Recombination term

Focusing on the recombination term in eq. 14 we see that this terra reduces to ... 

Considering these different limiting forms of the recombination term an Important tentative conclusion emerges the concentration dependence of the reciprocal relaxation time is a direct measure of the main ionic recombination process and yields therefore information on the ionic species present in solution. A linear dependence on total ion-pair concentration would therefore indicate unilateral triple ion formation or, if both kinds of triple ions are present as indicated by conductance, a sufficient difference in their stability. At this point it should be noted that the usual method of Fuoss and Draus... 

Experimentally all the limiting cases of the recombination term are encountered in all systems investigated up to now. In solutions of tetraalkylammonium salts in benzene the reciprocal relaxation time is even dependent on the square of total concentration (but here the quadrupoles may be comparable in concentration with ion-pairs) which would indicated a preponderance of quintuple and triple ions in the ionic recombination. 

The potential m, is defined similarly. As it is seen from equation (2.3.50), the mean force acting on a particle A at coordinate fhas both the contribution from direct interactions within a group of (m + m/)-particles and indirect interactions (integral terms). If the particle creation and recombination terms were absent, the steady-state solution of equation (2.3.47) would correspond to putting the fluxes and J m, equal zero. The corresponding set of... 

The recombination term of the reduced integral equation can be transformed into its differential analog as in Eq. (3.278). In the Markovian limit this differential equation reduces to the conventional one with the rate constant kr = fes(oo) [48] ... 

Summing this with the recombination term, we have the following equation for the free ions accumulation/recombination ... 

At t = 0, Qs = 0 and the measured photocurrent is entirely due to charging. At longer times the surface charge tends towards its steady state value, and the charging current falls to zero. The current due to charge transfer is proportional to Q so it is zero at t = 0 and increases with time towards its final steady state value. Since the recombination term also depends on Qs, the fraction of charge carriers at the surface that are transferred is determined by the ratio ktr/(ktr + krcc) for all values of t. 

The accumulated surface charge Qs t) oscillates periodically, and the time dependent charging, transfer and recombination terms are replaced by the sums of their steady state and periodic equivalents. 

The significance of the various terms in eqn. (426) are shown in Fig. 68. The only difference between this and the formula derived by Wilson, eqn. (415), is the presence of an additional loss term in the denominator which reflects recombination in the depletion layer. However, unlike the loss term representing diffusion out of the depletion layer into the bulk, the depletion recombination term decreases only slowly with increasing bias and plays a significant role even at comparatively large vs values. However, it is clear that, at comparatively large values of y (ca. 0.1) and reasonable values of the ratio (Dplk z)LD, very low efficiencies are found, even at high bias potentials. This is quite unreasonable, as will be seen below. 

We now consider the form of the expression for the collection efficiency in eqn. (426). It consists of a numerator 1 - e"3tv + (aLp/[aLp + l])e ,v = Xgm, a generating term, and a denominator that contains a depletion layer recombination term and a diffusion loss term. The last term is likely to be negligible at the higher potentials considered here and we ignore it. The recombination term in the denominator has the general form K/k zpB and... 

Here, k z is just the sum of the faradaic term and other surface recombination terms that are first order in ps. 

This has been designated the a region since it was the first observed temperature region. In this region the temperature dependence of the ratio (An/2Ad) and its dependence on the positive-ion concentration will be minimized since both recombination terms will be affected in the same manner. 

In Eq. (14) Ap (and An) represents small signal deviations from dc level, whereas in Eq. (1) it represents deviation from thermal equilibrium. The recombination term in Eq. (11) is then... 

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... 

Continuity equation approaches involving nonlinear forms for the electron diffusion and recombination terms are capable of reproducing some aspects of observed behavior [123, 126]. The challenge is to predictively relate the forms for recombination and diffusion to known material properties of the system. 

In a strong field, coefficient Kx) becomes a function of E due to the field induced ionization of molecules. Then we cross again the recombination term in (7.45) and get... 

In some applications, the carrier density may not vary a great deal with position or time. In such cases a simplification may be made to Eq. (3) by linearizing the recombination term around the operating carrier density. The resulting variation on the carrier rate equation is normally written as... 

This is identical to the Nemst-Planck Eq. (80) in the absence of an electric field term and a generation-recombination term. 

Based on the assumption that collisions change the ionic velocity but not their position, G is simply reduced to a charge generation-recombination term that will be neglected in processes involving transport. By recalling that / = qcV, one realizes that Eq. [61] is the continuity equation previously written (see Eq. [55]). 

In Equation 24, [F], [D], [R] denote the field, diffusion, and recombination terms, respectively. If we take the initial distribution of ion densities given by Equation 25, then the relative importance of the three terms can be evaluated for r = b as... 

Sensitivity of exclusion detectors. Fig. 3.20, was determined by calculating the dark current of detector according to the van Roosbroeck-Shockley model and including generation-recombination terms according to (1.85) and (1.86). The optical term (1.81) was subsequently added and the calculation was repeated. Signal current was... 

Ashley and Elliott [333] neglected recombination terms in the depleted part and left only Shockley-read and radiative generation to propose the following expression for electron concentration in the n region... 

For the non-plasticized polymer electrolyte, the light-dependent recombination term was introduced because of the high rate observed for equation 10.8, owing to the low ionic conductivity of the electrolyte. For the electrolytes plasticized with GBL, however, it would be expected that the J-V curves could be fitted using the simple one diode model, at least for samples containing higher amounts of salt, due to the high ionic conductivity of these electrolytes, and the data from transient absorption spectroscopy presented earlier. 

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