A structural model for equilibrium swollen networks

Department of Materials Science and Engineering, University of Cincinnati Cincinnati, OH 45221-0012, USA

Received: 5 April 2002
Accepted: 7 June 2002

Abstract

A tensile blob construction for branched structures is used to explain structural sizes larger than the strand length, as observed in neutron scattering data from equilibrium swollen networks. Under this model, equilibrium swollen networks display a base structural size, the “gel tensile blob” size, ξ, that follows the scaling relationship , where l is the monomer length, χ is the Flory interaction parameter and P is a power determined by the connectivity of the network and the degree of interpenetration. The gel tensile blobs compose a large-scale linear structure, whose length, L, follows the scaling relationship , where , Q is the equilibrium swelling ratio, is the strand length, is the entanglement length and f is the functionality of the cross-links. The variation of the swelling ratio with molecular weight can now be expressed as , which reduces to the correct expressions under the limits and .