R. Everaers, CONSTRAINED FLUCTUATION THEORIES OF RUBBER ELASTICITY - GENERAL RESULTS AND AN EXACTLY SOLVABLE MODEL, EUROPEAN PHYSICAL JOURNAL B, 4(3), 1998, pp. 341-350
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.