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 ∊. 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 (∊ < ∊G) and mean-field (∊ > ∊G) 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 ∊ < ∊G) critical percolation applies to an unentangled gel: G0 ∼ ∊2.6 and Q ∼ ∊−1.1. For ∊G < ∊ < ∊E we predict a mean-field unentangled regime with G0 ∼ ∊3 and Q ∼ ∊−8/5. For ∊ > ∊E entanglements raise the modulus and restrict the swelling of the mean-field gels, with G0 ∼ ∊14/3 and Q ∼ ∊−13/5.
All Science Journal Classification (ASJC) codes
- Organic Chemistry
- Polymers and Plastics
- Inorganic Chemistry
- Materials Chemistry