Propagation step kinetics

An important descriptor of a chain reaction is the kinetic chain length, ie, the number of cycles of the propagation steps (eqs. 2 and 3) for each new radical introduced into the system. The chain length for a hydroperoxide reaction is given by equation (10) where HPE = efficiency to hydroperoxide, %, and 2/ = number of effective radicals generated per mol of hydroperoxide decomposed. For 100% radical generation efficiency, / = 1. For 90% efficiency to hydroperoxide, the minimum chain length (/ = 1) is 14. 

Kinetics of the reaction of p-nitrochlorobenzene with the sodium enolate of ethyl cyanoacetate are consistent with this mechanism. Also, radical scavengers have no effect on the reaction, contrary to what would be expected for a chain mechanism in which aryl radicals would need to encounter the enolate in a propagation step. The reactant, /i-nitrophenyl chloride, however, is one which might also react by the addition-elimination mechanism, and the postulated mechanism is essentially the stepwise electron-transfer version of this mechanism. The issue then becomes the question of whether the postulated radical pair is a distinct intermediate. 

Solvent effects on radical polymerization have been reviewed by Coote and Davis,59 Coote et. Barton and Borsig,71 Gromov,72 and Kamachi" 1 A summary of kinetic data is also included in Beuennann and Buback s review.74 Most literature on solvent effects on the propagation step of radical polymerization deals with influences of the medium on rate of polymerization. 

In the case of cooperative processes, the formation of a nucleus, already discussed from the kinetical point of view, plays a crucial role. The steady state described by Eq. (1) depicts the formation of a triple helix as the simplest model by the formation of a nucleus Hx through fast pre-equilibria and subsequent propagation steps, Hx in this case is a triple-helical intermediate with x tripeptide units (that means x hydrogen bonds) in the helical state. The final product H3n 2 possesses two hydrogen bonds less than tripeptide units because the three single chains are staggered at one amino add residue each. 

The reaction kinetics In the case of HMDS suggests a two stage mechanism for the major dichloride consuming reaction. First a slow Na surface dependent build up of long lived active centers then a propagation step In which the Na surface is not rate determining. The reaction which occurs on the surface must be fast. 

Reactions of phenoxyl and aminyl radicals with RH and ROOH are chain propagation steps in oxidation inhibited by phenols and amines (see Chapter 14). Both reactions become important when their rates are close to the initiation rate (see Chapter 14). Mahoney and DaRooge [57] studied the oxidation of 9,10-dihydroanthracene inhibited by different phenols. He went on to estimate the values of rate constants ratio of the reaction of ArO with RH and the reaction In + In (reactions (9) and (10), see Chapter 14) by the kinetic study. The values of kw for the reaction... 

Equilibrium studies under anaerobic conditions confirmed that [Cu(HA)]+ is the major species in the Cu(II)-ascorbic acid system. However, the existence of minor polymeric, presumably dimeric, species could also be proven. This lends support to the above kinetic model. Provided that the catalytically active complex is the dimer produced in reaction (26), the chain reaction is initiated by the formation and subsequent decomposition of [Cu2(HA)2(02)]2+ into [CuA(02H)] and A -. The chain carrier is the semi-quinone radical which is consumed and regenerated in the propagation steps, Eqs. (29) and (30). The chain is terminated in Eq. (31). Applying the steady-state approximation to the concentrations of the radicals, yields a rate law which is fully consistent with the experimental observations ... 

Their algebraic formulation is inconsistent with their reaction scheme in that they represent the propagation step as kinetically of third order they use a steady-state treatment despite the fact that the limited yields obtained in these reactions show that this is inappropriate their equation for the DP as a function of [PJ is not of a form which has a maximum. For these and other reasons their treatment is not valid. (A simple explanation of the DP maximum is proposed in the Appendix to this Chapter.)... 

It is shown that the carbenium ions cannot be considered free except in a kinetic sense, but that they are strongly solvated by the solvent. Further, a clear mechanistic distinction is made between the nature of the propagation steps for carbenium and for onium ions, e.g., oxonium, which serves to explain the differences between the orders of magnitude of the corresponding rate-constants. 

It is a useful coincidence that the choice of a highly polar solvent for electrochemical reasons also has as a consequence that in such a solvent the rate of an ion-molecule reaction, as in the propagation step, characterised by kp+, is reduced considerably from what it is in a less polar solvent. This follows from Transition State Theory and has been explained in the present context [9,10]. In my reasoning, if the electrochemical imperative had not pointed to the use of the most polar solvent available, in order to obtain a monoeidic system, the kinetic imperative - the need to have rates adequately low for convenient measurement would have dictated the same choice. 

