Continuum Model of Heterogeneous Gels: Formation and Elastic Properties

(Received 27 November 1995, revised 21 May 1996, accepted 1 August 1996)

Abstract
A kinetic model of heterogeneous gel formation and a method to calculate gel stiffness are proposed, with application to the elastic properties of polyacrylamide gels. The model is based on assumptions about nucleation and growth of dense regions, governed by the concentration of monomer units (p₀) crosslink agent (c₀) and rate constants for chain propagation and curing. It is shown that at low c₀ the polymer and crosslink densities inside and outside an inclusion are almost the same and that the gel may be regarded as homogeneous. But the difference between densities increases sharply with c₀, giving growth of heterogeneities. Calculation of the elastic modulus was performed using a self-consistent method. Stiffness grows with p₀ at fixed c₀, but goes through a maximum as a function of c₀ at fixed p₀. The theoretical analysis is in qualitative agreement with the experimental data.