Charge-transfer impurity model

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. 

The proposed scenario is mainly based on the molecular approach, which considers conjugated polymer films as an ensemble of short (molecular) segments. The main point in the model is that the nature of the electronic state is molecular, i.e. described by localized wavefunctions and discrete energy levels. In spite of the success of this model, in which disorder plays a fundamental role, the description of the basic intrachain properties remains unsatisfactory. The nature of the lowest excited state in m-LPPP is still elusive. Extrinsic dissociation mechanisms (such as charge transfer at accepting impurities) are not clearly distinguished from intrinsic ones, and the question of intrachain versus interchain charge separation is not yet answered. 

The model shown in Scheme 2 indicates that a change in the formal oxidation state of the metal is not necessarily required during the catalytic reaction. This raises a fundamental question. Does the metal ion have to possess specific redox properties in order to be an efficient catalyst A definite answer to this question cannot be given. Nevertheless, catalytic autoxidation reactions have been reported almost exclusively with metal ions which are susceptible to redox reactions under ambient conditions. This is a strong indication that intramolecular electron transfer occurs within the MS"+ and/or MS-O2 precursor complexes. Partial oxidation or reduction of the metal center obviously alters the electronic structure of the substrate and/or dioxygen. In a few cases, direct spectroscopic or other evidence was reported to prove such an internal charge transfer process. This electronic distortion is most likely necessary to activate the substrate and/or dioxygen before the actual electron transfer takes place. For a few systems where deviations from this pattern were found, the presence of trace amounts of catalytically active impurities are suspected to be the cause. In other words, the catalytic effect is due to the impurity and not to the bulk metal ion in these cases. 

When sodium lignosulfonate or sulfur lignin are compounded, for instance, with iodine or bromine, complexes supposedly form (16-17). These systems are conductors with mixed ionic and electronic nature. Presumably they are charge transfer complexes, since the electronic conductivity predominates (18-19). These compounded materials form charge transfer structures (20). Water is supposed to introduce ionic conductivity to the system. Impurities affect conductivity, too (21). In any case, the main models of conductivity are probably based on the band model and/or the hopping model. 

The percolation model, which can be applied to any disordered system, is used for an explanation of the charge transfer in semiconductors with various potential barriers [4, 14]. The percolation threshold is realized when the minimum molar concentration of the other phase is sufficient for the creation of an infinite impurity cluster. The classical percolation model deals with the percolation ways and is not concerned with the lifetime of the carriers. In real systems the lifetime defines the charge transfer distance and maximum value of the possible jumps. Dynamic percolation theory deals with such case. The nonlinear percolation model can be applied when the statistical disorder of the system leads to the dependence of the system s parameters on the electrical field strength. 

At the early stages the photoconductivity of solid solutions of the leucobase of malachite green in various organic media was investigated [285]. In these systems, carrier transport occurs by direct interaction between the leucobase molecules. No direct participation of the organic matrix in the charge transfer was observed. A model was proposed which links charge transfer in these systems with impurity conduction in semiconductors. 

The screening-impurity model implies a strong-electron coupling. The strong polarization of the sp electronic density of the chalcogen by Li" ions induces a negative charge defect behind the transition-metal site and reinforces the local positive potential around it. This favors a localization of the transferred electron to this site. The more polarizable the anion, e.g., the Li-ZrSej system, the more important is the effect. 

We conclude that more work is need. In particular it would be useful to repeat the TB-LMTO-CPA calculations using also other methods for description of charge transfer effects, e.g., the so-called correlated CPA, or the screened-impurity model. One may also ask if a full treatment of relativistic effects is necessary. The answer is positive , at least for some alloys (Ni-Pt) that contain heavy elements. 

At about the same time as Reichman, Jarrett also published a model that explicitly included recombination in the SCR [55]. For a given impurity concentration, the numerical solutions for the photoconversion efficiency he obtained are completely defined by three parameters the optical absorption coefficient, the minority carrier lifetime in the depletion layer, Tr, and the charge transfer rate at... 

FIGURE 5.6 X-ray absorption spectrum of the Co L-edge of cobalt nanocrystals calculated from the single-impurity Anderson model, illustrating a charge transfer from metal nanocrystals to ligand molecules. Reprinted with permission from Ref. [19]. American Chemical Society. 

For donor and acceptor impurities in mixture A a dependence cr oc is typical. This does not fit the simple model of dissociation with constant coefficients Kb and Kr. Apparently the ionization process in this system passes through an intermediate stage involving the formation of charge-transfer complexes [19]. 

Analysis based on electrochemical impedance spectroscopy (EIS also called AC impedance spectroscopy) allows estimation of frequency behavior, quantification of resistance, and the ability to model equivalent circuits (ECs) of ES systems. The fundamental EC for a double-layer circuit, as discussed in Chapter 2, contains series resistance and double-layer capacitance. In addition, there is often a faradic parallel resistance from impurities in the carbon. In the pseudocapacitive case, the faradic resistance is a related reciprocal of the overpotential-dependent charge transfer [2,21]. 

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