Lecture 2, Fundamentals Hplc

Dr Cristina Legido-QuigleyLecturer in Pharmaceutical

Chemistry (Separation Science) at KCL

room [email protected]

HPLC THEORY

H.P.L.C High Pressure Liquid Chromatography?Highly Priced Liquid Chromatography?

High Performance Liquid Chromatography?

We will be dealing with chromatography from the 1970’s onwards. Prior to 1970, chromatography was anything but efficient, using

glass columns with wide-pore materials, mostly in a Normal Phase

manner.

•HPLC is a physical separation technique in which a sample dissolved in a liquid is injected into a column packed with small particles and it is separated into its constituent components

•HPLC is probably the most important and widely used analytical technique for quantitative analysis of organics and biomolecules

•HPLC is applicable to many kind of samples:

•Most useful for pharmaceuticals, biomolecules, and labile organics (also some ionic compounds)

•Annual sales of HPLC equipment world-wide> $ 1 billion; > 100.000 HPLC’s are in use today.

HPLC overview

History

Advantages of HPLC

The chromatographic process: general

Schematic layout for HPLC

Highpressurepump

Solvent supply bottle

Chromatogram

PC

Loop/injector SampleChromatographic

Column Detector Recorder

A test mixture

• The structures of the components of a test mix used for evaluating columns are shown below,

Thiourea Dimethyl Phthalate

Naphthalene Anisole

S

CNH2NH2 COOCH3

COOCH3

OCH3

Shows the chromatogram of the test mixture with the four eluting peaks. Column is an in-house packed Zorbax SB C8 100 x 0.32 mm id. Detection 210 nm. Temp 30° C, Flow: 8μl/min. Eluent 40% acetonitrile,

60% water. Injection 10 nanoL. Backpressure 159 bar.Instrument: Agilent 1100 Series CapLC.

min0 2 4 6 8 10 12 14

.

mAU

0

50

100

150

200

250

300

DAD1 C, Sig=210 Ref=360,100

anisoledimethyl

phthalate

thiourea

naphthalene

What can we see in the chromatogram?

Retention time tR

Capacity factor k’

Column efficiency N

Separation factor or selectivity α

Resolution Rs

THE PURNELL EQUATION

• The basic equation for RESOLUTION in HPLC gives the degree of separation of two peaks in a chromatogram as an empirical relationship, and is described as follows:

• Where tr1 and tr2 are the retention times of components 1 and 2 respectively, and w1 and w2 are the baseline widths of components 1 and 2 respectively. Assuming that w1 ≅ w2 then this equation reduces to:

• It does not however, show how resolution is related to the conditions of separation and cannot therefore be used directly to improve resolution.

( )21

122wwttR rr

s +−

=

wtR r

sΔ

=

Purnell showed that for column chromatography, the resolution Rs could be related to the capacity factor k’, the relative retention αand the efficiency in terms of the number of theoretical plates by the following equation:

Where (α-1)/α is the selectivity of the separation

k’2 / (1+ k’2) is the capacity factor term, and

√ N2 is the efficiency term.

2/2

/2

k1k1

41 NRS ⎟⎟

⎠

⎞⎜⎜⎝

⎛+

⎟⎠⎞

⎜⎝⎛ −

=α

α

THE PURNELL EQUATION

• This equations shows that it is possible to optimise resolution by altering the selectivity, the capacity factor, or the efficiency.

• The selectivity is altered by changing the relative retention α, which is a measure of the solvent efficiency. This can be accomplished by altering the stationary and mobile phases. Solvent efficiency depicts the separation of the band centres.

• Large values of capacity factor mean long retention times accompanied by broad peaks which are difficult to detect. With large values of k’ e.g. >5, the term k’2 / (1+ k’2) ---> 1 and therefore no longer plays a part in the resolution. Therefore, optimum values tend to be in the region of 2-5. k’ is mainly controlled by altering the mobile phase composition. Similar effects can be achieved by increasing the loading of the stationary phase.

THE PURNELL EQUATION

Can we increase efficiency to increase the resolution?

