Electrode kinetics relationship

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

Experimental studies of electrode kinetics resulted in the formnlation of the basic empirical relationship, the Volmer-Butler equation, (6.10) or (6.13), describing the dependence of the electric current on the electrode potential. This eqnation involves the potential E, the rate constants, and the concentrations. 

This is the basic relationship of electrode kinetics including the concentration overpotential. Equations (5.4.40) and (5.4.41) are valid for both steady-state and time-dependent currents. 

Oscillations have been observed in chemical as well as electrochemical systems [Frl, Fi3, Wol]. Such oscillatory phenomena usually originate from a multivariable system with extremely nonlinear kinetic relationships and complicated coupling mechanisms [Fr4], Current oscillations at silicon electrodes under potentio-static conditions in HF were already reported in one of the first electrochemical studies of silicon electrodes [Tul] and ascribed to the presence of a thin anodic silicon oxide film. In contrast to the case of anodic oxidation in HF-free electrolytes where the oscillations become damped after a few periods, the oscillations in aqueous HF can be stable over hours. Several groups have studied this phenomenon since this early work, and a common understanding of its basic origin has emerged, but details of the oscillation process are still controversial. 

M p = (z - l)F(pJRT. E is the electrode potential, is the standard potential, or more exactly the formal potential when activity effects cannot be neglected, and z is the charge number of the reactant. Thus, the current-electrode potential relationship characterizing the kinetics of an outer sphere electron-transfer reaction is given by (22) (/ is the current flowing through... 

In this chapter we derive the Butler-Vohner equation for the current-potential relationship, describe techniques for the study of electrode processes, discuss the influence of mass transport on electrode kinetics, and present atomistic aspects of electrodeposition of metals. 

There are two fundamentally different approaches to utilizing mass transport relationships to determine electrode kinetics. By determining electrode kinetics , we mean elucidating the dependence of the rate of the electrode reaction on the variables that affect it. For the reaction... 

The theoretical relationships for LSV and electrode kinetics were extensively developed by Matsuda and Ayabe [15]. Some theoretical peak potentials as a function of A, calculated by Nadjo and Saveant [29], are gathered in Table 14. The values in the third column were obtained by Parker [58] using the equation. 

In the previous edition of this book, Dryhurst and McAllister described carbon electrodes in common use at the time, with particular emphasis on fabrication and potential limits [1]. There have been two extensive reviews since the previous edition, one emphasizing electrode kinetics at carbon [2] and one on more general physical and electrochemical properties [3]. In addition to greater popularity of carbon as an electrode, the major developments since 1984 have been an improved understanding of surface properties and structure, and extensive efforts on chemical modification. In the context of electroanalytical applications, the current chapter stresses the relationship between surface structure and reproducibility, plus the variety of carbon materials and pretreatments. Since the intent of the chapter is to guide the reader in using commonly available materials and procedures, many interesting but less common approaches from the literature are not addressed. A particularly active area that is not discussed is the wide variety of carbon electrodes with chemically modified surfaces. 

This is the Nernst equation defined from the electrode kinetics considerations. Later, we derive the same relationship on purely thermodynamic grounds. 

Butler-Volmer equation — The Butler-Volmer or -> Erdey-Gruz-Volmer or Butler-Erdey-Gruz-Volmer equation is the fundamental equation of -> electrode kinetics that describes the exponential relationship between the -> current density and the -> electrode potential. Based on this model the -> equilibrium electrode potential (or the reversible electrode potential) can also be interpreted. 

We recall that the current is a very sensitive measure of the rate of an electrochemical reaction. It is therefore quite easy to determine the current-potential relationship without causing a significant change in the concentration of either reactants or products. Thus, measurements in electrode kinetics are conducted effectively under quasi-zero-order kinetic conditions. It would be wrong to infer from this that electrode reactions are independent of concentration. To determine the concentration dependence (i.e., the reaction order), one must obtain a series of HE or //ri plots and derive from them plots of log i versus logC. at different potentials, as shown in Fig. IF. The slopes in Fig. lF(b) yield the parameter p since p = (alog i/alogC.) is measured at constant potential E. Here, and in all further equations, we shall assume that T, P, and the concentration of all other species in solution are kept constant, to permit us to write the equations in a more concise form. 

From a phenomenological point of view, the study of electrode kinetics involves the determination of the dependence of current on potential. It is therefore appropriate that we start this book with a general qualitative description of such a relationship, as shown in Fig. lA. 

An experiment in electrode kinetics usually consists of determining the current-potential relationship under a given set of fixed conditions (temperature, concentrations). The measurement may then be repeated under a set of gradually changing conditions, to obtain the i/E plots as a function of temperature or concentration. 

The above does not imply that it is impossible to study the mechanism of alloy deposition it only shows that conclusions cannot be drawn from the usual interpretation of the directly observed current-potential relationship employed in the analysis of electrode kinetics. The partial currents for deposition of each of the alloying elements should be determined as a function of potential and other experimental parameters via determination of the atomic composition of the alloy and the FE. The FE during alloy deposition can be different from that of single-metal deposition of one or both metals involved in the process. Hence, the FE can be expected to depend on the composition of the alloy, and the thickness distribution may differ from that expected according to the current distribution." ... 

The theoretical interpretation of the first voltage drop at low current is based on the Butler-Volmer equation, which is derived by an analysis of electrode kinetics and provides a general description of the relationship between current density and surface overpotential for an electrochemical converter [46] ... 

Equation 3.26, derived by electrode kinetics, has the same form of an empirical equation proposed by Tafel [48, 49], which gives the relationship between... 

The boimdary conditions are described in more detail elsewhere. A zero-flux condition is imposed on the electrode for all species except the reactant Cu. A Tafel relationship with a concentration-dependent exchange current density was used to describe the electrode kinetics. The exchange current density was found from rotating disk experiments, and all other model parameters were taken from the literature. No parameters were adjusted for the simulations in the cell. 

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