Phase Behaviors in Compressible Polymer Blends.

We study phase behaviors in compressible polymer blends by using an equation of state in the framework of classical density-functional theory. The phase behaviors are explored by decomposing the compressible mixing of polymers into two steps: incompressible mixing as holding the volume and density relaxation at the given pressure. There exists both upper consolute pressure (UCP) and lower consolute pressure (LCP). LCP-type behaviors are driven by the entropy effect of asymmetric size of molecules, while UCP-type behaviors are driven by energetic interactions. The value of LCP follows a scaling of O(N-2), which can be improved to O(N-1.8) by taking into account the effects of random chain conformation. The volume of LCP-type polymers expands upon mixing, while that of UCP-type polymers contracts. A closed-loop phase coexisting curve may appear because of the interplay between UCP- and LCP-type behaviors. At the UCP/LCP boundary, the mixing free energy of density relaxation is much smaller than that of both UCP- and LCP-type behaviors. The contribution from incompressible mixing step always dominates the phase behaviors, while that from density relaxation step could distinguish UCP-type between LCP-type behaviors.