Static & Dynamic Light Scattering First quantitative experiments in 1869 by Tyndall (scattering of small particles in the air Tyndall effect) 1871 Lord Rayleigh started a quantitative study and theory Basic idea: incident monochromatic linearly polarized light beam incident on a sample. Assume No absorption Randomly oriented and positioned scatterers Isotropic scatterers Independently scattering particles (dilute) Particles small compared to wavelength of light Well remove some of these restrictions later Classical Wave description The incident electric field is E = Eocos(2x/ 2t/T) Interaction with molecules drives their electrons at the same f to induce an
oscillating dipole pinduced = Eocos(2x/ 2t/T) - = polarizability This dipole will radiate producing a scattered E field from the single molecule Eo 4 2 sin Escattered (r , t ) cos 2 x / 2 t / T 2 r dipole r Obs. Pt. Static (or time-average)Rayleigh scattering 1. E ~ 1/r so I ~ 1/r2 - necessary since I
~energy/time/area and A ~ r2 2. E ~ 1/2 dependence so I ~ 1/4 blue skies and red sunsets (sunrises) 3. Elastic scattering same f 4. sin dependence when = 0 or at poles of dipole no scattering max in horizontal plane 5. related to n , but how? Polarizability and index of refraction dn n 1 c dc Note that if n ~ 1 where c is the weight concentration dn dn 2 2 Then n 1 2 c ... so n 1 2 c 4 N dc
dc where N = number concentration So, dn dn c dc 2 N M or dc 2 N A For a particle in a solvent with nsolv, we have n2 n2solv = 4N so 2nsolv dn c nsolv dn
(n nsolv )(n nsolv ) / 4 N ~ M 4 dc N 2 N A dc Scattered Intensity Detect intensity, not E, where 2 2 I scatt I o 1 particle Eo 4 sin 2 4 2 2
r 16 sin 2 Eo r 2 4 Substituting for , we have 2 dn 4 M n sin 2 dc
r 2 4 N A2 2 I scatt I o 1 particle 2 2 solv Scattered Intensity II If there are N scatterers/unit volume and all are independent with N = NAc/M, then 2 dn 4 sin n Mc dc
N Ar 2 4 2 I scatt I scatt N I o per unit volume I o 1 particle 2 2 solv We define the Rayleigh ratio R: 2 dn 4 n Mc
2 I scatt , r dc R KMc 2 4 I o sin N A 2 2 solv Basic Measurement If the intensity ratio I/Io, nsolv, dn/dc, , c, , and r are all known, you can find M. Usually write Kc/R = 1/M Measurements are usually made as a function of concentration c and scattering angle
The concentration dependence is given by Kc 1 2 Bc R M where B is called the thermodynamic virial same as we saw before for c dependence of D (but called A) Angle Dependence If the scatterers are small (d < /20), they are called Rayleigh scatterers and the above is correct the scattering intensity is independent of scattering angle If not, then there is interference from the light scattered from different parts of the
single scatterer Different shapes give different particle scattering factors P() qR~ From P(q), we can get a Radius of Gyration for the scatterer Analysis of LS Data Measure I(, c) and plot Kc/R vs sin2(/2) + (const)c Extrapolations: c 0 0 Final result
Slope~RG intercept Slope~B Problems: Dust, Standard to measure Io, low angle measurement flare Polydispersity If the solution is polydisperse has a mixture of different scatterers with different Ms - then we measure an average M but which ci M i average? R K c KM wc ci So the weight-averaged M is measured! Possible averages: M i N i Number-average M N N
i M i ci M 2i Ni Mw Weight-average ci N i M i 2 3 M c M N i i i i Z-average Mz 2 M i ci
N i M i Dynamic Light Scattering - Basic ideas what is it? - The experiment how do you do it? - Some examples systems why do it? Double Slit Experiment Coherent beam Extra path length screen + = + = Light Scattering Experiment Scatterers in solution (Brownian motion)
Scattered light Laser at fo Narrow line incident laser Doppler broadened scattered light f 0 is way off scale fo f ~ 1 part in 10 - 10 10 15 f More Detailed Picture detector
Inter-particle interference Detected intensity Iaverage time How can we analyze the fluctuations in intensity? Data = g() = t = intensity autocorrelation function Intensity autocorrelation g() = t For small For larger g()
c What determines correlation time? Scatterers are diffusing undergoing Brownian motion with a mean square displacement given by = 6Dc (Einstein) The correlation time c is a measure of the time needed to diffuse a characteristic distance in solution this distance is defined by the wavelength of light, the scattering angle and the optical properties of the solvent ranges from 40 to 400 nm in typical systems Values ofc can range from 0.1 s (small proteins) to days (glasses, gels) Diffusion What can we learn from the correlation time? Knowing the characteristic distance and correlation time, we can find the diffusion coefficient D
According to the Stokes-Einstein equation k BT D 6 R where R is the radius of the equivalent hydrodynamic sphere and is the viscosity of the solvent So, if is known we can find R (or if R is known we can find Why Laser Light Scattering? 1. 2. 3. 4. 5. Probes all motion Non-perturbing Fast Study complex systems Little sample needed
Problems: Dust and best with monodisperse samples Aggregating/Gelling Systems Studied at Union College Proteins: Actin monomers to polymers and networks Study monomer size/shape, polymerization kinetics, gel/network structures formed, interactions with other actin-binding proteins Why? Epithelial cell under fluorescent microscope Actin = red, microtubules = green, nucleus = blue
Aggregating systems, cont BSA (bovine serum albumin) beta-amyloid +/- chaperones insulin what factors cause or promote aggregation? how can proteins be protected from aggregating? what are the kinetics? Polysaccharides: Agarose Carageenan Focus on the onset of gelation what are the mechanisms causing gelation? how can we control them? what leads to the irreversibility of gelation? Current Projects
1.-amyloid small peptide that aggregates in the brain believed to cause Alzheimers disease- 2. Insulin aggregation Current Projects EFFECTS OF ARGININE ON THE KINETICS OF BOVINE INSULIN AGGREGATION STUDIED BY DYNAMIC LIGHT SCATTERING By
Michael M. Varughese ********* Submitted in partial fulfillment of the requirements for Honors in the Department of Biological Sciences and done in conjunction with the Department of Physics and Astronomy UNION COLLEGE June, 2011
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