CONSTRAINED FLUCTUATION THEORIES OF RUBBER ELASTICITY - GENERAL RESULTS AND AN EXACTLY SOLVABLE MODEL

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. Th e model allows us to treat the constrained junction and the tube model within the same, transparent formalism! does not require any further approximations, and is particularly suited for the analysis of simulat ion data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the cons traints (but not the mean polymer conformations!) have to deform affin ely, a severe restriction that might also apply to other models. Compl ementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian lead s to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affin ely deforming constraints.