Statistical Mechanics of Swelling of Network Structures

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.