• The goal of most LC separations is to achieve baselineresolution for all key analytes (Rs > 1.5).

• Since the resolution Rs increases with the √ N, and N is proportional to the column length, doubling the column length will only increase the resolution by √ 2 i.e. 1.4. However, the cost would be a doubling of the analysis time assuming that the flow rate was held constant. Resolution is best increased by improving the efficiency of a separation, and this can be achieved by using small diameter particles, and/or a lower mobile phase velocity. This latter approach once again leading to longer analysis times. Column efficiency describes the band widths of the peaks being separated.

Glossary of HPLC terms

Time

Det

ecto

r res

pons

e

Time

Det

ecto

r res

pons

e

Time

Det

ecto

r res

pons

e

Time

Det

ecto

r res

pons

e

N = 3600 k’ = 0.8 α = 1.15

N = 3600 k’ = 2 α = 1.10

N = 1600 k’ = 2 α = 1.15

N = 3600 k’ = 2 α = 1.15 Rs=1.5

Rs=1.0

Rs=1.0

Rs=1.0

Diagram showing the effects of changing N, and α upon the resolution value Rs.

EXERCISE

N= 1600 or 3600

K’= 2 or 4

α= 1.15 or 1.10

N= 1600 or 3600

K’= 2 or 4

α= 1.15 or 1.10

N= 1600 or 3600

K’= 2 or 0.8

α= 1.15 or 1

BAND BROADENING THEORY• As a solute band passes through a column, the

width of band increases with time. In a uniform bed, the peak width increases with the square root of the length that the band has travelled.

L

W ≅ √L

• However, the distance between the centre of the two bands as they migrate through a column, increases in direct proportion to the length that the bands have traveled.

ΔL ≅ L• Since the distance between the bands

increases with the length traveled, but the width of each band only increases by the square root of this length, separation of these peaks will ultimately be achieved.

PLATE HEIGHT THEORY• Plate height theory is derived from

distillation theory and assumes that as the mobile phase travels through the packed column, a large number of equilibration steps take place. The column is imagined to be divided into N segments at which partitioning of the solute between the mobile and stationary phase is rapid and equilibration is reached before the solute moves on to the next plate. This imaginary segment is called a theoretical plate and if the column has a length L, then the height equivalent to a theoretical plate (HETP) is given by:

• The larger the value of N, (more efficient), the lower the value of H.E.T.P.

• By measuring the bandwidth and retention time, it is possible to calculate the number of theoretical plates using the following equation:

NLPTEH =....

2

2

2

2

16wttN rr ==

σ

Idealised Gaussian chromatogram showing how w and w1/2 are measured. The value w is obtained by extrapolating the tangents to the

inflection points down to the baseline

• In order to allow for peak tailing, the number of theoretical plates are often calculated using the equation containing the peak width at half height i.e.

22/1

2

55.5wtN r=

It was originally assumed that equilibration took place between the analyte and stationary and mobile phases, however, the equilibrium state can never be realised with the mobile phase in constant motion! A more realistic description of the movement of a solute through a packed column is given by the rate theory which allows for the fact that equilibration is not infinitely fast (as assumed by plate theory) and band shape depends upon the rate of elution.

• Probably the biggest shortcoming of the plate model is that it fails to relate the band broadening process to experimental parameters such as particle size, stationary phase film thickness and mobile phase velocity.

• A better understanding of the band broadening process is given by the

•Rate Theory of Chromatography.

Rate Theory of Chromatography• As a solute band moves through a packed column, the width of that

band will increases with time and the sample becomes diluted by the mobile phase. There are three dispersive processes that contribute to the band broadening process, namely:

• Eddy diffusion (sometimes referred to as streamline flow)• Axial molecular diffusion• Slow mass transfer between the mobile and stationary zones or

phases within the column• Because these three dispersive processes are both independent

and random, they can be summed to form the total variance produced by these processes.

