Kinetics of Living Polymerization with Propagation Rate Constants Depending on Degree of Polymerization

A study is presented on the kinetics of living polymerization in which the propagation rate constants decrease to zero at a certain degree of polymerization of the propagating chain. The general solution for the distribution function and the rate of polymerization is given and two special cases are discussed. When all the propagation rate constants are the same up to a critical degree of polymerization and null beyond it, the polymerization proceeds approximately as a normal living polymerization until the number-average degree of polymerization reach 85 to 90% of the critical value. When the propagation rate constants decrease linearly with the degree of polymerization, the distribution of living polymer is narrower than the usual Poisson distribution and the reaction order of the rate of polymerization with respect to monomer concentration is between first and second and is affected by the initial monomer and catalyst concentrations.