Statistical Mechanics of Swelling of Network Structures

TLDR

Previous theories on swelling of network polymers contain inaccuracies, with Flory–Rehner underestimating entropy and Kuhn–Pasternak–Kuhn overestimating it. The authors derive the entropy of swelling for networks of arbitrary functionality f, avoiding the inaccuracies of earlier models. They provide corrected expressions for the partial molal‑free energy of dilution, swelling equilibrium, and the influence of deformation. These corrections differ markedly from earlier results when cross‑link density is high and equilibrium swelling is small, while elastic deformation at constant volume remains unchanged.

Abstract

Inaccuracies in previously published theories dealing with the swelling of network polymers in solvents are pointed out. The treatment of Flory and Rehner, based on the tetrahedral model, is overly restrictive and leads to an entropy of swelling which is too small. A more recent treatment of Kuhn, Pasternak, and Kuhn introduces an error in the opposite direction. In the present paper the entropy of swelling a network of any degree of connectivity, or functionality f, is derived in a manner which avoids these inaccuracies. Corrected relationships are given for the partial molal-free energy of dilution, swelling equilibrium and the influence of deformation on swelling equilibrium. These differ appreciably from those previously given when the degree of interlinking (i.e., concentration of cross linkages if f=4) is large and the equilibrium degree of swelling therefore is small. Previous expressions for elastic deformation at constant volume are unaffected.