Rate constants free radical initiation

To study quantitatively the kinetics of lipid oxidation and antioxidation, a standard way of controlling and measuring the rate of free radical initiation is to use thermally labile azo compounds. These artificial initiators generate radicals at a reproducible, well-established and constant rate. In the presence of initiators such as a,a-azobisisobutyronitrile (AIBN) or benzoyl peroxide, the overriding initiation can be directly related to the rate of production of the initiator radical. Also, by using either water-soluble or lipid-soluble azo dyes, these compounds can initiate radicals at known specific micro-environments. 

Usually, free-radical initiators such as azo compounds or peroxides are used to initiate the polymerization of acrylic monomers. Photochemical (72—74) and radiation-initiated (75) polymerizations are also well known. At a constant temperature, the initial rate of the bulk or solution radical polymerization of acrylic monomers is first order with respect to monomer concentration and one-half order with respect to the initiator concentration. Rate data for polymerization of several common acrylic monomers initiated with 2,2 -azobisisobutyronittile (AIBN) [78-67-1] have been determined and are shown in Table 6. The table also includes heats of polymerization and volume percent shrinkage data. 

The thiol ( -dodecyl mercaptan) used ia this recipe played a prominent role ia the quaUty control of the product. Such thiols are known as chain-transfer agents and help control the molecular weight of the SBR by means of the foUowiag reaction where M = monomer, eg, butadiene or styrene R(M) = growing free-radical chain k = propagation-rate constant = transfer-rate constant and k = initiation-rate constant. 

Equation 6 would hold for a family of free radical initiators of similiar structure (for example, the frarw-symmetric bisalkyl diazenes) reacting at the same rate (at a half-life of one hour, for example) at different temperatures T. Slope M would measure the sensitivity for that particular family of reactants to changes in the pi-delocalization energies of the radicals being formed (transition state effect) at the particular constant rate of decomposition. Slope N would measure the sensitivity of that family to changes in the steric environment around the central carbon atom (reactant state effect) at the same constant rate of decomposition. 

It should be emphasized that the above equations, which relate reaction temperatures to calculated reactant or product energies, are equivalent to the more conventional linear free energy relationships, which relate logarithms of rate constants to calculated energies. It was felt that reactant temperatures would be more convenient to potential users of the present approach -those seeking possible new free radical initiators for polymerizations. 

The study of the detailed mechanism of free radical initiation (rate constant k ) and ozone decay (rate constant d) by the reaction with cyclohexane, cumene, and aldehydes gave the following results (7 = 298 K) ... 

Oxidative chain reactions of organic compounds are current targets of theoretical and experimental study. The kinetic theory of collisions has influenced research on liquid-phase oxidation. This has led to determining rate constants for chain initiation, branching, extension, and rupture and to establishing the influence of solvent, vessel wall, and other factors in the mechanism of individual reactions. Research on liquid-phase oxidation has led to studies on free radical mechanisms and the role of peroxides in their formation. 

A number of studies of simple reactions using DSC have given values for rate constants and activation energy in good agreement with those determined by methods utilising chemical analysis. An example of this is the work of Barrett18) on the thermal decomposition of free radical initiators. 

Several years later, DeSimone and co-workers (Guan et al., 1993) examined the decomposition of the free-radical initiator 2,2 azobis(isobutyro-nitrile) (AIBN, Scheme 4.6) in sc C02 as a function of pressure. The rate constant was found to increase with increasing pressure (reaching a maximum at approximately 250 bar). At higher pressures, the rate constant... 

A case classically associated with radical chain polymerization for which a (pseudo)steady state is assumed for the concentration of active centers this condition is attained when the termination rate equals the initiation rate (the free-radical concentration is kept at a very low value due to the high value of the specific rate constant of the termination step). The propagation rate, is very much faster than the termination rate, so that long chains are produced from the beginning of the polymerization. For linear chains, the polydispersity of the polymer fraction varies between 1.5 and 2. 

