Persistent radical effect kinetics

The polymerizations (a) and (b) owe their success to what has become known as the persistent radical effect."1 Simply stated when a transient radical and a persistent radical are simultaneously generated, the cross reaction between the transient and persistent radicals will be favored over self-reaction of the transient radical. Self-reaction of the transient radicals leads to a build up in the concentration of the persistent species w hich favors cross termination with the persistent radical over homotermination. The hoinolermination reaction is thus self-suppressing. The effect can be generalized to a persistent species effect to embrace ATRP and other mechanisms mentioned in Sections 9.3 and 9.4. Many aspects of the kinetics of the processes discussed under (a) and (b) are similar,21 the difference being that (b) involves a bimolecular activation process. 

The synthesis of mixed peroxides formed from /-butyl hydroperoxide and carbon-centred radicals has been studied. The reactions were strongly effected by solvents as well as catalytic amounts of Cun/Fem. The kinetic data suggest that the conditions for the Ingold-Fischer persistent radical effect are fulfilled in these cases.191 The use of Cu /Cu" redox couples in mediating living radical polymerization continues to be of interest. The kinetics of atom-transfer radical polymerization (ATRP) of styrene with CuBr and bipyridine have been investigated. The polymer reactions were found to be first order with respect to monomer, initiator and CuBr concentration, with the optimum CuBr Bipy ratio found to be 2 1.192 In related work using CuBr-A-pentyl-2-... 

Today, the subject is far from being mature. There are probably many more experimental manifestations of the effect than we are aware of, and there may be more kinetic peculiarities and variants. This is the reason we neither present a completely comprehensive description of all pertinent experimental findings nor a complete theory. Moreover, the particular subfield of living radical polymerizations involving the effect has become of practical importance. Hence, in the past few years, a large number of publications and patents have been published on this topic. These are covered in more detail in other parts of this issue, and here, we discuss only those aspects that are important for the operation of the persistent radical effect in living polymerizations. 

A second, and more chemical, verification is due to Finke et al.,21 who also invented the descriptive phrase persistent radical effect and gave a prototype example to the extreme. The thermal reversible 1,3-benzyl migration in a coenzyme B12 model complex leads to the equilibrium of Scheme 9. Earlier work had shown that the reaction involves freely diffusing benzyl and persistent cobalt macrocycle radicals, but the expected self-termination product bibenzyl of benzyl was missing. Extending the detection limits, the authors found traces of bibenzyl and deduced a selectivity for the formation of the cross-products to the self-termination products of 100 000 1 or 99.999%. Kinetic modeling further showed that over a time of 1000 years only 0.18% of bibenzyl would be formed, and this stresses the long-time duration of the phenomenon. 

A "persistent radical effect" is found if the cleavage of a molecule yields two radicals of which only one undergoes self-termination (i.e. recombination with a like radical) while the other does not and only decays by cross-termination (i.e. recombination with the other radical). As a consequence of this behaviour, there is a self-regulating effect on the reaction rates, and unusual kinetics result. 

The values of Katrp for numerous alkyl halide - copper catalyst combinations have been determined (21,27) using modified kinetic equations describing the accumulation of the deactivator XCu Ln due to the persistent radical effect.(28) Figure 3 shows that the values of Katrp for the same alkyl halide (ethyl 2-bromoisobutyrate, EtBriB, which mimics the dormant chains of a polymethacrylate) vary by more than seven orders of magnitude as the N-based ligand is changed. Since the solvent and the alkyl halide used in all measurements were the same, the values of Kbh and Kea (eq. 1) were constant and the variations in Katrp were cansed by differences in the electron transfer equilibrium constant and the halidophihcity of the Cu complexes. 

The kinetics of the stable free radical polymerization are controlled by the persistent radical effect which has been clearly elucidated by Fischer (1997,1999). 

ATRP a transition metal complex is needed for the activation of the alkyl-halide-ended macromolecules, and a wider range of temperatures can be applied. In both cases, the polymerization kinetics are governed by the activation-deactivation equilibrium and by the persistent radical effect [6]. The number-average degree of polymerization DP ) is calculated by the ratio of the initial monomer concentration to the initiator (i.e., alkoxyamine or alkyl halide) concentration, multiplied by monomer conversion. 

Very little information has been reported on the SI-ATRP kinetics, but it appears that incomplete monomer conversions are reached even after a long polymerization time of 24h [148, 153] this can be ascribed to the persistent radical effect and the accumulation of Cu(II) deactivator in the aqueous phase [6]. 

