Eur. Phys. J. B 6, 93-100 (1998)
https://doi.org/10.1007/s100510050530

Theory of gel point in real polymer solutions

Kohno Medical Institute, Tomitahama 26-14, Yokkaichi, Mie 512, Japan

Revised: 28 May 1998
Accepted: 12 June 1998
Published online: 15 November 1998

Abstract

We develop a new theory of gelation which takes into account (i) delay of the gel point and (ii) change of functionality due to ring formation. We show that the problem of finding the gel point in real polymer solutions reduces to the problem of calculating the total ring concentration and the extent of reaction of intermolecular reaction at the gel point. In this paper, we solve a special case of this problem, on the basis of the independence assumption between intermolecular reaction and cyclization which takes into account only (i) the delay of the gel point: making use of the asymptotic equality of the total ring concentration, we acquire an approximate solution for the gel point D_c as a function of the inverse concentration γ, the relative frequency of cyclization and dimension d. Applying the observed values of in linear polyesters, the theoretical result reproduces well the Wile and the Gordon-Scantlebury observations, showing the existence of a critical dilution beyond which gelation can not occur, and an asymptote . As the classical gel point is approached, the present theory reduces to the linear equation, which makes one-to-one correspondence with the real slope Δ, suggesting the inequality which is just what polymer chemists have quested for so far, with the physical meaning having remained unknown.