Electrode kinetics Butler-Volmer equation

Electrode kinetics electrode, kinetics, Butler-Volmer equation, -> charge transfer kinetics, - Marcus... 

Figure 5. Measurement and analysis of steady-state i— V characteristics, (a) Following subtraction of ohmic losses (determined from impedance or current-interrupt measurements), the electrode overpotential rj is plotted vs ln(i). For systems governed by classic electrochemical kinetics, the slope at high overpotential yields anodic and cathodic transfer coefficients (Ua and aj while the intercept yields the exchange current density (i o). These parameters can be used in an empirical rate expression for the kinetics (Butler—Volmer equation) or related to more specific parameters associated with individual reaction steps.(b) Example of Mn(IV) reduction to Mn(III) at a Pt electrode in 7.5 M H2SO4 solution at 25 Below limiting current the system obeys Tafel kinetics with Ua 1/4. Data are from ref 363. (Reprinted with permission from ref 362. Copyright 2001 John Wiley Sons.)...

Hydrogen evolution, the other reaction studied, is a classical reaction for electrochemical kinetic studies. It was this reaction that led Tafel (24) to formulate his semi-logarithmic relation between potential and current which is named for him and that later resulted in the derivation of the equation that today is called "Butler-Volmer-equation" (25,26). The influence of the electrode potential is considered to modify the activation barrier for the charge transfer step of the reaction at the interface. This results in an exponential dependence of the reaction rate on the electrode potential, the extent of which is given by the transfer coefficient, a. 

If the electrode reaction (1.1) is kinetically controlled, (1.8) mnst be snbstituted by the Butler-Volmer equation ... 

Considering kinetically controlled process at the electrode surface without lateral interactions between immobilized species, the following form of the Butler-Volmer equation holds ... 

Activation polarization arises from kinetics hindrances of the charge-transfer reaction taking place at the electrode/electrolyte interface. This type of kinetics is best understood using the absolute reaction rate theory or the transition state theory. In these treatments, the path followed by the reaction proceeds by a route involving an activated complex, where the rate-limiting step is the dissociation of the activated complex. The rate, current flow, i (/ = HA and lo = lolA, where A is the electrode surface area), of a charge-transfer-controlled battery reaction can be given by the Butler—Volmer equation as... 

The Butler-Volmer equation has yielded much that is essentia] to the first appreciation of electrode kinetics. It has not, however, been mined out. One has to dig deeper, and after electron transfer at one interface has been understood in a more general way, electrochemical systems or cells with two electrode/electrolyte interfaces must be tackled. It is the theoretical descriptions of these systems that provide the basis... 

The introduction of 0 in the equations for current density need by no means refer only to the adsorbed intermediates in the electrode reaction. What of other entities that may he adsorbed on the surface For example, suppose one adds to the solution an oiganic substance (e.g., aniline) and this becomes adsorbed on the electrode surface. Then, the 0 for the adsorbed organic substance must also be allowed for in the electrode kinetic equations. So, in Eq. (7.149), the value of 0 would really have to become a 0, where the summation is over all the entities that remain upon the surface and block off sites for the discharging entities. Many practical aspects of electrodics arise from this aspect of the Butler-Volmer equation. For example, the action of organic corrosion inhibitors partly arises in this way (adsorption and blocking of the surface of the electrode and hence reduction of the rate of the corrosion reaction per apparent unit area).67... 

The third exponential term in eqn. (187) is identical to the exponential term in the Butler—Volmer equation, eqn. (80), in the absence of specific adsorption. The first two exponential factors in eqn. (187) corresponding to the variation in the electrical part of the free energy of adsorption of R and O with and without specific adsorption A(AGr) and A(AG0), respectively. The explicit form of as, the activity of the adsorption site, and potential dependence of as, A(AGr) and A(AG0) is necessary for a complete description of the electrode kinetics. 

In this chapter we derive the Butler-Volmer 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. 

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. 

This equation (Tafel equation) is of fundamental importance in studies of electrode kinetics. It is actually an approximation of the - Butler-Volmer equation at... 

Volmer turned his attention to processes at - nonpo-larizable electrodes [iv], and in 1930 followed the famous publication (together with - Erdey-Gruz) on the theory of hydrogen - overpotential [v], which today forms the background of phenomenological kinetics of electrochemistry, and which resulted in the famous - Butler-Volmer equation that describes the dependence of the electrochemical rate constant on applied overpotential. His major work, Kinetics of Phase Formation , was published in 1939 [v]. See also the Volmer reaction (- hydrogen), and the Volmer biography with selected papers [vi]. 

