23125135 the-basics-of-nmr

The Basics of NMR

Chapter 1

INTRODUCTION

NMR Spectroscopy

Units Review

Nuclear magnetic resonance or NMR as it is abbreviated by scientists is a phenomenon which occurs when the nuclei of certain atoms are immersed in a static magnetic field and exposed to a second oscillating magnetic field Some nuclei experience this phenomenon and others do not dependent upon whether they possess a property called spin You will learn about spin and about the role of the magnetic fields in Chapter 2 but first lets review where the nucleus is

Most of the matter you can examine with NMR is composed of molecules Molecules are composed of atoms Here are a few water molecules Each water molecule has one oxygen and two hydrogen atoms If we zoom into one of the hydrogens past the electron cloud we see a nucleus composed of a single proton The proton possesses a property called spin which

1 can be thought of as a small magnetic field and 2 will cause the nucleus to produce an NMR signal

Not all nuclei possess the property called spin A list of these nuclei will be presented in Chapter 3 on spin physics

Spectroscopy

Spectroscopy is the study of the interaction of electromagnetic radiation with matter Nuclear magnetic resonance spectroscopy is the use of the NMR phenomenon to study physical chemical and biological properties of matter As a consequence NMR spectroscopy finds applications in several areas of science NMR spectroscopy is routinely used by chemists to study chemical structure using simple one-dimensional techniques Two-dimensional techniques are used to determine the structure of more

complicated molecules These techniques are replacing x-ray crystallography for the determination of protein structure Time domain NMR spectroscopic techniques are used to probe molecular dynamics in solutions Solid state NMR spectroscopy is used to determine the molecular structure of solids Other scientists have developed NMR methods of measuring diffusion coefficients

The versatility of NMR makes it pervasive in the sciences Scientists and students are discovering that knowledge of the science and technology of NMR is essential for applying as well as developing new applications for it Unfortunately many of the dynamic concepts of NMR spectroscopy are difficult for the novice to understand when static diagrams in hard copy texts are used The chapters in this hypertext book on NMR are designed in such a way to incorporate both static and dynamic figures with hypertext This book presents a comprehensive picture of the basic principles necessary to begin using NMR spectroscopy and it will provide you with an understanding of the principles of NMR from the microscopic macroscopic and system perspectives

Units Review

Before you can begin learning about NMR spectroscopy you must be versed in the language of NMR NMR scientists use a set of units when describing temperature energy frequency etc Please review these units before advancing to subsequent chapters in this text

Units of time are seconds (s)

Angles are reported in degrees (o) and in radians (rad) There are 2 radians in 360o

The absolute temperature scale in Kelvin (K) is used in NMR The Kelvin temperature scale is equal to the Celsius scale reading plus 27315 0 K is characterized by the absence of molecular motion There are no degrees in the Kelvin temperature unit

Magnetic field strength (B) is measured in Tesla (T) The earths magnetic field in Rochester New York is approximately 5x10-5 T

The unit of energy (E) is the Joule (J) In NMR one often depicts the relative energy of a particle using an energy level diagram

The frequency of electromagnetic radiation may be reported in cycles per second or radians per second Frequency in cycles per second (Hz) have units of inverse seconds (s-

1) and are given the symbols or f Frequencies represented in radians per second (rads) are given the symbol Radians tend to be used more to describe periodic circular motions The conversion between Hz and rads is easy to remember There are 2 radians in a circle or cycle therefore

2 rads = 1 Hz = 1 s-1

Power is the energy consumed per time and has units of Watts (W)

Finally it is common in science to use prefixes before units to indicate a power of ten For example 0005 seconds can be written as 5x10-3 s or as 5 ms The m implies 10-3 The animation window contains a table of prefixes for powers of ten

In the next chapter you will be introduced to the mathematical beckground necessary to begin your study of NMR

The Basics of NMR

Chapter 2

THE MATHEMATICS OF NMR

Exponential Functions Trigonometric Functions

Differentials and Integrals

Vectors

Matrices

Coordinate Transformations

Convolutions

Imaginary Numbers

The Fourier Transform

Exponential Functions

The number 271828183 occurs so often in calculations that it is given the symbol e When e is raised to the power x it is often written exp(x)

ex = exp(x) = 271828183x

Logarithms based on powers of e are called natural logarithms If

x = ey

ln(x) = y

Many of the dynamic NMR processes are exponential in nature For example signals decay exponentially as a function of time It is therefore essential to understand the nature of exponential curves Three common exponential functions are

y = e-xt

y = (1 - e-xt)

y = (1 - 2e-xt)

where t is a constant

Trigonometric Functions

The basic trigonometric functions sine and cosine describe sinusoidal functions which are 90o out of phase

The trigonometric identities are used in geometric calculations

Sin( ) = Opposite HypotenuseCos( ) = Adjacent Hypotenuse

Tan( ) = Opposite AdjacentThe function sin(x) x occurs often and is called sinc(x)

A differential can be thought of as the slope of a function at any point For the function

the differential of y with respect to x is

An integral is the area under a function between the limits of the integral

An integral can also be considered a sumation in fact most integration is performed by computers by adding up values of the function between the integral limits

Vectors

A vector is a quantity having both a magnitude and a direction The magnetization from nuclear spins is represented as a vector emanating from the origin of the coordinate system Here it is along the +Z axis In this picture the vector is in the XY plane between the +X and +Y axes The vector has X and Y components and a magnitude equal to

( X2 + Y2 )12

Matrices

A matrix is a set of numbers arranged in a rectangular array This matrix has 3 rows and 4 columns and is said to be a 3 by 4 matrix

To multiply matrices the number of columns in the first must equal the number of rows in the second Click sequentially on the next start buttons to see the individual steps associated with the multiplication

A coordinate transformation is used to convert the coordinates of a vector in one coordinate system (XY) to that in another coordinate system (XY)

Convolution

The convolution of two functions is the overlap of the two functions as one function is passed over the second The convolution symbol is The convolution of h(t) and g(t) is defined mathematically as

The above equation is depicted for rectangular shaped h(t) and g(t) functions in this animation

Imaginary Numbers

Imaginary numbers are those which result from calculations involving the square root of -1 Imaginary numbers are symbolized by i

A complex number is one which has a real (RE) and an imaginary (IM) part The real and imaginary parts of a complex number are orthogonal

Two useful relations between complex numbers and exponentials are

e+ix = cos(x) +isin(x)and

e-ix = cos(x) -isin(x)

Fourier Transforms

The Fourier transform (FT) is a mathematical technique for converting time domain data to frequency domain data and vice versa

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin Properties of Spin

Nuclei with Spin

Energy Levels

Transitions

Energy Level Diagrams

Continuous Wave NMR Experiment

Boltzmann Statistics

Spin Packets

T 1 Processes

Precession

T 2 Processes

Rotating Frame of Reference

Pulsed Magnetic Fields

Spin Relaxation

Spin Exchange

Bloch Equations

What is spin Spin is a fundamental property of nature like electrical charge or mass Spin comes in multiples of 12 and can be + or - Protons electrons and neutrons possess spin Individual unpaired electrons protons and neutrons each possesses a spin of 12

In the deuterium atom ( 2H ) with one unpaired electron one unpaired proton and one unpaired neutron the total electronic spin = 12 and the total nuclear spin = 1

Two or more particles with spins having opposite signs can pair up to eliminate the observable manifestations of spin An example is helium In nuclear magnetic resonance it is unpaired nuclear spins that are of importance

Properties of Spin

When placed in a magnetic field of strength B a particle with a net spin can absorb a photon of frequency The frequency depends on the gyromagnetic ratio of the particle

For hydrogen = 4258 MHz T

Nuclei with Spin

The shell model for the nucleus tells us that nucleons just like electrons fill orbitals When the number of protons or neutrons equals 2 8 20 28 50 82 and 126 orbitals are filled Because nucleons have spin just like electrons do their spin can pair up when the orbitals are being filled and cancel out Almost every element in the periodic table has an isotope with a non zero nuclear spin NMR can only be performed on isotopes whose natural abundance is high enough to be detected Some of the nuclei routinely used in NMR are listed below

Nuclei Unpaired Protons Unpaired Neutrons Net Spin (MHzT) 1H 1 0 12 4258

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

To understand how particles with spin behave in a magnetic field consider a proton This proton has the property called spin Think of the spin of this proton as a magnetic moment vector causing the proton to behave like a tiny magnet with a north and south pole

When the proton is placed in an external magnetic field the spin vector of the particle aligns itself with the external field just like a magnet would There is a low energy configuration or state where the poles are aligned N-S-N-S and a high energy state N-N-S-S

Transitions

This particle can undergo a transition between the two energy states by the absorption of a photon A particle in the lower energy state absorbs a photon and ends up in the upper energy state The energy of this photon must exactly match the energy difference between the two states The energy E of a photon is related to its frequency by Planks constant (h = 6626x10-34 J s)

In NMR and MRI the quantity is called the resonance frequency and the Larmor frequency

The energy of the two spin states can be represented by an energy level diagram We have seen that = B and E = h therefore the energy of the photon needed to cause a transition between the two spin states is

E = h B

When the energy of the photon matches the energy difference between the two spin states an absorption of energy occurs

In the NMR experiment the frequency of the photon is in the radio frequency (RF) range In NMR spectroscopy is between 60 and 800 MHz for hydrogen nuclei In clinical MRI is typically between 15 and 80 MHz for hydrogen imaging

CW NMR Experiment

The simplest NMR experiment is the continuous wave (CW) experiment There are two ways of performing this experiment In the first a constant frequency which is continuously on probes the energy levels while the magnetic field is varied The energy of this frequency is represented by the blue line in the energy level diagram

The CW experiment can also be performed with a constant magnetic field and a frequency which is varied The magnitude of the constant magnetic field is represented by the position of the vertical blue line in the energy level diagram

When a group of spins is placed in a magnetic field each spin aligns in one of the two possible orientations

At room temperature the number of spins in the lower energy level N+ slightly outnumbers the number in the upper level N- Boltzmann statistics tells us that

N-N+ = e-EkT

E is the energy difference between the spin states k is Boltzmanns constant 13805x10-23

JKelvin and T is the temperature in Kelvin

As the temperature decreases so does the ratio N- N+ As the temperature increases the ratio approaches one

The signal in NMR spectroscopy results from the difference between the energy absorbed by the spins which make a transition from the lower energy state to the higher energy state and the energy emitted by the spins which simultaneously make a transition from the higher energy state to the lower energy state The signal is thus proportional to the population difference between the states NMR is a rather sensitive spectroscopy since it is capable of detecting these very small population differences It is the resonance or exchange of energy at a specific frequency between the spins and the spectrometer which gives NMR its sensitivity

Spin Packets

It is cumbersome to describe NMR on a microscopic scale A macroscopic picture is more convenient The first step in developing the macroscopic picture is to define the spin packet A spin packet is a group of spins experiencing the same magnetic field strength In this example the spins within each grid section represent a spin packet

At any instant in time the magnetic field due to the spins in each spin packet can be represented by a magnetization vector

The size of each vector is proportional to (N+ - N-)

The vector sum of the magnetization vectors from all of the spin packets is the net magnetization In order to describe pulsed NMR is necessary from here on to talk in terms of the net magnetization

Adapting the conventional NMR coordinate system the external magnetic field and the net magnetization vector at equilibrium are both along the Z axis

T1 Processes

At equilibrium the net magnetization vector lies along the direction of the applied magnetic field Bo and is called the equilibrium magnetization Mo In this configuration the Z component of magnetization MZ equals Mo MZ is referred to as the longitudinal magnetization There is no transverse (MX or MY) magnetization here

It is possible to change the net magnetization by exposing the nuclear spin system to energy of a frequency equal to the energy difference between the spin states If enough energy is put into the system it is possible to saturate the spin system and make MZ=0

The time constant which describes how MZ returns to its equilibrium value is called the spin lattice relaxation time (T1) The equation governing this behavior as a function of the time t after its displacement is

Mz = Mo ( 1 - e-tT1 )

T1 is therefore defined as the time required to change the Z component of magnetization by a factor of e

If the net magnetization is placed along the -Z axis it will gradually return to its equilibrium position along the +Z axis at a rate governed by T1 The equation governing this behavior as a function of the time t after its displacement is

Mz = Mo ( 1 - 2e-tT1 )

The spin-lattice relaxation time (T1) is the time to reduce the difference between the longitudinal magnetization (MZ) and its equilibrium value by a factor of e

Precession

If the net magnetization is placed in the XY plane it will rotate about the Z axis at a frequency equal to the frequency of the photon which would cause a transition between the two energy levels of the spin This frequency is called the Larmor frequency

T2 Processes

In addition to the rotation the net magnetization starts to dephase because each of the spin packets making it up is experiencing a slightly different magnetic field and rotates at its own Larmor frequency The longer the elapsed time the greater the phase difference Here the net magnetization vector is initially along +Y For this and all dephasing examples think of this vector as the overlap of several thinner vectors from the individual spin packets

The time constant which describes the return to equilibrium of the transverse magnetization MXY is called the spin-spin relaxation time T2

MXY =MXYo e-tT2

T2 is always less than or equal to T1 The net magnetization in the XY plane goes to zero and then the longitudinal magnetization grows in until we have Mo along Z