• The original model which considered all the various mechanisms by which a solute band is broadened in a chromatography column was attributed to van Deemter at al. Although originally developed for Gas Chromatography, it was readily adapted for other forms of chromatography, including HPLC. The general form of the van Deemter equation is given below:

Where the A term represents the contribution to zone broadening by eddy diffusion, B represents the contribution from longitudinal diffusion (molecular diffusion in the axial direction) and C the contribution from slow mass transfer in both the stationary and mobile phases. Thecontribution to the dispersion process of each individual term will now be considered.

The efficiency of the column can be approximated by the following expression known as the Knox equation:

Rate Theory of Chromatography

CuuBAuH 1/3 ++=

Van Deemter equation

m

2pm1/3

p Dud

uD2ud2H

λ+

γ+λ=

This equation tries to account for all the kinetic processes that occur when a separation is undertaken. A, B and C are coefficients which relate to the three different processes. A being eddy diffusion, B/u the longitudinal axial diffusion,Cu tA more detailed view of the expanded Van Deemter equation is shown below,

where parameters are λ is the packing factor and dp the particle diameter. λ has a value between 0.5 and 1.0 dependant on how well the column is packed , the size of the particles and the particle size distribution. The smaller and more regular in size the particles, the smaller the λ value. Dm is the diffusion coefficient of the mobile phase. It also accounts for the Cs term which is the mass transfer in the stationary phase e mass transfer term and u the mean linear velocity.

Van Deemter plot

• The contributions to plate height H can be shown graphically:

H (μ

m)

Sum H

A

B

C0

3

6

9

0 31 2u (mm/s)

m

2pm1/3

p Dud

uD2ud2H

λ+

γ+λ=

The A term (home)• The A Term: Eddy Diffusion: When solute molecules migrate through a packed bed

they can migrate along different paths. These paths can be longer or shorter as the flow through a packed bed is more rapid in the wider channels than in narrower channels This dispersion is termed eddy diffusion.Flow path differences may be greater at the wall regions of the column where packing is more irregular, contributing in this way to a broader band width.

a) Start of separation b) End of separation

INTIAL BAND WIDTH

FINAL BAND WIDTH

Analyte

Packed Column

Diagram showing eddy diffusion as an analyte passes through a packed column

The B term• The B term: Longitudinal Diffusion: When the analyte within the mobile

phase travels through the column, it undergoes diffusion into the surrounding region. There are three geometrical axes from which the analyte can diffuse. The B term refers to longitudinal diffusion, that which

occurs along the length of the column.

MagnifiedSection

Flow Profile

LongitudinalDiffusion

AnalytePacked Column

. The longitudinal liquid diffusion is greatly diminished by employing high pressures and temperatures. Because liquids are incompressible the effect of pressure on longitudinal diffusion is insignificant in LC

uD2

uB mγ

=

The C term• The C term: Mass Transfer: The Cu term is the contribution to

band broadening from resistance to mass transfer. There are twoelements to this, mobile phase mass transfer and stationary phase mass transfer.

• The extended form of the Cu term is:

m

2p

Ddu λ

Cu =

MagnifiedSection

Flow Profile

Lateral Diffusion

AnalytePacked Column

The next figure shows the contribution from the lateral diffusion

• Mass transfer from stagnant mobile phase due to the diffusion into the pore.

MagnifiedSection

Packed Column

AnalyteBand width

Stagnant Phase Mass Transfer

The C term

Question 1. What does the retention factor, k', describe? a) The distribution of an analyte between the stationary and the mobile

phaseb) The migration rate of an analyte through a columnc) The velocity of the mobile phase

Question 2. What does the selectivity factor, alpha, describe? a) The proportional difference in widths of two chromatographic peaksb) The maximum number of different species which a column can separate

simultaneouslyc) The relative separation achieved between two species

Question 3. What useful information can be found from a Van Deemter plot? a) The selectivity factorb) Optimum mobile phase flow ratec) Optimum column temperature

BookHigh Performance Liquid Chromatography: Fundamental Principles and PracticeAuthors: W.J. Lough (Editor), Irving W. Wainer