A Monte Carlo study of polymer adsorption: random copolymers and random surfaces

We consider a model of random copolymer adsorption in which an n-edge self-avoiding walk in three dimensions interacts with a plane defining a half-space to which the walk is confined. Each vertex of the walk is randomly labelled A with probability p or B with probability 1 - p, and only vertices labelled A are attracted to the surface plane. The system is quenched, i.e. the labelling is fixed and then the thermodynamic properties are computed. We use Monte Carlo methods to investigate the behaviour of this system. We observe self-averaging of the energy as n increases, and investigate the location of the adsorption transition for various values of p. In addition, we compare the behaviour of this system with that of a homopolymer adsorbing at a randomly heterogeneous surface consisting of two types of sites, only one of which interacts with the monomers of the polymer.