Europhys. Lett.
Volume 76, Number 4, November 2006
Page(s) 677 - 682
Section Interdisciplinary physics and related areas of science and technology
Published online 18 October 2006
Europhys. Lett., 76 (4), pp. 677-682 (2006)
DOI: 10.1209/epl/i2006-10310-7

Elasticity of highly cross-linked random networks

S. Ulrich1, X. Mao2, P. M. Goldbart2 and A. Zippelius1

1  Institut für Theoretische Physik, Georg-August-Univeristät Göttingen 37073 Göttingen, Germany
2  Department of Physics, University of Illinois at Urbana-Champaign 1110 West Green Street, Urbana, IL 61801-3080, USA

received 21 August 2006; accepted in final form 19 September 2006
published online 18 October 2006

Starting from a microscopic model of randomly cross-linked particles with quenched disorder, we calculate the Landau-Wilson free energy ${\cal S}$ for arbitrary cross-link densities. Considering pure shear deformations, ${\cal S}$ takes the form of the elastic energy of an isotropic amorphous solid state, from which the shear modulus can be identified. It is found to be a universal quantity, not depending on any microscopic length-scales of the model.

82.70.Gg - Gels and sols.
61.41.+e - Polymers, elastomers, and plastics.
62.20.Dc - Elasticity, elastic constants.

© EDP Sciences 2006