Attachment reactions, diffusion controlled

After obtaining from the measured value of kl by this procedure, one can determine the attachment efficiency in the quasi-free state, rj = fe1f/fed.ff, by the same procedure as for scavenging reactions (see Eq. 10.11 et seq.). Mozumder (1996) classifies the attachment reactions somewhat arbitrarily as nearly diffusion-controlled, partially diffusion-controlled, and not diffusion-controlled depending on whether the efficiency p > 0.5, 0.5 > r > 0.2, or r < 0.2, respectively. By this criterion, the attachment reaction efficiency generally falls with electron mobility. Nearly diffusion-controlled reactions can only be seen in the liquids of the lowest mobility. Typical values of r] are (1) 0.65 and 0.72 respectively for styrene and p-C6H4F2 in n-hexane (2) 0.14 and 0.053 respectively for a-methylstyrene and naphthalene in isooctane (3) 1.8 X 10-3 for C02 in neopentane and (4) 0.043 and 0.024 respectively for triphenylene and naphthalene in TMS. 

It is natural to conclude that the high rate constants for electron attachment reactions in nonpolar liquids are associated with the high mobility of electrons. Early studies [96,104,105] of attachment to biphenyl and SFg emphasized the dependence of on mobility. This relationship is apparent if the expression for the rate constant for a diffusion-controlled reaction ... 

Many of these attachment reactions are also diffusion-controlled in other solvents of low electron mobility like, for example, n-hexane. It has been suggested that this is the case for all solvents for which 1 cm /Vs [118]. For this to be true, the rate constant k should scale as the mobility. For hexane, the rate constants for attachment to solutes like biphenyl, naphthalene, and difluorobenzene are close to 1 x 10 sec or one-third the value in cyclohexane. The mobility in -hexane is approximately one-third that in cyclohexane [2] thus k scales with fijj for these two solvents. 

An interesting example of a diffusion-controlled reaction is electron attachment to SFg. Early studies showed that in -alkanes, k increases linearly with over a wide range of mobilities from 10 to 1 cm /Vs [119]. Another study of the effect of electric field E) showed that in ethane and propane, k is independent of E up to approximately 90 kV/cm, but increases at higher fields [105]. This field is also the onset of the supralinear field dependence of the electron mobility [120]. Thus over a wide range of temperature and electric field, the rate of attachment to SFg remains linearly dependent on the mobility of the electron, as required by Eq. (15). 

Some electron transfer reactions have been studied in supercritical xenon. Two of them have been shown to be diffusion controlled and two are energy controlled. These reactions have been followed by changes in the optical absorption after the pulse. To carry out these studies requires that the rate of electron attachment to the solute be suffidendy fast to compete with ion recombination, which occurs on the picosecond time scale in pulse radiolysis. The solute hexafluo-robenzene satisfies this criterion the rate constant is sufficiently large (see Fig. 6) that millimolar concentrations will allow formation of anions. The rate constant for attachment to 4,4 -bipyridine (bipy) is also sufficiently large to satisfy this need. ° Another requirement for making these studies is to quench the excimers whose optical absorptions are strong and can interfere with detection of ions. As mentioned under Sec. 2, a small concentration of ethane (0.4%) is sufficient for this purpose. 

The formation reaction, 1, is very rapid. Absolute rate constants for electron attachment to four aromatic compounds in ethyl alcohol (4) are shown in Table I. These rate constants increase in order of increasing electron affinities of the aromatic molecule, but it should be noted that such a correlation may be fortuitous. The magnitude of the rate constants is equal to or near that of a diffusion controlled reaction, and a correlation with molecular size is also seen for this set of reactants. 

The termination reaction of free radical polymerization is a typical example of an intermacromolecular diffusion controlled reaction.3 Photophysical studies carried out in the 1980 s demonstrated for the first time that the reaction is solvent- and molecular weight-dependent. The experiments involved triplet quenching of probes attached to polymer chain ends. A benzil group was linked to the end of one PS sample (PS-B) and an anthryl group was linked to the end of a second PS sample (PS-A). The quenching rate coefficient kq of the benzil phosphorescence by anthryl groups is given by Eq. (3.26), where r0 is the lifetime of benzil phosphorescence in the absence of anthryl and ris the benzil phosphorescence lifetime in the presence of anthryl in concentration [A],... 

Interestingly, inverted behavior has been observed for reactions in solution between donors and acceptors that are not attached by molecular bridges. In a novel approach, the diffusion-control problem was avoided by monitoring charge recombination in geminate radical pairs (see Fig. 3). It is possible to extract the CR rate constant, k , from the quantum yield of radicals escaping from the geminate radical pair (Eq. 4), where is monitored with a cation radical trap such as dimethoxystilbene (DMS). 

Note that although the results reported by Yu and von Meerwall [65] and by Deng and Martin [66,67] showed a dependency of diffusion coefficient on molecular weight, the diffusion of reactive groups toward each other concerned with epoxy cure reactions (step-growth polymerisation reactions) is only controlled by segmental diffusion irrespective of the size of molecules to which they are attached. Neither molecular weight nor symmetry or composition play any role within overall diffusion control. 

Nowadays, most chemists know the name "Sand" only because it appears attached to a partic ilar equation in texts that describe chronopotentiometry. This technique can be useful in the diagnosis of electrode reactions (l). A current step i is Impressed across an electrochemical cell containing iinstirred solution, the potential of the working electrode is measured with respect to time and the transition time x is noted. According to the Sand equation, the product ix /2 should be constant for an uncomplicated linear diffusion-controlled electrode reaction at a planar electrode. 

Another demonstration of a continuous flow operation is the psi-shaped microreactor that was used for lipase-catalyzed synthesis of isoamyl acetate in the 1-butyl-3-methylpyridinium dicyanamide/n-heptane two-phase system [144]. The chosen solvent system with dissolved Candida antarctica lipase B, which was attached to the ionic liquid/n-heptane interfacial area because of its amphiphilic properties, was shown to be highly efficient and enabled simultaneous esterification and product removal. The system allowed for simultaneous esterification and product recovery showed a threefold reaction rate increase when compared to the conventional batch. This was mainly a consequence of efficient reaction-diffusion dynamics in the microchannel system, where the developed flow pattern comprising intense emulsification provided a large interfacial area for the reaction and simultaneous product extraction. Another lipase-catalyzed isoamyl acetate synthesis in a continuously operated pressure-driven microreactor was reported by the same authors [145]. The esterification of isoamyl alcohol and acetic acid occurred at the interface between n-hexane and an aqueous phase with dissolved lipase B from Candida antarctica. Controlling flow rates of both phases reestablished a parallel laminar flow with liquid-liquid boundary in the middle of the microchannel and a separation of phases was achieved at the y-shaped exit of the microreactor (Figure 10.25). The microreactor approach demonstrated 35% conversion at residence time 36.5 s at 45 °C and at 0.5 M acetic acid and isoamyl alcohol inlet concentrations and has proven more effective and outperformed the batch operation, which could be attributed to the favorable mass and heat transfer characteristics. 

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