Macromolecules, Vol.27, No.12, 3184-3190, 1994
Elastic-Modulus and Equilibrium Swelling of Near-Critical Gels
Scaling ideas are used to predict the modulus G0 of gels, just above the point of incipient gel formation, in the reaction bath as a function of the proximity to the gel point epsilon. The concentration dependence of the modulus when the gel is diluted in a good solvent is also calculated and used to predict the maximum swelling Q, obtained from the gel swollen at equilibrium with pure solvent. The Ginzburg criterion separates the critical (epsilon < epsilon(G)) and mean-field (epsilon > epsilon(G)) percolation regimes. We derive a new criterion for entanglement epsilon(E), which leads us to expect three regimes of behavior. Close to the gel point (for epsilon < epsilon(G)) critical percolation applies to an unentangled gel : G0 approximately epsilon2.6 and Q approximately epsilon-1.1. For epsilon(G) < epsilon < epsilon(E) we predict a mean-field unentangled regime with G0 approximately epsilon3 and Q approximately epsilon-8/5. For epsilon > epsilon(E) entanglements raise the modulus and restrict the swelling of the mean-field gels, with G0 approximately epsilon4/3 and Q approximately epsilon-13/5.