In the previous three chapters we considered the behaviour of polymers in bulk. In reality systems are never infinite and one always has to consider the presence of surfaces. When the polymer is close to or even attached to a surface its critical properties may change. When there is an interaction between the monomers and the surface interesting adsorption effects can occur. We now turn to a discussion of these phenomena.

Surface magnetism

Consider a (d > 1)-dimensional lattice, in which a polymer is restricted to be in a semi-infinite region, e.g. the region with x ≥ 0. We imagine a wall at x = 0 which is impenetrable. When the polymer is very far from this surface, i.e. in the bulk, its properties are hardly changed by the presence of the wall. As the polymer is placed closer and closer to the surface its properties may be modified. These effects can be expected to have a scaling behaviour depending on the ratio of the distance xcm of the centre of mass of the polymer from the surface and its radius RN. As we are interested in properties of the polymer on a coarse grained scale, let us immediately attach one of the monomers to the surface (figure 5.1). There are two ways to discuss the properties of such a polymer. The first one works directly with SAWs, while the other one uses, through the O(n)-connection, known properties of surface magnetism. Since we don't expect the general reader to know about surface critical behaviour, we will give a brief overview of the main ideas from this field (for a general review, see).