Diffusion recombination

Over long times, this displays the limiting form t 3/2 characteristic of the diffusive recombination of radicals. The various forms of h(t) which have been developed are shown in Fig. 40. There are significant differences between these forms and, in particular, the form of h(t) at short times must be 0(t+") where n > — 1. The partially reflecting form [eqn. (194)] is satisfactory as its limiting short-time dependence is U1/2, so too is the Noyes random flights form of h(t), though its theoretical justification is limited. The purely diffusive form of h(f), eqn. (193), is an unnecessary contrivance. 

The three terms on the left-hand side of (16.26) account, respectively, for the diffusion, recombination, and generation of holes under illumination. Without advancing into mathematical details, one obtains the hole current density at the interface between the bulk and the space charge region, i.e., the diffusion current density ydiff, as given by... 

There are two models which utilize this mechanism, the spur model [18, 16] and the blob model (diffusion-recombination model) [19, 20]. In spite of the fact that both models answer the question about the Ps precursor in the same way, they differ as to what constitutes the terminal part of the e+ track and how to calculate the probability of the Ps formation. 

Principles and Applications of Positron and Positronium Chemistry 5.5.2 Diffusion-recombination stage... 

Considering the diffusion-recombination stage below, we neglect an interaction between the thermalized positron and its blob. This approximation, as we discussed above, assumes that the appearance of a positive potential in the blob, caused by outdiffusion of electrons, is nearly cancelled by the negative potential caused by e+ screening inside the blob. In this case we can apply the prescribed diffusion method to obtain the solution of Eq. (17). Let us write Cj(r,t) in the following form ... 

What about the minority carrier injection process depicted in Figure 14 Here, contrasting with the process considered above, the hole injection step itself is usually very fast (see below). Then the current is limited by diffusion/recombination described by the Shockley equation [201] ... 

The diffusion/recombination mechanism results in considerable overpotential for (cathodic) current flow in the dark (again assuming an n-type semiconductor for illustration). Such a rate-limiting process was found to describe the charge transfer at n-GaAs in 6 M HCl containing Cu as the hole-injecting species [159, 176]. 

On the other hand, for secondary diffusive recombination, Eq. 21 would predict... 

Study of the effect of viscosity on the geminate diffusive recombination of radicals produced in the decomposition of diacetyl peroxide. 

The one-dimensional diffusion-recombination model neglects the transport in the electrolyte and shielding conditions. A standard, more general approach to multiple carrier transport problems [77] is solved using a set of equations that comprises ... 

The case of interest for DSC and solar cells in general is the diffusion-recombination impedance with a reflecting boundary condition at the end of the... 

Fig. 15 (a) Transmission line model for the generalized diffusion impedance, (b) Transmission line model for a porous electrode, (c) Transmission line impedance model for diffusion-recombination in a mesoporous Ti02 electrode, including also interfacial impedances and mass transport impedance in electrolyte... 

Here C is the chemical capacitance. is the macroscopic recombination resistance of the layer that was introduced in (20) and will be the object of detailed analysis in the remaining sections of this chapter. The impedance model for diffusion-recombination adopts the form [44]... 

Fig. 16 Diffusion-recombination transmission line with reflecting boundary conditions.

Note that k. in (5.25) depends similarly on R and D as the diffusive recombination rate constant in (5.20). During passage over the barrier the particle responds to a friction with the medium, due to the viscosity of the latter, that slows down the rate. D is the diffusion constant for the movement over the barrier. 

Figure 1.8 Contrasting direct photodissociation in the gas phase and in a soivent [adapted from Schwartz eta/. (1994)]. As we shall discuss, the coming back together of the two fragments owing to the "fence" presented by the solvent may initially be coherent in that the wave-packet describing the relative motion has not yet dephased, see Problem H. On a longer (>picosecond) time scale the recombination will be diffusive. When the fragments are polyatomic a diffusive recombination means that the fragments will lose their relative orientation. They can even recombine to a different isomer of the parent.

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