Statistical Thermodynamics of Rubber Elasticity

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Abstract
Two principal differences between the theories of rubberelasticity advanced by James and Guth and by other authors are examined in the light of certain fundamental concepts. First the distribution functions for molecular chain lengths in vulcanized rubber networks are considered from the point of view of symmetry. Assuming a relaxed network to be isotropic and a network subject to uniform stress in one direction to be transversely isotropic, it is possible to formulate very general mathematical forms with respect to which the actual distribution functions must be compatible. It is shown that the functions employed by Wall and by Flory and Rehner are consistent with the required general forms; those of James and Guth are incompatible with any degree of isotropy and suggest an aeolotropic structure for vulcanized rubber. It is also shown that the configurational entropy of vulcanization must be zero and quite independent of the statistical nature of the chains comprising the network, providing the network is not deformed macroscopically. The negative entropy of vulcanization derived by James and Guth arises from their erroneous identification of the configurational probability with the number of configurations which a microscopically specified network structure could assume, rather than with the total number of configurations for all network structures which are consistent with the requirements of the vulcanization process. The assertion of James and Guth that the configurations of the polymer chains are altered in some systematic manner by the introduction of cross‐linkages and their concept of ``internal pressure'' originate in this error. The present article attempts to clarify the currently prevalent confusion with respect to rubberelasticity theory.