Branching in free radical polymerization due to chain transfer, 2. Theory of the effect of polyfunctional transfer reagents

Polyfunctional chain transfer reagents applied in free radical polymerization have two effects on the polymer molecular weight. As in the case of monofunctional regulators the chain length is reduced; the polyfunctionality of the transfer reagents causes, however, branching and thus an increase in molecular weight. A general theory is developed on the basis of Cascade Theory to describe the polymer structure in dependence on the monomer conversion. The theory takes advantage of the graph theoretical concept of digraphs by which the directed chain reaction can be properly represented. Analytic equations are derived for the weight average molecular weight Mw, z‐average mean square radius of gyration 〈S2〉z and the average particle scattering factor Pz(μ). Furthermore, a simple equation is given for the condition of gelation. Special concern is given to the formation of fractions of branched and linear polymers during the polymerization process. The derived equations are discussed in terms of kinetic constants known for polystyrene. Gelation is shown to be possible for a chain transfer constant of Ctr = 22 if the number of functional groups per transfer molecule exceeds at least a value of 7.