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 e. 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 (e \textless to) and mean-field (e \textgreater to) percolation regimes. We derive a new criterion for entanglement 6e, which leads us to expect three regimes of behavior. Close to the gel point (for e \textless eo) critical percolation applies to an unentangled gel: Go e2·6 and Q r1·1. For íq \textless e \textless ce we predict a mean-field unentangled regime with G0 e3 and Q r8/5. For e \textgreater es entanglements raise the modulus and restrict the swelling of the mean-field gels, with Go e14’3 and Q r13/5.