Multicomponent Swelling of Polymer Networks

A mathematical model for treating multicomponent equilibrium in polymer networks is developed and tested against experimental data. Equations and numerical solution procedures for treating the full equilibrium problem of a binary mixed solvent in contact with a cross-linked polymeric network are provided. Case studies are presented for different values of the cross-link density (ρe) and Flory−Huggins interaction parameters (solute-1/solute-2 (χ12), solute-1/network-3 (χ13), and solute-2/network-3 (χ23)). Novel phenomena are observed in certain cases including decreasing concentration in the membrane with increasing component concentration in the contacting mixture. A simple renormalization procedure for capturing concentration dependence of the solute−network interaction parameters is proposed. Experiments on the swelling of poly(acrylonitrile-co-butadiene) (NBR rubber) by benzene−cyclohexane mixtures are also presented. Data obtained include cross-link densities from modulus measurements and interaction parameters χ13 and χ23 from pure component swelling. On the basis of these pure component data, no adjustable parameters are needed to predict the equilibrium swelling for the six different films studied. Model predictions based on pure component data using the renormalization approach show better agreement than the predictions based on constant interaction parameters.