ELASTIC-MODULUS AND EQUILIBRIUM SWELLING OF NEAR-CRITICAL GELS

Scaling ideas are used to predict the modulus G0 of gels, just above t he point of incipient gel formation, in the reaction bath as a functio n of the proximity to the gel point epsilon. The concentration depende nce of the modulus when the gel is diluted in a good solvent is also c alculated and used to predict the maximum swelling Q, obtained from th e 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 enta nglement epsilon(E), which leads us to expect three regimes of behavio r. Close to the gel point (for epsilon < epsilon(G)) critical percolat ion applies to an unentangled gel: G0 approximately epsilon2.6 and Q a pproximately epsilon-1.1. For epsilon(G) < epsilon < epsilon(E) we pre dict a mean-field unentangled regime with G0 approximately epsilon3 an d Q approximately epsilon-8/5. For epsilon > epsilon(E) entanglements raise the modulus and restrict the swelling of the mean-field gels, wi th G0 approximately epsilon4/3 and Q approximately epsilon-13/5.