Gel Formation and Molecular Weight Distribution in Long-Chain Polymers

In long-chain polymers an insoluble network or gel may be produced when a number of the separate molecules are linked together. A theoretical derivation is given of the relationship between the amount of gel formed and the degree of cross-linking, in terms of the initial molecular weight distribution. It is shown that whatever the initial molecular weight distribution, incipient gelling occurs when there is on the average one cross-linked monomer per weight average molecule. The shape of the gel-cross-linking curve depends on the ratio of z average, z+1, . . . average molecular weight to the weight average. From experimental values of the curve it becomes possible to determine many of the constants of the molecular weight distribution in the original polymer. Expressions are derived for the number average, weight average and z average of the polymer as a function of cross-linking prior to gel formation, as well as the number and weight averages of the sol fraction after gelation. The average molecular weight between cross-links in the gel is calculated. A number of other functions of the sol and gel fractions are also given.