Any transverse magnetization behaves the same way The transverse component rotates about the direction of applied magnetization and dephases T1 governs the rate of recovery of the longitudinal magnetization

In summary the spin-spin relaxation time T2 is the time to reduce the transverse magnetization by a factor of e In the previous sequence T2 and T1 processes are shown separately for clarity That is the magnetization vectors are shown filling the XY plane completely before growing back up along the Z axis Actually both processes occur simultaneously with the only restriction being that T2 is less than or equal to T1

Two factors contribute to the decay of transverse magnetization1) molecular interactions (said to lead to a pure pure T2 molecular effect) 2) variations in Bo (said to lead to an inhomogeneous T2 effectThe combination of these two factors is what actually results in the decay of transverse magnetization The combined time constant is called T2 star and is given the symbol T2 The relationship between the T2 from molecular processes and that from inhomogeneities in the magnetic field is as follows

1T2 = 1T2 + 1T2inhomo

We have just looked at the behavior of spins in the laboratory frame of reference It is convenient to define a rotating frame of reference which rotates about the Z axis at the Larmor frequency We distinguish this rotating coordinate system from the laboratory system by primes on the X and Y axes XY

A magnetization vector rotating at the Larmor frequency in the laboratory frame appears stationary in a frame of reference rotating about the Z axis In the rotating frame relaxation of MZ magnetization to its equilibrium value looks the same as it did in the laboratory frame

A transverse magnetization vector rotating about the Z axis at the same velocity as the rotating frame will appear stationary in the rotating frame A magnetization vector traveling faster than the rotating frame rotates clockwise about the Z axis A magnetization vector traveling slower than the rotating frame rotates counter-clockwise about the Z axis

In a sample there are spin packets traveling faster and slower than the rotating frame As a consequence when the mean frequency of the sample is equal to the rotating frame the dephasing of MXY looks like this

A coil of wire placed around the X axis will provide a magnetic field along the X axis when a direct current is passed through the coil An alternating current will produce a magnetic field which alternates in direction

In a frame of reference rotating about the Z axis at a frequency equal to that of the alternating current the magnetic field along the X axis will be constant just as in the direct current case in the laboratory frame

This is the same as moving the coil about the rotating frame coordinate system at the Larmor Frequency In magnetic resonance the magnetic field created by the coil passing an alternating current at the Larmor frequency is called the B1 magnetic field When the alternating current through the coil is turned on and off it creates a pulsed B1 magnetic field along the X axis

The spins respond to this pulse in such a way as to cause the net magnetization vector to rotate about the direction of the applied B1 field The rotation angle depends on the length of time the field is on and its magnitude B1

= 2 B1

In our examples will be assumed to be much smaller than T1 and T2

A 90o pulse is one which rotates the magnetization vector clockwise by 90 degrees about the X axis A 90o pulse rotates the equilibrium magnetization down to the Y axis In the laboratory frame the equilibrium magnetization spirals down around the Z axis to the XY plane You can see why the rotating frame of reference is helpful in describing the behavior of magnetization in response to a pulsed magnetic field

A 180o pulse will rotate the magnetization vector by 180 degrees A 180o pulse rotates the equilibrium magnetization down to along the -Z axis

The net magnetization at any orientation will behave according to the rotation equation For example a net magnetization vector along the Y axis will end up along the -Y axis when acted upon by a 180o pulse of B1 along the X axis

A net magnetization vector between X and Y will end up between X and Y after the application of a 180o pulse of B1 applied along the X axis

A rotation matrix (described as a coordinate transformation in 26 Chapter 2) can also be used to predict the result of a rotation Here is the rotation angle about the X axis [X Y Z] is the initial location of the vector and [X Y Z] the location of the vector after the rotation

Spin Relaxation

Motions in solution which result in time varying magnetic fields cause spin relaxation

Time varying fields at the Larmor frequency cause transitions between the spin states and hence a change in MZ This screen depicts the field at the green hydrogen on the water molecule as it rotates about the external field Bo and a magnetic field from the blue hydrogen Note that the field experienced at the green hydrogen is sinusoidal

There is a distribution of rotation frequencies in a sample of molecules Only frequencies at the Larmor frequency affect T1 Since the Larmor frequency is proportional to Bo T1 will therefore vary as a function of magnetic field strength In general T1 is inversely proportional to the density of molecular motions at the Larmor frequency

The rotation frequency distribution depends on the temperature and viscosity of the solution Therefore T1 will vary as a function of temperature At the Larmor frequency indicated by o T1 (280 K ) lt T1 (340 K) The temperature of the human body does not vary by enough to cause a significant influence on T1 The viscosity does however vary significantly from tissue to tissue and influences T1 as is seen in the following molecular motion plot

Fluctuating fields which perturb the energy levels of the spin states cause the transverse magnetization to dephase This can be seen by examining the plot of Bo experienced by the red hydrogens on the following water molecule The number of molecular motions less than and equal to the Larmor frequency is inversely proportional to T2

In general relaxation times get longer as Bo increases because there are fewer relaxation-causing frequency components present in the random motions of the molecules

Spin Exchange

Spin exchange is the exchange of spin state between two spins For example if we have two spins A and B and A is spin up and B is spin down spin exchange between A and B can be represented with the following equation

A( ) + B( ) A( ) + B( )

The bidirectional arrow indicates that the exchange reaction is reversible

The energy difference between the upper and lower energy states of A and of B must be the same for spin exchange to occur On a microscopic scale the spin in the upper energy state (B) is emitting a photon which is being absorbed by the spin in the lower energy state (A) Therefore B ends up in the lower energy state and A in the upper state

Spin exchange will not affect T1 but will affect T2 T1 is not effected because the distribution of spins between the upper and lower states is not changed T2 will be affected because phase coherence of the transverse magnetization is lost during exchange

Another form of exchange is called chemical exchange In chemical exchange the A and B nuclei are from different molecules Consider the chemical exchange between water and ethanol

CH3CH2OHA + HOHB CH3CH2OHB + HOHA

Here the B hydrogen of water ends up on ethanol and the A hydrogen on ethanol ends up on water in the forward reaction There are four senarios for the nuclear spin represented by the four equations

Chemical exchange will affect both T1 and T2 T1 is now affected because energy is transferred from one nucleus to another For example if there are more nuclei in the upper state of A and a normal Boltzmann distribution in B exchange will force the excess energy from A into B The effect will make T1 appear smaller T2 is effected because phase coherence of the transverse magnetization is not preserved during chemical exchange

Bloch Equations

The Bloch equations are a set of coupled differential equations which can be used to describe the behavior of a magnetizatiion vector under any conditions When properly integrated the Bloch equations will yield the X Y and Z components of magnetization as a function of time

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift Spin-Spin Coupling

The Time Domain NMR Signal

The Frequency Convention

Chemical Shift

When an atom is placed in a magnetic field its electrons circulate about the direction of the applied magnetic field This circulation causes a small magnetic field at the nucleus which opposes the externally applied field

The magnetic field at the nucleus (the effective field) is therefore generally less than the applied field by a fraction

B = Bo (1-)

In some cases such as the benzene molecule the circulation of the electrons in the aromatic orbitals creates a magnetic field at the hydrogen nuclei which enhances the Bo field This phenomenon is called deshielding In this example the Bo field is applied perpendicular to the plane of the molecule The ring current is traveling clockwise if you look down at the plane

The electron density around each nucleus in a molecule varies according to the types of nuclei and bonds in the molecule The opposing field and therefore the effective field at each nucleus will vary This is called the chemical shift phenomenon

Consider the methanol molecule The resonance frequency of two types of nuclei in this example differ This difference will depend on the strength of the magnetic field Bo used to perform the NMR spectroscopy The greater the value of Bo the greater the frequency difference This relationship could make it difficult to compare NMR spectra taken on spectrometers operating at different field strengths The term chemical shift was developed to avoid this problem

The chemical shift of a nucleus is the difference between the resonance frequency of the nucleus and a standard relative to the standard This quantity is reported in ppm and given the symbol delta

= ( - REF) x106 REF

In NMR spectroscopy this standard is often tetramethylsilane Si(CH3)4 abbreviated TMS The chemical shift is a very precise metric of the chemical environment around a nucleus For example the hydrogen chemical shift of a CH2 hydrogen next to a Cl will be different than that of a CH3 next to the same Cl It is therefore difficult to give a detailed list of chemical shifts in a limited space The animation window displays a chart of selected hydrogen chemical shifts of pure liquids and some gasses

The magnitude of the screening depends on the atom For example carbon-13 chemical shifts are much greater than hydrogen-1 chemical shifts The following tables present a few selected chemical shifts of fluorine-19 containing compounds carbon-13 containing compounds nitrogen-14 containing compounds and phosphorous-31 containing compounds These shifts are all relative to the bare nucleus The reader is directed to a more comprehensive list of chemical shifts for use in spectral interpretation

Spin-Spin Coupling

Nuclei experiencing the same chemical environment or chemical shift are called equivalent Those nuclei experiencing different environment or having different chemical shifts are nonequivalent Nuclei which are close to one another exert an influence on each others effective magnetic field This effect shows up in the NMR spectrum when the nuclei are nonequivalent If the distance between non-equivalent nuclei is less than or equal to three bond lengths this effect is observable This effect is called spin-spin coupling or J coupling

Consider the following example There are two nuclei A and B three bonds away from one another in a molecule The spin of each nucleus can be either aligned with the external field such that the fields are N-S-N-S called spin up or opposed to the external field such that the fields are N-N-S-S called spin down The magnetic field at nucleus A will be either greater than Bo or less than Bo by a constant amount due to the influence of nucleus B

There are a total of four possible configurations for the two nuclei in a magnetic field Arranging these configurations in order of increasing energy gives the following arrangement The vertical lines in this diagram represent the allowed transitions between energy levels In NMR an allowed transition is one where the spin of one nucleus changes from spin up to spin down or spin down to spin up Absorptions of energy where two or more nuclei change spin at the same time are not allowed There are two absorption frequencies for the A nucleus and two for the B nucleus represented by the vertical lines between the energy levels in this diagram

The NMR spectrum for nuclei A and B reflects the splittings observed in the energy level diagram The A absorption line is split into 2 absorption lines centered on A and the B absorption line is split into 2 lines centered on B The distance between two split absorption lines is called the J coupling constant or the spin-spin splitting constant and is a measure of the magnetic interaction between two nuclei

For the next example consider a molecule with three spin 12 nuclei one type A and two type B The type B nuclei are both three bonds away from the type A nucleus The magnetic field at the A nucleus has three possible values due to four possible spin configurations of the two B nuclei The magnetic field at a B nucleus has two possible values

The energy level diagram for this molecule has six states or levels because there are two sets of levels with the same energy Energy levels with the same energy are said to be degenerate The vertical lines represent the allowed transitions or absorptions of energy Note that there are two lines drawn between some levels because of the degeneracy of those levels

The resultant NMR spectrum is depicted in the animation window Note that the center absorption line of those centered at A is twice as high as the either of the outer two This is because there were twice as many transitions in the energy level diagram for this transition The peaks at B are taller because there are twice as many B type spins than A type spins

The complexity of the splitting pattern in a spectrum increases as the number of B nuclei increases The following table contains a few examples

Configuration Peak Ratios

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

This series is called Pascals triangle and can be calculated from the coefficients of the expansion of the equation

where n is the number of B nuclei in the above table

When there are two different types of nuclei three bonds away there will be two values of J one for each pair of nuclei By now you get the idea of the number of possible configurations and the energy level diagram for these configurations so we can skip to the spectrum In the following example JAB is greater JBC

An NMR sample may contain many different magnetization components each with its own Larmor frequency These magnetization components are associated with the nuclear spin configurations joined by an allowed transition line in the energy level diagram Based on the number of allowed absorptions due to chemical shifts and spin-spin couplings of the different nuclei in a molecule an NMR spectrum may contain many different frequency lines

In pulsed NMR spectroscopy signal is detected after these magnetization vectors are rotated into the XY plane Once a magnetization vector is in the XY plane it rotates about the direction of the Bo field the axis As transverse magnetization rotates about the Z axis it will induce a current in a coil of wire located around the X axis Plotting current as a function of time gives a sine wave This wave will of course decay with time constant T2 due to dephasing of the spin packets This signal is called a free induction decay (FID) We will see in Chapter 5 how the FID is converted into a frequency domain spectrum You will see in Chapter 6 what sequence of events will produce a time domain signal

Transverse magnetization vectors rotating faster than the rotating frame of reference are said to be rotating at a positive frequency relatve to the rotating frame () Vectors rotating slower than the rotating frame are said to be rotating at a negative frequency relative to the rotating frame (-)

It is worthwhile noting here that in most NMR spectra the resonance frequency of a nucleus as well as the magnetic field experienced by the nucleus and the chemical shift of a nucleus increase from right to left The frequency plots used in this hypertext book to describe Fourier transforms will use the more conventional mathematical axis of frequency increasing from left to right

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction The + and - Frequency Problem

