Electrode Potential Departs from Equilibrium Overpotential

Electrode Potential Departs from Equilibrium Overpotential 

When an electrode is made a part of an electrochemical cell through which current is flowing, its potential will differ from the equilibrium potential. If the equilibrium potential of the electrode (potential in the absence of external current) is E and the potential of the same electrode as a result of external current I flowing is E (/), then the difference r] between these two potentials 

The overpotential rj is required to overcome the hindrance of the overall electrode reaction, which is usually composed of the sequence of partial reactions. There are four possible partial reactions, as described in Sect. 3.1.1 and, thus, four types of rate control charge transfer, diffusion, chemical reaction, and crystallization. Four different kinds of overpotential are distinguished and the total overpotential rj can be considered to be composed of four components 

We first consider the case in which the charge transfer is the slow step. In this case, the rate of the electrode reaction is determined by the charge-transfer overpotential, rj = rjct. It is assumed here that 

Work on the development of the modern theory of the charge-transfer overpotential started when Eyring and Wynne-Jones and Eyring formulated the absolute rate theory on the basis of statistical mechanics [3,4], This expresses the rate constant k of a chemical reaction in terms of the activation energy AG, Boltzmann s constant k% and Planck s constant h 

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Electrode Potential Departs from Equilibrium Overpotential... 

Since in cathodic reactions is always smaller than c°, the concentration polarization has a negative sign, which adds to the activation overpotential in causing the electrode to depart from the equilibrium potential in the negative direction for an electronation reaction. 

Any servicing difficulties and delays, such as preconditions that must be satisfied before electron tunneling occurs, lead to a queue of electrons on the electrode. In other words, the excess charge qM on the electrode becomes more negative, and thus the potential difference across the interface departs from the equilibrium value. The overpotential, therefore, is determined by the electron queue. 

The difference between the potential, E, when a net current flows through the electrochemical ceU and the reversible half-ceU potential, e q, is called the electrode polarization or simply the overpotential or overvoltage, tj. The overvoltage represents the extent to which the electrode solution interface departs from the equilibrium potential value. 

To deduce the mathematical relationship between the electrochemical reaction rate (cathodic or anodic) and the overpotential is beyond the scope of our present chapter and is given in books such as that by Bockris and Reddy. Nevertheless, arguments can be presented which make the relationship which we shall present acceptable. Thus, if the current density at the equilibrium in the cathodic direction (electrons to the solution from the electrode) is then as we depart from the reversible potential by an amount n (the cathodic overpotential) there should be a change in the reaction rate which will be related to exponential function of the change in the energy of activation of the reaction (cf. the Arrhenius equation, rate = and the analogous Tafel relation,... 

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