Applications of generating functions to polymerization kinetics. 3. General procedure illustrated for propagation with monomer conversion

Abstract

The derivation of the product distribution function for the catalytic polymerization mechanism involving propagation with monomer conversion is used to illustrate the general procedure for obtaining the exact discrete distribution arising from a polymerization mechanism. The coupled differential equations arising from the polymerization mechanism are integrated using a generating function substitution. Due to the stepwise growth of polymer chains, this approach is generally applicable to problems in polymerization kinetics. The integrated rate law for the mechanism under consideration is similar to the Poisson distribution, except for a time dependent parameter which suppresses chain growth as time passes. This distribution function has a limiting value as time approaches infinity determined by the ratio of initial monomer and catalyst. The number-average and weight-average degrees of polymerization are also derived using an elementary technique involving generating functions. Catalytic polymerizations frequently give rise to chemical kinetics problems which are difficult to solve due to difficulty in integrating the coupled rate equations. The procedures outlined in this paper permit these problems to be overcome in many cases.