Phase Correction

Fourier Pairs

The Convolution Theorem

The Digital FT

Sampling Error

The Two-Dimensional FT

Introduction

A detailed description of the Fourier transform ( FT ) has waited until now when you have a better appreciation of why it is needed A Fourier transform is an operation which converts functions from time to frequency domains An inverse Fourier transform ( IFT ) converts from the frequency domain to the time domain

Recall from Chapter 2 that the Fourier transform is a mathematical technique for converting time domain data to frequency domain data and vice versa

The + and - Frequency Problem

To begin our detailed description of the FT consider the following A magnetization vector starting at +x is rotating about the Z axis in a clockwise direction The plot of Mx as a function of time is a cosine wave Fourier transforming this gives peaks at both + and - because the FT can not distinguish between a + and a - rotation of the vector from the data supplied

A plot of My as a function of time is a -sine function Fourier transforming this gives peaks at + and - because the FT can not distinguish between a positive vector rotating at + and a negative vector rotating at - from the data supplied

The solution is to input both the Mx and My into the FT The FT is designed to handle two orthogonal input functions called the real and imaginary components

Detecting just the Mx or My component for input into the FT is called linear detection This was the detection scheme on many older NMR spectrometers and some magnetic resonance imagers It required the computer to discard half of the frequency domain data

Detection of both Mx and My is called quadrature detection and is the method of detection on modern spectrometers and imagers It is the method of choice since now the FT can distinguish between + and - and all of the frequency domain data be used

An FT is defined by the integral

Think of f( ) as the overlap of f(t) with a wave of frequency

This is easy to picture by looking at the real part of f( ) only

Consider the function of time f( t ) = cos( 4t ) + cos( 9t )

To understand the FT examine the product of f(t) with cos( t) for values between 1 and 10 and then the summation of the values of this product between 1 and 10 seconds The summation will only be examined for time values between 0 and 10 seconds

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

The inverse Fourier transform (IFT) is best depicted as an summation of the time domain spectra of frequencies in f( )

Phase Correction

The actual FT will make use of an input consisting of a REAL and an IMAGINARY part You can think of Mx as the REAL input and My as the IMAGINARY input The resultant output of the FT will therefore have a REAL and an IMAGINARY component too

Consider the following function

f(t) = e-at e-i2 t

In FT NMR spectroscopy the real output of the FT is taken as the frequency domain spectrum To see an esthetically pleasing (absorption) frequency domain spectrum we want to input a cosine function into the real part and a sine function into the imaginary parts of the FT This is what happens if the cosine part is input as the imaginary and the sine as the real

To obtain an absorption spectrum as the real output of the FT a phase correction must be applied to either the time or frequency domain spectra This process is equivalent to the coordinate transformation described in Chapter 2

If the above mentioned FID is recorded such that there is a 45o phase shift in the real and imaginary FIDs the coordinate transformation matrix can be used with = - 45o The corrected FIDs look like a cosine function in the real and a sine in the imaginary

Fourier transforming the phase corrected FIDs gives an absorption spectrum for the real output of the FT This correction can be done in the frequency domain as well as in the time domain

NMR spectra require both constant and linear corrections to the phasing of the Fourier transformed signal

= m + b

Constant phase corrections b arise from the inability of the spectrometer to detect the exact Mx and My Linear phase corrections m arise from the inability of the spectrometer to detect transverse magnetization starting immediately after the RF pulse

In magnetic resonance the Mx or My signals are displayed A magnitude signal might occasionally be used in some applications The magnitude signal is equal to the square root of the sum of the squares of Mx and My

Fourier Pairs

To better understand FT NMR functions you need to know some common Fourier pairs A Fourier pair is two functions the frequency domain form and the corresponding

time domain form Here are a few Fourier pairs which are useful in NMR The amplitude of the Fourier pairs has been neglected since it is not relevant in NMR

Constant value at all time

Real cos(2 t) Imaginary -sin(2 t)

Comb Function (A series of delta functions separated by T)

Exponential Decay e-at for t gt 0

A square pulse starting at 0 that is T seconds long

Gaussian exp(-at2)

Convolution Theorem

To the magnetic resonance scientist the most important theorem concerning Fourier transforms is the convolution theorem The convolution theorem says that the FT of a convolution of two functions is proportional to the products of the individual Fourier transforms and vice versa

If f( ) = FT( f(t) ) and h( ) = FT( h(t) )

then f( ) g( ) = FT( g(t) f(t) ) and f( ) g( ) = FT( g(t) f(t) )

It will be easier to see this with pictures In the animation window we are trying to find the FT of a sine wave which is turned on and off The convolution theorem tells us that this is a sinc function at the frequency of the sine wave

Another application of the convolution theorem is in noise reduction With the convolution theorem it can be seen that the convolution of an NMR spectrum with a Lorentzian function is the same as the Fourier Transform of multiplying the time domain signal by an exponentially decaying function

The Digital FT

In a nuclear magnetic resonance spectrometer the computer does not see a continuous FID but rather an FID which is sampled at a constant interval Each data point making up the FID will have discrete amplitude and time values Therefore the computer needs to take the FT of a series of delta functions which vary in intensity

Sampling Error

The wrap around problem or artifact in a nuclear magnetic resonance spectrum is the appearance of one side of the spectrum on the opposite side In terms of a one dimensional frequency domain spectrum wrap around is the occurrence of a low frequency peak which occurs on the high frequency side of the spectrum

The convolution theorem can explain why this problem results from sampling the transverse magnetization at too slow a rate First observe what the FT of a correctly sampled FID looks like With quadrature detection the spectral width is equal to the

inverse of the sampling frequency or the width of the green box in the animation window

When the sampling frequency is less than the spectral width wrap around occurs

The two-dimensional Fourier transform (2-DFT) is an FT performed on a two dimensional array of data

Consider the two-dimensional array of data depicted in the animation window This data has a t and a t dimension A FT is first performed on the data in one dimension and then in the second The first set of Fourier transforms are performed in the t dimension to yield an f by t set of data The second set of Fourier transforms is performed in the t dimension to yield an f by f set of data

The 2-DFT is required to perform state-of-the-art MRI In MRI data is collected in the equivalent of the t and t dimensions called k-space This raw data is Fourier transformed to yield the image which is the equivalent of the f by f data described above

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction The 90-FID Sequence

The Spin-Echo Sequence

The Inversion Recovery Sequence

Introduction

You have seen in Chapter 5 how a time domain signal can be converted into a frequency domain signal In this chapter you will learn a few of the ways that a time domain signal can be created Three methods are presented here but there are an infinite number of

possibilities These methods are called pulse sequences A pulse sequence is a set of RF pulses applied to a sample to produce a specific form of NMR signal

The 90-FID Sequence

In the 90-FID pulse sequence net magnetization is rotated down into the XY plane with a 90o pulse The net magnetization vector begins to precess about the +Z axis The magnitude of the vector also decays with time

A timing diagram is a multiple axis plot of some aspect of a pulse sequence versus time A timing diagram for a 90-FID pulse sequence has a plot of RF energy versus time and another for signal versus time

When this sequence is repeated for example when signal-to-noise improvement is needed the amplitude of the signal after being Fourier transformed (S) will depend on T1 and the time between repetitions called the repetition time (TR) of the sequence In the signal equation below k is a proportionality constant and is the density of spins in the sample

S = k ( 1 - e-TRT1 )

Another commonly used pulse sequence is the spin-echo pulse sequence Here a 90o pulse is first applied to the spin system The 90o degree pulse rotates the magnetization down into the XY plane The transverse magnetization begins to dephase At some point in time after the 90o pulse a 180o pulse is applied This pulse rotates the magnetization by 180o about the X axis The 180o pulse causes the magnetization to at least partially rephase and to produce a signal called an echo

A timing diagram shows the relative positions of the two radio frequency pulses and the signal

The signal equation for a repeated spin echo sequence as a function of the repetition time TR and the echo time (TE) defined as the time between the 90o pulse and the maximum amplitude in the echo is

S = k ( 1 - e-TRT1 ) e-TET2

An inversion recovery pulse sequence can also be used to record an NMR spectrum In this sequence a 180o pulse is first applied This rotates the net magnetization down to the -Z axis The magnetization undergoes spin-lattice relaxation and returns toward its equilibrium position along the +Z axis Before it reaches equilibrium a 90o pulse is applied which rotates the longitudinal magnetization into the XY plane In this example

the 90o pulse is applied shortly after the 180o pulse Once magnetization is present in the XY plane it rotates about the Z axis and dephases giving a FID

Once again the timing diagram shows the relative positions of the two radio frequency pulses and the signal

The signal as a function of TI when the sequence is not repeated is

S = k ( 1 - 2e-TIT1 )

It should be noted at this time that the zero crossing of this function occurs for TI = T1 ln2

The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

The graphics window displays a schematic representation of the major systems of a nuclear magnetic resonance spectrometer and a few of the major interconnections This overview briefly states the function of each component Some will be described in detail later in this chapter

At the top of the schematic representation you will find the superconducting magnet of the NMR spectrometer The magnet produces the Bo field necessary for the NMR experiments Immediately within the bore of the magnet are the shim coils for homogenizing the Bo field Within the shim coils is the probe The probe contains the RF coils for producing the B1 magnetic field necessary to rotate the spins by 90o or 180o The RF coil also detects the signal from the spins within the sample The sample is positioned within the RF coil of the probe Some probes also contain a set of gradient coils These coils produce a gradient in Bo along the X Y or Z axis Gradient coils are used for for gradient enhanced spectroscopy (See Chapter 11) diffusion (See Chapter 11) and NMR microscopy (See Chapter 11) experiments

The heart of the spectrometer is the computer It controls all of the components of the spectrometer The RF components under control of the computer are the RF frequency source and pulse programmer The source produces a sine wave of the desired frequency The pulse programmer sets the width and in some cases the shape of the RF pulses The RF amplifier increases the pulses power from milli Watts to tens or hundreds of Watts The computer also controls the gradient pulse programmer which sets the shape and amplitude of gradient fields The gradient amplifier increases the power of the gradient pulses to a level sufficient to drive the gradient coils

The operator of the spectrometer gives input to the computer through a console terminal with a mouse and keyboard Some spectrometers also have a separate small interface for carrying out some of the more routine procedures on the spectrometer A pulse sequence is selected and customized from the console terminal The operator can see spectra on a video display located on the console and can make hard copies of spectra using a printer

The next sections of this chapter go into more detail concerning the magnet lock shim coils gradient coils RF coils and RF detector of nuclear magnetic resonance spectrometer

Magnet

The NMR magnet is one of the most expensive components of the nuclear magnetic resonance spectrometer system Most magnets are of the superconducting type This is a picture of a 70 Tesla superconducting magnet from an NMR spectrometer A superconducting magnet has an electromagnet made of superconducting wire Superconducting wire has a resistance approximately equal to zero when it is cooled to a temperature close to absolute zero (-27315o C or 0 K) by emersing it in liquid helium Once current is caused to flow in the coil it will continue to flow for as long as the coil is kept at liquid helium temperatures (Some losses do occur over time due to the

infinitesimally small resistance of the coil These losses are on the order of a ppm of the main magnetic field per year)

The length of superconducting wire in the magnet is typically several miles This wire is wound into a multi-turn solenoid or coil The coil of wire is kept at a temperature of 42K by immersing it in liquid helium The coil and liquid helium are kept in a large dewar This dewar is typically surrounded by a liquid nitrogen (774K) dewar which acts as a thermal buffer between the room temperature air (293K) and the liquid helium A cross sectional view of the superconducting magnet depicting the concentric dewars can be found in the animation window

The following image is an actual cut-away view of a superconducting magnet The magnet is supported by three legs and the concentric nitrogen and helium dewars are supported by stacks coming out of the top of the magnet A room temperature bore hole extends through the center of the assembly The sample probe and shim coils are located within this bore hole Also depicted in this picture is the liquid nitrogen level sensor an electronic assembly for monitoring the liquid nitrogen level

Going from the outside of the magnet to the inside we see a vacuum region followed by a liquid nitrogen reservoir The vacuum region is filled with several layers of a reflective mylar film The function of the mylar is to reflect thermal photons and thus diminish heat from entering the magnet Within the inside wall of the liquid nitrogen reservoir we see another vacuum filled with some reflective mylar The liquid helium reservoir comes next This reservoir houses the superconducting solenoid or coil of wire

Taking a closer look at the solenoid it is clear to see the coil and the bore tube extending through the magnet

Field Lock

In order to produce a high resolution NMR spectrum of a sample especially one which requires signal averaging or phase cycling you need to have a temporally constant and spatially homogeneous magnetic field Consistency of the Bo field over time will be discussed here homogeneity will be discussed in the next section of this chapter The field strength might vary over time due to aging of the magnet movement of metal objects near the magnet and temperature fluctuations Here is an example of a one line NMR spectrum of cyclohexane recorded while the Bo magnetic field was drifting a very significant amount The field lock can compensate for these variations

The field lock is a separate NMR spectrometer within your spectrometer This spectrometer is typically tuned to the deuterium NMR resonance frequency It constantly monitors the resonance frequency of the deuterium signal and makes minor changes in the Bo magnetic field to keep the resonance frequency constant The deuterium signal comes from the deuterium solvent used to prepare the sample The animation window contains plots of the deuterium resonance lock frequency the small additional magnetic field used to correct the lock frequency and the resultant Bo field as a function of time

while the magnetic field is drifting The lock frequency plot displays the frequency without correction In reality this frequency would be kept constant by the application of the lock field which offsets the drift

