Analysis of phase separation in compressible polymer blends and block copolymers

For the analysis of phase-separation behavior of compressible polymer blends and block copolymer melts, an equation-of-state (EOS) model is combined with the compressible random-phase approximation (RPA) formalism. The EOS model to be employed is obtained from extending an off-lattice model, recently given for interpreting compression response of pure polymers to pressure by Cho and Sanchez (CS), to polymer blends. The free energy for the CS model consists of an ideal free energy of Gaussian chains and a nonideal free energy that represents the excluded volume effects and the attractive interactions in given blend systems. This nonideal free energy yields the RPA interaction fields, with which monomer-monomer correlation functions for polymer blends or block copolymers are calculated to determine the condition of phase separation. it is shown that the theory can predict not only macrophase separation in some polymer blends but also microphase separation in the corresponding block copolymer melts. Especially, microphase separation upon heating, recently observed in several diblock copolymer melts; is shown to be driven by finite compressibility in given copolymer systems. The stability of diblock copolymer melts exhibiting microphase separation upon heating is also discussed in relation to the symmetry of phase diagrams.