Introduction to Dynamic Light Scattering with Applications Onofrio Annunziata Department of Chemistry Texas Christian University Fort Worth, TX, USA
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Introduction
to
Dynamic Light Scattering
with Applications
Onofrio AnnunziataDepartment of ChemistryTexas Christian University
Fort Worth, TX, USA
Outline
Introduction to dynamic light scattering
Particle sizing and particle-particle interactions
Particle sizing in Polydisperse systems
Mie scattering
Comparison with macroscopic-gradient techniques
A Technique mainly used to determine the diffusion coefficient of macromolecules and colloidal particles in solution.
The dominant practical application is in particle sizing (1-1000 nm).
Dynamic light scattering (DLS)Also known as
Quasielastic light scattering (QLS)
or
Photon Correlation Spectroscopy (PCS)
Techniques for particle size or mass
Light microscopy
Electron microscopy (SEM, TEM)
Atomic force microscopy (AFM)
Gel electrophoresis, SDS page
Mass spectrometry (EI, MALDI)
Size exclusion chromatography
Sedimentation
Osmotic pressureLight, neutron, X-ray scattering
Viscosity
Diffusion (DLS, NMR PGSE, Interferometry, Taylor dispersion, etc..)
Advantages:
noninvasive, nondestructive, relatively fast, versatile, sensitive to aggregates
Drawbacks:
Fairly poor resolution, not sensitive to chemical nature, relatively complex theory, particles are not visualized
Dynamic light scattering (DLS)
Instrument scheme
Detector
Brief History of DLS
Marian Smoluchowski(1872-1917)
Stochastic processesDensity fluctuations
Albert Einstein(1879-1955)
Brownian Motion
Lord Rayleigh(1842-1919)
Light Scattering
Fluctuations in the density of condensed media result in local inhomogeneities that give rise to light scattered at angles other than the forward direction.
Brief History of DLS
Benedek et al. (1965)First experimental report on pure fluidsnear critical point
Pecora (1964)Diffusion processes broadens frequency profile of the scattered electric field
Cummins et al. (1964)First experimental report on macromolecular solutions
K. S. Schmitz, An introduction to dynamic light scattering, Academic Press (1990)
DLS instruments commercially available
Wyatt Tech. Malvern
Brookhaven IC
PhotocorALV
Viscotek Precision Detectors
Brookhaven
Important References
G. D. J. Phillies, “Quasi-elastic Light Scattering”, Analytical Chemistry 62, 1049A-1057A (1990).
N. C. Santos, M.A.R.B. Castanho “Teaching Light Scattering”, Biophysical Journal 71, 1641-1650 (1996).
LASER
DETECTOR
CORRELATOR
COMPUTER
THERMOSTATEDCELL HOLDER
OPTICAL FIBER
IRIS
Scatteredintensity
Correlationfunction
DiffusionCoefficient
sample
DLS INSTRUMENT SCHEME
Scattering at 90°
( )Si t
( )g τ
D
IRIS
(test tubewith filtered
solution)
Incidentbeam
Cellholder
Sample
CELL-HOLDER SCHEME
MULTIANGLE SCHEME
LASERθ
Low AngleHigh Angle
90° Angle
Scattering Vector
0kSk
02| | | |
( / )Sk kn
πλ
= =
wave vector ofincident light
θ
λ Wavelength of incident light in vacuum
n Refractive index of the sample
(Elastic Scattering)
wave vector ofscattered light
0 Sq k k= −Scattering Vector
02| | | | 2sin
( / ) 2Sq q k kn
π θλ
⎛ ⎞= = − = ⎜ ⎟⎝ ⎠
The blue color of the sky is mainly caused by the scattered sunlight
The orange of the sky is mainly caused by the transmitted sunlight
Rayleigh Scattering
4
1Si λ∼
Elastic scattering of light by particles much smaller than the wavelength of the light. It occurs when light travels in transparent solids and liquids, but is most prominently seen in gases.
Rayleigh scattering is more effective at short wavelengths (the blue end of the visible spectrum).
Rayleigh Scattering of one particle
SE M∼
2 2| |SSi E M= ∼
The scattered electric field ES of a single particle is proportional to its numberof electrons and consequently to its molecular mass M.
Scattered field( particle)SE
IlluminatedVolume
Incident field
The particle size is assumed small compared to laser wavelength (size < λ / 10)
kiq rS
kE M e ⋅∑∼
(2 2)2| | j kiS
q r rS
j k
i M ME Ne ⋅ −= ∑∑∼ ∼
The scattered electric field ES of N identical particles must take into accountinter-particle interference.
