parameter sets. Since the molecular simulations do not use the mean-field assump-
tion, the quantitative consistence between two approaches validates the mean-field
assumption applied in the statistical thermodynamic theory (Hu et al.2003a).
Owning to the dilute effect of mixing entropy, the melting point of polymer
solutions will be depressed by the increase of solvent content. The depression speed
is related to the solvent quality. The solvent quality is reflected by the values of
mixing interaction parameters. The better the solvent quality is, the faster the
melting point drops down. Figure 11.2a demonstrates the theoretical phase
diagrams for the melting point depression of polymer solutions under various
solvent qualities, while Figure11.2bis the simulation results under parallel ther-
modynamic conditions. One can see that, again under the same scales of
coordinates, the simulation results are roughly consistent with the parallel theoreti-
cal predictions, except the second focusing point of the simulation curves. The first
focusing point of melting point curves is located at the pure polymer side. The
second focusing point occurs only in simulation curves, implying an invalidity of
the theoretical assumption that the mixing interaction parameter is independent
with the concentration. In Sect.8.3.4, we have introduced the theoretical efforts on
the correction of this assumption.
The interplay of phase separation and polymer crystallization in the multi-
component systems influences not only the thermodynamics of phase transitions,
but also their kinetics. This provides an opportunity to tune the complex morphology
of multi-phase structures via the interplay. In the following, we further introduce three
aspects of theoretical and simulation progresses: enhanced phase separation in the
blends containing crystallizable polymers; accelerated crystal nucleation separately in
the bulk phase of concentrated solutions, at interfaces of immiscible blends and of
solutions, and in single-chain systems; and interplay in diblock copolymers. In the
end, we introduce the implication of interplay in understanding biological systems.
Fig. 11.2 (a) Theoretical phase diagrams of melting point versus polymer volume fraction curves
of polymer solutions with the chain length 32 monomers. (b) Molecular simulation results under
parallel thermodynamic conditions. The reduced interaction parameter sets are labeled near the
liquid–solid coexistence curveTm(Ep/Ec,B/Ec) (Hu et al.2003a) (Reprinted with permission)
11.1 Complexity of Polymer Phase Transitions 225