Rate constant recombination calculation

In the case of partially diffusion-controlled recombination, which is described by Eq. (33), the recombination rate constant is calculated as [28]... 

The breakdown of the diffusion theory of bulk ion recombination in high-mobility systems has been clearly demonstrated by the results of the computer simulations by Tachiya [39]. In his method, it was assumed that the electron motion may be described by the Smoluchowski equation only at distances from the cation, which are much larger than the electron mean free path. At shorter distances, individual trajectories of electrons were simulated, and the probability that an electron recombines with the positive ion before separating again to a large distance from the cation was determined. The value of the recombination rate constant was calculated by matching the net inward current of electrons... 

A) Magnetic field dependence of the singlet recombination yield (proton radical pair for various rate constant (fc4i), calculated using Eq. (15-19). (B) Properties of the... 

The kinetics for P700 and P430 recombination was apparently non-exponential, as the semi-logarith-mic plot (not shown) was non-linear. The kinetics of the recombination reaction could be fitted to a linear plot by the application of a special case of a second-order reaction where the two reactants P700 and P430 existed in equal amounts throughout the reaction course The second-order rate constant was calculated to be 3T0 and the ty, was approximately 45 ms. 

Figure 13. Numerically calculated PMC potential curves from transport equations (14)—(17) without simplifications for different interfacial reaction rate constants for minority carriers (holes in n-type semiconductor) (a) PMC peak in depletion region. Bulk lifetime 10" s, combined interfacial rate constants (sr = sr + kr) inserted in drawing. Dark points, calculation from analytical formula (18). (b) PMC peak in accumulation region. Bulk lifetime 10 5s. The combined interfacial charge-transfer and recombination rate ranges from 10 (1), 100 (2), 103 (3), 3 x 103 (4), 104 (5), 3 x 104 (6) to 106 (7) cm s"1. The flatband potential is indicated.

Figure 14. PMC potential dependence, calculated from analytical formula (18) for different interfacial rate constants for minority carriers S = 1 cm, minority carrier flux toward interface I,- 1 cm-2s 1, a= 780enr1, L = 0.01 cm, 0=11.65 cmV, Ld = 2x 0"3cm), (a) sr = 0 and different charge-transfer rates (inserted in the figures in cm s 1), (b) Constant charge-transfer rate and different surface recombination rates (indicated in the figure).

Much of what is knotm about the structure response of the ECD is based on empirical observations. Clearly, the ability to correlate the response of the detector to fundamental molecular parameters would be useful. Chen and Wentworth have shorn that the information required for this purpose is the electron affinity of the molecule, the rate constant for the electron attachment reaction and its activation energy, and the rate constant for the, ionic recombination reaction [117,141,142]. in general, the direct calculation of detector response factors have rarely Jseen carried j out, since the electron affinities and rate constants for most compounds of interest are unknown. 

The long-time limit of k(t) defines the steady state rate constant of the bulk ion recombination, which for the totally diffusion-controlled recombination is calculated as [27]... 

Figure 6 Dependence of the electron-ion recombination rate constant on the external electric field F, calculated for different values of the electron mean free time r. The unit of Cis, and that of r is r l k-g,Tlnif. The simulation results of Morgan [45] for liquid methane at 120 K are shown by crosses. (From Ref. 48.)...

In the liquid phase, observed electron-ion recombination rate constants kr in a variety of nonpolar media were, as shown in Fig. 15, in good agreement with the values of k, calculated from the reduced Debye equation,... 

The dissociation rate is calculated after the assumption of the recombination rate constant of H with anion to be 10 ° M sec when the pita value is known. 

Let us assume that fci is equal to k9, the rate constant for the gas phase decomposition (15), where no cage effect is expected. This assumption does not always hold (15, 18). For example, it is known (18) that di-f erf-butyl peroxide (DPB) decomposes about 30% slower in the gas phase than in solution. We can calculate from our value of k8 and the known value of kg, from the work of Szwarc (7, 21), a value for the fraction of acetoxy radical pairs recombining, fR, where... 

Applying the laws of Brownian motion to the distribution of free ions and ion-pairs in the presence of a external electric field Onsager calculated the rate constants of recombination and dissociation for equilibrium [1] as ... 

Fig. 5-2. Dependence of bimolecular rate constant kobs of iodine atom recombination at 333°K on [NO] in the high-pressure region. The curve is calculated and the points are experimental (from Porter, Szab6, and Townsend350 with permission of the Royal Society).

The problem of restoring the function f(k), which characterizes the distribution of the recombining particles over the rate constants of their recombination, from the kinetics of ITL is discussed in detail in ref. 69. In this work a formalism has been used which is close to that described in Chap. 5. However, in ref. 69 the calculations have been carried out up to a very simple final formula. To follow ref. 69, let SN(k,t) be the number of luminescence centres with a recombination rate constant located between k and k + dk which have survived to time t, and let N0 be the total number of luminescence centres at the start of the recording of ITL. The values 5N(k,t) and i(k) are connected by the equation... 

Termination rate constants for alkyl and benzyl radicals in solution range between 109 and 1010 M 1 sec-1.85 These rates correspond quite closely to that calculated for a diffusion-controlled reaction, about 8 x 109 M x sec-1 for the common solvents at room temperature.86 Gas-phase rotating sector results are similar a newer method, however, shows that in the gas phase the rotating sector technique overestimates termination rates. Recombination is fastest for methyl radicals (1010,5 M-1 sec-1) and slower for others (-CF3, 109-7 at 146°C ... 

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