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

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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 DPw, respectively. For example, G is predicted to vanish for p→pc as (p–pc)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.