Disequilibrium 3: Internal Variables

In Chapters 2, 3, and 4, the usefulness of the concept chemical potential has been explored for describing and predicting movement of material from point to point in space—from a location where a component's potential is high to a location where its potential is lower. But chemical potential influences another type of material behavior as well, as in the example at the end of Chapter 2, the polymerization of vinyl chloride. The polymerization is a process that runs at a certain rate, like diffusion of salt, and the rate depends on the potential difference between the starting state and the end state; but unlike diffusion of salt, there is no overall movement from one location to a new location—the vinyl chloride simply polymerizes where it is. There are movements, of course, on the scale of the interatomic distances, but nothing corresponding to the 4 m of travel that appears in the discussion of the dike. If no travel is involved, it is not so easy to calculate a potential gradient along the travel path and go on to predict a rate of response. Yet there definitely is a rate of response, even with PVC polymerizing. The purpose of this chapter is to consider this matter; we shall then be equipped to begin considering nonhydrostatic conditions. The essential idea is to represent all possible degrees of polymerization along an axis, as in Figure 5.1. The figure is drawn to represent a condition where the chemical potential per kilogram is greater in the monomer form than in the dimer form, i.e., a condition where the material polymerizes spontaneously. Suppose we know the chemical potential per kilogram for all degrees of polymerization and also, at some temperature, the rates at which 2 forms from 1, 3 forms from 2, etc. (per kg of the starting form in a pure state). Then we arbitrarily pick a distance on the horizontal axis to separate point 1 from point 2.