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Introduction to Light Scattering A bulk analytical technique. What is light scattering?. In nature…. red sunsets. blue sky and clouds. What is light scattering?. In the lab…. Molar mass, M Size, r g Second virial coefficient, A 2 Translational diffusion coefficient, D T

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what is light scattering
What is light scattering?

In nature…

red sunsets

blue sky and clouds

what can light scattering measure
Molar mass, M

Size, rg

Second virial coefficient, A2

Translational diffusion coefficient, DT

- Can be used to calculate rh

What can light scattering measure?

For a solute in solution, light scattering can determine:

light and its properties


Light and its properties

Light is an oscillating wave of electric and magnetic fields

  • Polarization: direction
  • of electric field oscillation
how does light scatter

The oscillating charges

radiate light.

How much the charges move,

and hence how much light radiates, depends upon the matter’s polarizability.

How does light scatter?

When light interacts with matter, it causes charges to polarize.

index of refraction n
Index of refraction n

The polarizability of a material is directly

related to its index of refraction n.

The index of refraction is a measure of

the velocity of light in a material.

e.g., speed of light

For solutes, the polarizability is expressed as the specific

refractive index increment, dn/dc.

adding light
Adding light
  • Incoherent sum
  • Coherent sum
  • Interference:
isotropic scattering
For particles much smaller than the wavelength of the incident

light ( <10 nm for l = 690 nm), the amount of radiation scattered

into each angle is the same in the plane perpendicular to the


Isotropic scattering
angular dependence of light scattering
Angular dependence of light scattering

detector at 0°

scattered light

in phase

detector at q, scattered light


Intramolecular interference leads to a

reduction in scattering intensity as the

scattering angle increases.

how light scattering measures r g

Integrating over extended particle

involves integrating over mass


How light scattering measures rg

To calculate the angular distribution

of scattered light, integrate over

phase shifts from extended particle.

molar mass and radius
Molar mass and radius

Why isotropic if radius of gyration < 10 nm?

rg < 10 nm

isotropic scatterer

rg > 10 nm

basic light scattering principles
Principle 1

The amount of light scattered is directly proportional to the product of the polymer molar mass and concentration.

Principle 2

The angular variation of the scattered light is directly related to the size of the molecule.

Basic light scattering principles
basic light scattering equation
In the Rayleigh-Gans-Debye limit, the two light scattering

principles are embodied in the equation:

This equation also contains a correction due to concentration c. The correction is due to coherent intermolecular scattering, and contains information on the second virial coefficient.

Basic light scattering equation
definition of terms 1

K* .

n0 – solvent refractive index

NA – Avogadro’s number

l0 – vacuum wavelength of incident light

dn/dc - spec. refractive index increment

Definition of terms 1

R(q)– excess (i.e., from the solute alone) Rayleigh ratio.

The ratio of the scattered and incident light intensity,

corrected for size of scattering volume and distance

from scattering volume.

M– molar mass

definition of terms 2
c– solute concentration (g/ml)

P(q)– form factor or “scattering function”. P(q) relates the angular variation in scattering intensity to the mean square radius rg of the particle.

The larger rg, the larger the angular variation.

Note that P(0°) = 1.

A2– second virial coefficient, a measure of solute-solvent interaction. Positive for a “good” solvent.

Definition of terms 2
running an experiment 1 calibration

The detectors output voltages proportional to the light scattering intensities. The voltages must be converted to meaningful units.


1. Flow pure, filtered (0.02 mm) toluene through the flow cell.

ASTRA software measures the voltages from the 90° and laser monitor photodiodes with the laser on and off (dark voltages).

ASTRA then computes the calibration constant.

Running an experiment 1: Calibration
running an experiment 2 normalization

detector sensitivities vary.

each detector views a different scattering volume.

scattered light is refracted.

only the 90° detector is calibrated.


Fill flow cell with isotropic scatterer in actual solvent to be used.

ASTRA software measures voltages for each angle and:

Determines refraction angle from solvent index of refraction.

Determines angle and scattering volume corrections.

Normalizes each corrected detector voltage signal to the 90° detector.

Running an experiment 2: Normalization
online data collection
Online Data Collection

Record Rayleigh ratio varying angle (3 or 18 angles

for miniDAWN or DAWN) but measuring concentration.

online data analysis
Online Data Analysis
  • Perform fit of angular data to retrieve M and rg.
  • Assess quality of fit using a Debye plot.
batch data collection
Batch Data Collection

excess scattering

solvent scattering

+ detector offset

Record Rayleigh ratio varying

- angle (3 or 18 angles for miniDAWN or DAWN)

- concentration (multiple injections of known c).

batch data analysis
Batch Data Analysis
  • Perform global fit of data to light scattering equation to retrieve M, rg, and A2.
  • Assess quality of fit using a Zimm plot.
zimm plot of a protein
Zimm Plot of a Protein

Molar Mass (MM) : (7.714±0.01)e+4 g/mol (0.16%)

RMS Radius (Rz) : 2.6±2.2 nm (84%)

2nd virial coefficient : (1.413±0.06)e-4 mol mL/g2 (3%)

Aqueous microbatchZimm Plot of BSA monomer

radius results light scattering viscometry
Rg or RMS radius – mass average (root mean square) distance of each point in a molecule from the molecule’s center of gravity.

*lower limit 10nm

Rh or Hydrodynamic radius – radius of a sphere with the same diffusion coefficient or viscosity as “our” sample.

*lower limit 1nm

Radius Results: Light Scattering &Viscometry
hydrodynamic radius












Hydrodynamic Radius

Theoretical Examples

what can qels measure
Diffusion constant, DT

Size, rh


Conformation, rh vs. rg

What can QELS Measure?
what is a qels experiment
What is a QELS Experiment?

Scattered light intensity is measured through time

how qels works interference of light


Constructive interference

Destructive interference

How QELS Works: Interference of Light

Particles diffuse due to Brownian motion, resulting in light intensities which fluctuate with time.

what is translational diffusion
What is translational diffusion?

Diffusion of molecules ---- Brownian Motion

Translational diffusions: signal change

Rotational diffusions: no signal change

timescale of motion
Timescale of Motion

kB – Boltzmann’s constant

T – temperature (Kelvin)

h – viscosity of solvent

rh – hydrodynamic radius

what affects translational diffusion

DT  1/fs

DT  1/

DT  1/fh

Asphericity slows it down

Attached solvent and/or interparticle interactions create drag

Viscous solvent slows it down.

…and if concentration too high, ‘viscosity effects’

DT  T

DT  1/R

High temperature

speeds it up

Small particles move faster

What affects translational diffusion?