On the Nitroxide Quasi‐Equilibrium in the Alkoxyamine‐Mediated Radical Polymerization of Styrene

Abstract

Summary: 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, kc[P][N] = kd[PN], where P, N and PN are living, nitroxide radicals and dormant species respectively, with kinetic constants kc and kd, 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, kc[P][N] = kd[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 physico‐chemical 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.Validity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.imageValidity of the rigorous nitroxide quasi‐equilibrium assumption as a function of the nitroxide equilibrium constant.

Copolymer Composition Deviations from Mayo–Lewis Conventional Free Radical Behavior in Nitroxide Mediated Copolymerization

“…Due to this, the contribution of alkoxyamine decomposition to R p is significant only in the first case (first row), as evidenced by the differences between the M1 and M2 curves. This observation is consistent with what has been found before in early experimental investigations of monomolecular (alkoxyamine initiated) NMP of styrene by several authors, and further analyzed by simulations in more general terms, which can be summarized as follows: for a given value of the nitroxide radical equilibrium constant, there is a minimum rate R TSI of continuous initiation for which the rate of polymerization becomes independent of the alkoxyamine concentration, since the additional flux of radicals provided by the continuous initiation is sufficient to maintain true nitroxide‐equilibrium condition. If the equilibrium constant is increased, the minimum rate R TSI needed to reach true equilibrium conditions must be increased.…”

Exploring the Full Potential of Reversible Deactivation Radical Polymerization Using Pareto-Optimal Fronts

“…NMP is one of the first discovered RDRP systems, due to the pioneering work of Rizzardo et al [36]. Since then, numerous studies have been devoted to clarify the mechanism and the kinetics of NMP [37][38][39][40][41][42], focusing mostly on styrene and acrylates as monomers. In NMP, an alkoxyamine initiator (R0X), undergoes a homolytic cleavage at elevated temperature, which releases a R0 species and a nitroxide radical (X), also called the persistent radical.…”

Simulation of Styrene Polymerization by Monomolecular and Bimolecular Nitroxide‐Mediated Radical Processes over a Range of Reaction Conditions

“…Although the process is well understood with the help of kinetic expressions based on the quasi‐steady state (QSS) of living radicals and the quasi‐steady equilibrium (QSE) of persistent radicals derived by the groups of Fukuda6–12 and Fischer,13–20 the effects of side reactions, the study of polymerization conditions outside the theoretical bounds imposed by the QSS approach, and the estimation of kinetic parameters embedded into monomolecular or bimolecular NMRP processes can be more easily and accurately addressed with complete mathematical models, based on detailed reaction mechanisms, where the QSS and QSE assumptions are not needed. An analysis of the applicability and limitations of the QSS and QSE assumptions in monomolecular NMRP has been recently offered by Saldívar‐Guerra et al21 Also, Tang et al22 have recently reevaluated the persistent radical effect (PRE) and proposed new equations to extend the PRE treatment to higher conversions. The model used in the present paper is more general and it contains the models by Fisher and Fukuda6–20 and Tang et al22 as particular cases.…”

“…Estimates of kinetic rate constants for the NMRP of 2,2,6,6‐tetramethyl‐1‐piperidinoxyl (TEMPO) and other controllers have been reported before 6–28. However, some of these are specific for a single temperature (e.g., ref.…”