Random recombination reaction

Figure 4. Scheme of the random recombination reaction via F-pairs. 

The observation of MFEs in f-pairs is important as this is how most ordinary chemical reactions take place. Most recombination reactions of organic free radicals do not occur through photochemically generated RPs with initially pure spin states, but instead through the random encounter of radicals in solution (think of the classic termination reaction in free radical chain reactions). 

This resemblance is highly significant if one considers that 10,359 structural isomers exist for saturated hydrocarbons with 16 C atoms (Lederberg, 1972). Apparently the meteoritic hydrocarbons were made by FTT reactions, or some other process of the same extraordinary selectivity. The Miller-Urey reaction, incidentally, shows no such selectivity. Gas chromatograms of hydrocarbons made by electric discharges in methane show no structure whatsoever in the region around Cjg (Ponnamperuma et al., 1969). Apparently all 10 possible isomers are made in comparable yield, as expected for random recombination of free radicals. 

As seen in Table 2.3.2, a plot of 1/DP against time will be almost linear, assuming a small zip length and a random initiation reaction. When the initiation reaction is an end scission, or when the termination is a recombination reaction, other dependencies must be applied. 

In Sect. 3, the Noyes approach to analysing reaction rates based on the molecular pair approach is discussed [5]. Both this and the diffusion equation analysis are identical under conditions where the diffusion equation is valid and when the appropriate recombination reaction rate for a molecular pair is based on the diffusion equation. Some comments by Naqvi et al. [38] and Stevens [455] have obscured this identity. The diffusion equation is a valid approximation to molecular motion when the details of motion in a cage are no longer of importance. This time is typically a few picoseconds in a mobile liquid. When extrapolating the diffusion equation back to such times, it should be recalled that the diffusion is a continuum form of random walk [271]. While random walks can be described with both a distribution of jump frequencies and distances, nevertheless, the diffusion equation would not describe a random walk satisfactorily over times less than about five jump periods (typically 10 ps in mobile liquids). Even with a distribution of jump distances and frequencies, the random walk model of molecular motion does not represent such motion adequately well as these times (nor will the telegrapher s or Fokker-Planck equation be much better). It is therefore inappropriate to compare either the diffusion equation or random walk analysis with that of the molecular pair over such times. Finally, because of the inherent complexity of molecular motion, it is doubtful whether it can be described adequately in terms of average jump distances and frequencies. These jump characteristics are only operational terms for very complex quantities which derive from the detailed molecular motion of the liquid. For this very reason, the identification of the diffusion coefficient with a specific jump formula (e.g. D = has been avoided. 

Recalling the spin-sorting nature of the radical pair mechanism, we can anticipate that in the absence of nuclear spin relaxation, random recombination will eventually lead to exact cancellation of the + polarization when the + polarization in A is transferred to A (making the usual assumption that chemical reaction preserves nuclear spin orientation). In such a situation, polarization in A could only be observed in a time-resolved experiment before all the radicals had recombined. Relaxation of the nuclei A , however, allows some of the escape polarization to "leak away preventing complete cancellation (II). Thus, unless the radical lifetime is very much smaller than the nuclear... 

Although a reaction scheme involving disproportionation as a significant random recombination route is not strictly cyclic, it can lead to partial cancellation of the A polarization as indicated by the arrows in equation (32). In the limit of very slow relaxation, a maximum of half of the f polarization in A can be cancelled by the opposite phase + polarization in the radicals. The remainder of the escape polarization ends up in the other disproportionation product (A ). This type of reaction leads to much simpler CIDNP time dependence than the A + B back reaction because no net polarization can arise in radical pairs consisting of identical free radicals. 

The process took place on Ni/Cr203 between 373 and 525 K and must require the dissociative chemisorption of the methanes followed by random recombination not surprisingly, deactivation was found at all temperatures." The reaction between normal and deuterated n-butane has also been studied on a number of supported platinum catalysts." Little or no exchange was seen between light methylcyclo-hexane and deuterated n-octane (or the reverse) over Pt/Si02 at 755 K either in the presence or absence of hydrogen or deuterium because of rapid conversion to other molecules reaction did however take place between them at lower temperatures, and on Pt/Al203 it occurred both on the metal and the support. ... 

The observed inhibition on Pt has been ascribed to [144, 145] (1) simple geometric blocking, (2) a decrease in the number of pairs of uncovered Pt atoms, which decreases the H -P H recombination reaction, and (3) a change of electronic states of uncovered Pt atoms. Protopopoff and Marcus [147] have analyzed in detail the blocking effects of sulfur on H2 evolution on Pt(llO) and Pt(lll) electrodes. For random adatoms distribution, the zones of deactivation overlap, and this process can be analyzed by using a simple statistical treatment [148]. For severd Pt/Maj systems, considerable H2 evolution takes place when the UPD of H is completely blocked. This provides an additional proof that there is no connection between the UPD H and the intermediates in H2 evolution. 

A fourth assay measures the rate of interconversion of ortho and para hydrogen. Since any type of rupture of the hydrogen-hydrogen bond that permits random recombination will be detected by this assay, it was suggested that this is the most specific measurement of hydrogenase. However, the finding that a D2O medium substitutes the exchange reaction (HD formation) for the ortho-para conversion indicates that... 

The methodology of stochastic treatment of e-ion recombination kinetics is basically the same as for neutrals, except that the appropriate electrostatic field term must be included (see Sect. 7.3.1). This means the coulombic field in the dielectric for an isolated pair and, in the multiple ion-pair case, the field due to all unrecombined charges on each electron and ion. All the three methods of stochastic analysis—random flight Monte Carlo (MC), independent reaction time (IRT), and the master equation (ME)—have been used (Pimblott and Green, 1995). 

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