Elasticity of highly cross-linked random networksS. 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 for arbitrary cross-link densities. Considering pure shear deformations, 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.
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