Prediction of molecular weight distributions in branched polymers

Abstract

AbstractA theoretical treatment of long branching in radical polymerization in a continuous stirred tank reactor is presented. The treatment takes into account radical termination by disproportionation and/or combination, transfer to polymer and/or additive of low molecular weight, residence time, and injection of polymer. In the absence of added polymer, the molecular weight distribution depends upon four parameters which can be expressed as P̄n and ratios of the rate of polymerization to the rate at which radicals (a) leave the reactor, (b) combine, and (c) transfer to polymer. The kinetic equations were converted into a differential equation which was solved numerically to give polymer and radical moments. An analytical solution is presented for the case where combination is absent. P̄w/P̄n is predicted to increase smoothly in a markedly exponential manner with increasing polymer transfer, combination, P̄n, and mean residence time. At no stage do any of the moments become infinite unless the residence time is infinite. For polymers of wide distribution, the second and higher radical moments can exceed the corresponding polymer moments so that most of the large molecules leave the reactor as radicals. Beasley's and Nicolas's treatments are shown to be limiting cases at low polymer transfer.