Kinetics of charge transfer

The classical circuit element that gives rise to semicircles is a charge transfer resistance shunted by a double-layer capacitance. Indeed the values of the capacitance deduced from the semicircular features are typical of those for a double-layer capacitance. The barrier to charge transfer can be either a barrier to electron transfer at the electrode/polymer interface or a barrier to ion transfer (perhaps through resolvation) at the polymer/electrolyte interface. We now derive expressions for the charge transfer resistance in either case. 

We start with the electron transfer at the electrode interface with electrochemical rate constants ki and k-i before the small perturbation 

The kinetic term in Eqn. 46 for the charge transfer resistance may have important consequences. Near the standard electrochemical potential of the couple, rate constants are roughly equal and possibly large enough so that Rct is small the system behaves reversibly. However for very reduced systems, ki is very small, and hence Rct can be large. Similarly for very oxidized systems, k-i is very small, and again Rct can be large. It is important to realize that systems which are kinetically labile close to the standard electrode potential may show kinetic barriers at extremes in reduction or oxidation. 

Turning to the polymer electrolyte interface, we use a similar treatment. Before the step the system is in balance, and we have 

Equation 48 for Rct shows that for a consant electrolyte concentration given by s, as the Donnan exclusion develops with oxidation, has to increase to provide counterions. Hence Rct decreases monotonically as oxidation takes place. This is true for normal polymers. Ren and Pickup made polymers containing polystyrenesulphonate counterion. For these polymers mobile cation must be incorporated when the polymer is reduced and expelled when the polymer is oxidized. Now the Donnan potential is largest for the reduced coat and smaller for the oxidized coat. For this case Rct increases with oxidation. 

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The electrochemistry of a polymer-modified electrode is determined by a combination of thermodynamics and the kinetics of charge-transfer and transport processes. Thermodynamic aspects are highlighted by cyclic voltammetry, while kinetic aspects are best studied by other methods. These methods will be introduced here, with the emphasis on how they are used to measure the rates of electron and ion transport in conducting polymer films. Charge transport in electroactive films in general has recently been reviewed elsewhere.9,11... 

The kinetics of charge transfer between metallic electrodes and conducting polymer films have proved to be difficult to investigate, and little reliable data exist. Charge-transfer limitations have been claimed in cyclic voltammetry, and Butler-Volmer kinetics have been used in a number of... 

The Role of the Electronic Factor in the Kinetics of Charge-Transfer Reactions German, E. D. Kuznetsov, A. M. 24... 

In the case of layer compounds as electrode materials the kinetics of charge transfer were also studied in some detail taking into account surface recombination which plays an important role here . In the presence of suitable redox systems some materials show very little corrosion . This is due to the morphology of the crystal surfaces and it is generally assumed that corrosion occurs only at steps of different crystal planes . Accordingly, it is not surprising that the highest efficiencies were obtained with some of these materials (Table 1) . The steps also play an important role in the fill factor as determined by surface recombination measurements . ... 

Potential differences at the interface between two immiscible electrolyte solutions (ITIES) are typical Galvani potential differences and cannot be measured directly. However, their existence follows from the properties of the electrical double layer at the ITIES (Section 4.5.3) and from the kinetics of charge transfer across the ITIES (Section 5.3.2). By means of potential differences at the ITIES or at the aqueous electrolyte-solid electrolyte phase boundary (Eq. 3.1.23), the phenomena occurring at the membranes of ion-selective electrodes (Section 6.3) can be explained. 

This chapter will be concerned with the kinetics of charge transfer across an electrically charged interface and the transport and chemical processes accompanying this phenomenon. Processes at membranes that often have analogous features will be considered in Chapter 6. The interface that is most often studied is that between an electronically conductive phase (mostly a metal electrode) and an electrolyte, and thus these systems will be dealt with first. 

The kinetics of charge transfer across the phase boundary between... 

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

The changes in the potential profile of the interfacial region because specific adsorption do indeed affect the electrode kinetics of charge transfer processes, particularly when these have an inner sphere character [13, 26] (see Fig. 1.12). When this influence leads to an improvement of the current response of these processes, the global effect is called electrocatalysis. ... 

VI. KINETICS OF CHARGE TRANSFER AND TRANSPORT 1. Three Experimental Situations... 

Figure 5 A schematic representation of the kinetics of charge-transfer dissociation proposed by Braun.

In the present article, various fundamental photoelectrochemical effects are quantitatively described and discussed, with the main emphasis on the kinetics of charge transfer processes. Although in principle the same reaction mechanisms are valid for extended semiconductor electrodes and particles, different factors govern the reaction rate, as will be discussed in detail. Finally, a brief overview of various applications will be given. 

The nonideality of both polarized ITIES and nonpolarized ITIES, the latter of which is usually employed as a reference ITIES to define the potential of the organic phase, often poses experimental difficulty in obtaining reliable kinetic parameters of charge transfer and double layer capacitance. It is worth considering in depth the degree of ideality of both ITIES before dealing with the kinetics of charge transfer at ITIES. 

Z. Samec, Kinetics of charge transfer, in Liquid-Liquid Interfaces, eds. A. G. Volkov and D. W. Deamer (CRC press, Boca Raton, 1996), pp. 155. 

All solid surfaces exhibit structural features that can have significant effects on the kinetics of charge transfer reactions and on the stability of the interfacial region. In the case of metals, the most significant structural features for "smooth" surfaces are emergent dislocations, kink sites, steps, and ledges. It has long been known, for example, that the kinetics of some electrodissolution and electrodeposition reactions depend on the density of such sites at the surface, but the exact mechanisms by which the effects occur have not been established. The role of "adion" in these processes is also unclear, as is the sequence of the dehydration-electronation-adsorption-diffusion-incorporation processes, even for the simplest of metals. 

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