Monte Carlo simulation of kinetics and chain-length distribution in radical polymerization

Abstract

In this paper, the Monte Carlo method for numerically simulating the kinetics and chain-length distribution in radical polymerization is described. Because the Monte Carlo method is not subject to the assumption of steady-state, it is particularly suitable for studying the kinetic behaviour before the steady-state has been reached and for systems in which the steady-state assumption may be violated. Illustrative applications of the algorithm given in this paper not only demonstrate convincingly both the feasibility and usefulness of the algorithm, but also provide some new insight into the illustrative examples. For the case of pseudostationary radical polymerization such as rotating-sector and pulsed-laser initiations, we have found that the pseudostationary radical concentration can be reached after two or three initiation periods. However, the number-average chain-length xn reaches the pseudostationary value much slower than the radical concentration. It is oscillatively reaching the pseudostationary value, and the amplitudes of the oscillations are decreasing with time. We have also found that the chain-length distribution of the resulting polymer in the case of pseudostationary radical polymerization with termination by combination has stronger periodic modulation. Hence, it should be easier to locate the points of inflection in practice. Therefore, the rate constant of propagation, kp, can be determined precisely for systems which are dominated by a combination-type of termination.