Self avoiding walks

In the discussion in the previous chapter we neglected the fact that polymers are almost always immersed in a solvent. A good solvent is defined as a solvent in which it is energetically more favourable for the monomers of the polymer to be surrounded by molecules of the solvent than by other monomers. As a consequence, one can imagine that there exists round each monomer a region (the excluded volume) in which the chance of finding another monomer is very small. This will lead to a more open, more expanded structure for the polymer than if the excluded volume effects were absent.

The most popular model to describe this effect is the self avoiding walk. Here one considers only the subset of random walks which never visit the same site again. An example is given in figure 2.1. When one compares this figure with that of a random walk, the excluded volume effect is obvious.

Thus, the equilibrium properties of a polymer with excluded volume effects are studied by making averages over the set of all N-step self avoiding walks (SAW) (we will encounter a ‘continuum version’ of the SAW model in chapter 4). All energy effects are taken into account by limiting the set of allowed configurations to the self avoiding ones. For the moment all SAWs therefore have the same energy and thus when we calculate averages, we weight all configurations equally. Note that the self avoidance constraint doesn't come from the fact that no two monomers can be in the same place, as is often stated.