Bimolecular initiation

Scheme 7 Unimolecular and bimolecular initiation mechanisms induced by photochemical and thermal processes, respectively...

The bimolecular initiation leads to much more complex results. The essential difference between the former kinetic scheme and the bimolecular initiation (or a similar kinetic scheme) lays in the dependence in the latter case of Mn and Mw on the rate of addition of monomer. Increasing the rate of addition results in a higher Mw and produces, therefore, a polymer of higher intrinsic viscosity. 

Using the same toluene-benzoyl peroxide system Nakatsuka (105) measured polymerization rate and molecular weight as functions of temperature (40° and 58°) and of the concentration of.three retarders p-nitrophenol, 2,4-dinitrophenol and picric acid. Results were consistent with a kinetic scheme postulating (among other things) bimolecular initiation involving peroxide and monomer and spontaneous unimolecular termination of growing polymer chains. 

Non-activated double bonds, e.g. in the allylic disulfide 1 (Fig. 10.2) in which there are no substituents in conjugation with the double bond, require high initiator concentrations in order to achieve reasonable polymerisation rates. This indicates that competition between addition of initiator radicals (R = 2-cyanoisopropyl from AIBN) to the double bond of 1 and bimolecular side reactions (e.g. bimolecular initiator radical-initiator radical reactions outside the solvent cage with rate = 2A t[R ]2 where k, is the second-order rate constant) cannot be neglected. To quantify this effect, [R ] was evaluated using the quadratic Equation 10.5 describing the steady-state approximation for R (i.e. the balance between the radical production and reaction). In Equation 10.5, [M]0 is the initial monomer concentration, k is as in Equation 10.4 (and approximately equal to the value for the addition of the cyanoisopropyl radical to 1-butene) [3] and k, = 109 dm3 mol 1 s l / is assumed to be 0.5, which is typical for azo-initiators (Section 10.2). The value of 11, for the cyanoisopropyl radicals and 1 was estimated to be less than Rpr (Equation 10.3) by factors of 0.59, 0.79 and 0.96 at 50, 60 and 70°C, respectively, at the monomer and initiator concentrations used in benzene [5] ... 

At high temperatures, both simplifications and complications of the above mechanism occur. Bimolecular initiation processes (involving at least one unsaturated molecule) cannot be excluded (see, for example, ref. 15). Transfer processes must be included since chains are no longer long. H abstraction from alkenes generates not only allylic type radicals, but also vinylic type radicals. As the temperature increases, allylic type radicals become thermally unstable. As the activation energy of unimolecular fissions of radicals is much higher than that of bimolecular processes such as metatheses, when the temperature increases the relative concentration of the p- radicals, compared with that of the thermally stable / and Y- radicals, decreases. Therefore, termination processes involve mainly / radicals (except for H- radicals, because they are very reactive and recombine in a third-order process) and Y-radicals. Finally, the addition of the most concentrated / and Y- radicals to unsaturated molecules can play a role, because this process is followed by a very fast unimolecular fission. For reasons of size limitation, the addition of radicals (e.g. H- and CH3-) will mainly be considered. Of course, the above a priori hypotheses about relative radical concentrations or reaction rates must be checked a posteriori, when numerical calculations have been carried out. 

In the third article of the series the authors set out to determine the kinetic initiation parameters and the lifetime of the ionic chain carriers. The values of kj were cmnputed frmn the measured rates of carbenium icm formation assuming bimolecular initiation. This assumption is unacceptable a priori since the interaction between Brjinsted acids and olefins in solvents like the one used in this work has been shown to involve kinetic patterns whidi are almost always more complicated than a simple first order in each reactant (see Sect. III-B). As for the calculation of the mean lifetime of the active species based on the expression... 

At low temperatures the polymerization process is only initiated by UV-, y- or x-irradiation via excitation of the monomer molecules. However, in order to understand the relatively high quantum yield obtained in the bimolecular initiation reaction of Eq. (9) we have to consider a metastable long-lived excited state M, which represents... 

Thioxanthiones (TX) absorb strongly in the near-ultraviolet region of the spectrum, and their reaction with amines comprises a bimolecular initiator system competitive with photodissociative initiators [138 150. The photochemistry and photophysics of TX in the presence of amines are similar to that observed for other aromatic ketones, and can be summarized by the scheme proposed by Davidson [148] (Scheme 17). 

