Chemistry Reference
In-Depth Information
The basic method yields good measurements of
M
w
but the heterogeneity
parameters are generally found not to be credible for statistical copolymers. This
may be due to a dependence of
dn/dc
on polymer molecular weight, at low
molecular weights
[3]
.
3.2.6
Radius of Gyration from Light-Scattering Data
A radius of gyration in general is the distance from the center of mass of a body
at which the whole mass could be concentrated without changing its moment of
rotational inertia about an axis through the center of mass. For a polymer chain,
this is also the root-mean-square distance of the segments of the molecule from
its center of mass. The radius of gyration is one measure of the size of the random
coil shape which many synthetic polymers adopt in solution or in the amorphous
bulk state. (The radius of gyration and other measures of macromolecular size
and shape are considered in more detail in Section 1.13.)
The radius of gyration,
r
g
, of a polymer in solution will depend on the molecu-
lar weight of the macromolecule, on its constitution (whether or not and how it is
branched), and on the extent to which it is swollen by the solvent. An average
radius of gyration can be determined from the angular dependence of the intensi-
ties of scattered light.
We saw in
Section 3.2.3
that the light scattered from large particles is less
intense than that from small scatterers except at zero degrees to the incident
beam. This reduction in scattered light intensity depends on the viewing angle (cf.
Fig. 3.4b
), on the size of the solvated polymer, and on its general shape (whether
it is rodlike, a coil, and so on). A general relation between these parameters can
be derived
[4]
, and it is found that the effects of molecular shape are negligible at
low viewing angles. The relevant equation (for zero polymer concentration) is
2
Kc
R
θ
5
1
M
w
16
π
r
g
sin
2
2
1
?
lim
c
1
1
(3-58)
2
3
λ
-
0
The limiting slope of the zero concentration line of the plot of
Kc/R
θ
against
sin
2
2
M
w
Þ
2
θ
/
2(
Fig. 3.5
) gives
ð
16
π
=
3
λ
r
g
:
The mutual intercept of the zero con-
centration and zero angle lines gives
M
2
1
w
and the limiting slope of the zero angle
line can be used to obtain the second virial coefficient as indicated by
Eq. (3-47)
.
Fo
r a
polydisperse polymer, the average molecular weight from light scatter-
ing is
M
w
, but the radius of gyration which is estimated is the
z
average.
;
3.3
Dilute Solution Viscometry
The viscosity of dilute polymer solutions is considerably higher than that of the
pure solvent. The viscosity increase depends on the temperature, the nature of the
solvent and polymer, the polymer concentration, and the sizes of the polymer
