Elastic Modulus and Equilibrium Swelling of Near-Critical Gels

Michael Rubinstein, Ralph H. Colby

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39 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)3184-3190
Number of pages7
Issue number12
StatePublished - Jun 1 1994

All Science Journal Classification (ASJC) codes

  • Organic Chemistry
  • Polymers and Plastics
  • Inorganic Chemistry
  • Materials Chemistry


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