Elastic Modulus and Equilibrium Swelling of Near-Critical Gels

Scaling ideas are used to predict the modulus Go of gels, just above the point of incipient gel formation, in the reaction bath as a function of the proximity to the gel point t. 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 ( t < t ~ ) and mean-field ( t> t ~ ) percolation regimes. We derive a new criterion for entanglement €E, which leads us to expect three regimes of behavior. Close to the gel point (for t < €0) critical percolation applies to an unentangled gel: Go- P and Q- t-l.l. For EG < E < we predict a mean-field unentangled regime with Go- t3 and Q N d5. For t> €E entanglements raise the modulus and restrict the swelling of the mean-field gels, with Go- t I4 l3 and Q- t-I3l5. 1.