Butler-Volmer equation, electrochemical reaction

This is the most commonly employed form of the Butler -Volmer equation as it does not involve the unmeasurable surface concentration terms. It must be remembered, however, that equation (1.35) is only applicable under the conditions where [0]0 [O ] and [R]0 =t- [R ]- We must now examine this equation in some detail, as its form dictates the nature of a number of electrochemical techniques for exploring reaction mechanisms. 

Thus, cyclic or linear sweep voltammetry can be used to indicate whether a reaction occurs, at what potential and may indicate, for reversible processes, the number of electrons taking part overall. In addition, for an irreversible reaction, the kinetic parameters na and (i can be obtained. However, LSV and CV are dynamic techniques and cannot give any information about the kinetics of a typical static electrochemical reaction at a given potential. This is possible in chronoamperometry and chronocoulometry over short periods by applying the Butler Volmer equations, i.e. while the reaction is still under diffusion control. However, after a very short time such factors as thermal... 

If the electrochemical reaction obeys the Butler-Volmer equation, the current density j at an electrode potential [Pg.146]

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. 

Butler27 and Volmer28 advanced Tafel s equation by relating overpotentials to activation barriers. The quantitative relationship between current and overpotential is called the Butler-Volmer equation (eqn (32)), and is valid for electrochemical reactions that are rate limited by charge transfer. 

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.)...

For the forward reaction, the sign of b is negative, so 77 reduces the EMF. Equations 15.65, 15.68, and 15.69 can be combined and rearranged to give the Butler-Volmer equation (Eq. 15.70) for the net current density, i, of an electrode process involving a single electrochemical step ... 

Derivation of the Butler-Volmer equation in terms of electrode reaction rate constants is given in most electrochemical texts.1,3 7 15... 

There is a good economic reason for this. Look back at the Butler Volmer equation (Eq. 7.24) the larger the ifl (Le., the better the catalysis), the smaller the overpotential needed to get a given rate of reaction. However, the smaller the overpotential, the less the total cell potential, and hence the kilowatt hours, to produce a given amount of a substance in an electrochemical reactor. 

Our chapter has two broad themes. In the first, we will consider some aspects of quantum states relevant to electrochemical systems. In the second, the theme will be the penetration of the barrier and the relation of the current density (the electrochemical reaction rate) to the electric potential across the interface. This concerns a quantum mechanical interpretation of Talel s experimental work of 1905, which led (1924-1930) to the Butler-Volmer equation. 

It is an experimental fact that whenever mass transfer limitations are excluded, the rate of charge transfer for a given electrochemical reaction varies exponentially with the so-called overpotential rj, which is the potential difference between the equilibrium potential F0 and the actual electrode potential E (t) = E — Ed). Since for the electrode reaction Eq. (1) there exists a forward and back reaction, both of which are changed by the applied overpotential in exponential fashion but in an opposite sense, one obtains as the effective total current density the difference between anodic and cathodic partial current densities according to the generalized Butler-Volmer equation ... 

Since the electrochemical reactions are supposed to take place at the electrodeelectrolyte interface, then the Butler-Volmer equation, regulating the electrochemical kinetics, sets the boundary condition, whilst j (production rate) in Equation (3.37) is replaced with J (current density produced), as explained in detail in Section 3.7.2. 

Here the subscripts s and m denote solid (electrodes and current collectors) and membrane (electrolyte) respectively. Note that these two equations can be treated as only one equation with variable a and source terms. The R s are the volumetric transfer currents due to electrochemical reaction which are non-zero only in the catalyst layers and can be calculated from the Butler-Volmer equation for anode and cathode sides as ... 

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]. 

The Nemst equation is a thermodynamic expression of the equilibrium state of an electrochemical reaction. It can give the value of the thermodynamic electrode potential for electrochemical reactions as well as point out the reaction direction. However, it cannot show the reaction rate. To connect the reaction rate and the electrode potential, one needs to use the Butler-Volmer equation. 

HOR and the ORR involve two and four electrons, respectively. Since the Butler-Volmer equation is important for expressing the relationship between the current density of an electrochemical reaction and the overpotential, the rate-determining step (RDS) of a multi-electron reaction can be simplified as a pseudo-elementary reaction involving multiple electrons. The Butler-Volmer equation for this reaction is usually written as follows ... 

This is of course also true if we need to consider the general electrochemical reaction Eq. (92). If the applied driving force (cf. electrical experiment) is an electrical potential gradient, Eq. (97) leads to the well-known non-linear Butler-Volmer equation.79 We will become acquainted with equally important kinetic equations for the cases of the tracer and the chemical experiment.172... 

The rate of electron transfer and its potential dependence can be described by the Butler-Volmer equation (20) (see Section 2). An electron transfer often initiates a cascade of homogeneous chemical reactions by producing a reactive radical anion/cation. The mechanism can be described mathematically by a rate equation for each species these form part of the electrochemical model. The rate law of the overall sequence is probed by the voltammetric experiment. 

The region of kinetic control of electrochemical reactions is characterized by current densities that are exponential functions of potential. For a single reversible reaction, the Butler-Volmer equation... 

The relationship between overpotential and current density of a single, activation-controlled electrochemical reaction is the Butler-Volmer equation, Eq. (10). As the equation shows, the rates of anodic and cathodic partial reactions are exponentially dependent on the overpotential. The net current is the sum of the anodic and cathodic partial currents. 

This is one of the few electrode reactions that does not follow the Butler-Volmer equation. The reason is that the dual-site dissociatidn of the H2 molecule is the rate-controlling step. But although this is a non-electrochemical step, the reaction rate is still a function of the potential, because the hydrogen oxidation is self-... 

E and the reversible equilibrium potential of the electrochemical reaction Thus the driving force for the electrochemical reaction is not the absolute potential it is the activation overpotential riaof This relationship between the current density and activation overpotential has been further developed and resulted in the Butler-Volmer equation ... 

Therefore, the current density depends on the exchange current density ( o), transfer coefficient ( p), overpotential r ), and temperature (r). Fig. 7 represents typical current-overpotential curves based on Eq. (39). The net current is the result of the combined effects of the forward (anodic) and reverse (cathodic) currents. Although the Butler-Volmer equation for an electrochemical reaction in PEMFC is valid over the full potential range, simpler approximate equations may often be used for limited conditions. Thus, for the common value dp = 1/2, Eq. (39) becomes... 

As described above, if this electrochemical reaction is driven out of equilibrium with the thermodynamic force ry, a current / will flow. One of the great successes of electrochemistry is its ability to provide a quantitative description of the charge transfer current characteristics. Max Volmer (1885—1965) and John Alfred Valentine Butler (1899—1977) proposed the following relation, which is known today as the Butler—Volmer equation, between the over potential 7j and the current density j (Fig. 3.4) ... 

Figures 26.2 and 26.3 show typical current density-overpotential plots where i varies exponentially with r s, in accordance with the Butler-Volmer equation. In Figure 26.2, the effect of varying P on )-r 5 curves is shown (as P decreases, i increases at a given value of 1I5). The increase in current density at a given for increasing values of i is shown in Figure 26.3. From these two figures it can be concluded that electrochemical reactions that follow Butler-Volmer kinetics will be facile when the kinetic parameter p is small and the value of is large.

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