Gel Point Properties in Batch Free-Radical Vinyl/Divinyl Copolymerization

摘要

Gelation is a critical phenomenon, and various simple relationships are expected to hold. On the other hand, it is important to clarify the required conditions for the validity of the relationships. In this theoretical study, the effects of the primary chain connection statistics and the primary chain length distribution change during batch free-radical vinyl/divinyl copolymerization on the gel point properties are investigated systematically. The weight fraction distribution at the gel point always conforms to the power-law distribution,W(P)proportional to P(-alpha)with alpha = 1.5, as long as the classical chemical kinetics is valid in a closed reaction system. When the primary chain connection statistics is independent of chain length, the cross-linking density, rho(g), of the gel molecule right at the gel point is given by rho g=2/P over bar wp,acc, where P over bar wp,acc is the weight-average chain length of all primary chains. The random cross-linking is a special case that belongs to this category. The distribution of the pendant double bonds among polymer molecules having different molecular weights is nonrandom, except for the special cases with equal reactivity of all types of double bonds for which the random cross-linking applies.