Phase diagram of selectively cross-linked block copolymers shows chemically microstructured gel

Abstract

We study analytically the intricate phase behavior of cross-linked AB diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints. Gelation, i.e., spatially random localisation of polymers forming a system-spanning cluster, is driven by increasing the number parameter mu of irreversible, type-selective cross-links between random pairs of A blocks. Self-assembly into a periodic pattern of A/B-rich microdomains (microphase separation) is controlled by the AB incompatibility chi inversely proportional to temperature. Our model aims to capture the system's essential microscopic features, including an ensemble of random networks that reflects spatial correlations at the instant of cross-linking. We identify suitable order parameters and derive a free-energy functional in the spirit of Landau theory that allows us to trace a phase diagram in the plane of mu and chi Selective cross-links promote microphase separation at higher critical temperatures than in uncross-linked diblock copolymer melts. Microphase separation in the liquid state facilitates gelation, giving rise to a novel gel state whose chemical composition density mirrors the periodic AB pattern. (C) 2015 AIP Publishing LLC.