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Inelastic Scattering

Inelastic Scattering. Raman. Compton. Acoustic Mode Scattering. Bragg and Brillouin. Why the sky is blue?. Rayleigh Scattering.

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Inelastic Scattering

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  1. Inelastic Scattering Raman Compton

  2. Acoustic Mode Scattering Bragg and Brillouin

  3. Why the sky is blue?

  4. Rayleigh Scattering Rayleigh scattering refers to the scattering of light off of the molecules of the air, and can be extended to scattering from particles up to about a tenth of the wavelength of the light.

  5. Mie Scattering The scattering from molecules and very tiny particles (< 1 /10 wavelength) is predominantly Rayleigh scattering. For particle sizes larger than a wavelength, Mie scattering predominates.

  6. Mie scattering is not strongly wavelength dependent and produces the almost white glare around the sun when a lot of particulate material is present in the air. It also gives us the the white light from mist and fog.

  7. SAXS/WAXS WAXS DLS SLS SALS Photons Rayleigh Scattering Neutrons SANS SPIN-ECHO

  8. ESRF- EUROPEAN SYNCHROTRON RADIATION FACILITIES X-RAYS SOURCE ILL : INSTITUT LAUE LANGEVIN NEUTRONS SOURCE ESRF RING ILL REACTOR GRENOBLE, FRANCE

  9. Elastic and Quasi-Elastic Light Scattering Elastic: Mw, Rg, A2 , form factor P(q), Persistence Length, etc. Dynamic: relaxation times, Diffusion Coefficients, Mobilities, etc.

  10. SAXS/WAXS X-Ray Scattering 2-D detector up to 600 Å resolution Nano-Structures: x-rays Scattering Form factor, Anisotropy, Polyelectrolytes, Nano-materials : Copolymers, Colloids, Micelles, Polymer Liquid Crystals, etc.

  11. 2 1.5 1 0.5 0 0 0.05 0.1 0.15 0.2 Intensity vs wavevector q Elastic Scattering Size and Shape Mw (Molecular Weight Rg (Radius of Gyration) A2 (Virial Coefficient) o-1 q(A ) Light scattering, SANS, SAXS Dynamic Scattering: Diffusion Coefficient D or Hydrodynamic Radius Rh

  12. SALT-FREE POLYELECTROLYTE CHAINS (Electrostatic Forces) 4 3.5 3 2.5 D=2p/q* I(q) 2 1.5 1 D=2p/q* 0.5 Dilute : q*~c 1/3 0 0 0.05 0.1 0.15 0.2 Uniform or Cubic distribution Semi-dilute : q*~c 1/2 Parallel Arrangement SAXS REPULSION Scattering Peak ! Expansion of the Chain q* o-1 q(A )

  13. (1/3) : Uniform / Cubic Arrangement (1/2) : Cylindrical 2-D Arrangement

  14. Variation of qmax as a Function of Xanthan Concentration Xanthan “Salt-Free” Solutions -1 10 -2 10 -3 10 -4 10 -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 XANTHAN/LS/SAXS q-SAXS Range ) °-1 (A max q 0.497 q =0.34*C max q-Light Scattering Range 3 C (g/cm ) E. Sadlik, M. Villetti, M. de Souza, V. Soldi and R. Borsali (in preparation )

  15. Sample [Solutions, Gels, Melts ] Polarizer Beam Stop (Polymers, Colloïds, etc.) Laser l Q Pinhole Lens Scattering Angle Analyzer Pinhole q=(4p/l)n sin(Q/2) Lens Wavevector Detection (Optical Fiber) Computer Dynamic I(q,t) Correlator Static Photons Count <I(q)> LIGHT SCATTERING - EXPERIMENTAL SET UP

  16. The wave-vector q

  17. Quasi-Elastic Light Scattering or... SLS - Static Light Scattering The amount of light scattered is directly proportional to the product of the weight-average molar mass and the macromolecule (solute) concentration, i.e., LS ~ Mw·c • R(Q) is the excess intensity of scattered light at angle Q • c is the sample concentration • Mw is the weight-average molecular weight (molar mass) • A2 is a second viral coefficient • K* is an optical parameter equal to • 4p2n2 (dn/dc)2 / (lo4NA) • n is the solvent refractive index and dn/dc is the refractive index increment • NA is Avogadro’s number • lo is the wavelength of the scattered light in vacuum. Based on Zimm’s formalism, the Rayleigh-Debye-Gans light scattering model for dilute polymer solutions can be expressed as equation below:

  18. The function P(Q) describes the angular dependence of scattered light. The expansion of 1/ P(Q) to first order gives: 1/ P(Q) = 1 + (16p2/3l2) <rg2>. sin2(Q/2) + f4 sin4(Q/2) +... At low angles the angular dependence of light scattering depends only on the mean square radius <rg2> (alternatively called radius of gyration) and is independent of molecular conformation or branching. Zimm plot A plot of K*c /R(Q) vs. sin2(Q/2) yields a curve whose intercept gives Mw and whose slope at low angles gives <rg2>.

  19. ZIMM DIAGRAM KC/I(q) = (1/Mw)(1+q2Rg2/3) + 2A2C KC/I(q) C->0 KC/I(q) = (1/M) (q ->0 ; C ->0) KC/I(q) = (1/M)(1+q2Rg2/3) ; (C ->0) b -> Slope = Rg2/3M b q->0 KC/I = (1/Mw)+ 2A2C ; (q->0) a a -> Slope = 2A2 C2 C1 C4 C3 (1/M) q2+k’C Measure of I(q) as a function of Concentration and Scattering Angle allows the determination of: The Molecular Weight : Mw The Radius of Gyration : Rg The Second Virial Coefficient : A2 & The Form Factor : P(q)

  20. [PVP] = 30 mM

  21. O coeficiente viral A2 [HA]=0.1mg/mL [PVP]=30mM [SDS]=7mM

  22. Photon Correlation Spectroscopy or... DLS - Dynamic Light Scattering

  23. Solvent Polymer solution

  24. DYNAMIC LIGHT SCATTERING Linear & Cyclic PS-PI in heptane

  25. Stokes Einstein equation

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