On most NMR spectrometers the deuterium lock serves a second function It provides the =0 reference The resonance frequency of the deuterium signal in many lock solvents is

well known Therefore the difference in resonance frequency of the lock solvent and TMS is also known As a consequence TMS does not need to be added to the sample to set =0 the spectrometer can use the lock frequency to calculate =0

Shim Coils

The purpose of shim coils on a spectrometer is to correct minor spatial inhomogeneities in the Bo magnetic field These inhomogeneities could be caused by the magnet design materials in the probe variations in the thickness of the sample tube sample permeability and ferromagnetic materials around the magnet A shim coil is designed to create a small magnetic field which will oppose and cancel out an inhomogeneity in the Bo magnetic field Because these variations may exist in a variety of functional forms (linear parabolic etc) shim coils are needed which can create a variety of opposing fields Some of the functional forms are listed in the table below

Shim Coil Functional Forms

Shim Function

By passing the appropriate amount of current through each coil a homogeneous Bo magnetic field can be achieved The optimum shim current settings are found by either minimizing the linewidth maximizing the size of the FID or maximizing the signal from the field lock On most spectrometers the shim coils are controllable by the computer A computer algorithm has the task of finding the best shim value by maximizing the lock signal

Sample Probe

The sample probe is the name given to that part of the spectrometer which accepts the sample sends RF energy into the sample and detects the signal emanating from the sample It contains the RF coil sample spinner temperature controlling circuitry and gradient coils The RF coil and gradient coils will be described in the next two sections The sample spinner and temperature controlling circuitry will be described here

The purpose of the sample spinner is to rotate the NMR sample tube about its axis In doing so each spin in the sample located at a given position along the Z axis and radius from the Z axis will experience the average magnetic field in the circle defined by this Z and radius The net effect is a narrower spectral linewidth To appreciate this phenomenon consider the following examples

Picture an axial cross section of a cylindrical tube containing sample In a very homogeneous Bo magnetic field this sample will yield a narrow spectrum In a more inhomogeneous field the sample will yield a broader spectrum due to the presence of lines from the parts of the sample experiencing different Bo magnetic fields When the sample is spun about its z-axis inhomogeneities in the X and Y directions are averaged out and the NMR line width becomes narrower

Many scientists need to examine properties of their samples as a function of temperature As a result many instruments have the ability to maintain the temperature of the sample above and below room temperature Air or nitrogen which has been warmed or cooled is passed over the sample to heat or cool the sample The temperature at the sample is monitored with the aid of a thermocouple and electronic circuitry maintains the temperature by increasing or decreasing the temperature of the gas passing over the sample More information on this topic will be presented in Chapter 8

RF Coils

RF coils create the B1 field which rotates the net magnetization in a pulse sequence They also detect the transverse magnetization as it precesses in the XY plane Most RF coils on NMR spectrometers are of the saddle coil design and act as the transmitter of

the B1 field and receiver of RF energy from the sample You may find one or more RF coils in a probe

Each of these RF coils must resonate that is they must efficiently store energy at the Larmor frequency of the nucleus being examined with the NMR spectrometer All NMR coils are composed of an inductor or inductive elements and a set of capacitive elements The resonant frequency of an RF coil is determined by the inductance (L) and capacitance (C) of the inductor capacitor circuit

RF coils used in NMR spectrometers need to be tuned for the specific sample being studied An RF coil has a bandwidth or specific range of frequencies at which it resonates When you place a sample in an RF coil the conductivity and dielectric constant of the sample affect the resonance frequency If this frequency is different from the resonance frequency of the nucleus you are studying the coil will not efficiently set up the B1 field nor efficiently detect the signal from the sample You will be rotating the net magnetization by an angle less than 90 degrees when you think you are rotating by 90 degrees This will produce less transverse magnetization and less signal Furthermore because the coil will not be efficiently detecting the signal your signal-to-noise ratio will be poor

The B1 field of an RF coil must be perpendicular to the Bo magnetic field Another requirement of an RF coil in an NMR spectrometer is that the B1 field needs to be homogeneous over the volume of your sample If it is not you will be rotating spins by a distribution of rotation angles and you will obtain strange spectra

Gradient Coils

The gradient coils produce the gradients in the Bo magnetic field needed for performing gradient enhanced spectroscopy diffusion measurements and NMR microscopy The gradient coils are located inside the RF probe Not all probes have gradient coils and not all NMR spectrometers have the hardware necessary to drive these coils

The gradient coils are room temperature coils (ie do not require cooling with cryogens to operate) which because of their configuration create the desired gradient Since the vertical bore superconducting magnet is most common the gradient coil system will be described for this magnet

Assuming the standard magnetic resonance coordinate system a gradient in Bo in the Z direction is achieved with an antihelmholtz type of coil Current in the two coils flow in opposite directions creating a magnetic field gradient between the two coils The B field at the center of one coil adds to the Bo field while the B field at the center of the other coil subtracts from the Bo field

The X and Y gradients in the Bo field are created by a pair of figure-8 coils The X axis figure-8 coils create a gradient in Bo in the X direction due to the direction of the current through the coils The Y axis figure-8 coils provides a similar gradient in Bo along the Y axis

Quadrature Detector

The quadrature detector is a device which separates out the Mx and My signals from the signal from the RF coil For this reason it can be thought of as a laboratory to rotating frame of reference converter The heart of a quadrature detector is a device called a doubly balanced mixer The doubly balanced mixer has two inputs and one output If the input signals are Cos(A) and Cos(B) the output will be 12 Cos(A+B) and 12 Cos(A-B) For this reason the device is often called a product detector since the product of Cos(A) and Cos(B) is the output

The quadrature detector typically contains two doubly balanced mixers two filters two amplifiers and a 90o phase shifter There are two inputs and two outputs on the device Frequency and o are put in and the MX and MY components of the transverse magnetization come out There are some potential problems which can occur with this device which will cause artifacts in the spectrum One is called a DC offset artifact and the other is called a quadrature artifact

Digital Filtering

Many newer spectrometers employ a combination of oversampling digital filtering and decimation to eliminate the wrap around artifact Oversampling creates a larger spectral or sweep width but generates too much data to be conveniently stored Digital filtering eliminates the high frequency components from the data and decimation reduces the size of the data set The following flowchart summarizes the effects of the three steps by showing the result of performing an FT after each step

Lets examine oversampling digital filtering and decimation in more detail to see how this combination of steps can be used to reduce the wrap around problem

Oversampling is the digitization of a time domain signal at a frequency much greater than necessary to record the desired spectral width For example if the sampling frequency fs is increased by a factor of 10 the sweep width will be 10 times greater thus eliminating wraparound Unfortunately digitizing at 10 times the speed also increases the amount of raw data by a factor of 10 thus increasing storage requirements and processing time

Filtering is the removal of a select band of frequencies from a signal For an example of filtering consider the following frequency domain signal Frequencies above fo could be removed from this frequency domain signal by multipling the signal by this rectangular function In NMR this step would be equivalent to taking a large sweep width spectrum and setting to zero intensity those spectral frequencies which are farther than some distance from the center of the spectrum

Digital filtering is the removal of these frequencies using the time domain signal Recall from Chapter 5 that if two functions are multiplied in one domain (ie frequency) we must convolve the FT of the two functions together in the other domain (ie time) To filter out frequencies above fo from the time domain signal the signal must be convolved with the Fourier transform of the rectangular function a sinc function (See Chapter 5) This process eliminates frequencies greater than fo from the time domain signal Fourier transforming the resultant time domain signal yields a frequency domain signal without the higher frequencies In NMR this step will remove spectral components with frequencies greater than +fo and less than -fo

Decimation is the elimination of data points from a data set A decimation ratio of 45 means that 4 out of every 5 data points are deleted or every fifth data point is saved Decimating the digitally filtered data above followed by a Fourier transform will reduce the data set by a factor of five

High speed digitizers capable of digitizing at 2 MHz and dedicated high speed integrated circuits capable of performing the convolution on the time domain data as it is being recorded are used to realize this procedure

Safety

There are some important safety considerations which one should be familiar with before using an NMR spectrometer These concern the use of strong magnetic fields and cryogenic liquids

Magnetic fields from high field magnets can literally pick up and pull ferromagnetic items into the bore of the magnet Caution must be taken to keep all ferromagnetic items away from the magnet because they can seriously damage the magnet shim coils and probe The force exerted on the concentric cryogenic dewars within a magnet by a large metal object stuck to the magnet can break dewars and magnet supports The kinetic energy of an object being sucked into a magnet can smash a dewar or an electrical connector on a probe Small ferromagnetic objects are just as much a concern as larger ones A small metal sliver can get sucked into the bore of the magnet and destroy the homogeneity of the magnet achieved with a set of shim settings

There are additional concerns regarding the effect of magnetic fields on electronic circuitry specifically pacemakers An individual with a pacemaker walking through a strong magnetic field can induce currents in the pacemaker circuitry which will cause it to fail and possibly cause death A person with a pacemaker must not be able to inadvertently stray into a magnetic field of five or more Gauss Although not as important as a pacemaker mechanical watches and some digital watches will also be affected by magnetic fields Magnetic fields of approximately 50 Gauss will erase credit cards and magnetic storage media

The liquid nitrogen and liquid helium used in NMR spectrometers are at a temperature of 774 K and 42 K respectively These liquids can cause frostbite which is not a concern

unless you are filling the magnet If you are filling the magnet or if you are operating the spectrometer suffocation is another concern you need to be aware of If the magnet quenches or suddenly stops being a superconductor it will rapidly boil off all its cryogens and the nitrogen and helium gasses in a confined space can cause suffocation

The Basics of NMR

Chapter 8

PRACTICAL CONSIDERATIONS

Introduction Sample Preparation

Sample Probe Tuning

Determining a 90 Degree Pulse

Field Shimming

Phase Cycling

1-D Hydrogen Spectra

Integration

SNR Improvement

Variable Temperature

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

In previous chapters you have learned the basic theory of nuclear magnetic resonance This chapter emphasizes some of the spectroscopic techniques While some of these may

be easy for you to understand based on the simple theory you have learned in previous chapters there may be specific points discussed which are less obvious because they are based on theories not presented in this hypertext book

When comparing two NMR spectra always keep in mind the subtle differences in the way the spectra were recorded One obvious example is the effect of field strength As the Bo field increases in magnitude (ie 15T 47T 7T) the signal-to-noise ratio generally increases The shape of the spectrum may also change For example consider the hydrogen NMR spectrum from three coupled nuclei A B and C with the following chemical shifts and J coupling constants

Nuclei (ppm)

Interaction J (Hz)

Compare the 100 MHz and 400 MHz NMR spectra The spectral lines from the B type spins are colored red You can see how easy it would be to make the wrong choice as to the structure of the molecule based on the 100 MHz spectrum although the chance of error might be reduced if you had further information eg the relative areas under the peaks This topic is described in a later section of this chapter

Sample Preparation

NMR samples are prepared by dissolving an analyte in a deuterium lock solvent Several deuterium lock solvents are available Some of these solvents will readily absorb moisture from the atmosphere and give water signal in your spectrum It is therefore advisable to keep bottles of these solvents tightly capped when not in use

Most routine high resolution NMR samples are prepared and run in 5 mm glass NMR tubes Always fill your NMR tubes to the same height with lock solvent This will minimize the amount of magnetic field shimming required The animation window depicts a sample tube filled with solvent such that it fills the RF coil

The concentration of your sample should be great enough to give a good signal-to-noise ratio in your spectrum yet minimize exchange effects found at high concentrations The exact concentration of your sample in the lock solvent will depend on the sensitivity of the spectrometer If you have no guidelines for a specific spectrometer use one drop of analyte for liquids and one or two crystals for solid samples

The position of spectral absorption lines can be solvent dependent Therefore if you are comparing spectra or trying to identify an unknown sample by comparison to reference spectra use the same solvent The hydrogen NMR spectrum of ethanol is a good example of this solvent dependence Compare the positions of the CH3 CH2 and OH absorption lines in a hydrogen NMR spectrum of ethanol in the lock solvents CDCl3 and D2O Notice also that the relative peak heights are not the same in the two spectra This is because the linewidths are not equal The area under a peak not the height of a peak is proportional to the number of hydrogens in a sample This point will be emphasized later in this chapter

Variations in the polarity and dielectric constant of the lock solvent will also effect the tuning of the probe The correction of these effects are covered in the next section of this chapter on sample probe tuning

Sample Probe Tuning

Variations in the polarity and dielectric constant of the lock solvent will affect the probe tuning For this reason the probe should be tuned whenever the lock solvent is changed Tuning the probe entails adjusting two capacitors on the RF probe One capacitor is called the matching capacitor and the other the tuning capacitor The matching capacitor matches the impedance of the loaded probe to that of the 50 Ohm cable coming from the spectrometer The tuning capacitor changes the resonance frequency of the RF coil