Rayleigh Scattering of many particles
Scattered field
SE
N = number of particles
Rayleigh Scattering from particle-solvent mixtures
* 2S Ni c MM< > ∼ ∼ c =N M / V (mass concentration)
Ideal Solutions (random structure)
Real Solutions (structure affected by particle-particle interactions)
* ( )SS S qii< > =< > S(q) (Structure Factor)
0lim ( ) 1c
S q→
=
The time-averaged spatial positions of the particles represent the solution structure
0
1lim ( )( / ) 1 2 ...q
RTS qM c M cB→
= =∂Π ∂ + +
Π (Osmotic pressure)
B > 0 particle-particle net repulsion
Second virial coefficient B
B is used to characterize particle-particle interactions
*S Si i< *
S Si i>B < 0
particle-particle net attraction
Second virial coefficient and protein crystallization
1 2 ...BK cR
cM
= + +(Rayleigh ratio)
22 2
4
4
A
n dnKN dcπ
λ⎛ ⎞= ⎜ ⎟⎝ ⎠
2
,std
std S std
SiR n Rn i
⎛ ⎞= ⎜ ⎟⎝ ⎠
c (mg/mL)0 102 4 6 8
K c
/ R
(10-
5m
ol/g
)
4
5
6
7
8
9NaCl 0%NaCl 2%NaCl 4%NaCl 5% B > 0
B < 0
B << 0
Lysozyme (acetate buffer pH 4.5)
crystals
aggregation
soluble
Protein crystallization slot
B (10-4 mol mL g-2)
Successful crystallization is obtained for B values slightly negative
SuccessfulProtein
Crystallization
Particles in solution are moving scatterers
Incident light(LASER)
IlluminatedVolumeparticle
Time-dependentScattered intensity
phasedifference
Dynamic light Scattering
( )2| | j kiq r rS S
j ki E e ⋅ −= ∑∑∼
Particles in solution are moving due toBrownian Motion
Dynamic light Scattering
Brownian Motion
2( ) (0)[ ]6
rD rττ
−< >=
(0)r( )r τ
Dynamic Light Scattering
Dynamic Structure Factor
[ (0) ( )]1( , ) (0) ( ) j kiq r rS S
j kF q E E e
Nττ τ ⋅ −=< ⋅ > < >∑∑∼
How the solution structure at time τ correlateswith the solution structure at time 0?
Field autocorrelation function
( )(1) 2( , )( , ) exp( ,0)
F qg q qF q
Dττ τ= = −
D = diffusion coefficient of particles
22[ ( ) (0)](1) [ (0) ( )] 6( , )
q r riq r rg q e eτττ
− < − >⋅ −= < >=
2[ ( ) (0)]6
r rD ττ
< − >=
( )r τ
(0)r
( )(1) 2( , )( , ) exp( ,0)
F qg q q DF q
ττ τ= = −
Gaussian Random variable
Field autocorrelation function
Field autocorrelation function
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
q 2 D τ
g(1
) ( τ
) ( )(1) 2( , ) expg q q Dτ τ= −
Strong correlationτ = 0, g(1) =1
No correlationτ → ∞, g(1) = 0
Shortτ
Longτ
(1) ( ) (0) ( )S Sg E Eτ τ< ⋅ >∼
(1) ( ) 1g τ ≈ (1) ( ) 0g τ ≈
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50
q 2 D 1 τ
g(1
) ( τ
)
fast particles (1)slow particles (2)
D 1 = 10 D 2
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50
q 2 D 1 τ
g(1
) ( τ
)( ) ( )1
1) 22
( 2exp exp. .0 8 0 2g q qD Dτ τ= − + −
Fast vs slow particles
Mixture of Slow and Fast particles
Field autocorrelation function
45
46
47
48
49
50
0 20 40 60 80 100
t (s)
i S (
kcou
nts/
s )
1
2
0 1 2 3
q 2 D τ
g(2
) ( τ
)( ) 2(2) 2( , ) 1 expg q q Dτ α τ⎡ ⎤= + −⎣ ⎦
The DLS Detector probes iS( t )This is a stochastic function
Intensity autocorrelation function
(2) ( ) (0) ( )S Sg i iτ τ< ⋅ >∼
The correlator calculatesIntensity autocorrelation function
(2) (1) 2( ) 1 | ( ) |g gτ β τ= +(Siegert equation)
1β < Coherence factor
0
1
ν-ν0i S
( ν)
2
2Dq
0
1
q 2 D τ
g(1
) ( τ
)
(1) 2( ) 2 ( )iSg e i dπν ττ π ν ν= ∫ 2 (1)1( ) ( )
2i
Si e g dπν τν τ τπ
−= ∫
Correlation function and Light scattering spectrum
Why Light Scattering is quasielastic
Related Documents
