Surface overpotential

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

Two simplifications of the Buder-Vohner expression are often encountered. First, at low surface overpotentials equation 22 can be written as... 

This limit is called linear kinetics. On the other hand, if the surface overpotential is large, one of the exponential terms is negligible. This limit is called Tafel kinetics. The relationship was found empirically. In the anodic Tafel region... 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

It is convenient to distinguish three components of the overpotential, r. Two of these are associated respectively with mass-transfer restrictions in the electrolyte near the electrode (concentration overpotential, f/c), and with kinetic limitations of the reaction taking place at the electrode surface (surface overpotential, rjs) the third one is related to ohmic resistance. 

The second component of the overpotential, rjs, is associated with the passage of reacting species and electrons across the electric double layer, discharge of the reacting species, and changes in the electrode surface structure. Following Newman (N8a), this component is called the surface overpotential. It depends on the reaction rate, the species concentrations in the double layer, and the kinetic characteristics of the electrode reaction at the surface in question. 

The ohmic contribution to the overpotential can be minimized by suitable placement of the reference electrode, but the surface overpotential cannot be reduced similarly. In making limiting-current measurements, the surface overpotential, or rather its rate of increase with current density, should be low enough to permit observation of a long, clearly defined limiting-current plateau. 

Therefore, criteria in the selection of an electrode reaction for mass-transfer studies are (1) sufficient difference between the standard electrode potential of the reaction that serves as a source or sink for mass transport and that of the succeeding reaction (e.g., hydrogen evolution following copper deposition in acidified solution), and (2) a sufficiently low surface overpotential and rate of increase of surface overpotential with current density, so that, as the current is increased, the potential will not reach the level required by the succeeding electrode process (e.g., H2 evolution) before the development of the limiting-current plateau is complete. 

For most of the reactions frequently employed in limiting-current studies, the surface overpotential is not negligible. A criterion for assessing its magnitude is the exchange-current density i0, which is a measure of the reaction rate at the equilibrium potential of the electrode (i.e., when anodic and cathodic rates are equal). 

Figure 3a is an illustration of the effect of surface overpotential on the limiting-current plateau, in the case of copper deposition from an acidified solution at a rotating-disk electrode. The solid curves are calculated limiting currents for various values of the exchange current density, expressed as ratios to the limiting-current density. Here the surface overpotential is related to the current density by the Erdey Gruz-Volmer-Butler equation (V4) ... 

It is clear from the calculated limiting-current curves in Fig. 3a that the plateau of the copper deposition reaction at a moderate limiting-current level like 50 mA cm 2 is narrowed drastically by the surface overpotential. On the other hand, the surface overpotential is small for reduction of ferri-cyanide ion at a nickel or platinum electrode (Fig. 3b). At noble-metal electrodes in well-supported solutions, the exchange current density appears to be well above 0.5 A/cm2 (Tla, S20b, D6b, A3e). At various types of carbon, the exchange current density is appreciably smaller (Tla, S17a, S17b). 

In limiting-current measurements, the counterelectrode is sometimes used as a reference electrode. In that case, the surface overpotential of the counterelectrode contributes to the recorded overpotential that is, the potential of the reference electrode is now current dependent. Unless precautions are taken (e.g., the area of the counterelectrode is much larger than that of the working electrode), a properly defined limiting-current plateau may not be obtained. 

Potentiostatic current sources, which allow application of a controlled overpotential to the working electrode, are used widely by electrochemists in surface kinetic studies and find increasing use in limiting-current measurements. A decrease in the reactant concentration at the electrode is directly related to the concentration overpotential, rj0 (Eq. 6), which, in principle, can be established directly by means of a potentiostat. However, the controlled overpotential is made up of several contributions, as indicated in Section III,C, and hence, the concentration overpotential is by no means defined when a given overpotential is applied its fraction of the total overpotential varies with the current in a complicated way. Only if the surface overpotential and ohmic potential drop are known to be negligible at the limiting current density can one assume that the reactant concentration at the electrode is controlled by the applied potential according to Eq. (6). 

A steep rise of current to the plateau. This rise would be complete within approximately 200 mV, if surface overpotential were negligible. (See, e.g., Fig. 3a, illustrating cathodic deposition of copper in which the experimental current-voltage curve indicates an appreciable surface overpotential, and Fig. 3b, illustrating cathodic reduction of ferricyanide in which the surface overpotential is negligible.)... 

In many cases mass transfer is not the sole cause of unsteady-state limiting currents, observed when a fast current ramp is imposed on an elongated electrode. In copper deposition, in particular, as a result of the appreciable surface overpotential (see Section III,C) and the ohmic potential drop between electrodes, the current distribution below the limiting current is very different from that at the true steady-state limiting current. 

Greek Letters he t. Concentration overpotential (V) Surface overpotential (V)... 

In this review, the reference electrode used is defined as a platinum metal electrode exposed to hydrogen at the same temperature and electrolyte (e.g.. Nation) as the solution of interest. With this reference electrode, the electrode overpotential defined in eq 10 is the same as having the reference electrode located next to the reaction site but exposed to the reference conditions (i.e., it carries its own extraneous phases with it). Typical values for the reference conditions are those in the gas channels. If the reference electrode is exposed to the conditions at the reaction site, then a surface overpotential can be defined... 

For the kinetic region, the values of the theoretical and experimental Tafel slopes have been shown to agree with Uc equal to i.9.io.i5o.i52-i57 If eq 13 were to be written with respect to the surface overpotential, as defined by eq 11, instead of the electrode overpotential, then it would read... 

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