On exact and approximate methods of calculating an overall termination rate coefficient from chain length dependent termination rate coefficients

Abstract

AbstractIn this paper is tackled the problem of calculating the overall termination rate coefficient 〈kt〉 which follows from values of kti, j, by which is denoted the rate coefficient for termination between two free radicals of degrees of polymerization i and j, respectively. The significance of this problem is that polymerization experiments yield 〈kt〉 values, whereas microscopic models predict Kti,j values. An assumption‐free method is presented for computing the steady state 〈kt〉 corresponding to a set of Kti,j values. Parallel to this, approximate methods for calculating steady state 〈kt〉 values are developed: the so‐called short‐long approximation is used, and coarse graining of the radical chain length distribution is applied. Calculations are firstly carried out using a microscopic termination model which describes an intermediate conversion polymerization system, and then a set of calculations are performed with low conversion conditions in mind. Comparison of the completely exact solutions with the various approximate solutions reveals which of the approximate and therefore more tractable models is suitable for accurate, microscopic modeling of polymerization kinetics at the different physical conditions envisaged. In this respect the credentials of one of the coarse grain approaches are found to be persuasive. Also executed are calculations probing how values of 〈kt〉 depend on factors, such as the rate of propagation and of chain transfer to monomer, not traditionally regarded as having anything to do with termination rates; interesting results emerge. Because calculations are carried out with real systems very much in mind, the latter (and other) results are felt to be genuinely relevant to the mechanism of actual free radical polymerizations.