In contrast, recent kinetic investigation of the polymerization of spacerless G2 dendron-substi-tuted styrene and methylmethacrylate, respectively, in solution lead to the unexpected conclusion that above a certain critical monomer concentration a strong increase in the rate of the free radical polymerization is observed [21]. The results can be explained by self-organization of the growing polymer chain to a spherical or columnar superstructure in solution, depending on the degree of polymerization (DP, Fig. 2). The rate constants and low initiator efficiency lead one to conclude that the self-assembled... 

As would be predicted from Equation 1, the rate of dissociation of free radical initiators is decreased by the application of pressure. Thus azobisisobuty-ronitrile dissociates with a rate constant equal to 4.47 X 1(H sec." at 1500 atm. but at 1 atm. the dissociation rate constant is 5.5 X 10 sec. (8). Studies concerning the effect of pressure on the decomposition of benzoyl peroxide reveal that the rate of this reaction also decreases with increasing pressure (II, 18). The extent to which the radical-induced decomposition of this peroxide at high pressures affects the rate is not clear, but it appears that some complications arise from this cause. 

As indicated earlier, G=0.7 for free radical initiation and about 0.1 for the free ions. The termination rate constants are 3 X 10 M sec for free radicals and 2 x 10 M sec for the free ions. The propagation rate constants have been determined to be 30, 4 X 10 and about 10 sec for free radical, cationic and anionic polymerization, respectively. 

The second step of initiation [Eq. (8.83)], being slower than the first [Eq. (8.82)], is rate-determining for initiation (unlike in the case of free-radical chain polymerization) and so though the amide ion produced upon chain transfer to ammonia can initiate polymerization it is but only at a rate controlled by the rate constant, ki, for initiation. Therefore, this chain transfer reaction may be considered as a true kinetic-chain termination step and the application of steady-state condition gives Eq. (8.90). 

For long chain lengths, many molecules of hydroperoxide are formed per free radical initiating the reaction before termination occurs and hence variations of over-all rate constant K essentially reflects changes in the rate of propagation, i.e. in eq. (8)... 

The rate coefficients for hydroxyperoxide decomposition to free radicals is different from that for hydroperoxides. Therefore, addition of hydroperoxide to ketone changes the rate of free radical formation. This was first found for the system cyclohexanone—t-butyl hydroperoxide [168] with chlorobenzene as solvent. The rate of initiation increases with ketone concentration at a constant concentration of hydroperoxide. The... 

One possible way of overcoming this problem is to introduce into the reaction mixture a compound that decomposes at a constant rate to free radicals (X ) capable of extracting a hydrogen atom from the PUFAs (RH) and consequently initiating the autoxidation process. The compounds most frequently used for this are the so-called azo-initiators (X-N=N=X), which thermally decompose to highly reactive carbon-centered radicals. ... 

However, a commercially feasible process for bulk polymerization in a continuous stirred tank reactor has been developed by Montedison Fibre [103,104]. The heat of reaction is controlled by operating at relatively low-conversion levels and supplementing the normal jacket cooling with reflux condensation of unreacted monomer. Operational problems with thermal stability are controlled by using a free radical redox initiator with an extremely high decomposition rate constant. Since the initiator decomposes almost completely in the reactor. 

Most copolymerizations in the presence of a free radical initiator obey the simple copolymerization equation. Equation (22-22). Consequently, the copolymerization parameters calculated from this equation can be interpreted directly as the ratios of two rate constants. Since they are relative reactivities, they must be influenced by the polarity, the resonance stabilization, and the steric effects of the monomers. In these cases, resonance stabilization effects are generally stronger than polarity influences, and these, in turn are greater than effects due to steric hindrance. 

To develop their model, Wen and McCormick adopted a number of simplifying assumptions. These are (1) initiation produces two equally reactive radicals, (2) chain transfer reactions are neglected, (3) the rate constants for radicals of different sizes are assumed identical, (4) the propagation rate constant kp, termination rate constant kp and the rate constant for radical trapping kb are all simple functions of free volume as shown below, and (5) there is no excess free volume. The material balance equations for the initiator, the functional group, the active radical, and the trapped radical concentrations... 

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