Eur. Phys. J. B 4, 341-350 (1998)
https://doi.org/10.1007/s100510050389

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France and Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany

Corresponding author: ^a Ralf.Everaers@curie.fr

Received: 28 November 1997
Accepted: 31 March 1998
Published online: 15 August 1998

Abstract

We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The 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 simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints.