Diffusion-controlled copolymerization kinetics

Abstract

The Smoluchowski equation is used to derive equations for predicting the values of diffusion controlled propagation and termination rate coefficients in copolymerization. None of the resulting expressions are any more complicated than the analogous homopolymerization results. Diffusion controlled propagation rate coefficients in copolymerization are predicated to depend only very weakly on chain end type, and thus the propagation kinetics of high conversion copolymerizations are expected to be considerably simpler than those of low conversions. In considering termination, expressions for the rate coefficient for termination by ‘reaction diffusion’ are first of all derived. It is possible that under some conditions (for example, high conversions) these expressions describe the overall rate of termination, but in general, overall rates of termination will be determined by rates of center of mass diffusion, which are chain length dependent. For this reason the reaction diffusion results are incorporated into a more general treatment of termination in which chain end motion is both by translational and reaction diffusion; this treatment is envisaged as applying from intermediate conversions onward. Considerable effort is subsequently invested in developing simple descriptions of copolymerization in which rate coefficients (and in particular those for termination) are allowed to be chain length dependent. An important feature of this paper is that for every parameter usilized, a means of associating to it a value appropriate for a real system is discussed; in most cases this association is readily carried out.