| The goal of this project is to apply a variational method recently developed by the applicant and collaborators to the study of copolymers near selective interfaces. The object of interest is a copolymer consisting of a random concatenation of hydrophobic and hydrophilic monomers, located near a linear interface separating oil and water acting as solvents. The energy of the copolymer is given by an interaction Hamiltonian that rewards matches and penalizes mismatches of the monomers and the solvents. It is known that the quenched free energy has a phase transition along a critical curve in parameter space, separating a localized phase (in which the copolymer stays close to the interface) and a delocalized phase (in which the copolymer wanders away from the interface). One goal of the project is to derive a variational formula for this critical curve, and to settle a conjecture for the weak interaction limit that has been open for ten years. Another goal is to extend the analysis to a copolymer near a random interface, as found in an oil-water micro-emulsion. |
