Parameters of the swelling equation and network structure

Abstract

The functionality of a crosslink which appears in the swelling equation differs from the chemical functionality and represents the number average of elastically-active chains issuing from an elastically-active cross-link, independently of the type of the crosslinking process. Relationships have been derived for the polycondensation of an ƒ-functional monomer, for alternating copoly-condensation of two monomers, and for the crosslinking of primary chains which allow the determination of the effective functionality ƒ_e either from the composition of the gel phase or its calculation by means of crosslinking statistics based on the theory of cascade processes (Gordon–Good). In close proximity of the gel point, ƒ_e is always three and its increase is the faster the more positive the substitution effect in the monomer unit. Up to comparatively low values of the gel fraction (10–20 %), ƒ_e in most cases does not depart too much from three and increases steeply to the final value only at a virtually negligible sol fraction.