Relation between Energy Contribution to Elastic Force and Strain Dependence of Modulus for Polybutadiene Vulcanizates

It is well known that the modulus G = r/(λ - λ^?2) varies with deformation, thus deviating from the predictions of statistical theories of rubber elasticity which require it to be constant. It has also been found that there is a nonnegligible energy contribution to the elastic force. It is postulated that these two phenomena are related because both arise from energetic interaction between chains.

Based on the lateral order of chains indicated by x-ray fiber diagrams of elongated noncrystallizable elastomers, it is suggested that energetic interaction of chains is induced by strain orientation. Proportionality between these two is assumed. The orientation distribution functions of end-to-end vectors and of statistical chain segments are considered. The proportionality constants are determined from the energy contribution to the strain dependence of the coefficient of thermal expansion. With the aid of these constants the modulus, corrected for energy contribution, is calculated. The observed and calculated elongation dependence of G agree reasonably well.

It is concluded that an energy interaction between aligned chains can account for the deviation of the observed stress elongation relation from the predictions of entropy elasticity theories.