Malvern Zetasizer Nano Series, User Manual

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Static light scattering - theory
The molecular weight is determined by measuring the sample at different
concentrations and applying the
Rayleigh equation . The Rayleigh equation
describes the intensity of light scattered from a particle in solution.
The Rayleigh equation is :
.
R
q
: The Rayleigh ratio - the ratio of scattered light to incident light of the
sample.
.
M : Sample molecular weight.
.
A
2
: 2
nd
Virial Coefficient.
.
C : Concentration.
.
P
q
: Scattering angle.
.
K : Optical constant as defined below.
N
A
: Avogadro’s constant.
R
g
: Radius of gyration.
l
o
: Laser wavelength.
n : Solvent refractive index..
dn/dc : The differential refractive index increment. This is the change in
refractive index as a function of the change in concentration. For many
sample/solvent combinations this may be available in literature; while for
novel combinations the dn/dc can be measured by use of a differential
refractometer.
The standard approach for molecular weight measurements is to first measure the
scattering intensity of the analyte used relative to that of a well described
‘standard’ pure liquid with a known Rayleigh ratio.
A common standard used in Static light scattering is Toluene , for the simple
reason that the Rayleigh ratios of toluene are suitably high for precise
measurements, are known over a range of wavelengths and temperatures and,
maybe more importantly, Toluene is relatively easy to obtain. The Rayleigh ratio
of Toluene can be found in many reference books, but for reference purposes the
expression used to calculate the sample Rayleigh ratio from a toluene standard is
given below.
C H A P T E R 1 4 Z e t a s i z e r N a n o S e r i e s
P a g e 1 4 . 2
M A N 0 3 1 7