Model for charge transfer

Figure 11. Structure model for charge transfer reaction at a Pt site...

Some of the earlier works devoted to rationalize the dependence of the observed ET rate constant on the applied potential were based on basic models for charge transfer in polar media. Two of the main issues arising from these considerations are the structure of the liquid liquid boundary and the distribution of the electrostatic potential. In the pioneering work by Samec in 1979, the potential dependence of was considered assuming a model involving two diffuse layers separated by an ion-free compact layer [7]. The region delimited by the inner layer establishes the distance for maximum probabiKty of ET (/ ). In this case, the element SR is estimated by the space volume of the ion of radius aoi located in one of the reaction plane and certain molecular volume adjacent to the phase boundary. 

Figure 8b. Modified Butler model for charge transfer with adsorption.

Fig. 17 Tunneling model for charge transfer across semiconductor-electrolyte interfaces.

Most of the present implementations of the CPA on the ab-initio level, both for bulk and surface cases, assume a lattice occupied by atoms with equal radii of Wigner-Seitz (or muffin-tin) spheres. The effect of charge transfer which can seriously influence the alloy energetics is often neglected. Several methods were proposed to account for charge transfer effects in bulk alloys, e.g., the so-called correlated CPA , or the screened-impurity model . The application of these methods to alloy surfaces seems to be rather complicated. 

It should be mentioned that one can detect two types of equilibrium in the model of charge transfer in the absorbate - adsorbent system (i) complete transition of chemisorbed particles into the charged form and (ii) flattening of Fermi level of adsorbent and energy level of chemisorbed particles. The former type takes place in the case of substantially low concentration of adsorbed particles characterized by high affinity to electron compared to the work function of semiconductor (for acceptor adsorbates) or small value of ionization potential (for donor adsorbates). The latter type can take place for sufficiently large concentration of chemisorbed particles. 

Prior to addressing the results of simulations on the issues exposed in the last section, we will now develop in this section a simple model perspective [5c,21,22,43]. Its purpose is both to shed light on the interpretation in terms of solvation of those results and to emphasize the interconnections (and differences) that may exist. The development given below is suitable for charge transfer reaction systems, which have pronounced solute-solvent electrostatic coupling it is not appropiate for, e.g., neutral reactions in which the solvent influence is mainly of a collisional character. (Although we do not pursue it here, the various frequencies that arise in the model can be easily evaluated by dielectric continuum methods [21,431). 

A simple modification of the IAM model, referred to as the K-formalism, makes it possible to allow for charge transfer between atoms. By separating the scattering of the valence electrons from that of the inner shells, it becomes possible to adjust the population and radial dependence of the valence shell. In practice, two charge-density variables, P , the valence shell population parameter, and k, a parameter which allows expansion and contraction of the valence shell, are added to the conventional parameters of structure analysis (Coppens et al. 1979). For consistency, Pv and k must be introduced simultaneously, as a change in the number of electrons affects the electron-electron repulsions, and therefore the radial dependence of the electron distribution (Coulson 1961). 

Historically, crystal field theory was the first theoretical model (11, 86, 101, 123) used to explain d-d transition energies in metal complexes. Its usefulness is restricted to those complexes whose bonding is largely ionic, and its mqjor deficiency arises from its inability to account for charge transfer transitions. The iterative extended Hiickel and the ab initio, limited basis set, Hartree-Fock calculations are capable of de-... 

We mentioned the main models for generation, transfer, and recombination of the charge carriers in polymers. Very often, these models are interwoven. For example, the photogeneration can be considered in the frame of the exciton model and transport in the frame of the hopping one. The concrete nature of the impurity centers, deep and shallow traps, intermediate neutral and charged states are specific for different types of polymers. We will try to take into account these perculiarities for different classes of the macro-molecules materials in the next sections. 

The factors that influence cross sections for charge-transfer reactions have not yet been completely assessed. Several theoretical models have been developed.176179 For asymmetric charge-transfer processes of the type... 

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