Second order recombination

The conductivity K induced by radiation absorption at dose rate I (eV°=cm-3 s-1) is given by K = uc, where c the is free ion concentration and u is the sum of mobilities of positive and negative carriers. The establishment of steady state requires equal rates of generation and recombination, or IGR /100 = kc2 where k is the second-order recombination rate constant. Eliminating c between these... 

Bakale et al. [397] pulse irradiated the hydrocarbons cyclopentane, cyclohexane and n-hexane with 0.9 MeV electrons of duration 10 or 100 ns. The transient conductivity decreased approximately exponentially with time for low doses of radiation. The first-order decay of the conductance is probably due to electrons reacting with impurities. With higher doses, the conductance decays approximately as inverse time, characteristic of a second-order recombination of free ions. No evidence for time-dependent geminate ion-pair recombination effects was observed. 

The stationary state concentration of radicals was shown to be proportional to the square root of the dose rate indicating that, as might be expected, the radicals, which are produced at a uniform rate, disappear by a second order recombination reaction... 

The conclusion drawn from Worked Problem 6.14 is that changing the type of termination step from gas to surface alters the kinetics. This is because the order with respect to the radical differs between the second order recombination of the gas phase termination and surface termination where diffusion to the surface or adsorption on the surface is rate determining and first order. If, however, the rate-determining step in surface termination were bimolecular recombination on the surface, the order would not change between gas and surface termination. This is because both recombinations would now have the same order, i.e. 2 4[R ]2 and 2 7[R ]2, with the total rate of termination if both contributed being 2(k + 7)[R ]2. 

Fig. 8. Outline of the time-scale of the processes observed during an electron transfer reaction observed through thermal lensing. Processes which occur in times below ca. 0.5 ps are very fast , beyond the temporal resolution of the thermal lensing technique they would appear as a step function in the kinetics of heat release. The slowest processes which would be observed in this case are the second-order recombinations of free ions, which take place in time scales of ps to several ms.

Bowman and coworkers characterized the subpicosecond dynamics of titanium dioxide sols employing particle sizes of about 2 nm prepared by hydrolysis of titanium tetraisopropoxide [6]. From their spectral results the authors inferred that the average lifetime of an electron/hole pair is 23 5 ps, and substantial electron/hole recombination occurs within the first 30 ps. A second-order recombination rate constant of (1.8 0.7) x 1CT10 cm3 s 1 for trapped electrons with holes has been obtained [6a]. 

Processes such as cross-linking, second-order termination of radical species, and polymerization are all examples of recombination. Here, we consider second-order recombination, where two molecules or radical fragments may join to form a new molecule of higher degree of polymerization. 

FIGURE 18.19 Evolution of an initially normal distribution by second-order recombination. 

As pointed out previously, an upper limit is placed upon (C) by second-order recombination processes, so that the radical concentration cannot grow without limit. At pressures near the first explosion limit this restriction is unimportant. Thus if we assume that the reaction H -f- H -f M proceeds at every tenth triple collision (that is, A = 3 X 10 liters2/mole -sec) then the lifetime of an II atom at 750 K when M = 8 mm Hg and H = 0.8 mm Hg ( ) is about 0.2 sec [t = l/fc(M)(H)]. This is much slower than the rate of branching in the H2 + O2 system (see page 457). 

Equation (XIV.G.3) represents, of course, one special case among many possible examples of chain-branching reactions. Variations of this equation may be obtained by adding terms that represent homogeneous first-order termination ka C) to Eq. (XIV.6.3) or wall-initiation terms to the auxiliary boundary equation (XIV.6.4). The addition of terms which are second-order in radicals, such as second-order recombination in the gas phase, or second-order branching leads to equations which are nonlinear and which may only be solved cither numerically or by approximation. 

Noyes has made numerical solutions of the case of special interest at higher pressures, that of the second-order recombination of radicals in the gas phase competing with first-order wall recombination. The interesting result here may be stated in terms of the effective thickness over which the wall exerts an appreciable effect. Noyes finds that r , where D is the diffusion coefficient, /c, the constant rate of initiation of radicals, and fc<2 is the rate constant for homogeneous second-order termination of radicals. Within the shell of thickness Vw near the wall, it may be assumed, if the surface is an efficient radical trap, that the concentration of radicals is essentially zero, while outside this shell the concentration of radicals may be assumed to correspond to that which is unperturbed by the walls. 

A simple way of arriving at a result which also takes into account the efficiency of the surface is to say that the wall will exert its effect out to a distance which point is determined by the condition that a radical starting there has an equal chance of being captured on the wall or of undergoing second-order recombination in the gas phase. 

Dynamic equilibrium concentration of chain carriers (radicals), [R], generated by ionizing irradiation at the dose rate P, is defined by the second-order recombination kinetics ... 

As in dissociation, at different pressures the second-order recombination rate constant... 

The simple mechanisms consisting of reactions (1), (2) and (3), (plus the second order recombination term at low pressures), together with vibrational quenching steps, give a satisfactory description of the O -t-NO -f M reaction. Since the excited state of NO2 in the O NO -f-M emission is believed to be the same as that excited in fluorescence by irradiation of the rate constant ratio for fluorescence and... 

Equation (II) has several useful properties. (1) The observed decay of atoms is independent of concurrent first-order atom decay processes, e.g. heterogeneous decay, and of second-order atom recombination (fcg[M]), provided first-order decay dominates this recombination. It may be helpful to increase the first-order decay (e.g. by adding NO to O atoms, NO -1- O -I- M NOj -f M) in order to suppress second-order recombination. (2) Any variation of with distance along the flow tube does not affect the results, provided is not a function of [R]. (3) The fixed observation point may be at room temperatures, whilst the reaction zone containing the reactant inlets is at an elevated temperature. The results then give a value for k at the elevated temperature. These useful properties have been exploited in series of studies over wide temperature ranges of rate constants for atom -f molecule recombination reactions, and for atom molecule transfer reactions. - - - - ... 

Chain termination most likely occurs by reaction with the primary initiating radical or with another propagating chain. The calculated stability of any species containing a double bond precludes their participation in chain growth. Thus, the second-order recombination of difluorocarbene. 

Accounting for high pressures (of several tens of torr and higher) and taking the second-order recombination rate constant kj.ec 10 cm mol s (see [219]), the disproportionation rate constant can be measured from the known absolute values and the temperature dependence of A. The results of such calculations for several alkyl radical pairs are given in Table 10. The activation energy for disproportionation reactions is seen to be usually low. 

Whenever possible the fourth point has been taken into consideration and radical concentrations have been corrected for losses due to recombination or other decay reactions of the (secondary) radicals under consideration. In the case of 6 polyamide fibers [5, 11, 17, 18] the radical decay is a second order recombination reaction with the rate constant depending on type, location, and mobility of the radicals (see Section III below). 

Kinetic Study of the Photochromism of 2 -Hexaphenyl-l,l -Biimidazolyl with Electron Spin Resonance. Taro Hayashi, Koko Maeda, and Makoto Takeuchi (Univ. Ochanomizu, Tokyo). BuU. Chem. Soc. Japan 37 (11), 1717-18 (1964) (Eng.). The tide reaction, followed by the E.S.R. spectrum, involves a second-order recombination of triphenylimidazolyl radicals. 

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