A typical kinetic scheme for homogeneous systems is considered, which includes radical initiation (ki), monomer propagation (fep), bimolecular termination by radical combination (k,), and RAFT reaction, i.e., addition reaction to a dormant chain ( add) fragmentation of the radical intermediate (kfrag)- In addition, bimolecular termination by combination of radicals with the radical intermediates (fe ,) has been included. The methodology first proposed by Fischer to study the persistent radical effect in NMLP is used to find an analytical solution for the mass balances on the different species (radicals, R", intermediate radicals, T", and dormant chains, D). In particular, by plotting the solution in a log-log scale, it has been shown that it becomes possible to identify distinct time intervals or regions where the different... 

In the group of Fischer, a considerable amount of work was dedicated to the kinetic description of NMP. They introduced the concept of the so-called persistent radical effect (PRE) (49,50). The PRE relies on the limited buildup of the concentration of deactivator, which in the case of NMP is the nitroxide, the persistent radical. On the basis of the PRE, it can be predicted which conditions will lead to narrow MMDs, and to a small fraction of irreversibly terminated dead chains. 

Thus, the rate of polymerization is internally first order in monomer, externally first order with respect to initiator and activator, Cu(I), and negative first order with respect to deactivator, XCu However, the kinetics may be more complex because of the formation of XCu species via the persistent radical effect. The actual kinetics depend on many factors, including the solubility of activator and deactivator, their possible interactions, and variations of their structures and reactivities with concentrations and composition of the reaction medium. It should also be noted that the contribution of persistent radical effect at the initial stages might be affected by the mixing method, solubility of the metal compoimd and ligand, etc (239-242). 

Based on the persistent radical effect described by Fischer [59], NMP is apphcable to a rather large number of monomers. The performance of a wide range of nitroxide and derived alkoxyamines has been presented in numerous experimental and theoretical studies on polymerization mechanism and kinetics [54, 60-64], A simple selfregulation operates between transient and stable radicals at the outset of the reaction, coupling reactions between transient radicals occur leading to an excess of stable radical. Then, bimolecular termination reactions are reduced and become negligible. 

The ACOMP continuously computed conversion data for experiments at 90 °C with different concentration of Cu Br (0,0.025, and 0.05 equiv vs. Cu Br) made possible to observe the persistent radical effect (PRE) kinetics at the early polymerization stages. 

For the polymerization of tert-butyl acrylate, the monomer consumption followed the first-order kinetics, while that of MMA could be described with a kinetics model that includes the persistent radical effect. The control over the reaction could be preserved for monomer conversions of up to 90%, and poly(methyl methacrylate) s (PMMAs) with narrow molecular weight distributions (PDI below 1.3) were obtained. Conventional experiments with an oil bath showed a limited reproducibility and furthermore failed to yield polymers with similar narrow molecular weight distributions (for high conversions). This observation was refereed to the superiority of the uniform, noncontact, and internal heating mode of micro-wave irradiation. 

Hanns Fischer elaborated kinetics describing at least some CRPs in terms of persistent radical effect (PRE) (the term coined by Finke). This is an application of the theory explaining the phenomena of self-regulation of the radical reactions that are related to Scheme 21. The principle, as Fischer says, is simple. 

The persistent radical effect (PRE) is a kinetic effect observed when transient and persistent radicals are formed with equal or similar rates. The cross-coupling of these radicals proceeds with high selectivity and dominates the homo-coupling of the transient radicals. The first example of PRE was most likely observed in 1936 by Bachmann and Wiselogle during experiments on thermolysis of pentaarylethanes. 

The first kinetic analysis of this phenomenon was made in 1986 by Fischer, who also highlighted its importance in living radical polymerization. The first numerical simulation of PRE in the context of NMP was performed by Johnson et al The term persistent radical effect was proposed in 1992 by Daikh and Finke. " Several excellent reviews eovering the applications of PRE in organic and polymer chemistry are available. ... 

In the course of NMP, the persistent radical effect (PRE) leads to a steady increase in excess nitroxide. This slows the polymerization rate down and leads to longer polymerization times. As shown by Matyjaszewski, Fukuda and Miura/ introduction of a conventional radical initiator which slowly decomposes under the reaction conditions considerably enhances the conversion rate. Even a low rate of external initiation ( 1% of the initial internal initiation, reaction 1, Scheme 4.5) leads to a considerable reduction in the polymerization time while the livingness, polydispersity and controlled degree of polymerization remain virtually unchanged. The extra radicals reduce the concentration of persistent nitroxides rather than initiating new chains. The kinetic aspects of additional initiation were studied by Fukuda et alP and Fischer et In summary, if the rate R of generation of additional... 

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