Classical Theories of Rubber Elasticity

This chapter describes three molecular theories of rubber elasticity. Section 2.1 outlines the elementary theory of Kuhn and Treloar, which is of particular importance since it presents the basic elements of rubberlike elasticity in a very transparent way. Section 2.2 presents the phantom network model developed by James and Guth, and section 2.3 presents the affine network model developed by Wall and Flory. Historical aspects of the theories have been given in an article by Guth and Mark, and in a book prepared as a memorial to Guth. Finally, the major features of both theories are briefly summarized in a review. Separately, the James-Guth theory has been reviewed by Guth and by Flory, and the phantom network model of section 2.2 is based on the Flory treatment. The affine network model has been described in detail in Flory’s 1953 book. This model is described in section 2.3 by generalizing the phantom network model (as was done in one of Flory’s subsequent studies). The simple, elementary statistical theory described in section 2.1 paved the way to the current understanding of rubber elasticity. Further progress in the understanding of rubberlike systems was possible, however, only as a result of the two more precise and accurate theories: the phantom network and the affine network theories. Despite their differences, these two theories and the corresponding molecular models have served as basic reference points in this area for more than four decades. They still serve this purpose for the interpretation and explanation of experimental data. The differences between the assumptions and the predictions of the two models have led to serious disagreements during their development, as may be seen from the original papers cited earlier. The main point of disagreement was the magnitude of the front factor that appeared in the expression for the elastic free energy and the stress. For tetrafunctional networks, the James-Guth phantom network theory predicts one-half the value of the front factor obtained by the Wall-Flory affine network theory.