Abstract
A molecular theory is presented in this paper which gives a method of analysis for mechanical properties of filler-reinforced elastomers, based on the conception of a internal deformation and a statistical theory of rubber-like elasticity. The internal deformation is determined more strictly and more accurately than an old theory by author and Furukawa under the condition of minimizing the free energy of the system for a position and a given external deformation. From the theory, formulae for tension, swelling tension, Young's moduli, local stress distribution, strain birefringence, condition for swelling equilibrium, and so on are derived. Moreover as an application of the equilibrium theory, a rate theory is derived which gives a method of analysis for non-equilibrium properties such as stress relaxation and hysteresis loops of the filler-reinforced elastomers. The characteristic of the basic theory (which the equilibrium theory is called hereafter) is uniquely determined from character of the internal deformation and of the statistical theory of rubber-like elasticity, but this is only one of rate theories in which various treatments are possible about many mechanisms of rate processes.
