Termination step kinetics

We shall consider these points below. The mechanism for cationic polymerization continues to include initiation, propagation, transfer, and termination steps, and the rate of polymerization and the kinetic chain length are the principal quantities of interest. 

Autooxidation. Liquid-phase oxidation of hydrocarbons, alcohols, and aldehydes by oxygen produces chemiluminescence in quantum yields of 10 to 10 ° ein/mol (128—130). Although the efficiency is low, the chemiluminescent reaction is important because it provides an easy tool for study of the kinetics and properties of autooxidation reactions including industrially important processes (128,131). The light is derived from combination of peroxyl radicals (132), which are primarily responsible for the propagation and termination of the autooxidation chain reaction. The chemiluminescent termination step for secondary peroxy radicals is as follows ... 

When the initiation and termination reactions are the reverse of one another, the kinetic form is usually simpler than when the two are independent. Also, the transition-state composition follows directly from the rate law, which is why the term well-behaved is applied. Imagine, for example, that the termination step in the system most recently presented was the recombination of two sulfate radical ions rather than Eq. (8-38) ... 

The chemical mechanisms of transition metal catalyses are complex. The dominant kinetic steps are propagation and chain transfer. There is no termination step for the polymer chains, but the catalytic sites can be activated and deactivated. The expected form for the propagation rate is... 

Torkelson and coworkers [274,275] have developed kinetic models to describe the formation of gels in free-radical pol5nnerization. They have incorporated diffusion limitations into the kinetic coefficient for radical termination and have compared their simulations to experimental results on methyl methacrylate polymerization. A basic kinetic model with initiation, propagation, and termination steps, including the diffusion hmitations, was found to describe the gelation effect, or time for gel formation, of several samples sets of experimental data. 

From these relations it can be concluded that ksi > k 3 > k, which implies that the concentrations of SO4 and HO2 radicals are relatively large compared to that of OH. It is striking, however, that for kinetic reasons this mechanism does not involve termination steps (78) and (89) which are widely favoured in the chemistry of HO2 and OH radicals... 

For purposes of kinetic analysis, the termination step may be written... 

The gegen ion, K+, has been dismissed from the scheme in consideration of the comparatively high dielectric constant of the liquid ammonia medium.) The associated kinetic equations are equivalent to Eqs. (44) and (45). It will be observed that the termination step (51) is essentially a chain transfer with solvent. A similar process has... 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

A simple kinetic scheme which involves the initiation propagation and termination steps may be represented as under ... 

Because of the precise control of the redox steps by means of the electrode potential and the facile measurement of the kinetics through the current, the electrochemical approach to. S rn I reactions is particularly well suited to assessing the validity of the. S rn I mechanism and identifying the side reactions (termination steps of the chain process). It also allows full kinetic characterization of the reaction sequence. The two key steps of the reaction are the cleavage of the initial anion radical, ArX -, and conversely, formation of the product anion radical, ArNu -. Modeling these reactions as concerted intramolecular electron transfer/bond-breaking and bond-forming processes, respectively, allows the establishment of reactivity-structure relationships as shown in Section 3.5. 

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

Abstract. Auto-accelerated polymerization is known to occur in viscous reaction media ("gel-effect") and also when the polymer precipitates as it forms. It is generally assumed that the cause of auto-acceleration is the arising of non-steady-state kinetics created by a diffusion controlled termination step. Recent work has shown that the polymerization of acrylic acid in bulk and in solution proceeds under steady or auto-accelered conditions irrespective of the precipitation of the polymer. On the other hand, a close correlation is established between auto-acceleration and the type of H-bonded molecular association involving acrylic acid in the system. On the basis of numerous data it is concluded that auto-acceleration is determined by the formation of an oriented monomer-polymer association complex which favors an ultra-fast propagation process. Similar conclusions are derived for the polymerization of methacrylic acid and acrylonitrile based on studies of polymerization kinetics in bulk and in solution and on evidence of molecular associations. In the case of acrylonitrile a dipole-dipole complex involving the nitrile groups is assumed to be responsible for the observed auto-acceleration. 

To illustrate the conditions under which a system that includes chain propagating, chain branching, and chain terminating steps can generate an explosion, one chooses a simplified generalized kinetic model. The assumption is made that for the state condition just prior to explosion, the kinetic steady-state assumption with respect to the radical concentration is satisfactory. The generalized mechanism is written as follows ... 

At this point, it can be concluded that the direct and indirect electrochemical approach of the reaction in the case of aryl halides has provided a quantitative kinetic demonstration of the mechanism and the establishment of the nature of the side-reactions (termination steps in the chain process). In poor H-atom donor solvents, the latter involve electron-transfer reduction of the aryl radical. 

It is remarkable that the initial description of the mechanism, although based on qualitative evidence, has so successfully passed the test of time and of quantitative investigations. The latter have allowed a more precise description of the kinetics and the assignment of the termination steps, but the core of the mechanism, i.e. the propagation loop (103), has essentially remained untouched (see, however, the discussion at the end of this section). 

