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Analysis of Anomalous Swelling by a Rubber Elasticity Model for Entangled Networks

A complete equation of the swelling activity parameter (S) as a function of swelling deformation (λs ) is derived by using a non-Gaussian elastic network model, including a tube concept and the Flory–Rehner model, and by following McKenna's criterion that takes into account the disparity between the Flory–Huggins interaction parameters for cross-linked and uncross-linked polymers. However, only a part of tube at the network chain size scale is extended to that for a large-scale structure according to the “gel tensile blob” model for equilibrium swollen networks. This approach is basically best for the “ideal regular network + simple structured good-solvent” binary systems due to its model character. As a result, it reproduces well the literature data of S versus λs 2 with a maximum/inflection measured for such actual systems.