Condensation and gelation: Clarification of Stockmayer's analogy

Abstract

To explore the analogy, originally noted by Stockmayer, between vapor condensation and gelation in ``three‐dimensional'' chemical polymerizations, we here explore the special case of reversible gelation in more detail. We show how the partition function of a one component system the molecules of which reversibly form branched‐chain clusters can be adapted, under certain approximations, to display its correspondence to Stockmayer's formulation of the molecular size distribution in branched‐chain polymers formed from random chemical polymerization of polyfunctional monomers. Thus, we obtain, for the reversible case, a statistical thermodynamic counterpart to Stockmayer's purely statistical calculations concerning gelation by relating his ``extent of reaction'' α to the thermodynamic variables temperature and density. The relation between Stockmayer's gelation theory and Mayer's condensation theory is accordingly clarified. A key step in this analysis involves the use of Hill's criterion for a ``bond.'' The similarity of condensation to gelation is noted to be particularly close in the case of liquids with directional interactions which saturate at low coordination numbers. In such cases, of which water is the outstanding example, the condensation‐gelation analogy provides a helpful physical picture of the liquid state.