Chemistry Reference
In-Depth Information
C
6
θ
4
C
5
C
4
C
3
C
2
C=0
LINE
θ
3
C
1
θ
2
θ
1
θ
= 0 LINE
sin
2
θ
4
2
bc
5
bc
6
sin
2
θ/
2 + bc
FIGURE 3.5
Zimm plot
for simultaneous extrapolation of
light-scattering data to zero angle (
θ
)
and zero concentration (c). The symbols are defined in the text.
, experimental points;
x
K
extrapolated points; x, double extrapolation.
with the corresponding sin (
/
2) ordinates. The zero
an
gle and zero concentration
lines intercept at the ordinate and the intercept equals
M
2
1
θ
w
:
In many instances, Zimm plots will curve sharply downward at lower values
of sin(
/
2). This is usually caused by the presence of either (or both) very large
polymer entities or large foreign particles like dust. The large polymers may be
aggregates of smaller molecules or very large single molecules. If large molecules
or aggregates are fairly numerous, the plot may become banana shaped. Double
extrapolation of the “zero” lines is facilitated in this case by using a negative
value of
b
to spread the network of points.
It is obviously necessary to clarify the solvent and solutions carefully in order
to avoid spurious scattering from dust particles. This is normally done by filtra-
tion through cellulose membranes with 0.2- to 0.5-
θ
m-diameter pores.
If a laser light-scattering photometer is used, the scattered light can be
observed at angles only a few degrees off the incident beam path. In that case
extrapolation to zero angle is not needed and the Zimm plot can be dispensed
with. The turbidities at several concentrations are then plotted according to
Eq. (3-53)
. A single concentration observation is all that is needed if the concen-
tration is low (the
A
3
c
2
term in
Eq. 3-53
becomes negligible) and if the second
virial coefficient
A
2
is known. However,
A
2
is weakly dependent on molecular
weight and better accuracy is generally realized if the scattered light intensities
are measured at several concentrations.
μ
