Kinetic analysis based on the excluded-volume effect for radical polymerization

When the potential of average force based on the excluded volume affects the relative motions of the polymer radicals, the specific rate for bimolecular reaction between them can be approximated as k_t = const. (ns)^?a, where a = 0.153(2b ? 1), b being a constant in the Mark-Houwink equation, and n and s being degrees of polymerization. Introduction of such a rate into kinetic equation yields a relative molecular weight distribution: G(n) = (n/m)^2–2a exp {ph(m^1–a ? n^1–a)}, where m = (2/ph)^1/(1–a) is a degree of polymerization for the maximum in G(n) and ph is a parameter denoting kinetic character. Further, the relationship between polymerization rate R_p, monomer concentration [M], and initiator concentration [ε] is found to be: where σ is a parameter denoting primary radical termination and η and η? are viscosities for an arbitrary solvent and ?-solvent, respectively. These relationships are sufficiently applicable to the data obtained in the polymerizations of styrene and methyl methacrylate.