  
|
     
|
The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 4 Issue 3 (1998) pp 341-350
Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model
R. Everaers (a)
Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France and Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany
Received: 28 November 1997 / Received in final form and accepted: 31 March 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.
PACS. 05.40.+j Fluctuation phenomena, random processes, and Brownian motion - 62.20.Dc Elasticity, elastic constants - 61.41.+e Polymers, elastomers, and plastics
(a) Present address: Institut Curie, Section de recherche, 11 rue Pierre et Marie Curie, 75231 Paris Cedex 05, France. email: Ralf.Everaers@curie.fr
Article in PDF-Format (348 KB)
Online publication: August 17, 1998
LINK Helpdesk
© EDP Sciences, Springer-Verlag 1998