J. Phys. I France
Volume 5, Numéro 6, June 1995
Page(s) 657 - 669
DOI: 10.1051/jp1:1995158
J. Phys. I France 5 (1995) 657-669

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

Andrey V. Dobrynin

Department of Physics and Astronomy, University of Rochester, Rochester, New York 146270011, U.S.A.

(Received 3 August 1994, revised 29 November 1994, accepted 16 February 1995)

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 $Q_{\alpha\beta}({\bf q})$ is proportional to the square of the one-replica correlation function $Q_{\alpha\beta}G_{\alpha\alpha}^2({\bf q})$, where $Q_{\alpha\beta}$ is a matrix describing the metric properties of the replica space. The phase diagram for this class of copolymer systems is calculated.

© Les Editions de Physique 1995