Partition Function of Bulk Polymers. I

Abstract

This paper develops a theory which interrelates several aspects of the behavior of rubberlike materials through the extension of statistical mechanical treatments which have been developed for fluids. An additional term of the partition function of bulk polymers is found. This term decreases as the temperature increases. It has been possible partially to evaluate this added term by replacing important portions of it with thermodynamic expressions appropriate to liquids. This eliminates the necessity of attempting to evaluate series which would be difficult at low temperatures. In this way it is shown with a minimum of approximation how it is that the well-known and simple theory of rubber is valid at high temperatures and tends to show deviations as the temperature decreases. It further shows that the probability of finding a chain far removed from its most probable position decreases with decreasing temperature. It is hoped that these techniques can be used to explain some of the changes which occur in solid polymers as the temperature is lowered.