Equilibrium electrode potential charge-exchange reactions

During the determination of standard electrode potentials an electrochemical equilibrium must always exist at the phase boundaries, e.g. that of the elec-trode/electrolyte. From a macroscopic viewpoint no external current flows and no reaction takes place. From a microscopic viewpoint or a molecular scale, a continuous exchange of charges occurs at the phase boundaries. In this context Fig. 6 demonstrates this fact at the anode of the Daniell element. 

The values of exchange current density observed for different electrodes (or reactions) vary within wide limits. The higher they are (or the more readily charges cross the interface), the more readily will the equilibrium Galvani potential be established and the higher will be the stability of this potential against external effects. Electrode reactions (electrodes) for which equilibrium is readily established are called thermodynamically reversible reactions (electrodes). But low values of the exchange current indicate that the electrode reaction is slow (kinetically limited). 

A common source of error in fuel cell modeling is poor use of input data which must be relevant for the studied condition. For example, the exchange current density for the charge transfer reaction have to be valid for the reference concentrations and reference electrode potential used for the calculation of the concentration overpotential, since this will determine the convergence to the correct equilibrium currents. If possible, values for transport properties must also follow the same reference state to avoid unnecessary sources of inconsistency. 

Thus, the exchange current density, i0, is a useful arbiter of the dynamic nature of the electrode reaction. The larger the i0, the faster the exchange of ions and charge takes place, although because it is equilibrium, there is no net electronation or deelectronation current. We will see shortly that i0 determines the rate of electrode reactions at any potential A —and indeed leads to the study of electrodes acting as catalysts. 

When a metal, M, is immersed in a solution containing its ions, M, several reactions may occur. The metal atoms may lose electrons (oxidation reaction) to become metaUic ions, or the metal ions in solution may gain electrons (reduction reaction) to become soHd metal atoms. The equihbrium conditions across the metal-solution interface controls which reaction, if any, will take place. When the metal is immersed in the electrolyte, electrons wiU be transferred across the interface until the electrochemical potentials or chemical potentials (Gibbs ffee-energies) on both sides of the interface are balanced, that is, Absolution electrode Until thermodynamic equihbrium is reached. The charge transfer rate at the electrode-electrolyte interface depends on the electric field across the interface and on the chemical potential gradient. At equihbrium, the net current is zero and the rates of the oxidation and reduction reactions become equal. The potential when the electrode is at equilibrium is known as the reversible half-ceU potential or equihbrium potential, Ceq. The net equivalent current that flows across the interface per unit surface area when there is no external current source is known as the exchange current density, f. 

The exchange current Iq is a measure of the rate of exchange of charge between oxidized and reduced species at any equilibrium potential without net overall change. The rate constant k, however, has been defined for a particular potential, the formal standard potential of the system. It is not in itself sufficient to characterize the system unless the transfer coefficient is also known. However, Eq. (2.21) can be used in the elucidation of the electrode reaction mechanism. The value of the transfer coefficient can be determined by measuring the exchange current density as a function of the concentration of the reduction or oxidation species at a constant concentration of the oxidation of reduction species, respectively. A schematic representation of the forward and backward currents as a function of overvoltage, 7] = E - E, is shown in Fig. 2.6, where the net current is the sum of the two components. 

---