Gelation in concentrated critically branched polymer solutions. Percolation scaling theory of intramolecular bond cycles

Abstract

Cyclization effects lead to deviations from the classical Flory–Stockmayer theory of gelation and are taken into account by percolation theory. Nonclassical “critical exponents”β and γ should therefore occur for gel fraction G and molecular weight DP_w, respectively. For example, G is predicted to vanish for p→p_c as (p–p_c)^β with β≃ 0.4 instead of the Flory–Stockmayer prediction β= 1. Our present knowledge of these critical exponents of percolation theory is reviewed. We estimate theoretically the width of the critical region where the exponents β and γ should deviate from their classical values, and discuss the influence of nonclassical exponents on the molecular weight distribution function and the tail-cutting effects.