Chemistry Reference
In-Depth Information
3.2.4
Light-Scattering Instrumentation
Light-scattering photometers include a light source and means for providing a col-
limated light beam incident on the sample, as well as for detecting the intensity
of scattered light as a function of a (usually) limited series of angles. A cell
assembly to hold the solution and various components for control and readout of
signals are also included. Scattered light is detected with a photomultiplier. At
any angle, solvent scattering is subtracted from solution scattering to ensure that
the scattering that is taken into account in the molecular weight calculation is due
to solute alone.
Since the square of the specific refractive index increment (
dn/dc
) appears
in the light-
sc
attering equations, this value must be accurately known in order
to measure
M
w
:
(
An
error of
x
%in
dn/dc
will result in a corresponding error
of about 2
x
%in
M
w
:
) The value of
dn/dc
is needed at infinite dilution, but
there is very little concentration dependence for polymer concentrations in the
normal range used for light scattering. The required value can therefore be
obtained from
n
2
c
5
Δ
n
0
n
c
5
dn
dc
(3-57)
where
n
and
n
0
are the refractive indices of solution with concentration
c
and of
solvent, respectively. In practice,
dn/dc
values may be positive or negative.
Their absolute values are rarely
0.2 cm
3
/g. Thus, if a solution of 10 g/liter con-
.
10
2
3
centration is being used, the
n
2
n
0
value would be 2
3
and this would
10
2
5
have to be measured within
1%. Conventional
refractometers are not suitable for measurements of this accuracy, and a direct
measurement of
6
2
3
to obtain
dn/dc
6
Δn
is obviously preferable to individual measurements of
n
and
n
0
. The preferred method for measuring
dn/dc
is differential refractometry,
which measures the refraction of a light beam passing through a divided cell
composed of solvent and solution compartments that are separated by a transpar-
ent partition.
3.2.5
Light Scattering from Copolymers
[2]
The foregoing analysis of the scattering of light from polymer solutions relied on
the implicit assumption that all polymer molecules had the same refractive index.
This rule does not hold for copolymers since the intensity of light scattered at a
particular angle from a solution with given concentration depends not only on the
mean molecular weight of the solute but also on the heterogeneity of the chemical
composition of the polymer. The true weight average molecular weight of a
binary copolymer can be determined, in principle, by measuring the scattering of
light from its solutions in at least three solvents with different refractive indices.
These measurements also yield estimates of parameters that characterize the het-
erogeneity of the chemical composition of the solute.