As an example, the propagation steps for the reductive alkylation of alkenes are shown in Scheme 7.1. For an efficient chain process, it is important (i) that the RjSi radical reacts faster with RZ (the precursor of radical R ) than with the alkene, and (ii) that the alkyl radical reacts faster with the alkene (to form the adduct radical) than with the silicon hydride. In other words, the intermediates must be disciplined, a term introduced by D. H. R. Barton to indicate the control of radical reactivity [5]. Therefore, a synthetic plan must include the task of considering kinetic data or substituent influence on the selectivity of radicals. The reader should note that the hydrogen donation step controls the radical sequence and that the concentration of silicon hydride often serves as the variable by which the product distribution can be influenced. 

The revealed mechanism of ter Meer reaction is well-founded. It helps us to understand the peculiarities of nucleophilic substitution reactions having the chain ion-radical mechanism and involving the interaction of radicals with anions at the chain propagation steps. It also demonstrates how the knowledge of kinetics and mechanism can be used to find new ways of initiating and optimizing the reactions important for technical practice. The ter Meer reaction turns out to be a reaction having one name and mechanism. This differs from, say, aromatic nitration, which has one name bnt different mechanisms. 

The low tendency of 1,2-disubstituted ethylenes to polymerize is due to kinetic considerations superimposed on the thermodynamic factor. The approach of the propagating radical to a monomer molecule is sterically hindered. The propagation step is extremely slow because of steric interactions between the P-substituent of the propagating species and the two substituents of the incoming monomer molecule ... 

It is instructive to sketch this reaction as in Figure 10-1. The chain is fed by initiation reactions that create CHs and terminated by reactions that destroy CHy- to form C2H6. However, the major processes by which the reaction proceeds are the two propagation steps that alternately create and destroy the two chain-propagating radicals CH3 and CHsCOv Thus we have the notion of a chain of reactions, which is a kinetic chain of propagation reaction steps that feed reactants into the chain and spit out stable products. This is a kinetic chain reaction, which is different from the polymerization chain of reactions, which we wiU introduce in the next chapter (although those reactions form both kinetic and polymer chains). 

That work has shown that deuterium substitution produced very large kinetic isotope effects on the initiation step (a) and much smaller but still sizable effects on propagation step (d) ... 

Kinetic Isotope Effect in Propagation Step (d) Step (d), e.g.,... 

The alkylation of quinoline by decanoyl peroxide in acetic acid has been studied kineti-cally, and a radical chain mechanism has been proposed (Scheme 207) (72T2415). Decomposition of decanoyl peroxide yields a nonyl radical (and carbon dioxide) that attacks the quinolinium ion. Quinolinium is activated (compared with quinoline) towards attack by the nonyl radical, which has nucleophilic character. Conversely, the protonated centre has an unfavorable effect upon the propagation step, but this might be reduced by the equilibrium shown in equation (167). A kinetic study revealed that the reaction is subject to crosstermination (equation 168). The increase in the rate of decomposition of benzoyl peroxide in the phenylation of the quinolinium ion compared with quinoline is much less than for alkylation. This observation is consistent with the phenyl having less nucleophilic character than the nonyl radical, and so it is less selective. Rearomatization of the cr-complex formed by radicals generated from sources other than peroxides may take place by oxidation by metals, disproportionation, induced decomposition or hydrogen abstraction by radical intermediates. When oxidation is difficult, dimerization can take place (equation 169). 

From this equation, it is clear that concentration of the solvent, S, influences a number of sites on the template which are occupied by the monomer, M. As the result of monomer units association with the template, the orientation of the substrate takes place and some special type of structure can be created. The structures, in which the monomer is aligned in a regular manner on the polymer template, were described by Chapiro in the case of polymerization of acrylic acid and acrylonitrile and details are described below. The ordered structure increases concentration of monomer at the reaction site, affects distances between pre-oriented monomer molecules, and changes a steric hindrance. This change in structure leads to the change in the kinetics of the polymerization reaction and it is responsible for stereo-control of the propagation step. 

The autoxidation of hydrocarbons catalyzed by cobalt salts of carboxylic acid and bromide ions was kinetically studied. The rate of hydrocarbon oxidation with secondary hydrogen is exactly first order with respect to both hydrocarbon and cobalt concentration. For toluene the rate is second order with respect to cobalt and first order with respect to hydrocarbon concentration, but it is independent of hydrocarbon concentration for a long time during the oxidation. The oxidation rate increases as the carbon number of fatty acid solvent as well as of cobalt anion salt are decreased. It was suggested that the cobalt salt not only initiates the oxidation by decomposing hydroperoxide but also is responsible for the propagation step in the presence of bromide ion. 

Later, other authors utilized the differences found in the optical activity of monomer and polymer to carry out kinetic investigations on the free-radical polymerisation (70,72,120) and copolymerization (71), and tried to achieve the steric control of the propagation step of free-radical polymerization and copolymerization (13, 14, 39, 73, 98) using optically active monomers and initiators. 

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