Exchange current density concentration dependence

Exchange current density is dependent on the concentrations of reactants and products ... 

The exchange current density still depends on the concentration of the redox components. A constant, describing the rate of a redox reaction not dependent on concentration, is defined in Eq. (6.16) and could be recommended for comparisons and tabulation... 

The exchange current density for methanol oxidation depends on the methanol concentration, i.e. ... 

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. 

The dimensionless limiting current density N represents the ratio of ohmic potential drop to the concentration overpotential at the electrode. A large value of N implies that the ohmic resistance tends to be the controlling factor for the current distribution. For small values of N, the concentration overpotential is large and the mass transfer tends to be the rate-limiting step of the overall process. The dimensionless exchange current density J represents the ratio of the ohmic potential drop to the activation overpotential. When both N and J approach infinity, one obtains the geometrically dependent primary current distribution. 

Figure 11.3 Dependence of the exchange current density jo for the deposition of silver on the concentration of cyanide. Data taken from Ref. 2.

The activation overpotentials for both electrodes are high therefore, the electrochemical kinetics of the both electrodes can be approximated by Tafel kinetics. The concentration dependence of exchange current density was given by Costamagna and Honegger.The open-circuit potential of a SOFC is calculated via the Nernst equation.The conductivity of the electrolyte, i.e., YSZ, is a strong function of temperature and increases with temperature. The temperature dependence of the electrolyte conductivity is expressed by the Arrhenius equation. 

The exchange current density is the electrode reaction rate at the equilibrium potential (identical forward and reverse reaction rates) and depends on the electrode properties and operation. The typical expression for determining the exchange current density is the Arrhenius law (3.23), where the constant A depends on the gas concentration. Costamagna et al. [40] provide the following expressions for the anodic and cathodic exchange current density, respectively ... 

Here subscripts a and c denote anode and cathode respectively, iref is the reference exchange current density, y is the concentration dependence exponent, [ ] and [ ]ref represent the local species concentration and its reference concentration, respectively. Anode transfer current, Ra, is the source in the electric potential equations at the anode/electrolyte interface with positive sign on membrane (electrolyte) side and negative sign on solid (anode) side. Similarly, near the cathode interface, the source on membrane (electrolyte) side is negative of the cathode transfer current, Rc and that on solid (cathode) side is positive of Rc. The activation over-potentials, in Equations (5.35) and (5.36) are given by... 

Equation 38E shows that the exchange current density is a function of the concentration of both reactants and products. This relationship is also implicit in Eq. 34E, considering that the rate constants in this equation depend exponentially on, which itself is a function of... 

The exchange current density, which governs the rate of attainment of electrode equilibrium, varies enormously from one potential-determining redox couple to another. It varies not only with the initial concentration but also with the ratio of oxidant to reductant [Equation (14-14)]. In titrations performed at great dilution, the equilibrium near the end point may be reached slowly. Therefore, it may be advantageous to select a method of end-point detection that is not dependent on equilibrium near the end point. 

The exchange current density /q is assumed to depend on the surface concentration of metal ion, according to... 

According to eq. (2.21), the exchange current density of kink atoms, io,kink. depends on the concentration of kink atoms kink- As long as the surface profile of a crystal face, which depends on the pretreatment and includes an arbitrary number of steps populated by kinks, the exchange current density of kink atoms is not a constant quantity, but depends on step density L or on the surface topography. It cannot be considered as a system property. 

Taking into account that the exchange current density depends on the concentration of reacting ion, it follows that the growth of dendrites12,21,22 inside the diffusion layer of the macroelectrode is in fact under mixed activation-diffusion control. Hence, it can be expected that the process on the microelectrodes placed on the surface of the inert macroelectrode can be under mixed control. This is because the charge transfer occurs on the microelectrodes, while the mass-transfer limitations are related to the diffusion layer of the macroelectrode. 

A similar expression is obtained for a nonelementary reaction. The exchange current density Iq expresses the rate of the forward and backward step at the reversible electrode potential and depends on concentration. Equation (9) is usually rewritten in terms of ig in electrode kinetics... 

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