Adsorption of polymers on a random surface.

Abstract

We investigate the adsorption of a polymer on a planar, random surface. For this we use a generalization of de Gennes's boundary condition to a random one, and path-integral methods. For weak randomness, the chain size is reduced slightly from its value in the absence of randomness. But as one increases the randomness or chain length, the chain size becomes \ensuremath{\sim}R, where R is the correlation length of the potential. If the length or the randomness exceeds a certain critical value, the chain is found to collapse in the direction perpendicular to the surface, to a thickness zero, so that it becomes a two-dimensional object.