A Monte Carlo study of adsorption of random copolymers on random surfaces

We study the adsorption problem of a random copolymer on a random surface in which a 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 randonfly labelled A with probability p(p) or B with probability 1 - p(p), and only vertices labelled A are attracted to the surface plane. Each lattice site on the plane is also labelled either A with probability p(s) or B with probability 1 - p(s), and only lattice sites labelled A interact with the walk. We study two variations of this model: in the first case the A-vertices of the walk interact only with the A-sites on the surface. In the second case the constraint of selective binding is removed; that is, any contact between the walk and the surface that involves an A-labelling, either from the surface or from the walk, is counted as a visit to the surface. The system is quenched in both cases, i.e. the labellings of the walk and of the surface are fixed as thermodynamic properties are computed. We present Monte Carlo simulation results which provide evidence for second-order transitions in both cases. We observe that in both cases the adsorption location depends on both p(s) and p(p), the dilution of the interactive sites on the surface and the walk. We compare critical properties for the two cases and find that the adsorption location varies for different models while the crossover exponent is independent of the details of the models.