with the theoretical predictions (solid lines); but once approaching to the coexis-
tence curves, the simulated binodals shift up. This shifting-up implies that, the
thermal fluctuations for crystallization are enhanced near the melting point, making
a more significant contribution to the driving forces for phase separation. As a
result, the phase separation is enhanced near the melting point (Ma et al. 2007 ).
11.3 Accelerated Crystal Nucleation in the Concentrated Phase
Let us switch our perspective to the other side, and see how the prior phase
separation affects polymer crystal nucleation. We know that polymer crystallization
normally needs a relatively large degree of supercooling. If liquid-liquid phase
separation happens before a polymer solution has reached a sufficient degree of
supercooling, the practical concentration for polymer crystallization will be
changed.
As demonstrated in Fig.11.4, we designed three sets of energy parameters for the
solutions of polymers each containing 128 monomers in the cubic lattice space 64^3.
They display the same equilibrium melting points near the concentration 0.125 in the
semi-dilute solution region, but clearly different critical points for phase separation.
Fig. 11.4 Comparison in the theoretical phase diagrams of phase separation and polymer crystalli-
zation in polymer solutions, and the kinetic phase diagrams of crystal nucleation. The energy
parameters are set asEp/Ec¼1.0 andB/Ec¼0.076 for the labeledC1 curves,Ep/Ec¼1.072 and
B/Ec¼0.03 forC2,andEp/Ec¼1.275 andB/Ec¼0.1 forC3. Three solution series share the
same melting points (solid lines) at polymer concentrationf¼0.125, but different depths of critical
points for phase separation. Thedashed linesare binodals, and thedotted linesare spinodals. The
data points are the onset temperatures for the uprising of crystallite numbers on isothermal crystalli-
zation. Thestraight linesare drawn to guide the eyes (Zha and Hu 2007 ) (Reprinted with permission)
228 11 Interplay Between Phase Separation and Polymer Crystallization