On the nitroxide quasi-equilibrium in the alkoxyamine-mediated radical polymerization of styrene

The range of validity of two popular versions of the nitroxide quasi-equilibrium (NQE) approximation used in the theory of kinetics of alkoxyamine mediated styrene polymerization, are systematically tested by simulation comparing the approximate and exact solutions of the equations describing the system. The validity of the different versions of the NQE approximation is analyzed in terms of the relative magnitude of (dN/dt)/(dP/dt). The approximation with a rigorous NQE, k(c)[P][N] = k(d)[P-N], where P,N and P-N are living, nitroxide radicals and dormant species respectively, with kinetic constants k(c) and k(d), is found valid only for small values of the equilibrium constant K (10(-11)-10(-12) mol (.) L-1) and its validity is found to depend strongly of the value of K. On the other hand, the relaxed NQE approximation of Fischer and Fukuda, k(c)[P][N] = k(d)[P-N](0) was found to be remarkably good up to values of K around 10(-8) mol (.) L-1. This upper bound is numerically found to be 2-3 orders of magnitude smaller than the theoretical one given by Fischer. The relaxed NQE is a better one due to the fact that it never completely neglects dN/dt. It is found that the difference between these approximations lies essentially in the number of significant figures taken for the approximation; still this subtle difference results in dramatic changes in the predicted course of the reaction. Some results confirm previous findings, but a deeper understanding of the physicochemical phenomena and their mathematical representation and another viewpoint of the theory is offered. Additionally, experiments and simulations indicate that polymerization rate data alone are not reliable to estimate the value of K, as recently suggested.