Statistics of Irreversible Termination in Homogeneous Anionic Polymerization

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Abstract
The effect of irreversible termination on the molecular weight distribution of a polymer prepared by homogeneous anionic polymerization is examined for cases in which the initiator is monofunctional and initiation is instantaneous. A general procedure for the calculation of the chain length distribution, as well as its moments, is presented. The procedure is then illustrated by an exact treatment of an isothermal batch polymerization for which we obtain the ratio rσ(t) of the weight to number average molecular weights as a function of the fraction of monomer consumed, the initial ratio σ of the terminator concentration to that of the initiator, the ratio ρ of the rate constant for termination to the rate constant for propagation, and the average degree of polymerization at time t, 〈n1〉t. When σ is much less than unity, and the limiting number average D.P. 〈n1〉∞ is very large, rσ(t) approaches the following value as the reaction nears completion: rσ(∞) = 1+σρ(2+ρ)—1.

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