Light ScatteringLight Scattering(pp. 53-63 in Shaw and pp. 193-(pp. 53-63 in Shaw and pp. 193-244 in Hiemenz and Rajagopalan)244 in Hiemenz and Rajagopalan)

• Introduction

• Rayleigh Scattering

• Debye Scattering, Zimm Plots

• Dynamic Light Scattering

IntroductionIntroduction

Absorbed Transmitted

Scattered

Turbidityl

o

eII

Information Obtained

•Particle mass•non-perturbed•absolute determination•instantaneous

•Particle size and shape•Dynamic information (diffusion constants)

When there isno absorption

Rayleigh Scattering• particles small (< /20, about 20-25 nm)• refractive index similar to medium

Debye Scattering• particles relatively large • refractive index similar to medium

Mie Scattering• few constraints on size or refractive index• easily applied only to spherical particles, or particles where geometry is known

(NOT discussed here)

Experimental Apparatus

Rayleigh Scattering

Rayleigh found the following relationshipfor point scatterers (i.e. particle size < /20):

)cos1(

)cos1(8

2

2

2

4

242

o

o

IrI

R

IrI

Why is the sky blue?(red=700 nm, blue=400 nm)

Vertically vs. horizontally polarised light

Insert Shaw Fig. 3.6

KHBcM

Hc

BcMR

Kc

BcMKc

R

Ndcdnn

K

BcMdcdnn

Nc

IrI

A

Ao

316

21

21

)2/1(

)]/([2

)cos1()2/1(

)]/([2

4

22

22

4

22

Assumptions

•scatterers are isotropic,dielectric, non-absorbing•n is not too large•size of scatterers is small cf. light wavelength

Find an expression for and replacein the Rayleigh equation...

Comparison to osmotic pressuremeasurements:

•Instantaneous, kinetics possible•covers a different particle size range

Debye ScatteringDebye Scattering

If particle size>/20 we get interference effects...

Use a correction factor P()

n

iig

g

rn

R

R

P

BcMPR

Kc

1

22

2

2

22

1

2sin

3

161

)(1

21

)(1

Correction term derived from X-rayscattering theory...

Physical meaning of radius of gyration...

average radius swept out by a chainof n particles (e.g. polymer, protein…)

centre of mass

n1

n3

n2

r1

r3r2

2sin

3

1612

1 2

2

22

gRBc

MRKc

Zimm Plots

No interference effect,just like Rayleigh eqn.

slope givesi.e. particle size info.

particle MW info--Zimm plot

lim

0c

lim

0

lim

0

0

c

RKc 2

22

3

16

M

Rg

M1

2

gR

kc

2sin 2

2B

c=0

=0

(+ Overheads)

Dynamic effects

2

2/1 2sin

4

cn

D oo