Rate of photochemical initiation

A similar analysis for the photochemical rate replaces the rate of thermal initiation, 2 1[Br2][M], by the rate of photochemical initiation 2/abs, giving... 

At constant light intensity, the rate of photochemical initiation, rlnit, is constant. Therefore integration yields... 

In photochemistry, a mole of light quanta is called an Einstein. Thus an Einstein of light quanta of frequency v or wavelength X has energy Np hv (or NA hc/X), where Naw is Avogadro s number, h is Planck s constant, and c is the speed of light. The rate of photochemical initiation may then be expressed (Ghosh, 1990)... 

By experimentally determining the rate of photochemical initiation, from an examination of the rate of inhibited n-decanal oxidation, and by determining the concentration of peroxidic species (obtained by the rotating sector method), it is possible to calculate the propagation (k3) and rupture (ft6) coefficients which, at 5°C, are... 

The rate of photochemical initiation is given by the product of the intensity of absorbed light (in moles of light quanta per liter and second) and the primary quantum yield. A good survey on different photoinitiators and their photodecomposition by UV light was given by Gruber (55). 

An important application of photochemical initiation is in the determination of the rate constants which appear in the overall analysis of the chain-growth mechanism. Although we shall take up the details of this method in Sec. 6.6, it is worthwhile to develop Eq. (6.7) somewhat further at this point. It is not possible to give a detailed treatment of light absorption here. Instead, we summarize some pertinent relationships and refer the reader who desires more information to textbooks of physical or analytical chemistry. The following results will be useful ... 

Tetralin hydroperoxide (1,2,3,4-tetrahydro-l-naphthyl hydroperoxide) and 9,10-dihydroanthracyl-9-hydroperoxide were prepared by oxidizing the two hydrocarbons and purified by recrystallization. Commercial cumene hydroperoxide was purified by successive conversions to its sodium salt until it no longer increased the rate of oxidation of cumene at 56°C. All three hydroperoxides were 100% pure by iodometric titration. They all initiated oxidations both thermally (possibly by the bi-molecular reaction, R OOH + RH — R O + H20 + R (33)) and photochemically. The experimental conditions were chosen so that the rate of the thermally initiated reaction was less than 10% of the rate of the photoreaction. The rates of chain initiation were measured with the inhibitors 2,6-di-ter -butyl-4-methylphenol and 2,6-di-fer -butyl-4-meth-oxyphenol. None of the hydroperoxides introduced any kinetically first-order chain termination process into the over-all reaction. 

The authors have concerned themselves particularly with the initicd rate of photochemical oxidation of aldehydes in order to eliminate any possible kinetic effects of the products formed. To clarify the reaction mechanism at the initial time, the authors studied the effect on the initial rate of the aldehyde concentration, oxygen pressure, intensity of light absorbed, and temperature. 

For NO t > 0-5 ppb (typical of urban and polluted rural sites in the eastern USA and Europe) Equations (3) and (4) represent the dominant reaction pathways for HO2 and RO2 radicals. In this case the rate of ozone formation is controlled largely by the rate of the initial reaction with hydrocarbons or CO (Equations (1) and (2)). Analogous reaction sequences lead to the formation of various other gas-phase components of photochemical smog (e.g., formaldehyde (HCHO) and PAN) and to the formation of organic aerosols. 

If a problem appears to be due to unwanted radical-radical interactions, then it might be necessary to slow the initiation processes. This can be achieved by adjusting the temperature of the reaction, the decomposition temperature of the initiator and the rate of introduction of the initiator. In case of photochemical initiation, the power of the lamp could have an influence or for redox processes, one of the reagents could be introduced more slowly. 

In many cases a chemical compound may, depending on the conditions of the photochemical reaction, behave either as a photo-initiator or as a photosensitizer. Benzophenone is a typical example. For this reason some authors do not distinguish between these two classes of compounds, assuming that their positive influence on the changes of the rate of photochemical reactions represents the sensitization of these reactions. 

Photochemical studies have shown that below 172°C a stationary state is established, but this temperature is too low for the rate of thermal initiation to be sufficient. 

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 decomposition of an initiator seldom produces a quantitative yield of initiating radicals. Most thermal and photochemical initiators generate radicals in pairs. The self-reaction of these radicals is often the major pathway for the direct conversion of primary radicals to non-radical products in solution, bulk or suspension polymerization. This cage reaction is substantial even in bulk polymerization at low conversion when the medium is essentially monomer. The importance of the process depends on the rate of diffusion of these species away from one another. 

In order to estimate the extent of ozone depletion caused by a given release of CFCs, computer models of the atmosphere are employed. These models incorporate information on atmospheric motions and on the rates of over a hundred chemical and photochemical reactions. The results of measurements of the various trace species in the atmosphere are then used to test the models. Because of the complexity of atmospheric transport, the calculations were carried out initially with one-dimensional models, averaging the motions and the concentrations of chemical species over latitude and longitude, leaving only their dependency on altitude and time. More recently, two-dimensional models have been developed, in which the averaging is over longitude only. 

Photochemically induced polymerizations in which the molecular weight is termination-controlled are exceptions to the rule that the average degree of polymerization diminishes with temperature. The rate of initiation at fixed intensity of illumination is virtually independent of temperature, hence din Xn/dT = Ep — Et/2)/RT j which is a positive quantity. 

Reaction selectivity of the parent ortho-QM has also been explored with a variety of amino acid and related species.30 In these examples, the rates of alkylation and adduct yields were quantified over a range of temperatures and pH values. The initial QM3 was generated by exposing a quaternary benzyl amine (QMP3) to heat or ultraviolet radiation (Scheme 9.10). Reversible generation of QM3 was implied by subsequent exchange of nucleophiles at the benzylic position under alternative photochemical or thermal activation.30 Report of this work also included the first suggestion that the reversible nature of QM alkylation could be used for controlled delivery of a potent electrophile. 

Using l,8-diphenyloctatetra-l,3,5,7-ene, (DOT), as a model compound either in dilute, ( 10-5m), hexane or ethanol solutions or incorporated into a film of undegraded PVC confirmed that in the presence of HC1 it underwent a photochemical reaction which resembled that of the polyenes in thermally degraded PVC. The results indicated that the initial rates of reactions proceeding in either solvent showed a second order dependence on HC1 pressure and that the reaction was considerably slower in ethanol than in hexane. Further, when cast in PVC films, the characteristic absorption maxima of DOT were shifted about 16nm to longer wavelengths compared with their absorption in hexane and there... 

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