Current density-overpotential coefficients

Figure 2.4 Current density—overpotential curves of 0 -i- nae <- / reaction at three different electron-transfer coefficients (a = 0.25, 0.5, and 0.75, respectively), calculated according Eqn (Z28a) using the parameter values of = / =8.314 J mol, T=298 K, F=96,487 CmoP, and /=1.0x 10 Acm . (For color version of this...

Tills must be regarded as the fundamental equation of electrode kinetics, and it shows the way in which current density varies with exchange current density, overpotential, and the transfer coefficients. In the laboratory it is, however, more common to use one of the three limiting forms of Equation (1.31). The first two apply at high overpotentials. At high positive overpotentials / > /, and the second term may be ignored the anodic current density if then given by... 

In order to obtain a definite breakthrough of current across an electrode, a potential in excess of its equilibrium potential must be applied any such excess potential is called an overpotential. If it concerns an ideal polarizable electrode, i.e., an electrode whose surface acts as an ideal catalyst in the electrolytic process, then the overpotential can be considered merely as a diffusion overpotential (nD) and yields (cf., Section 3.1) a real diffusion current. Often, however, the electrode surface is not ideal, which means that the purely chemical reaction concerned has a free enthalpy barrier especially at low current density, where the ion diffusion control of the electrolytic conversion becomes less pronounced, the thermal activation energy (AG°) plays an appreciable role, so that, once the activated complex is reached at the maximum of the enthalpy barrier, only a fraction a (the transfer coefficient) of the electrical energy difference nF(E ml - E ) = nFtjt is used for conversion. 

Fig. 5.2 Dependence of the relative current density j/j0 on the overpotential rj according to Eq. (5.2.28). Various values of the charge transfer coefficient a are indicated at each curve. Dashed curves indicate the partial current densities (Eqs 5.2.11 and 5.2.12 for a = 0.5). (According to K. Vetter)...

In the first case, the rate of deposition depends on the equilibrium concentration of ad-atoms, on their diffusion coefficient, on the exchange current density and on the overpotential. In the second case, the rate of deposition is a function, besides of the geometric factors of the surface, of the exchange current and the overpotential. This mechanism is valid, for example, in the deposition of silver from a AgN03 solution. 

Consider the reaction with two consecutive electron-transfer steps described by Eq. (11.12). (a) Show that, if j0,2 j0,1, there is an intermediate range of negative overpotentials in which the apparent transfer coefficient is (2 — ai) and the apparent exchange current density 2j0,i (see Fig. 11.1). (b) Derive the form of the Tafel plot for jo,i > jo,2-... 

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.)...

Faraday s constant (96,487 C/mol) overpotential total current current density exchange current density ratio of ohmic constriction to inter-facial resistance surface exchange coefficient volume-specific interfacial resistance in a composite thickness utilization length characteristic length of a porous microstructure... 

This equation gives the relationship between the current density i and the charge-transfer overpotential rj in terms of two parameters, the exchange current density Iq and the transfer coefficient a. Eigure 6.7 depicts the variation of the partial current densities and the net current density with overpotential. It can be seen that for large... 

The overpotentia] measured at a current density of 10-5 A/cm2 was +0.236 V. The decay of the overpotential with the cut off of the current was observed as listed Table P.l. Calculate the double-layer capacitance, the exchange current density, and the transfer coefficient for the electrochemical reaction. (Kim)... 

For a given overpotential, the effective current density depends on the magnitude of the charge-transfer coefficient a as well as on the exchange current density iu. If the overpotential is high enough—that is, if either —(a Frj/RT) or (a Fr/)/RT > 1—then one of the partial current densities in the Butler-Volmer equation overrules the other ... 

Figure 1 a explains schematically in a linear and a semilogarithmic plot of current densities i versus overpotentials how charge-transfer coefficients a are determined by extrapolating the slopes of the semilogarithmic current... 

Equation (80) relates the current density that flows through the electrode—electrolyte interface due to the electrode reaction to the overpotential in terms of two kinetic parameters, the exchange current density, j0, and the transfer coefficient, a. 

Arrhenius plots of conductivity for the four components of the elementary cell are shown in Fig. 34. They indicate that electrolyte and interconnection materials are responsible of the main part of ohmic losses. Furthermore, both must be gas tight. Therefore, it is necessary to use them as thin and dense layers with a minimum of microcracks. It has to be said that in the literature not much attention has been paid to electrode overpotentials in evaluating polarization losses. These parameters greatly depend on composition, porosity and current density. Their study must be developed in parallel with the physical properties such as electrical conductivity, thermal expansion coefficient, density, atomic diffusion, etc. 

Consider two half-cell reactions, one for an anodic and the other for a cathodic reaction. The exchange current densities for the anodic and the cathodic reactions are lO-6 A/cm2 and 1(T2 A/cm2, respectively, with transfer coefficients of 0.4 and 1, respectively. The equilibrium potential difference between the two reactions is 1.5 V. (a) Calculate the cell potential when the current density of 1CT5 A/cm2 flows through the self-driving cell, neglecting the concentration overpotentials. The solution resistance is 1000 Q cm2, (b) What is the cell potential when the current density is 10-4 A/cm2 (Kim)... 

To make Tafel plots (Figure 8.15) [124,125] subsequent to the subtraction of the ohmic losses (iR), the electrode overpotential, p, is plotted versus ln(.//./0). For systems controlled by standard electrochemical kinetics, the slope at a high overpotential gives the anodic and the cathodic transference coefficients, aA and ac, respectively, and the intercept gives the exchange current density, J0. 

Tafel plot — Figure 1. Calculated charge transfer current density j as a function of - overpotential r assuming a transfer coefficient a = 0.5 and an exchange current density jo = 0.1 A cm2, and, in simplified... 

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