Chemistry Reference
In-Depth Information
The important features of the approximate relationships (
96
) and (
98
) were
verified by the exact numerical calculations. An exponential dependence of the
interfacial tension reduction on the block copolymer molecular weight as well as on
the total homopolymer volume fraction was predicted that can explain the remark-
able effectiveness of using large molecular weight diblocks as surfactants for
concentrated mixtures of immiscible homopolymers. For small
N
, a linear depen-
dence of
Dg
on
N
(
98
) was also predicted by the exact numerical calculations.
Moreover, a linear dependence of
Dg
on the block copolymer volume fraction was
predicted by the exact numerical solution, as shown by (
96
) and (
98
).
The homopolymer profile thickness was calculated numerically to increase
exponentially with copolymer molecular weight and linearly with copolymer con-
centration. The increasing width (or decreasing slope) of the homopolymer profiles,
as compared to the total polymer profiles (homopolymer plus copolymer segments),
reflected the necessity to accommodate the increased amount of the copolymer at
the interface.
Noolandi (personal communication) suggested that the theory can be applied to
the experimental system PS/PS-
b
-PVE/PVE of [
45
], i.e., to a concentrated system
without solvent, by letting the total polymer volume fraction,
f
p
, go to 1 in (
96
) and
(
98
). For the temperature of 145
C in the experiments,
w ¼
0.0388 [
245
], and for the
degree of polymerization of the diblock (
N
¼
261), (
98
) becomes:
583
d
Dg
0
:
b
f
c
(99)
with
d
being the width at the half height of the copolymer profile, which is a
parameter related to the thickness of the interface but it was not determined by the
simplified theory.
In order to compare the data with the theory, Noolandi and Hong, Anastasiadis
et al. [
45
] assumed that the same volume fraction of copolymer exists in both bulk
phases and, by using the bulk densities of PS and PB, they plotted the interfacial
tension increment,
Dg ¼ g g
0
, as a function of the copolymer bulk volume
fraction, as shown in Fig.
29
.
The interfacial tension increment,
Dg ¼ g g
0
, was linear with the copolymer
volume fraction, calculated for low concentration of the copolymer additive as
suggested by theory for concentrations below the CMC. The slope of the fitted line
was
37.0, and thus
d
was estimated to be 38 nm, or 63.5
b
when the geometric
mean of the Kuhn statistical segment lengths of the two segments was used as
0.6 nm. This value of
d
(
63.5 monomer units) was about 24% of the contour
length of the copolymer chains and, thus, indicated an extended configuration of the
copolymer chains.
Noolandi and Hong [
71
,
281
] pointed out that both copolymer concentration
and molecular weight are equally important in reducing the interfacial tension.
They noted, however, that the interfacial tension surface (
g
plotted against N and
f
c
) is bounded by a CMC curve because blocks of large molecular weights tend
to form micelles in the bulk of the homopolymers rather than segregating to the
