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 crosslink agent and rate constants for chain propagation and curing. It is shown that at low 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 , giving growth of heterogeneities. Calculation of the elastic modulus was performed using a self-consistent method.
Stiffness grows with at fixed , but goes through a maximum as a function of at fixed .
The theoretical analysis is in qualitative agreement with the experimental data.