Theory of molecular size distribution In multichain polymers

Abstract

Expressions are derived for the most probable distribution of molecular sizes in multi-chain polymers formed by the self-condensation of the monomer A—R—X f − 1 , where A and X are functional groups and X may be either A or B. It is assumed that all functional groups of the same kind are chemically equivalent and that intramolecular condensation may be neglected. For the case A—R—B f − 1 the results are identical with those of Flory, although it is shown that this is fortuitous and due to a cancellation of two errors in Flory's method. For the case R—A f the results differ significantly from expressions derived by Flory and sources of error in previous work are discussed. In theory, the mole and weight fractions of individual x-mers vary continuously with the extent of reaction α over the entire range up to α max = 2/f. The ratio of the weight average to the number average degree of polymerization is finite for all values of α below α max . The critical point for the formation of infinitely large (wall-to-wall) molecules occurs, not at α = 1/(f − 1) as predicted by Flory, but at α = 2/f. The prediction of actual gel points is discussed in terms of the largest molecule which can have a physically meaningful existence at any fixed value of α.