A new approach to the theory of rubber elasticity

Current polymer network theories do not explain the experimental behaviour clearly. The use of Gaussian distribution might be the reason of this limitation. The approximation of the distribution of the chain vector by a Gaussian function implies non-vanishing probability for chains at full extension and beyond. In the stress-strain relation, the first derivative with respect to strain of the logarithm of the distribution function is involved. For Gaussian distribution this derivative deviates very much from that of the actual distribution especially at higher extensions. The properties of the said derivatives for different distributions were examined. It is observed that the use of the Langevin distribution might be more realistic. A new approach is suggested on this basis. The tensile force per unit cross section, τ, for an extension ratio α at constant volume has the form where an average chain contributes a length L in each of the three mutually perpendicular directions and contains n equivalent free links of length l each. The expression contains no unknown parameter. This equation has great similarity with the empirical Mooney-equation and gives much better agreement with experimental results.