J. Phys. I France
Volume 5, Numéro 10, October 1995
Page(s) 1241 - 1246
DOI: 10.1051/jp1:1995194
J. Phys. I France 5 (1995) 1241-1246

A Field Theory for Polymeric Networks with Excluded Volume

Thomas A. Vilgis and Michael P. Solf

Max-Planck-Institut für Polymerforschung, Postfach 3148, 55021 Mainz, Germany

(Received 5 May 1995, received in final form 24 July 1995, accepted 16 August 1995)

In this note we present a fiel theory for Gaussian phantom networks with excluded volume interaction. Contrary to earlier work which was formulated solely in terms of chain variables, the Deam-Edwards Hamiltonian of a polymeric network is transformed to a special case of a dn-dimensional anisotropic O( m) field theory in the limit $n,m \to 0$. Using Flory-type arguments we predict the size of the network. Its density and the vulcanization threshold are computed from the saddle point approximation. For an elastic affine deformation we find from our mean-field calculation that the essential parts of the free energy agree with the result predicted earlier by Deam and Edwards.

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