Most spectrometers have a probe tuning mode of operation This mode of operation presents a display of reflected power vs frequency on the screen The goal is to adjust the display so that the reflected power from the probe is zero at the resonance frequency of the nucleus you are examining

As the polarity and dielectric constant of the lock solvent changes so does the bandwidth of the RF probe This is significant because it affects the amount of RF power needed to produce a 90 degree pulse The larger the bandwidth the more power is needed to produce the 90 degree rotation

Determinining a 90o Pulse

As pointed out in the previous section of this chapter changes in the polarity and dielectric constant of the lock solvent affect the bandwidth of the RF probe which in turn affects the amount of RF power needed to produce a 90 degree rotation Most NMR spectrometers will not allow you to change the RF power but they will permit you to change the pulse length Therefore if the bandwidth of the RF probe increases you will need to increase the RF pulse width to produce a 90 degree pulse

To determine the pulse width needed to produce a 90 degree pulse you should perform the following experiment using a sample which has a single absorption line and a relatively short T1 Record a series of spectra with incrementally longer RF pulse widths Fourier transform the time domain signals and plot these lines as a function of pulse

width The peak height should vary sinusoidally with increasing pulse width The 90 degree pulse width will be the first maximum The 180 degree pulse width will be the first zero crossing Many spectrometers have routines which will automatically record the data necessary to produce these plots

You should also be aware of the effect of varying the width of the RF pulse on the distribution of frequencies being delivered to your sample Recall from the discussion of the convolution theorem in Chapter 5 that the Fourier pair of a sine wave which is turned on and off is a sinc function centered at the frequency of the sine wave When you apply an RF pulse of width t in the time domain you apply a distribution of frequencies to your sample Not all of these frequencies will have sufficient B1 magnitude to produce a 90 degree rotation The range of frequencies from the center of the distribution to the first zeros in the distribution is +- 1t As your pulse width increases the width of the distribution of frequencies in your pulse decreases If the distribution is too narrow you may not be applying the desired rotation to the entire sample

Field Shimming

The purpose of shimming a magnet is to make the magnetic field more homogeneous and to obtain better spectral resolution Shimming can be performed manually or by computer control It is not the intent of this section to teach you a step-by-step procedure for shimming but to present you with the basic theory so that you can with the aid of your NMR instruction manual shim your magnet The reader is encouraged to write down or save the current shim settings before making changes to any of the current shims coil settings

Broad lines asymmetric lines and a loss of resolution are indications that a magnet needs to be shimmed The shape of an NMR line is a good indication of which shim is misadjusted Consider a single narrow NMR line If we zoom in on this line we might see the following shape The following series of spectra depict the appearance of this spectral line in the presence of various inhomogeneities

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

In general asymmetric lineshapes result from mis-adjusted even-powered Z shims This can be seen by looking at the shape of a Z2 shim field As you go further away from the center of the sample in the +Z or -Z direction the field increases giving more components of the spectral line at higher fields The higher the power of the Z inhomogeneity the further away the asymmetry is from the center of the line

Symmetrically broadened lines are from mis-adjusted odd-powered Z shims Consider the shape of the Z3 shim field The top of the sample (+Z) is at a higher field resulting in higher field spectral components while the bottom (-Z) is at a lower field giving more lower field spectral components Transverse shims (XY) will cause large first order or second order spinning sidebands when the sample is spun The shape of these inhomogeneities cause the sample when it is spun to experience a periodic variation in the magnetic field Those shims (XY or X2-Y2) causing a spinning sample to experience two variations per cycle will create second order spinning sidebands

Phase Cycling

There are a few artifacts of the detection circuitry which may appear in your spectrum if you record a single FID and Fourier transform it Phase cycling is the technique used to eliminate these artifacts The artifact will be introduced first followed by the technique used to eliminate it

Electronic amplifiers often have small offsets in their output when no signal is being put in This is referred to as the DC offset of the amplifier A DC offset in the time domain is equivalent to a peak at zero frequency in the frequency domain If there is an FID on top of a DC offset its Fourier transform will have an additional peak at zero frequency in the spectrum This picture has been simplified by presenting only the real part of the signal

The DC offset could be eliminated by spending thousands of dollars on better quality amplifiers Alternatively the artifact can be removed by taking an FID recorded with a 90 degree pulse applied along +X an FID recorded with a 90 degree pulse applied along -X (note the phase change in the FID) multiplying the FID recorded with a 90 degree pulse along -X by -1 adding the two FIDs and Fourier transforming This process only costs a little extra time and a few extra lines of computer code

Another type of artifact is caused by having unequal gains on the real and imaginary outputs of the quadrature detector For a Fourier transform to produce a proper spectrum it requires true real and imaginary inputs When the inputs are equal in amplitude there are no negative frequency artifacts in the spectrum If the two inputs are different the negative frequency components of a signal do not cancel You can tell a negative frequency artifact because it appears to be the mirror image (but smaller) of a peak from the opposite sign end of the spectrum

Negative frequency artifacts can be removed by recording an FID with Mx or the real signal (My or the imaginary signal) from channel 1 (2) of the quadrature detector Another FID is recorded with Mx or the real signal (My or the imaginary signal) from channel 2 (1) of the quadrature detector The two FIDs are then averaged As a result the amplitude of the real and imaginary inputs to the FT are equal so when the FIDs are Fourier transformed there are no negative frequency artifacts

The averaging described above can be achieved by applying a 90 degree pulse about +X and a 90 degree pulse about +Y and adding the two resulting FIDs together To eliminate all possible errors from different combinations of these types of pulses phase cycling is applied Phase cycling adds together eight FIDs recorded with the following phases to eliminate all the possible quadrature artifacts

There are several parameters in addition to the ones already discussed in this chapter which must be set before a spectrum can be recorded These include the width of the spectrum number of data points in the spectrum and the receiver gain Some of these are automatically set to default values on some spectrometers You are encouraged to refer to Chapter 5 for a deeper appreciation of the significance of these parameters

Once an FID is recorded and Fourier transformed the resultant spectrum must be phased so that all the absorption lines are positive You are encouraged to review Chapter 5 for an explanation of the need to phase correcting a spectrum There are various automatic and manual phase correction algorithms on most NMR spectrometers

Here are a few examples of simple hydrogen NMR spectra to demonstrate the capabilities of NMR spectroscopy As you become more knowledgeable about NMR you will learn the relationship between peak locations peak splitting and molecular structure in NMR spectra

Molecule Formula Solvent Spectrum

cyclohexane C6H12 CDCl3

benzene C6H6 CDCl3

toluene C6H5CH3 CDCl3

ethyl benzene C6H5CH2CH3 CDCl3

acetone CH3(C=O)CH3 CDCl3

methyl ethyl ketone CH3(C=O)CH2CH3 CDCl3

water H2O D2O

ethanol CH3CH2OH CDCl3

ethanol CH3CH2OH D2O

1-propanol CH3CH2CH2OH CDCl3

2-propanol (CH3)2CHOH CDCl3

t-butanol (CH3)3COH CDCl3

2-butanol CH3CH2CH(OH)CH3 CDCl3

pyridine C5H5N CDCl3

Integration

In addition to chemical shift and spin-spin coupling information there is one additional piece of information which the chemist can use in determining the structure of a molecule from an NMR spectrum This information is the relative area of absorption peaks in the spectrum Here an absorption peak is defined as the family of peaks centered at a particular chemical shift For example if there is a triplet of peaks at a specific chemical shift the number is the sum of the area of the three The rule is that peak area is proportional to the number of a given type of spins in the molecule and in the sample An example should help you understand this relationship

Consider the methyl ethyl ketone (CH3CH2(C=O)CH3) molecule and its hydrogen NMR spectrum When the -CH2- ( = 225 ppm) -CH3 ( = 20 ppm) and CH3- ( = 09 ppm) peaks are integrated we get the following spectrum The areas under the three types of peaks on this spectrometer are 263939 Dividing each number by 13 we obtain a 233 ratio which is proportional to the number of -CH2- to -CH3 to CH3- hydrogens

There are a few assumptions which were made in presenting this rule

The T1 and T2 values of all the spins are equal There is no spin decoupling being performed The signal-to-noise ratio is good There is no sloping baseline in the spectrum

Spin decoupling will be discussed in Chapter 9

You may correct for a sloping baseline by performing a baseline correction to the spectrum A poor signal-to-noise ratio may be improved by performing signal averaging discussed next

SNR Improvement

The signal-to-noise ratio (SNR) of a spectral peak is the ratio of the average height of the peak to the standard deviation of the noise height in the baseline Often spectroscopists approximate this quantity as the average peak height divided by the amplitude of the noise in the baseline The signal to noise ratio may be improved by performing signal averaging Signal averaging is the collection and averaging together of several spectra The signals are present in each of the averaged spectra so their contribution to the resultant spectrum add Noise is random so it does not add but begins to cancel as the number of spectra averaged increases The signal-to-noise improvement from signal averaging is proportional to the square root of the number of spectra (N) averaged

SNR N12

Because of the need to perform phase cycling you will need to have the number of averages equal to a multiple of the minimum number of phase cycling steps Compare the results of averaging together the following number of spectra of a very dilute solution of methyl ethyl ketone

N N12 Spectrum

16 400

80 894

800 2828

Many NMR spectrometers have the ability to control the temperature of the sample in the probe A schematic representation of the variable temperature hardware on an NMR spectrometer is depicted in the animation window All of these spectrometers permit you to set the temperature to values above room temperature by just entering the desired temperature You should be careful not to exceed the maximum temperature allowable for your probe because doing so will melt adhesives and components in the probe Controlling the temperature below room temperature requires the use of hardware to cool the gas flowing over the sample If this gas is air it must be dry air to avoid condensation of water on the sample Once the sample and probe have been cooled or heated you should slowly return the probe to room temperature Do not expose a cold probe to the moist atmosphere condensation will result

Troubleshooting

By now you may realize that an NMR spectrometer is a complex piece of instrumentation with many sub systems which must be functioning properly in order to record a useable NRM spectrum The intent of this section is to provide you with a systematic method of identifying a problem with the spectrometer Once a problem is identified you are not necessarily expected to be able to solve it but you will at least be able to describe the steps you took to diagnose the problem when speaking to a system administrator or a service representative from the manufacturer of your spectrometer Click on this icon to start the diagnosis process in the animation window

Cryogen Fills

Superconducting magnets require liquid nitrogen (N2) and liquid Helium (He) Because it is difficult to make a perfect dewar to hold these cryogens they need to be periodically replenished Liquid nitrogen is typically filled every 7 to 10 days and liquid helium every 200 to 300 days Cryogen fills must be performed correctly to avoid injury to you and the magnet The injuries to you from cryogenic liquids were described in Chapter 7 Injury to a magnet could include breaking a seal on a dewar or quenching a magnet Both forms of magnet injuries are repairable but at the least entail recharging the magnet at the most they can entail replacing the magnet

When filling the magnet with liquid nitrogen you must be sure not to exceed the recommended fill pressure and rate for your magnet If your magnet has two liquid nitrogen ports one should be used for filling and the other for venting the boil-off gaseous nitrogen and overfill liquid nitrogen A piece of tubing is typically placed on the vent port to direct the overfill liquid nitrogen away from the magnet seals probe and electronics It is highly recommended that your liquid nitrogen tanks be made of non-magnetic stainless steel

Liquid helium fills are typically a two-person operation Because they are done so infrequently it is good to review the process before each fill The fill requires a supply dewar of liquid helium a special liquid helium transfer line and a tank of pure compressed helium gas Liquid helium is transferred from the liquid helium supply dewar up through the transfer line into the helium dewar of the magnet

The transfer line goes into the top of the liquid helium supply dewar but should never rest on the bottom of the dewar The bottom of the dewar may contain frozen water oxygen and nitrogen which will be forced into your magnet if the transfer line touches the bottom during the transfer process The compressed helium gas mentioned earlier is for pressurizing the liquid helium supply dewar with about 2 to 4 psi of pressure Gauges on helium supply dewars can be very inaccurate so do not count on them to give you an accurate reading A helium pressure above the liquid forces the Helium into the magnet dewar

The transfer line is usually inserted into the magnet until it contacts a transfer flange in the bottom of the magnet The nitrogen ports on the magnet should be plugged with a check valve during filling of the helium dewar of the magnet This step prevents cryopumping a process whereby nitrogen water and oxygen are condensed out of the atmosphere into the nitrogen dewar due to the magnet stacks being cooled by the helium Many labs loosely plug the helium vents with tissue during the fill This cuts down on cryopumping should the flow of the venting He drop

The best way to determine if the magnet is full is to look for a change in the gas cloud coming out of the magnet vents When the magnet is full the cloud becomes very thick with a deep white center plume with a slight blue tint The helium vents on the magnet should be closed promptly after the magnet is full

Unix Primer

Most NMR spectrometers are controlled by a computer workstation The NMR program which gives your spectrometer the look and feel you are used to is running on this computer This computer is most likely running a UNIX operating system The operating system is equivalent to DOS on a Microsoft system or OS-5 on a Macintosh system Although you may be able to perform all the file transfer and manipulation commands from your NMR program you may find it useful to know a few UNIX commands This chapter is intended to give you enough information about UNIX to perform simple tasks in the UNIX operating system

