A simplified data treatment for dead-end and high conversion polymerization kinetics

A simplified approximation method for the treatment of dead-end and high conversion polymerization kinetics is presented. The method is based on the treatment of dead-end polymerization first described by Tobolsky. In appropriate circumstances, by contrast with Tobolsky's method, this method provides measurements of k_d and k_p/k_t^1/2 without recourse to the measurement of the monomer conversion at infinite time. Kinetic studies of free radical polymerizations are normally confined to measurements of initial rates. At low conversions the predictions of the general mechanism for chain-growth polymerization involving initiation, propagation, and termination steps are generally obeyed. Thus the polymerization rate should be first order in the vinyl monomer and half-order in the initiator concentrations. At high conversions, however, large deviations which can be ascribed to various effects can occur; for example, (1) the effect of the increasing viscosity of the polymerization medium on the termination rate constant k_t, and possibly also on the propagation rate constant k_p, which have been considered by North¹ and Cardenas and O'Driscoll,² or (2) depletion of the initiator as the polymerization progresses. This depletion will occur in all polymerizations but its significance will depend on the magnitude of the rate constant for initiator decomposition (k_d) and the period of polymerization. Appropriate conditions will lead to limiting monomer conversion even after infinite polymerization time; this phenomenon has been called dead-end polymerization by Tobolsky.³ Free radical polymerizations to high conversion are particularly important in the industrial context when initial kinetics are obviously inadequate. Suitable treatment of the conversion/time relationship is highly desirable. Senogles and Woolf⁴ have examined the polymerization of n-lauryl methacrylate at 60°C with 2-azobisisobutyronitrile as initiator under dead-end conditions. Here we propose a modification of Tobolsky's treatment of such polymerizations by using an approximation for the exponential decay in the initiator concentration. This method permits easy manipulation of the experimental data and the estimation of values for the kinetic parameters in favorable circumstances without recourse to the measurement of the conversion at infinite time or the evaluation of complicated functions of the monomer conversion. The method thus allows the duration of the laboratory experimentation to be significantly shortened and the complexity of the subsequent data analysis to be considerably reduced.