This mechanism is denoted as an EC mechanism (Testa and Reinmuth, 1961 Bott, 1997). Thus homogeneous kinetic terms may be combined with the expressions for diffusion and convection [i.e. a modified version of (18)] to give the temporal variation of the concentration of a species in an electrode reaction mechanism. In order to model the voltammetric response associated with this mechanism, a knowledge of , a, ko and k is required, or deduced from a theoretical-experimental comparison, and the set of concentrationtime equations for species A, B and C must be solved subject to the constraints of the Butler-Volmer equation and the experimental design. Considerable simplification of the theory is achieved if the kinetics for the forward and reverse processes associated with the E step are fast, which is a good approximation for many organic reactions. Section 7 describes the approaches used to solve the equations associated with electrode reaction mechanisms, thus enabling theoretical simulation of voltammetric responses to be achieved. 

The charge-transfer kinetics of an electrochemical electrode can be formally treated on the basis of the Butler-Volmer equation. The overvoltage t/ct is then given by... 

The net rate of electrochemical current generation in an electrode section is given by the Butler-Volmer equation, a fundamental relation in electrode kinetics [109],... 

It is fair to say that the effect of ultrasound upon the fundamental electron transfer processes at an electrode have been less widely studied than the effects upon mass transport phenomena. Electrode kinetics is defined by the Butler—Volmer equation, which by a series of practical assumptions reduces to the Tafel equation [44],... 

The electron transfer process across the electrode/electrolyte interface is a heterogeneous reaction. The rate at which electron transfer takes place across that interface is described in terms of a heterogeneous electron transfer rate constant. The kinetics can be described via the Butler-Volmer equation ... 

A theoretical current-potential curve (/7/q vs. fj) is given in Fig. 7.3 for r] = 0.5. It should be emphasized here that Eq. (7.11) is only valid in this simple form if the current is really kinetically controlled, i.e. if diffusion of the redox species toward the electrode surface is sufficiently fast. According to the Butler-Volmer equation (Eq. 7.11) the current increases exponentially with potential in both directions. In this aspect charge transfer processes at metal electrodes differ completely from those at semiconductors. When the overpotential is sufficiently large, erj/kT 1. one of the exponential terms in Eq. (7.11) can be neglected compared to the other. In this case we have either... 

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] ... 

Bockris Reddy (1970) describes the Butler-Volmer-equation as the "central equation of electrode kinetics . In equilibrium the adsorption and desorption fluxes of charges at the interface are equal. There are common principles for the kinetics of charge exchange at the polarisable mercury/water interface and the adsorption kinetics of charged surfactants at the liquid/fluid interface. Theoretical considerations about the electrostatic retardation for the adsorption kinetics of ions were first introduced by Dukhin et al. (1973). 

The Butler-Volmer equation describes the kinetics for electrochemical reactions that are controlled by the transfer of charge across the interface. It has been derived here in a simpKfied way. For a more complete discussion of charge transfer reactions and of electron tunneling, the reader is referred to the volume of this series dealing with electrode kinetics. 

Fig. 4 Electrode kinetics as expressed by the Butler-Volmer equation (a) symmetrical curve when a = 0.5 and (b) symmetrical curve when a f=0.5.

In the case of energy producing power sources, the equifibrium shifts to one side, resulting in the flow of net current and the subsequent loss of equifibrium at the electrode. A system of this nature is said to be polarized. The net current that flows through the polarized system at any given overpotential is <=(electroactive species in the bulk and at the electrode interface are equal which reduces Eq.(3.23) to the Butler-Volmer equation (3.28), which is a fundamental equation in electrode kinetics. 

This is the well-known Butler-Volmer equation for electrode kinetics in the absence of mass transfer effects between electrode and electrolyte. 

The existence of the EDL at an interface is of crucial importance for all interfacial electrochemical phenomena, in particular for the kinetics of electrode reactions. In most cases the principal factors influencing their rate are the overall potential difference across the interface (e.g. according to the Butler-Volmer equation for a simple ET reaction) and the specific adsorption of reactants, reaction products or intermediates. However, there are important cases in which the diffuse layer plays a dominant role [47, 48]. 

It is obvious that this reaction can only lead to metal dissolution, if the metal electrode potential is negative from the hydrogen electrode potential. This is the reason for the classification of metals into noble metals (the equilibrium potential is more positive than the standard hydrogen potential) and non-noble metals (the equilibrium potential is more negative than the standard hydrogen potential). The kinetic of the total process can be described by the Butler-Volmer equation for the two partial reactions. 

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