Statistical Mechanics of Cross-Linked Polymer Networks II. Swelling

The interaction of solvents with cross-linked network structures, such as occur in vulcanized rubber, is subjected to a statistical mechanical treatment based on the model and procedure presented in the preceding paper. The activity of the solvent is expressed as a function of its concentration in the swollen network, and of the degree of cross-linking. The maximum degree of swelling of the network in contact with the pure solvent is related to the degree of cross-linking. The heat of interaction of the solvent with the network can be calculated from the temperature coefficient of maximum swelling. The theory leads to the conclusion that the swelling capacity should be diminished by the application of an external stress. Furthermore, the modulus of elasticity should decrease inversely with the cube root of the swelling volume.