Copolymer Melts in Disordered Media

Abstract

The symmetric AB block copolymer melt in a gel matrix with preferential adsorption of A monomers on the gel gives an example of a random-field system, which is described near the point of the microphase separation transition by the random field Landau-Brazovskii Hamiltonian. By using the technique of the 2-nd Legendre transform, the phase diagram of the system is calculated. We found that the preferential adsorption of the copolymer on the gel results in two effects: a) It decreases the temperature of the first order phase transition between disordered and ordered phase. b) There exists a region on the phase diagram at some small but finite value of the adsorption energy in which the replica symmetric solution for two replica correlation function is unstable with respect to replica symmetry breaking. We interpret this state as a glassy state and calculate a spinodal line of this transition. We also consider the stability of the lamellar phase in the weak segregation limit by mapping the copolymer Hamiltonian onto the Hamiltonian of the random field XY model. We suggest that the long range order is always destroyed by weak randomness.