Glass Transition Versus Microphase Separation: a Phenomenological Replica-Field Theory for AB Copolymer Systems

Abstract

We present a phenomenological replica-field theory for symmetric AB copolymer systems with the A-block near its glass transition point. Using a variational principle based on the second Legendre transformation we prove that the interaction between composition fluctuations, due to the loss mobility of the A monomers, results in the elimination of microphase separation. Instead of a microphase separation there is a third-order phase transition between the homogeneous state and a glass-like state with broken replica symmetry of the two-replica density-density correlation function. We show that near the point of the glass transition two-replica correlation function Q αβ (q) is proportional to the square of the one-replica correlation function Q αβ G αα 2 (q), where Q αβ is a matrix describing the metric properties of the replica space. The phase diagram for this class of copolymer systems is calculated