Adsorption and localization of random copolymers subject to a force: The Morita approximation

We discuss directed walk models of random copolymers, either adsorbed at a surface or localized at an interface between two immiscible liquids. We consider the response to an applied force which can cause desorption or delocalization into a bulk phase, and calculate the critical force as a function of temperature. The randomness is quenched and, even for directed models, we cannot usually treat; the quenched system analytically so we resort to an approximation in which the quenched average is approximated by an annealed average with a side condition which ensures the correct proportion of the types of comonomers. We argue that this approach gives the exact result for the quenched system in some cases and a bound in others.