The UNIX file system is divided into directories which are equivalent to folders in some operating systems Because UNIX is a multi-user system there must be a way to keep your directories separate (and safe) from someone elses To achieve this there are accounts with passwords and ownership of directories For example you have an account which has a password Logging on under your account gives you access to your directories and to other directories for which you have access (permission)

The most useful but least used command in UNIX is man This is short for manual and gives you on-line help on every UNIX command The more you use it the easier it is to use The animation window contains a table of a few simple UNIX commands Entries in italics are examples and can be any string of characters or numbers

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction Decoupling

Population Inversion

1-D C-13 Spectra

Introduction

Many of the molecules studied by NMR contain carbon Unfortunately the carbon-12 nucleus does not have a nuclear spin but the carbon-13 (C-13) nucleus does due to the presence of an unpaired neutron Carbon-13 nuclei make up approximately one percent of the carbon nuclei on earth Therefore carbon-13 NMR spectroscopy will be less sensitive (have a poorer SNR) than hydrogen NMR spectroscopy With the appropriate concentration field strength and pulse sequences however carbon-13 NMR spectroscopy can be used to supplement the previously described hydrogen NMR information Advances in superconducting magnet design and RF sample coil efficiency have helped make carbon-13 spectroscopy routine on most NMR spectrometers

The sensitivity of an NMR spectrometer is a measure of the minimum number of spins detectable by the spectrometer Since the NMR signal increases as the population difference between the energy levels increases the sensitivity improves as the field strength increases The sensitivity of carbon-13 spectroscopy can be increased by any technique which increases the population difference between the lower and upper energy levels or increases the density of spins in the sample The population difference can be increased by decreasing the sample temperature or by increasing the field strength Several techniques for increasing the carbon-13 signal have been reported in the NMR literature

Unfortunately or fortunately depending on your perspective the presence of spin-spin coupling between a carbon-13 nucleus and the nuclei of the hydrogen atoms bonded to the carbon-13 splits the carbon-13 peaks and causes an even poorer signal-to-noise ratio This problem can be addressed by the use of a technique known as decoupling addressed in the next section

Decoupling

The signal-to-noise ratio in an NMR spectrometer is related to the population difference between the lower and upper spin state The larger this difference the larger the signal We know from chapter 3 that this difference is proportional to the strength of the Bo magnetic field

To understand decoupling consider the familiar hydrogen NMR spectrum of HC-(CH2CH3)3 The HC hydrogen peaks are difficult to see in the spectrum due to the splitting from the 6 -CH2- hydrogens If the effect of the 6 -CH2- hydrogens could be removed we would lose the 1615201561 splitting for the HC hydrogen and get one peak We would also lose the 131 splitting for the CH3 hydrogens and get one peak The process of removing the spin-spin splitting between spins is called decoupling Decoupling is achieved with the aid of a saturation pulse If the affect of the HC hydrogen is removed we see the following spectrum Similarly if the affect of the -CH3

hydrogens is removed we see this spectrum

A saturation pulse is a relatively low power B1 field left on long enough for all magnetization to disappear A saturation pulse applied along X rotates magnetization clockwise about X several times As the magnetization is rotating T2 processes cause the magnetization to dephase At the end of the pulse there is no net Z X or Y magnetization It is easier to see this behavior with the use of plots of MZ MX and MY as a function of time Since the B1 pulse is long its frequency content is small It therefore can be set to coincide with the location of the -CH2- quartet and saturate the -CH2- spin system By saturating the -CH2- spins the -CH2- peaks and the splittings disappear causing the height of the now unsplit HC- and -CH3 peaks to be enhanced

Now that the concept of decoupling has been introduced consider the carbon-13 spectrum from CH3I The NMR spectrum from the carbon-13 nucleus will yield one absorption peak in the spectrum Adding the nuclear spin from one hydrogen will split

the carbon-13 peak into two peaks Adding one more hydrogen will split each of the two carbon-13 peaks into two giving a 121 ratio The final hydrogen will split each of the previous peaks giving a 1331 ratio If the hydrogen spin system is saturated the four lines collapse into a single line having an intensity which is eight times greater than the outer peak in the 1331 quartet since 1+3+3+1=8 In reality we see a single line with a relative intensity of 24 Where did the extra factor of three come from

The answer to the question raised in the previous paragraph is the nuclear Overhauser effect (NOE) To understand the NOE consider a set of coupled hydrogen and carbon-13 nuclei Assume that the red-green nuclei are carbon-13 and the blue-pink nuclei are hydrogen

T1CC is T1 relaxation due to interactions between carbon-13 nuclei T1HH is T1 relaxation due to interactions between hydrogen nuclei T1CH is T1 relaxation due to interactions between carbon-13 and hydrogen nuclei

MZ(C) is the magnetization due to carbon-13 nuclei Mo(C) is the equilibrium magnetization of carbon-13 MZ(H) is the magnetization due to hydrogen nuclei Mo(H) is the equilibrium magnetization of hydrogen

The equations governing the change in the Z magnetization with time are

If we saturate the hydrogen spins MZ(H) = 0

Letting the system equilibrate d MZ(C) dt = 0

Rearranging the previous equation we obtain an equation for MZ(C)

Note that MZ(C) has increased by Mo(H) T1CC T1CH which is approximately 2 Mo(C) giving a total increase of a factor of 3 relative to the total area of the undecoupled peaks This explains the extra factor of three (for a total intensity increase of 24) for the carbon-13 peak when hydrogen decoupling is used in the carbon-13 spectrum of CH3I

The following spin-echo sequence has been modified to decouple the hydrogen spins from the carbon-13 spins The signal is recorded as the second half of the echo

Another method of improving the NMR signal in systems with spin-spin coupling is population inversion To understand the concept of a population inversion recall from Chapter 3 that Boltzmann statistics tell us that there are more spins in the lower spin state than the upper one of a two spin state system Population inversion is the interchange of the populations of these two spin states so that there are more spins in the upper state then the lower one

To understand how a population inversion improves the signal-to-noise ratio in a spectrum consider the CHI3 molecule CHI3 will have four energy levels (L1 L2 L3 and L4) due to C-H spin-spin coupling There are two carbon-13 absorption frequencies f1 and f2 and two hydrogen absorption frequencies f3 and f4 The population distribution between the four levels is such that the lowest state has the greatest population and the highest the lowest population The two intermediate states will have populations between the outer two as indicated by the thickness of the levels in the accompanying diagram The four lines in the spectrum will have intensities related to the population difference between the two levels spanned by the frequency The two carbon-13 absorption lines (f1 and f2) will have a lower intensity than the hydrogen lines (f3 and f4) due to the smaller population difference between the two states joined by f1 and f2

If the populations of L3 and L1 are inverted or interchanged with a frequency selective 180 degree pulse at f3 the signal at f2 will be enhanced because of the greater population

difference between the states joined by f2 It should be noted that the signal at f1 will be inverted because the upper state of the two joined by f1 has a greater population than the lower one An example of a population inverting pulse sequence designed to enhance the carbon-13 spectral lines is depicted in the animation window The 180 degree pulse at f3

has a narrow band of frequencies centered on f3 that selectively rotates only the magnetization at f3 by 180 degrees

1-D C-13 Spectra

The following table of compounds contains links to their corresponding one-dimensional carbon-13 NMR spectra The spectra were recorded on a 300 MHz NMR spectrometer with a delay time between successive scans of two seconds This relatively short delay time may cause differences in the peak heights due to variations in T1 values Other differences may be caused by variations in the nuclear Overhauser effect In spectra recorded with deuterated chloroform (CDCl3) as the lock solvent the three peaks at = 75 are due to splitting of the CDCl3 carbon-13 peak by the nuclear spin = 1 deuterium nucleus

benzene C6H6 CDCl3

t-butnol (CH3)3COH CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction J-resolved

Examples

Introduction

In Chapter 6 we saw the mechanics of the spin echo sequence Recall that a 90 degree pulse rotates magnetization from a single type of spin into the XY plane The magnetization dephases and then a 180 degree pulse is applied which refocusses the magnetization

When a molecule with J coupling (spin-spin coupling) is subjected to a spin-echo sequence something unique but predictable occurs Look at what happens to the molecule A2-C-C-B where A and B are spin-12 nuclei experiencing resonance The NMR spectrum from a 90-FID sequence looks like this

With a spin-echo sequence this same molecule gives a rather peculiar spectrum once the echo is Fourier transformed Here is a series of spectra recorded at different TE times The amplitude of the peaks have been standardized to be all positive when TE=0 ms

To understand what is happening consider the magnetization vectors from the A nuclei There are two absorptions lines in the spectrum from the A nuclei one at +J2 and one at -J2 At equilibrium the magnetization vectors from the +J2 and -J2 lines in the spectrum are both along +Z

A 90 degree pulse rotates both magnetization vectors into the XY plane Assuming a rotating frame of reference at o = the vectors precess according to their Larmor frequency and dephase due to T2 When the 180 degree pulse is applied it rotates the magnetization vectors by 180 degrees about the X axis In addition the +J2 and -J2 magnetization vectors change places because the 180 degree pulse also flips the spin state of the B nucleus which is causing the splitting of the A spectral lines

The two groups of vectors will refocus as they evolve at their own Larmor frequency In this example the precession in the XY plane has been stopped when the vectors have refocussed You will notice that the two groups of vecotrs do not refocus on the -Y axis The phase of the two vectors on refocussing varies as a function of TE This phase varies as a function of TE at a rate equal to the size of the spin-spin coupling frequency Therefore measuring this rate of change of phase will give us the size of the spin-spin coupling constant This is the basis of one type of two-dimensional (2-D) NMR spectroscopy

J-resolved

In a 2-D J-resolved NMR experiment time domain data is recorded as a function of TE and time These two time dimensions will referred to as t1 and t2 For the A2-C-C-B molecule the complete time domain signals look like this

This data is Fourier transformed first in the t2 direction to give an f2 dimension and then in the t1 direction to give an f1 dimension

Displaying the data as shaded contours we have the following two-dimensional data set Rotating the data by 45 degrees makes the presentation clearer The f1 dimension gives

us J coupling information while the f2 dimension gives chemical shift information This type of experiment is called homonuclear J-Resolved 2-D NMR There is also heteronuclear J-resolved 2-D NMR which uses a spin echo sequence and techniques similar to those described in Chapter 9

The application of two 90 degree pulses to a spin system will give a signal which varies with time t1 where t1 is the time between the two pulses The Fourier transform of both the t1 and t2 dimensions gives us chemical shift information The 2-D hydrogen correlated chemical shift spectrum of ethanol will look like this There is a wealth of information found in a COSY spectrum A normal (chemical shift) 1-D NMR spectrum can be found along the top and left sides of the 2-D spectrum Cross peaks exist in the 2-D COSY spectrum where there is spin-spin coupling between hydrogens There are cross peaks between OH and CH2 hydrogens and also between CH3 and CH2 hydrogens hydrogens There are no cross peaks between the CH3 and OH hydrogens because there is no coupling between the CH3 and OH hydrogens

Heteronuclear correlated 2-D NMR is also possible and useful

Examples

The following table presents some of the hundreds of possible 2-D NMR experiments and the data represented by the two dimensions The interested reader is directed to the NMR literture for more information

2-D Experiment (Acronym) Information

Homonuclear J resolved J

Heteronuclear J resolved JAX X

Homoculclear correlated spectroscopy (COSY) A A

Heteronuclear correlated spectroscopy (HETCOR) A X

Nuclear Overhauser Effect (2D-NOE) H JHH H JHH

2D-INADEQUATE A + X X

The following table of molecules contains links to their corresponding two-dimensional NMR spectra The spectra were recorded on a 300 MHz NMR spectrometer with CDCl3 as the lock solvent

Molecule Formula Type Spectrum

methyl ethyl ketone CH3(C=O)CH2CH3 COSY

ethanol CH3CH2OH COSY

1-propanol CH3CH2CH2OH COSY

2-propanol (CH3)2CHOH COSY

2-butanol CH3CH2CH(OH)CH3 COSY

ethyl benzene C6H5CH2CH3 COSY

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

ADVANCED SPECTROSCOPIC TECHNIQUES

Introduction Diffusion

Spin Relaxation Time

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Nuclear magnetic resonance spectroscopy is one of the richest spectroscopies available In previous chapters you have seen how it can be used to elucidate chemical structure In this chapter you will see some of the other more advanced applications of NMR Two of these techniques solid state NMR and gradient enhanced spectroscopy will assist us further in the determination of molecular structure Two additional techniques will assist us in studying molecular dynamics or the rotational and translational motions of molecules The last technique NMR microscopy will enable us to determine the spatial distribution of nuclear spins in a sample

Diffusion

Diffusion is the motion of particles due to Brownian motion The diffusion coefficient D is a measure of the diffusion The pulsed-gradient spin-echo sequence permits us to measure the diffusion coefficient The sequence is in theory capable of measuring both the rotational and translational diffusion coefficients but is used primarily for studying translational diffusion

To understand how the pulsed-gradient spin-echo sequence allows us to measure diffusion consider the timing diagram for the sequence This sequence is very similar to the spin echo sequence introduced in Chapter 6 except that two gradient pulses have been applied These two gradient pulses are identical in amplitude G and width The two gradient pulses are separated by a time and are placed symmetrically about the 180 degree pulse

