Introduction to Light Scattering
A bulk analytical technique
What is light scattering?
In nature…
blue sky and clouds
red sunsets
What is light scattering?
In the lab…
What can light scattering
measure?
For a solute in solution, light scattering can determine:
•
•
•
•
Molar mass, M
Size, rg
Second virial coefficient, A2
Translational diffusion coefficient, DT
- Can be used to calculate rh
Light and its properties
Light is an oscillating wave of electric and magnetic fields
• Polarization: direction
of electric field oscillation
• Intensity:
How does light scatter?
When light interacts with matter, it causes charges to polarize.
The oscillating charges
radiate light.
How much the charges move,
and hence how much light radiates,
depends upon the matter’s polarizability.
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
• Incoherent sum
• Coherent sum
• Interference:
How light scattering measures M
coherent:
incoherent:
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
polarization.
Angular dependence of light
scattering
detector at 0°
scattered light
in phase
detector at q, scattered light
out-of-phase
Intramolecular interference leads to a
reduction in scattering intensity as the
scattering angle increases.
Definitions
How light scattering measures rg
To calculate the angular distribution
of scattered light, integrate over
phase shifts from extended particle.
Integrating over extended particle
involves integrating over mass
distribution.
Conformation: rh vs. rg
3-arm star polymer
solid sphere

rg
rh
 0.77

rg
rh
 1.4
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 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.
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.
K*
M – molar mass
.
n0 – solvent refractive index
NA – Avogadro’s number
l0 – vacuum wavelength of incident light
dn/dc - spec. refractive index increment
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.
Running an experiment 1:
Calibration
Why?
The detectors output voltages
proportional to the light
scattering intensities. The
voltages must be converted to
meaningful units.
How?
1. Flow pure, filtered (0.02 mm) toluene through the flow cell.
2. ASTRA software measures the voltages from the 90° and laser
monitor photodiodes with the laser on and off (dark voltages).
3. ASTRA then computes the calibration constant.
Running an experiment 2:
Normalization
Why?
• detector sensitivities vary.
• each detector views a
different scattering volume.
• scattered light is refracted.
• only the 90° detector is
calibrated.
How?
1. Fill flow cell with isotropic scatterer in actual solvent to be used.
2. ASTRA software measures voltages for each angle and:
a. Determines refraction angle from solvent index of refraction.
b. Determines angle and scattering volume corrections.
c. Normalizes each corrected detector voltage signal to the 90°
detector.
Online Data Collection
Record Rayleigh ratio varying angle (3 or 18 angles
for miniDAWN or DAWN) but measuring concentration.
Online Data Analysis
1. Perform fit of angular data to retrieve M and rg.
2. Assess quality of fit using a Debye plot.
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
1. Perform global fit of
data to light scattering
equation to retrieve M,
rg, and A2.
2. Assess quality of fit
using a Zimm plot.
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
Aqueous microbatch Zimm Plot of BSA monomer
(3%)
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
27
Hydrodynamic Radius
Theoretical Examples
Rh
_
H2O
Rh
+
H2O
+
H2O
H2O
+
H2O
28
What can QELS Measure?
•
•
•
•
Diffusion constant, DT
Size, rh
Polydispersity
Conformation, rh vs. rg
29
What is a QELS Experiment?
Scattered light intensity is measured through time
30
How QELS Works:
Interference of Light
Diffusion!
Constructive interference
Destructive interference
Particles diffuse due to Brownian motion, resulting in
light intensities which fluctuate with time.
31
What is translational diffusion ?
Diffusion of molecules ---- Brownian Motion
Rotational diffusions: no
signal change
Translational diffusions:
signal change
32
Timescale of Motion
kB – Boltzmann’s constant
T – temperature (Kelvin)
h – viscosity of solvent
rh – hydrodynamic radius
33
What affects translational diffusion?
DT  1/h
DT  1/fh
Viscous solvent slows it
down.
…and if concentration too
high, ‘viscosity effects’
Attached solvent and/or
interparticle interactions
create drag
DT  1/fs
DT  T
Asphericity slows it down
DT  1/R
High temperature
speeds it up
Small particles move faster
34