Energy Contribution to Rubber Elasticity

Stress-temperature measurements were performed for natural rubber at both ``infinitesimal'' (<10%) and finite (<100%) strains. Data are used to calculate the internal-energy contribution to the elastic stress fe by several thermoelastic equations. A unified derivation of these equations is given, which leads naturally to a new equation based on the temperature coefficient of shear modulus of the rubber. It is demonstrated that the dependence of the relative energy contribution fe/f on deformation as previously reported arises because of the difficulty in obtaining extremely accurate data in the low-strain regions. Calculation of the same data by our new equation shows fe/f to be independent of deformation for the region of strains in which the statistical theory of rubber elasticity applies. Thus the postulate of additivity of configurational free energy, basic to the derivation of the statistical theory, is vindicated. Finally it is shown that the stress-temperature measurements are sensitive to the sample geometry. For butt-jointed samples, which are believed to approach uniform stress distribution, the relative energy contribution is found to be approximately 15% for natural rubber.