Molecular weight development in free-radical polymerization with polyfunctional chain-transfer agents, 2 - Substitution effects

摘要

The analytic expression for the weight-average molecular weight development proposed in the first part of this series([1]) is extended to account for the substitution effects of the functional groups in a polyfunctional chain-transfer agent. The obtained functional form of the matrix formula, (P) over bar (w) = W{D-w + (I + T) SPE (I - TSPE)(-1) D-f} is essentially the same as for equal reactivity model, but the N x N square matrixes, S and in the equal reactivity model is now expanded to N x f and fN x fN matrixes, respectively, to account for the different reactivities of f functional groups. The number of chain types, is extrapolated to infinity to obtain the (P) over bar (w)-value for free-radical polymerization. Practically, such extrapolation can be conducted with calculated (P) over bar (w)-values for only three different N-values. Illustrative calculations show that the obtained results agree with those from the Monte Carlo method. The present approach provides newer insight into the branched structure formation during complex polymerization reactions. [GRAPHICS] Average chain-length developments under conditions C2s and D2s. The symbols are the MC simulation results taken from ref.([7]) [References: 8]