Copolymers near a Linear Selective Interface

Abstract

A copolymer is a polymer consisting of different types of monomer. In this chapter we consider a two-dimensional directed copolymer, consisting of a random concatenation of hydrophobic and hydrophilic monomers, near a linear interface separating two immiscible solvents, oil and water (see Fig. 9.1). We will be interested in the quenched path measure (of the type defined in (1.3)). We will show that, as a function of the strength and the bias of the interaction between the monomers and the solvents, this model has a phase transition between a localized phase, where the copolymer stays near the interface, and a delocalized phase, where the copolymer wanders away from the interface. The critical curve separating the two phases has interesting properties, some of which remain to be clarified. The main techniques used are the subadditive ergodic theorem, the method of excursions, large deviations and partial annealing estimates.