Phase transition in a heteropolymer chain at a selective interface

We consider the localization transition of a heteropolymer chain without volume interactions consisting of two types of links hydrophobic (A) and hydrophilic (B) at a selective oil-water interface: the A links are repelled from the water into the oil whereas B links prefer to be located in the water. We study the behavior of the free energy near the point of transition from a delocalized (Gaussian) to a localized (adsorbed) regime for two basic models: chains with periodic (A-B-A-B-...) and annealed random sequences of links. We show that the transition is sensitive to the type of direct repulsive interaction of the links with the interface, and can be of fourth order in particular cases.