Theory of molecular size distribution In multichain polymers

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—Xf − 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—Bf − 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—Af 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 αmax = 2/f. The ratio of the weight average to the number average degree of polymerization is finite for all values of α below αmax. 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.