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Inelastic Scattering - PowerPoint PPT Presentation


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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Inelastic Scattering

Raman

Compton


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Acoustic Mode Scattering

Bragg and Brillouin


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Why the sky is blue?


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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.


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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.


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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.


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SAXS/WAXS

WAXS

DLS

SLS

SALS

Photons

Rayleigh Scattering

Neutrons

SANS

SPIN-ECHO


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ESRF- EUROPEAN SYNCHROTRON RADIATION FACILITIES

X-RAYS SOURCE

ILL : INSTITUT LAUE LANGEVIN

NEUTRONS SOURCE

ESRF RING

ILL

REACTOR

GRENOBLE, FRANCE


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Elastic and Quasi-Elastic Light Scattering

Elastic: Mw, Rg, A2 , form factor P(q), Persistence Length, etc.

Dynamic: relaxation times, Diffusion Coefficients, Mobilities, etc.


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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.


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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


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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

)


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(1/3) : Uniform / Cubic Arrangement

(1/2) : Cylindrical 2-D Arrangement


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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 )


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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


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The wave-vector q


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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:


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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>.


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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)


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[PVP] = 30 mM


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O coeficiente viral A2

[HA]=0.1mg/mL

[PVP]=30mM [SDS]=7mM


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Photon Correlation Spectroscopy or...

DLS - Dynamic Light Scattering


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Solvent

Polymer solution


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DYNAMIC LIGHT SCATTERING

Linear & Cyclic PS-PI in heptane


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Stokes Einstein equation


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