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Transcript

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 We’ll remove some of these restrictions later Classical Wave description • The incident electric field is E = Eocos(2px/l – 2pt/T) • Interaction with molecules drives their electrons at the same f to induce an oscillating dipole pinduced = a Eocos(2px/l – 2pt/T) - a = polarizability • This dipole will radiate producing a scattered E field from the single molecule a Eo 4p 2 sin Escattered (r , t ) cos 2p x / l 2p t / T 2 rl 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/l2 dependence so I ~ 1/l4 – blue skies and red sunsets (sunrises) 3. Elastic scattering – same f 4. sin dependence – when = 0 or p – at poles of dipole – no scattering – max in horizontal plane 5. a 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 4p Na dc dc where N = number concentration • So, dn dn c a dc 2p N or a M dc 2p N A • For a particle in a solvent with nsolv, we have n2 – n2solv = 4pNa so a (n nsolv )(n nsolv ) / 4p N ~ 2nsolv dn c n dn a solv M 4p dc N 2p N A dc Scattered Intensity • Detect intensity, not E, where 2 a Eo 4p sin 2 4 2 2 r l 16 p a sin 2 Eo r 2l 4 2 I scatt I o 1 particle • Substituting for a, we have 2 I scatt I o 1 particle dn 4p M n sin 2 dc r 2l 4 N A2 2 2 2 solv Scattered Intensity II • If there are N scatterers/unit volume and all are independent with N = NAc/M, then 2 I scatt I scatt N I o per unit volume I o 1 particle 4p sin n 2 2 2 solv dn Mc dc N Ar 2l 4 • We define the Rayleigh ratio Rq: 2 dn 4p n Mc 2 I scatt ,q r dc Rq KMc 2 4 I o sin N Al 2 2 solv Basic Measurement • If the intensity ratio Iq/Io, nsolv, dn/dc, l, c, , and r are all known, you can find M. • Usually write Kc/Rq = 1/M • Measurements are usually made as a function of concentration c and scattering angle q • The concentration dependence is given by Kc 1 2 Bc Rq M where B is called the thermodynamic virial – same as we saw before for c dependence of D (but called A) q Angle Dependence • If the scatterers are small (d < l/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(q) qR~q From P(q), we can get a Radius of Gyration for the scatterer Analysis of LS Data • Measure I(q, c) and plot Kc/Rq vs sin2(q/2) + (const)c – Extrapolations: c q 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 M’s - then we measure an average M – but which ci M i average? Rq 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 Ni M i 2 3 M c M N i i i i Z-average Mz M i ci Ni M i 2 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 Df 0 is way off scale fo Df ~ 1 part in f 1010 - 1015 More Detailed Picture detector q Inter-particle interference Detected intensity Iaverage time How can we analyze the fluctuations in intensity? Data = g(t) = <I(t) I(t + t)>t = intensity autocorrelation function Intensity autocorrelation • g(t) = <I(t) I(t + t)>t t For small t For larger t t g(t) tc t What determines correlation time? • Scatterers are diffusing – undergoing Brownian motion – with a mean square displacement given by <r2> = 6Dtc (Einstein) • The correlation time tc 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 of tc can range from 0.1 ms (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 kBT D 6ph R where R is the radius of the equivalent hydrodynamic sphere and h is the viscosity of the solvent • So, if h is known we can find R (or if R is known we can find h 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, con’t – 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.b-amyloid – small peptide that aggregates in the brain – believed to cause Alzheimer’s disease- Current Projects 2. Insulin aggregation • 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 • • •