Long linear polymer molecules in solution can adsorb at a surface, and this phenomenon is important in many applications of polymers. It is associated with the phenomenon of steric stabilization, where colloids are stabilized by adsorbed polymer layers on their surfaces. As colloidal particles approach one another, the polymer layers interact and lose entropy, giving rise to an entropically driven stabilizing effect.
A model of polymer adsorption which has been studied for many years is a self-avoiding walk on a lattice (such as the simple cubic lattice) confined to lie either in or on one side of a specified plane (eg the plane z=0) representing the surface on which adsorption can occur. The energy of the system is proportional to the number of vertices of the walk in this surface. For a homopolymer all vertices of the walk behave in the same way (ie they all have the same potential for interaction with the surface) and this problem is now quite well-understood. It is known that the system exibits a phase transition, corresponding to adsorption. In the desorbed phase the fraction of vertices of the walk which are in the surface goes to zero as the length of the walk goes to infinity, while in the adsorbed phase this fraction goes to a positive constant.
Recently there has been considerable interest in the problem of copolymer adsorption, where one monomer interacts with the surface, and the other doesn't. One can consider regular copolymers, such as the alternating copolymer ABABAB... and the diblock copolymer AAA...ABBB...B, or random copolymers where the sequence of comonomers is determined by some random process. Many papers have appeared recently on both types of problem.