Statistical Mechanics of Rubber

It is shown in this paper that above the second-order transition the partition function of a rubber can be represented to a reasonably good approximation by the product of the partition function of a liquid formed of molecules similar to the chain elements and the partition function of the noninteracting chains divided by the partition function of a perfect gas. In terms of the free energy this means that the free energy of rubber will be equal to the sum of the free energy of the chain network without interactions and that of a liquid formed of the chain elements alone minus the free energy of a perfect gas having the same number of molecules as the rubber has chain elements. This same procedure has permitted the calculation of the free energy and partial pressure of a rubber solution. This is, however, by no means the only possible application. All the thermodynamic properties of elastomer solvent systems can be obtained. This is a generalization of the methods previously used in the statistical studies of rubber and rubber solvent mixtures.