Chemistry Reference
In-Depth Information
There are a number of factors that determine the state of the block copolymer in
a phase-separated system. The entropy of mixing of the block copolymers with the
homopolymers favors a random distribution of the copolymers. On the other hand,
localization of the block copolymers to the interface displaces the homopolymers
away from each other, thus, lowering the enthalpy of mixing. In addition, each
block of the copolymer will prefer to extend into its compatible homopolymer to
lower the block copolymer homopolymer enthalpy of mixing. Besides suffering an
entropy loss as a whole because of the confinement to the interphase, there is a
further entropy loss for the blocks of the copolymer arising from the restriction of
the blocks into their respective homopolymer regions. Finally, extension of the
copolymer chains, as well as the effect of the excluded volume at the interphase for
the homopolymers, lead to further loss of entropy. In their theoretical development,
Noolandi and Hong [
70
] included the contributions to the free energy from all these
effects, and obtained the concentration of the block copolymer at the interface as
well as the associated reduction in the interfacial tension.
It is clear that similar considerations for the enthalpy and entropy of mixing of
block copolymers could favor micellar aggregation rather than random distribution
in the bulk of the homopolymers. In this case, the micelles could compete with the
interfacial region for copolymer chains and the amount in each state would depend
on the relative reduction in the free energy as well as the surface area. Since no
complete treatment of this complicated case was given in the Noolandi and Hong
paper [
70
], their results should be reliable only for low copolymer concentrations
below the CMC. Their mean-field calculation cannot adequately describe the
critical crossover regime from a random copolymer distribution to aggregation
(micelle formation) and, thus, they only gave a rough estimate of the CMC.
The reduction in interfacial tension with increasing block copolymer concentra-
tion was calculated for a range of copolymer and homopolymer weights as well as
for different initial concentrations of solvent in their systems. The calculated
interfacial density profiles showed greater exclusion of the homopolymers from
the interfacial region as the molecular weight of the copolymer increased. This
greater localization of the copolymer resulted in a greater reduction in the interfa-
cial tension as the block molecular weight increased for both infinite and finite
molecular weights of the corresponding homopolymers.
The theory, however, generally overestimates the interfacial tension reduction
upon addition of the copolymer. An attempt to model the exact polymer system
studied by Gaillard et al. [
215
,
266
] (PS/PBD/styrene/PS-
b
-PBD, discussed in Sect.
4.2
) showed a disagreement between theory and experiment. The calculated inter-
facial tension fell to zero for a copolymer concentration (weight fraction with
respect to one of the two homopolymers of equal weight) of ca. 10
4
, while the
measurements indicated that interfacial tension decreased much more slowly with
increasing block copolymer concentration, and reached a constant value for ca. 5%.
Possible reasons for this discrepancy were discussed in the original paper [
70
]. The
use of the spinning drop method to measure the interfacial tension for the demixed
polymer solutions and the effect of the rotational speed on possible shift in the
position of the block copolymer at the interphase were emphasized, together with