The function of the gradient pulses is to dephase magnetization from spins which have diffused to a new location in the period These pulses have no effect on stationary spins For example a stationary spin exposed to the first gradient pulse applied along the Z axis will acquire a phase in radians given by

= 2 z Gz dt The spin will acquire an equal but opposite phase from the second pulse since the pulses are on different sides of the 180 degree RF pulse Thus their effects cancel each other out

Consider the following illustration of the effect of the gradient pulses on the phase of stationary and moving spins The illustration presents the phase of a diffusing spin relative to that of a reference spin and a stationary spin The reference spin is one which experiences no gradient pulses The stationary spin is not diffusing during the time illustrated by the sequence The diffusing spin moves along Z during the sequence The blue line in the timing diagram represents the time of the 180 degree pulse in the spin echo sequence When you put the illustration into motion the stationary spin comes back into phase with the reference one indicating a positive contribution to the echo The diffusing spin does not come back into phase with the reference spin so it diminishes the echo height

The relationship between the signal (S) obtained in the presence of a gradient amplitude Gi in the i direction and the diffusion coefficient in the same direction is given by the following equation where So is the signal at zero gradient

SSo = exp[-(Gi )2 Di ( - 3)]

The diffusion coefficient is typically calculated from a plot of ln(SSo) versus (G )2 ( - 3) Diffusion in the x y or z direction may be measured by applying the gradient respectively in the x y or z direction

The spin-lattice and spin-spin relaxation times T1 and T2 respectively of the components of a solution are valuable tools for studying molecular dynamics You saw in Chapter 3 that T1

-1 is proportional to the number of molecular motions at the Larmor frequency while T2

-1 is proportional to the number of molecular motions at frequencies less than or equal to the Larmor frequency When we are dealing with solutions these motions are predominantly rotational motions

There are many pulse sequences which may be used to measure T1 and T2 The inversion recovery 90-FID and spin-echo sequences may be used to measure T1 Each technique has its own advantages and disadvantages The spin-echo sequence may be used to measure T2

T1 MeasurementRecall the timing diagram for an inversion recovery sequence first presented in Chapter 6

S = k ( 1 - 2eTIT1 )

If the curve is well defined (ie if there is a high density of data points recorded at different TI times) the T1 value can be determined from the zero crossing of the curve which is T1 ln2

Alternatively the relaxation curve as a function of TI may be fit using the equation

S = So (1 - 2e-TIT1)

This approach is favored when there are fewer data points as a function of TI

T1 may also be determined from a 90-FID or spin-echo sequence which is repeated at various repetition times (TR) For example if the 90-FID sequence is repeated many times at TR1 and then many times at TR2 TR3 etc the plot of signal as a function of TR will be an exponential growth of the form

S = k ( 1 - eTRT1 )

This data may be fit to obtain T1

The difficulty with fitting this data and the inversion recovery data is a lack of knowledge of the value of the equilibrium magnetization or signal So Other techniques have been proposed which do not require knowledge of the equilibrium magnetization or signal

T2 Measurement Measurement of the spin-spin relaxation time requires the use of a spin-echo pulse sequence The echo amplitude S as a function of echo time TE is exponentially decaying Plotting ln(SSo) versus TE yields a straight line the slope of which is -1T2

A linear least squares algorithm is often used to find the slope and hence T2 value This approach can result in lead to large errors in the calculated T2 values when the data has noise The later points in the decay curve have poorer signal-to-noise ratio than the earlier points but are given equal weight by the linear least squares algorithm The solution to this problem is to use a non-linear least squares procedure

Solid State

We saw in Chapter 4 that the magnitude of the chemical shift is related to the extent to which the electron can shield the nucleus from the applied magnetic field In a spherically symmetric molecule the chemical shift is independent of molecular orientation In an asymmetric molecule the chemical shift is dependent on the orientation The magnetic field experienced by the nucleus varies as a function of the orientation of the molecule in the magnetic field The NMR spectrum from a random distribution of fixed orientations such as in a solid would look like this The larger signal at lower field strength is due to the fact that there are more perpendicular orientations In a nonviscous liquid the fields at the various orientations average out due to the tumbling of the molecule

The anisotropic chemical shift is one reason why the NMR spectra of solid samples display broad spectral lines Another reason for broad spectral lines is dipolar broadening A dipolar interaction is one between two spin 12 nuclei The magnitude of the interaction varies with angle and distance r As a function of the magnetic field B experienced by the red nucleus is

(3cos2 - 1)

A group of dipoles with a random distribution of orientations as in a solid gives this spectrum The higher signal at mid-field strength is due to the larger presence of orientations perpendicular to the direction of the Bo field This signal is made up of components from the red and blue nuclei in the dipole In a nonviscous liquid the interaction averages out due to the presence of rapid tumbling of the molecule

When the angle in the above equation is 547o 1253o 2347o or 3053o the dipole interaction vanishes The angle 547o is called the magic angle m

If all the molecules could be positioned at m the spectrum would narrow to the fast tumbling limit

Since this is not possible the next best thing is to cause the average orientation of the molecules to be m

Even this is not exactly possible but the closest approximation is to rapidly spin the entire sample at an angle m relative to Bo In solid state NMR samples are placed in a special sample tube and the tube is placed inside a rotor The rotor and hence the sample are oriented at an angle m with respect to the Bo magnetic field The sample is then spun at a rate of thousands of revolutions per second

The spinning rate must be comparable to the solid state line width The centrifigal force created by spinning the sample tube at a rate of several thousands of revolutions per second is enough to destroy a typical glass NMR sample tube Specially engineered sample tubes and rotors are needed

Microscopy

NMR microscopy is the application of magnetic resonance imaging (MRI) principles to the study of small objects Objects which are studied are typically less than 5 mm in diameter NMR microscopy requires special hardware not found on conventional NMR spectrometers This includes gradient coils to produce a gradient in the magnetic field along the X Y and Z axes gradient coil drivers RF pulse shaping software and image processing software Resultant images can have 20 to 50 m resolution The reader interested in more information on NMR microscopy is encouraged to read the authors hypertext book on MRI entitled The Basics of MRI located at httpwwwcisriteduhtbooksmri

Solvent Suppression

Occasionally it becomes necessary to eliminate the signal from one constituent of a sample An example is an unwanted water signal which overwhelms the signal from the desired constituent If T1 of the two components differ this may be accomplished by using an inversion recovery sequence presented in Chapter 6 To eliminate the water signal choose the TI to be the time when the water signal passes through zero

TI = T1 ln2

In this example a TI = 1 s would eliminate the water signal

Another method of eliminating a solvent absorption signal is to saturate it In this procedure a saturation pulse similar to that employed in C-13 NMR (See Chapter 9) is used to decouple hydrogen coupling The frequency of the saturation pulse is set to the

solvent resonance The width of the saturation pulse is very long so its bandwidth is very small causing it to affect only the solvent resonance

Field Cycling NMR

Field cycling NMR spectroscopy is used to obtain spin-lattice relaxation rates R1 where R1 = 1T1

as a function of magnetic field or Larmor frequency Therefore field cycling NMR finds applications in the study of molecular dynamics The animation window contains an example of results from a field cycling NMR spectrometer The plot represents the R1 value of the hydrogen nuclei in various concentration aqueous solutions of Mn+2 at 25o as a function of the proton Larmor frequency

Many different techniques have been used to obtain R1 as a function of magnetic field Some techniques move the sample rapidly between different magnetic field strengths One of the more popular techniques keeps the sample at a fixed location and rapidly varies the magnetic field the sample experiences This technique is referred to as rapid field cycling NMR spectroscopy

The principle behind a rapid field cycling NMR spectrometer is to polarize the spins in the sample using a high magnetic field Bp The magnetic field is rapidly changed to the value at which relaxation occurs Br Br is the value at which R1 is to be determined After a period of time the magnetic field is switched to a value Bd at which detection of a signal occurs Bd is fixed so that the operating frequency of the detection circuitry does not need to be changed The signal an FID is created by the application of a 90o RF pulse The timing diagram for this sequence can be found in the animation window

The FT of the FID represents the amount of magnetization present in the sample after relaxing for a period in Br A plot of this magnetization as a function of is an exponentially decaying function starting from the equilibrium magnetization at Bp and going to the value at Br When a single type of spin is present the relaxation is monoexponential with rate constant R1 at Br

When Br is very large compared to Bd Bp is often set to zero and the plot of this magnetization as a function of is an exponentially growing function

Glossary

Artifact A feature which appears in an NMR spectrum of a molecule which should not be present based on the chemical structure and pulse sequence used [Chapter 7]

Chemical Screening

The screening of an applied magnetic field experienced by a nucleus due to the electron cloud around an atom or molecule [Chapter 4]

Chemical Shift A variation in the resonance frequency of a nuclear spin due to the chemical environment around the nucleus Chemical shift is reported in ppm [Chapter 4]

Coil One or more loops of a conductor used to create a magnetic field In NMR the term generally refers to the radiofrequency coil [Chapter 7]

Convolution A mathematical operation between two functions [Chapter 2]

Complex Data Numerical data with a real and an imaginary component [Chapter 2]

Continuous Wave (CW) A form of spectroscopy in which a constant amplitude electromagnetic wave is applied [Chapter 3]

Coordinate Transformation A change in the axes used to represent some spatial quantity [Chapter 2]

Cryopumping The condensation of air onto a surface cooled by a cryogenic liquid [Chapter 8]

Dephasing Gradient A magnetic field gradient used to dephase transverse magnetization [Chapter 11]

Digital Filtering A feature found on may newer spectrometers which eliminates wraparound artifacts by filtering out the higher frequency components in the time domain spectrum [Chapter 7]

Doubly balanced mixer An electrical device often referred to as a product detector which is used in NMR to convert signals from the laboratory frame of reference to the rotating frame of reference [Chapter 7]

Echo A form of magnetic resonance signal from the refocusing of transverse magnetization [Chapter 6]

Echo Time ( TE ) The time between the 90 degree pulse and the maximum in the echo in a spin-echo sequence [Chapter 6]

Exchange Chemical The interchange of chemically equivalent components on a molecule [Chapter 3]

Exchange Spin The interchange of spin state between two nuclei [Chapter 3]

Figure-8 Coil A magnetic field gradient coil shaped like the number eight [Chapter 7]

Free induction decay ( FID ) A form of magnetic resonance signal from the decay of transverse magnetization [Chapter 4]

Fourier transform ( FT ) A mathematical technique capable of converting a time domain signal to a frequency domain signal and vice versa [Chapter 5]

Gradient ( G ) A variation in some quantity with respect to another In the context of NMR a magnetic field gradient is a variation in the magnetic field with respect to distance [Chapter 7]

Gyromagnetic Ratio The ratio of the resonance frequency to the magnetic field strength for a given nucleus [Chapter 3]

Imaginary Component The component of a signal perpendicular to the real signal [Chapter 5]

Imaging Sequence A specific set of RF pulses and magnetic field gradients used to produce an image [Chapter 11]

Inversion Recovery Sequence A pulse sequence producing signals which represent the longitudinal magnetization present after the application of a 180o inversion RF pulse [Chapter 6

Inversion Time (TI) The time between the inversion pulse and the sampling pulse(s) in an inversion recovery sequence [Chapter 6]

K-Space That image space represented by the time and phase raw data The Fourier transform of k-space is the magnetic resonance image [Chapter 5]

Larmor frequency The resonance frequency of a spin in a magnetic field The rate of precession of a spin packet in a magnetic field The frequency which will cause a transition between the two spin energy levels of a nucleus [Chapter 3]

Longitudinal Magnetization The Z component of magnetization [Chapter 3]

Lorentzian Lineshape A function obtained from the Fourier transform of an exponential function [Chapter 5]

Magnitude The length of a magnetization vector In NMR the square root of the sum of the squares of the Mx and My components ie the magnitude of the transverse magnetization [Chapter 2]

Magnetic Resonance Imaging (MRI) An imaging technique based on the principles of NMR [Chapter 11]

Negative Frequency Artifact The appearance of smaller in amplitude peaks in one half of the spectrum which are the mirror image of ones in the opposite half [Chapter 8]

Net Magnetization Vector

A vector representing the sum of the magnetization from a spin system [Chapter 3]

Nuclear Magnetic Resonance (NMR) A spectroscopic technique used by scientists to elucidate chemical structure and molecular dynamics [Chapter 1]

Pixel Picture element [Chapter 1]

Precess A rotational motion of a vector about the axis of a coordinate system where the polar angle is fixed and the azmuthal angle changes steadily [Chapter 3]

Proportionality Constant A constant used to convert one set of units to another [Chapter 8]

Pulse Sequence A series of RF pulses andor magnetic field gradients applied to a spin system to produce a signal whose behavior gives information about some property of the spin system [Chapter 4]

Quadrature Detection Detection of Mx and My simultaneously as a function of time [Chapter 9]

Radio Frequency A frequency band in the electromagnetic spectrum with frequencies in the millons of cycles per second [Chapter 3]

Raw data The Mx and My data as a function of time andor other parameters in an NMR pulse sequence This is also called k-space data [Chapter 10]

