Inelastic Scattering. Raman. Compton. Acoustic Mode Scattering. Bragg and Brillouin. Why the sky is blue?. Rayleigh Scattering.
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Acoustic Mode Scattering
Bragg and Brillouin
Why the sky is blue?
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.
ESRF- EUROPEAN SYNCHROTRON RADIATION FACILITIES
ILL : INSTITUT LAUE LANGEVIN
Elastic and Quasi-Elastic Light Scattering
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
SALT-FREE POLYELECTROLYTE CHAINS (Electrostatic Forces)
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
The wave-vector q
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
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)
[PVP] = 30 mM
O coeficiente viral A2
Photon Correlation Spectroscopy or...
DLS - Dynamic Light Scattering
DYNAMIC LIGHT SCATTERING
Linear & Cyclic PS-PI in heptane
Stokes Einstein equation