TABLE OF CONTENTS The salient fact about polymer chains is that, on a molecular scale, they are very long. Linear polymers consist of chains whose lengths can vary from hundreds to many thousands of monomer units. The statistical mechanics of systems composed of such large molecules can be quite complex and, if pursued with a degree of rigor and completeness, soon becomes intractable to analytic methods.
But it is the great length of the polymer chain that distinguishes it from other systems, and it is of interest to focus on this fact. Accordingly, it is customary to adopt a simple model that assumes that a polymer chain consists of a large sequence of identical segments joined together at their ends by chemical bonds, each segment being rigid, but having at least some freedom to rotate in space relative to its adjoining segments. Such a chain has many possible conformations, and the analogy to a random flight is clear. Figure 13.1 is then interpreted as a possible conformation of a long-chain molecule, and figure 13.2 then shows the angular relation among adjacent monomer segments. In this model, all the results of random flight theory carry over to polymer statistics.
However, some caveats are in order because polymer segments consist of groups of atoms and are not geometric lines. There are intramolecular interactions among these groups that are not accounted for in the theory of random flights. An important effect of these interactions is that segments cannot go through...
