Radical lifetimes

To arrive at an expression for the radical lifetime, we return to Eq. (6.24), which may be interpreted as follows ... 

If we multiply the time elapsed per monomer added to a radical by the number of monomers in the average chain, then we obtain the time during which the radical exists. This is the definition of the radical lifetime. The number of monomers in a polymer chain is, of course, the degree of polymerization. Therefore we write... 

The radical lifetime is an average quantity, indicated by the overbar. 

Since the radical lifetime provides the final piece of information needed to independently evaluate the three primary kinetic constants-remember, we are still neglecting chain transfer-the next order of business is a consideration of the measurement of r. 

To gain some additional familiarity with the concept of radical lifetime and to see how this quantity can be used to determine the absolute value of a kinetic constant, consider the following example. 

The rate of initiation was measured directly and radical lifetimes were determined using the rotating sector method. The following results were obtained.f... 

Substituents on the methine chain can stabilize the dye radical cation if the substituent (like methyl) is located on the high electron density carbons. However, no significant stabilization occurs when alkyl groups are on the alternate positions (like 9, 11 for the dication in Fig. 9). Current results for several dyes including die arbo cyanines and carbocyanines indicate that electronic stabilization of the dication radical lengthens the radical lifetime and also enhances the reversibiUty of the dimerization process (37). 

Overhauser limit (Gloss and Gloss, 1969 Gloss, 1969 Gloss and Trifunac, 1969) (v) polarization was obsei ved in radical systems where the radical lifetimes were longer than the nuclear relaxation times in the individual radicals involved (Ward and Lawler, 1967 Lawler, 1967 Fischer, 1969). 

Table I. Trace gas rate constants and lifetimes for reaction with ozone, hydroxyl radical, and nitrate radical. Lifetimes are based upon [O3]=40ppb [HO ]=1.0x10 molecules cm (daytime) [NO3 ]=10ppt (nighttime).

Evidence indicates [28,29] that in most cases, for organic materials, the predominant intermediate in radiation chemistry is the free radical. It is only the highly localized concentrations of radicals formed by radiation, compared to those formed by other means, that can make recombination more favored compared with other possible radical reactions involving other species present in the polymer [30]. Also, the mobility of the radicals in solid polymers is much less than that of radicals in the liquid or gas phase with the result that the radical lifetimes in polymers can be very long (i.e., minutes, days, weeks, or longer at room temperature). The fate of long-lived radicals in irradiated polymers has been extensively studied by electron-spin resonance and UV spectroscopy, especially in the case of allyl or polyene radicals [30-32]. 

Ex-situ generation. In this approach the radicals are generated away from the epr cavity under well-defined voltammetric conditions and then transferred into the epr cell (usually via a flow system). Such a method imposes a restriction on the radical lifetimes observable due to the dead time involved between generation and detection. 

The most recent values for Arrhenius parameters are those of Dainton and Burns128, who performed a very careful study of the photochemical formation of phosgene, investigating the effects of light intensity, temperature and concentration and determined radical lifetimes by the rotating sector technique. 

The rotating sector method requires the introduction of the parameter is, defined as the average lifetime of a growing radical under steady-state conditions. The radical lifetime is given by the steady-state radical concentration divided by its steady-state rate of disappearance ... 

Consider now what occurs on the entry of a radical into a particle that already has a radical. For most reaction systems, the radical concentration in a polymer particle is 10-6 M or higher. This is a higher radical concentration than in the homogeneous polymerization systems and the radical lifetime here is only a few thousandths of a second. The entry of... 

It is known that hydrophobic surroundings can stabilize free radicals lifetimes of up to an hour were measured for otherwise very reactive radicals. This may be of importance for the enzyme mechanism. 

Short HO radical lifetimes in the dark prevent the collection of ambient air samples for later analysis, except perhaps for the case of filter collection techniques that use a spin-trapping reagent (28). Furthermore, rapid reactivity of HO with surfaces mandates careful attention to the sampling train used to move ambient air into a more amenable analysis environment. 

It would lie beyond the scope of this treatment to describe the various methods now available for determining radical concentrations. Most of them are difficult to apply to the gas phase and none of them is really useful unless (a) the intensity / is very high, i.e. over 1018 quanta.ml-1.sec-1 and (b) experimental conditions are such that radical lifetimes are at least 10 4 second or more. In a way these two conditions are mutually exclusive. 

There is currently significant debate about the mechanism of substrate oxidation by Q [62, 80, 81, 89]. Studies examining the MMO-catalyzed oxidation of nor-carane, of which the products derived from radical and cationic rearrangements clearly differ, indicated that both radical and cationic species are involved in product formation with a radical lifetime on the order of 20-150 ps [79, 90]. There is, furthermore, evidence suggesting that compound P may be able to effect alkene epoxidation directly [91]. Thus, in analogy with P450, multiple mechanisms and oxidants may be involved in the oxygenation of different substrates by MMO. 

Unlike the arylmethyl radicals, diphenyl ketyl radicals have substantial extinction coefficients for the D0 —> Dx absorption and emission that shows the expected mirror image relationship to the absorption band. Ketyl radical lifetimes are generally in the 10-ns range and show only minor temperature dependence. Deuterium substitution of the hydroxy group has a pronounced effect on lifetime,... 

---