Inelastic Scattering. Raman. Compton. Acoustic Mode Scattering. Bragg and Brillouin. Why the sky is blue?. Rayleigh Scattering.
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Bragg and Brillouin
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.
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.
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.
ILL : INSTITUT LAUE LANGEVIN
Elastic: Mw, Rg, A2 , form factor P(q), Persistence Length, etc.
Dynamic: relaxation times, Diffusion Coefficients, Mobilities, etc.
up to 600 Å
Nano-Structures: x-rays Scattering
Form factor, Anisotropy, Polyelectrolytes, Nano-materials : Copolymers, Colloids, Micelles, Polymer Liquid Crystals, etc.
Intensity vs wavevector q
Size and Shape
Mw (Molecular Weight
Rg (Radius of Gyration)
A2 (Virial Coefficient)
Light scattering, SANS, SAXS
Dynamic Scattering: Diffusion Coefficient D or
Hydrodynamic Radius Rh
Dilute : q*~c 1/3
Uniform or Cubic distribution
Semi-dilute : q*~c 1/2
Scattering Peak !
Expansion of the Chain
(1/3) : Uniform / Cubic Arrangement
(1/2) : Cylindrical 2-D Arrangement
Variation of qmax as a Function
of Xanthan Concentration
Xanthan “Salt-Free” Solutions
q-Light Scattering Range
E. Sadlik, M. Villetti, M. de Souza, V. Soldi and R. Borsali (in preparation )
Sample [Solutions, Gels, Melts ]
LIGHT SCATTERING - EXPERIMENTAL SET UP
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
Based on Zimm’s formalism, the Rayleigh-Debye-Gans light scattering model for dilute polymer solutions can be expressed as equation below:
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.
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>.
KC/I(q) = (1/Mw)(1+q2Rg2/3) + 2A2C
KC/I(q) = (1/M) (q ->0 ; C ->0)
KC/I(q) = (1/M)(1+q2Rg2/3) ; (C ->0)
b -> Slope = Rg2/3M
KC/I = (1/Mw)+ 2A2C ; (q->0)
a -> Slope = 2A2
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)
DLS - Dynamic Light Scattering
Linear & Cyclic PS-PI in heptane