A number of ex situ spectroscopic techniques, multinuclear NMR, IR, EXAFS, UV-vis, have contributed to rationalise the overall mechanism of the copolymerisation as well as specific aspects related to the nature of the unsaturated monomer (ethene, 1-alkenes, vinyl aromatics, cyclic alkenes, allenes). Valuable information on the initiation, propagation and termination steps has been provided by end-group analysis of the polyketone products, by labelling experiments of the catalyst precursors and solvents either with deuterated compounds or with easily identifiable functional groups, by X-ray diffraction analysis of precursors, model compounds and products, and by kinetic and thermodynamic studies of model reactions. The structure of some catalysis resting states and several catalyst deactivation paths have been traced. There is little doubt, however, that the most spectacular mechanistic breakthroughs have been obtained from in situ spectroscopic studies. 

The kinetics of redox-initiated polymerizations generally fall into two categories depending on the termination mode. Many of these polymerizations proceed in the same manner as other polymerizations in terms of the propagation and termination steps the only difference is the source of radicals for the initiation step. For these polymerizations where termination is by bimolecular reaction of propagating radicals, the initiation and polymerization rates will be given by appropriate expressions that are very similar to those developed previously ... 

Some redox polymerizations involve a change in the termination step from the usual bimolecular reaction to monomolecular termination involving the reaction between the propagating radicals and a component of the redox system. This leads to kinetics that are appreciably different from those previously encountered. Thus, in the alcohol-Ce4+ system (Eq. 3-39), termination occurs according to... 

The kinetics of radiation-initiated polymerizations follow in a relatively straightforward manner those of photolytic polymerization. The initiation rate is determined by the radiation intensity and the concentration and susceptibility of the compound that radiolyzes to yield the initiating species (ionic and/or radical). The final expression for Rp is determined by the exact details of the initiation, propagation, and termination steps. 

A chain reaction, 4 —> 6 + C obeys the rate expression r = What initiation and termination steps will predict these kinetics Repeat for r = kC. ... 

The preliminary work has already indicated the existence of large deuterium kinetic isotope effects in the oxidation of 1. However, the real extent of the isotope effects could be determined only later, when the role of disproportionation of HO2 (e) as a termination step, and that of inhibitors in obtaining pseudo first-order rates (Eq. 11) were fully understood ). 

The iGLE also presents a novel approach for studying the reaction dynamics of polymers in which the chemistry is driven by a macroscopic force that is representative of the macroscopic polymerization process itself The model relies on a redefined potential of mean force depending on a coordinate R which corresponds locally to the reaction-path coordinate between an n-mer and an (n -t 1 )-mer for R = nl. The reaction is quenched not by a kinetic termination step, but through an (R(t))-dependent friction kernel which effects a turnover from energy-diffusion-limited to spatial-diffusion-Iimited dynamics. The iGLE model for polymerization has been shown to exhibit the anticipated qualitative dynamical behavior It is an activated process, it is autocatalytic, and it quenches... 

The cyclotrimerization of isocyanates is initiated by anionic type of catalysts and proceeds via propagation, transfer and termination steps ( ). It was found that in the case where the cyclotrimerization reaction proceeds with a long kinetic chain length, the kinetics of the reaction followed second order with respect to the isocyanate as measured by the disappearance of the isocyanate groups and was first order with respect to the initial concentration of the catalyst ( ,5). ... 

In consideration of the kinetic law obtained, Rp i0 of magnitude range, one can conclude that the common polymerization mechanism, based on bimolecular termination reactions, is no longer valid for these multifunctional systems when irradiated in condensed phase. Indeed, for conventional radical-induced polymerizations, the termination step consists of the interaction of a growing polymer radical with another radical from the initiator (R), monomer (M) or polymer (P) through recombination or disproportionation reactions ... 

The state of aggregation of the polymerising system represents another important factor which may affect the kinetics of polymerisation. It is well known (96,97) that many radical polymerisations are enhanced by increase in the viscosity of the po-lymerisingsystem, and this phenomenon was explained by a decrease in the rate of termination step which may become diffusion-controlled. In fact, the effect of viscosity should be observed at any stage of radical polymerisation, and this problem has been discussed recently by Benson and North (98, 99). Of course, this type of acceleration cannot be observed when the growth involves living polymers and therefore such an explanation does not apply to polymerisation of NCA, particularly since no termination resulting from active end-active end interaction takes place in these processes. 

While this review discloses the kinetic and stereochemical features of soluble Ziegler-Natta catalysts, we have little information on the structure of the active center. The steric environments of active centers must be very important in determining the monomer reactivity, regiospecificity and stereospecificity of soluble catalyst. The influence of ligands such as the aluminum components on the rates of chain propagation and chain-terminating steps should be correlated to the electronic structure of... 

---