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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
blue sky and clouds
In the lab…
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.
light ( <10 nm for l = 690 nm), the amount of radiation scattered
into each angle is the same in the plane perpendicular to the
detector at 0°
detector at q, scattered light
Intramolecular interference leads to a
reduction in scattering intensity as the
scattering angle increases.
Why isotropic if radius of gyration < 10 nm?
rg < 10 nm
rg > 10 nm
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
n0 – solvent refractive index
NA – Avogadro’s number
l0 – vacuum wavelength of incident light
dn/dc - spec. refractive index incrementDefinition 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
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
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
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
Record Rayleigh ratio varying angle (3 or 18 angles
for miniDAWN or DAWN) but measuring concentration.
+ detector offset
Record Rayleigh ratio varying
- angle (3 or 18 angles for miniDAWN or DAWN)
- concentration (multiple injections of known c).
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
*lower limit 10nm
Rh or Hydrodynamic radius – radius of a sphere with the same diffusion coefficient or viscosity as “our” sample.
*lower limit 1nmRadius Results: Light Scattering &Viscometry
Scattered light intensity is measured through time
Diffusion of molecules ---- Brownian Motion
Translational diffusions: signal change
Rotational diffusions: no signal change
kB – Boltzmann’s constant
T – temperature (Kelvin)
h – viscosity of solvent
rh – hydrodynamic radius
Asphericity slows it down
Attached solvent and/or interparticle interactions create drag
Viscous solvent slows it down.
…and if concentration too high, ‘viscosity effects’
speeds it up
Small particles move fasterWhat affects translational diffusion?