Radical-induced decomposition is thermodynamically favorable (Ea = 37.5 kCal), and is also more consistent with the characteristics of bimolecular initiation by hydroperoxides originally proposed by Russell (356), the kinetics measured in lipid oxidation systems, and significant epoxide products reported in many studies. Most importantly, the radical-induced decomposition described in Reaction 63 provides a powerful cascade of reactive radicals to fuel the very rapid increase in oxidation during the bimolecular rate period. 

There are two important rules in selecting initiation reactions. The first is that unimolecular fission reactions, because of their high A-factors (/ 1016 1 sec"1) will generally be faster than bimolecular reactions for which A-factors run about 109 1 1/mole-sec. At 1 atm of reactant the ratio of rates for initiation is of the order of 109 in favor of the first-order processes. A rough rule of thumb is that the bimolecular initiations will be significant only if they have activation energies at least 40 kcal less... 

Coming back to the a(C-C)/(3(C-H) primary split ratio (Table 3), it would be valuable to compare these values with that obtained either in the thermal pyrolysis of propene or in chemical activated systems. For example, in shock tube experiments (1650-2300 K), the dominant bimolecular initiation reaction leads to the C-C bond rupture, although a possible contribution of the 3(C-H) bond rupture cannot be excluded (50). This is also observed in the decomposition of hot propene formed from ethylcarbene f(E)(C3H ) s 414 kJ/mol] a(C-C)/ P(C-H) = 22 (51). Conversely, hot propene formed by the addition of singlet methylene to ethylene [(EXCsH ) s 464—492 kJ/mol) gives rise to C-H bond... 

Here, in spite of the chain sequence of steps, the reaction is apparent first-order. However, it can be seen that the apparent first-order rate constant is a combination of the rate constants of the individual elementary steps. A comparison of this example with the contents of Table 1.3 shows that the Rice-Herzfeld mechanism corresponds in this case to Two Active Centers with Second-Order Cross-Termination Chain. The apparent first-order behavior here is a consequence of the particular kinetics of the initiation and termination steps. It is not difficult to show that various combinations of unimolecular or bimolecular initiation with bimolecular or even termolecular termination can result in apparent orders that range from 0 to 2 (M.F.R. Mulcahy, Gas Kinetics, John Wiley, New York, 1973, pp. 87-92). 

The hypothesis of a bimolecular initiation reaction for liquid phase autoxida-tions was extended beyond cyclohexanone as a reaction partner. Also other substances featuring abstractable H-atoms are able to assist in this radical formation process. The initiation barrier was found to be linearly dependent on the C-H bond strength, ranging from 30 kcal/mol for cyclohexane to 5 kcal/mol for methyl linoleate [14, 15]. Substrates that yield autoxidation products that lack weaker C-H bonds than the substrate (e.g., ethylbenzene) do not show an exponential rate increase as the chain initiation rate is not product enhanced [16]. 

Write down the bimolecular initiation reaction of normal butane with oxygen. 

Table XIV-2.5.b gives the kinetic parameters of five categories of bimolecular initiation reactions concerning primary (p), secondary (s), tertiary (t), allylic (a) and vinylic (v) H atoms. The A factor is relative to one H atom.

Calculate the kinetic parameters for the bimolecular initiation reactions of propane. There are two reactions ... 

This computer program calculates the kinetic parameters of elementary reactions (bimolecular initiations, addition of a free radical to an unsaturated molecule, unimolecular decomposition, cyclization, oxidation of a radical, metathesis and branching) using structure-reactivity correlations. It is part of the EXGAS system. Information cf EXGAS. 

A bimolecular initiating system, based in 2,2 -azobisisobutyronitrile was reported by Michl and co workers [26]. It consists of weakly solvated lithium in combination with the cyanopropyl radical (from AIBN). The combination can initiate polymerizations of olefins. The reaction was illustrated as follows ... 

The position of the equilibrium constant in reactions with TEMPO depends on the nature of the radical, the solvent and the temperature. These polymerizations can be initiated by either bimolecular initiators or by unimolecular ones. The bimolecular initiators utilize common free radical sources such as benzoyl peroxide or azobisisobutyronitrile to start the reaction. The carbon-centered initiating radicals that form in turn react with TEMPO. This can be illustrated as follows ... 

Since the overall rate is proportional to and includes an additional factor of [f-BuOOH] arising from the propagation sequence, the combined initiation mechanism is in accord with the observed rate law. A similar situation involving Mn(II) and Mn(III) species - both active in bimolecular initiation with -BuOOH -applies to the reaction catalyzed by [Mn(acac)3] which obeys the same type of rate law as [Co(dpm)2]. 

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