Real The component of a signal perpendicular to the imaginary signal [Chapter 2]

Repetition Time The time between repetitions of the basic sequence in a pulse sequence [Chapter 6]

Resonance An exchange of energy between two systems at a specific frequency [Chapter 3]

RF Coil An inductor-capacitor resonant circuit used to set up B1 magnetic fields in the sample and to detect the signal from the sample [Chapter 7]

RF Pulse A short burst of RF energy which has a specific shape

Rotation Matrix A matrix used to describe the rotation of a vector [Chapter 3]

Sample Probe That portion of the NMR spectrometer containing the RF coils and into which the sample is placed [Chapter 7]

Saddle Coil A coil geometry which has two loops of a conductor wrapped around opposite sides of a cylinder [RF Chapter 7]

Spin A fundamental property of matter responsible for NMR and MRI [Chapter 3]

Spin Density The concentration of spins [Chapter 6]

Spin-Echo An NMR sequence whose signal is an echo resulting from the refocusing of magnetization after the application of 90o and 180o RF pulses [Chapter 6]

Spin-Lattice Relaxation The return of the longitudinal magnitization to its equilibrium value along the +Z axis [Chapter 3]

Spin-Lattice Relaxation Time ( T1 ) The time to reduce the difference between the longitudinal magnitization and its equilibrium value by a factor of e [Chapter 3]

Spin Packet A group of spins experiencing the same magnetic field [Chapter 3]

Spin-Spin Relaxation The return of the transverse magnitization to its equilibrium value (zero) [Chapter 3]

Spin-Spin Relaxation Time The time to reduce the transverse magnetization by a factor of e [Chapter 3]

Sinc Pulse An RF pulse shaped like Sin(x)x [Chapter 5]

Superconduct To have no resistance A perfect superconductor can carry an electrical current without losses [Chapter 7]

T2 Pronounced T-2-star The spin-spin relaxation time composed of contributions from molecular interactions and inhomogeneities in the magnetic field [Chapter 3]

Timing Diagram A multiaxis plot of some aspects of a pulse sequence as a function of time [Chapter 6]

Transverse magnetization The XY component of the net magnetization [Chapter 3]

List of Symbols

Symbol Definition

Aring Angstrom (10-10 meters)

Bo Static magnetic field

B1 The radio frequency magnetic field

C Contrast

C Electrical eapacitance

COSY 2-D correlated spectroscopy

CW Continuous wave

D Deuterium

D Diffusion coefficient

Chemical shift

Magnetic field gradient pulse width

Magnetic field gradient pulse separation

Chemical shift

E Energy

f Frequency

FID Free induction decay

FT Fourier transform

Gi Magnetic field gradient in the i direction

Gyromagnetic ratio

h Plancks constant

H Hydrogen

IFT Inverse Fourier transform

IM Imaginary part of a complex number

J Joule

J Spin-spin coupling constant

k Boltzmann constant

k kilo (103)

k Proportionality constant

K Kelvin temperature

L Electrical Inductance

m milli (10-3)

M mega (106)

micro (10-6)

Mo Equilibrium magnetization

MX X component of magnetization

MY Y component of magnetization

MZ Z component of magnetization

MXY Transverse component of magnetization

MRI Magnetic resonance imaging

Resonance frequency in Hertz

N Number of averages

N+ Spin population in low energy state

N- Spin population in high energy state

NMR Nuclear magnetic resonance

Resonance frequency in radians per second

Ohm impedance

314159

Phase angle

ppm Parts per million

R1 Spin-lattice relaxation rate

RE Real part of a complex number

RF Radio frequency

s Second

Chemical shielding constant

SAR Specific absorption rate

Sinc Sin(x)x

SNR Signal-to-noise ratio

T Temperature

T Tesla

T1 Spin-lattice relaxation time

T2 Spin-spin relaxation time

T2 T2 star

T2inhomo Inhomogeneous T2

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

X X axis in laboratory coordinate system

X Rotating frame X axis

Y Y axis in laboratory coordinate system

Y Rotating frame Y axis

Z Z axis in laboratory coordinate system

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

complicated molecules These techniques are replacing x-ray crystallography for the determination of protein structure Time domain NMR spectroscopic techniques are used to probe molecular dynamics in solutions Solid state NMR spectroscopy is used to determine the molecular structure of solids Other scientists have developed NMR methods of measuring diffusion coefficients

The versatility of NMR makes it pervasive in the sciences Scientists and students are discovering that knowledge of the science and technology of NMR is essential for applying as well as developing new applications for it Unfortunately many of the dynamic concepts of NMR spectroscopy are difficult for the novice to understand when static diagrams in hard copy texts are used The chapters in this hypertext book on NMR are designed in such a way to incorporate both static and dynamic figures with hypertext This book presents a comprehensive picture of the basic principles necessary to begin using NMR spectroscopy and it will provide you with an understanding of the principles of NMR from the microscopic macroscopic and system perspectives

Units Review

Before you can begin learning about NMR spectroscopy you must be versed in the language of NMR NMR scientists use a set of units when describing temperature energy frequency etc Please review these units before advancing to subsequent chapters in this text

Units of time are seconds (s)

Angles are reported in degrees (o) and in radians (rad) There are 2 radians in 360o

The absolute temperature scale in Kelvin (K) is used in NMR The Kelvin temperature scale is equal to the Celsius scale reading plus 27315 0 K is characterized by the absence of molecular motion There are no degrees in the Kelvin temperature unit

Magnetic field strength (B) is measured in Tesla (T) The earths magnetic field in Rochester New York is approximately 5x10-5 T

The unit of energy (E) is the Joule (J) In NMR one often depicts the relative energy of a particle using an energy level diagram

The frequency of electromagnetic radiation may be reported in cycles per second or radians per second Frequency in cycles per second (Hz) have units of inverse seconds (s-

1) and are given the symbols or f Frequencies represented in radians per second (rads) are given the symbol Radians tend to be used more to describe periodic circular motions The conversion between Hz and rads is easy to remember There are 2 radians in a circle or cycle therefore

2 rads = 1 Hz = 1 s-1

The Basics of NMR

Chapter 2

Vectors

Matrices

Convolutions

Imaginary Numbers

ex = exp(x) = 271828183x

x = ey

ln(x) = y

y = e-xt

y = (1 - e-xt)

y = (1 - 2e-xt)

Vectors

( X2 + Y2 )12

Matrices

Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Nuclei with Spin

Energy Levels

Transitions

Spin Packets

T 1 Processes

Precession

T 2 Processes

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The Basics of NMR

Chapter 2

Vectors

Matrices

Convolutions

Imaginary Numbers

ex = exp(x) = 271828183x

x = ey

ln(x) = y

y = e-xt

y = (1 - e-xt)

y = (1 - 2e-xt)

Vectors

( X2 + Y2 )12

Matrices

Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Nuclei with Spin

Energy Levels

Transitions

Spin Packets

T 1 Processes

Precession

T 2 Processes

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

x = ey

ln(x) = y

y = e-xt

y = (1 - e-xt)

y = (1 - 2e-xt)

Vectors

( X2 + Y2 )12

Matrices

Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Nuclei with Spin

Energy Levels

Transitions

Spin Packets

T 1 Processes

Precession

T 2 Processes

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Vectors

( X2 + Y2 )12

Matrices

Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Nuclei with Spin

Energy Levels

Transitions

Spin Packets

T 1 Processes

Precession

T 2 Processes

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Nuclei with Spin

Energy Levels

Transitions

Spin Packets

T 1 Processes

Precession

T 2 Processes

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Spin Relaxation

Spin Exchange

Bloch Equations

Properties of Spin

Nuclei with Spin

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

2H 1 1 1 654 31P 1 0 12 1725 23Na 1 2 32 1127 14N 1 1 1 308 13C 0 1 12 1071 19F 1 0 12 4008

Energy Levels

Transitions

E = h B

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

CW NMR Experiment

N-N+ = e-EkT

Spin Packets

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

T1 Processes

Mz = Mo ( 1 - e-tT1 )

Mz = Mo ( 1 - 2e-tT1 )

Precession

T2 Processes

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

MXY =MXYo e-tT2

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

= 2 B1

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Spin Relaxation

Spin Exchange

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

A( ) + B( ) A( ) + B( )

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

NMR SPECTROSCOPY

Chemical Shift

B = Bo (1-)

= ( - REF) x106 REF

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Spin-Spin Coupling

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

AB2 121

AB3 1331

AB4 14641

AB5 15101051

AB6 1615201561

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Phase Correction

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Fourier Pairs

The Digital FT

Sampling Error

Introduction

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

=1 =2 =3 =4 =5 =6 =7 =8 =9 =10

Phase Correction

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

f(t) = e-at e-i2 t

= m + b

Fourier Pairs

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Gaussian exp(-at2)

Convolution Theorem

The Digital FT

Sampling Error

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The 90-FID Sequence

S = k ( 1 - e-TRT1 )

S = k ( 1 - e-TRT1 ) e-TET2

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

S = k ( 1 - 2e-TIT1 )

The Basics of NMR

Chapter 7

NMR HARDWARE

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Magnet

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Field Lock

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Shim Coils

Shim Function

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Safety

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The Basics of NMR

Chapter 8

Sample Probe Tuning

Field Shimming

Phase Cycling

Integration

SNR Improvement

Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Nuclei (ppm)

Interaction J (Hz)

Sample Preparation

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Sample Probe Tuning

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Field Shimming

Shim Spectrum

X Y ZX or ZY

XY or X2-Y2

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Phase Cycling

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

benzene C6H6 CDCl3

water H2O D2O

Integration

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

SNR Improvement

SNR N12

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

N N12 Spectrum

16 400

80 894

800 2828

Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

The Basics of NMR

Chapter 9

CARBON-13 NMR

1-D C-13 Spectra

Introduction

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Decoupling

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

1-D C-13 Spectra

benzene C6H6 CDCl3

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Examples

Introduction

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

J-resolved

Examples

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

pyridine C5H5N COSY

The Basics of NMR

Chapter 11

Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Diffusion

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

SSo = exp[-(Gi )2 Di ( - 3)]

S = k ( 1 - 2eTIT1 )

S = So (1 - 2e-TIT1)

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

S = k ( 1 - eTRT1 )

Solid State

(3cos2 - 1)

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Microscopy

Solvent Suppression

TI = T1 ln2

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Field Cycling NMR

Glossary

Chemical Screening

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

List of Symbols

Symbol Definition

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

C Contrast

CW Continuous wave

D Deuterium

Chemical shift

E Energy

f Frequency

Gyromagnetic ratio

h Plancks constant

H Hydrogen

J Joule

k kilo (103)

m milli (10-3)

M mega (106)

micro (10-6)

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

Ohm impedance

314159

Phase angle

RF Radio frequency

s Second

Sinc Sin(x)x

T Temperature

T Tesla

T2 T2 star

Rotation angle

TE Echo Time

TI Inversion Time

TR Repetition Time

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

1-D One-dimensional

2-D Two-dimensional

The Basics of NMR

Chapter 1

INTRODUCTION

NMR

Spectroscopy

Units Review

NMR

Spectroscopy

Units Review

The Basics of NMR

Chapter 2





Vectors

Matrices


Convolutions

Imaginary Numbers





Vectors

Matrices


Convolution

Imaginary Numbers

Fourier Transforms

The Basics of NMR

Chapter 3

SPIN PHYSICS

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions




Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

Spin

Properties of Spin

Nuclei with Spin

Energy Levels

Transitions


CW NMR Experiment


Spin Packets

T1 Processes

Precession

T2 Processes



Spin Relaxation

Spin Exchange

Bloch Equations

The Basics of NMR

Chapter 4

NMR SPECTROSCOPY

Chemical Shift

Spin-Spin Coupling



Chemical Shift

Spin-Spin Coupling



The Basics of NMR

Chapter 5

FOURIER TRANSFORMS

Introduction



Phase Correction

Fourier Pairs


The Digital FT

Sampling Error


Introduction



Phase Correction

Fourier Pairs

Convolution Theorem

The Digital FT

Sampling Error


The Basics of NMR

Chapter 6

PULSE SEQUENCES

Introduction

The 90-FID Sequence



Introduction

The 90-FID Sequence



The Basics of NMR

Chapter 7

NMR HARDWARE

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

Hardware Overview

Magnet

Field Lock

Shim Coils

Sample Probe

RF Coils

Gradient Coils

Quadrature Detector

Digital Filtering

Safety

The Basics of NMR

Chapter 8


Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

Introduction

Sample Preparation

Sample Probe Tuning


Field Shimming

Phase Cycling


Integration

SNR Improvement


Troubleshooting

Cryogen Fills

Unix Primer

The Basics of NMR

Chapter 9

CARBON-13 NMR

Introduction

Decoupling

NOE


1-D C-13 Spectra

Introduction

Decoupling

NOE


1-D C-13 Spectra

The Basics of NMR

Chapter 10

2-D TECHNIQUES

Introduction

J-resolved

COSY

Examples

Introduction

J-resolved

COSY

Examples

The Basics of NMR

Chapter 11


Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Introduction

Diffusion


Solid State

Microscopy

Solvent Suppression

Field Cycling NMR

Glossary

List of Symbols

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