Overpotentials definition

It must be emphasized that Equations (5.24) and (5.25) stem from the definitions of Fermi level, work function and Volta potential and are generally valid for any electrochemical cell, solid state or aqueous. We can now compare these equations with the corresponding experimental equations (5.18) and (5.19) found to hold, under rather broad temperature, gaseous composition and overpotential conditions (Figs. 5.8 to 5.16), in solid state electrochemistry ... 

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. 

The current is zero at equilibrium. Indeed, = 0 is one definition of equilibrium (see Chapter 2). As the potential is shifted away from V equilibrium so the electrode is polarized (cf Section 6.1). We recall that the deviation of the potential from its equilibrium value is termed the overpotential q (as defined by equation (6.1)). The portion of the Tafel graph at extreme overpotentials represents insufficient flux at the electrode in effect, the potential is so extreme that extra charge could flow if sufficient flux were available but, because of solvent viscosity, rate of solution stirring, etc., the flux is simply not large enough for the behaviour to follow the Tafel equation. 

Figure 7.17 shows a summary of the available conditions of water electrolysis [72]. For each configuration there exists a range of performance. Conventional electrolyzers, which nevertheless are still the most common in the current production of H 2 on the intermediate and small scale, show high overpotential and a relatively small production rate. Membrane (SPE) and advanced alkaline electrolyzers show very similar performance, with somewhat lower overpotential but a much higher production rate. Definite improvements in energy consumption would come from high temperature (steam) electrolysis, which is, however, still far from optimization because of a low production rate and problems of material stability. 

Charge transfer resistance, 1056 Charge transfer overpotential, 1231 Charge transfer, partial. 922. 954 Charges in solution, 882 chemical interactions, 830 Charging current. 1056 Charging time, 1120 Chemical catalysis, 1252 Chemical and electrochemical reactions, differences, 937 Chemical equilibrium, 1459 Chemical kinetics, 1122 Chemical potential, 937, 1058 definition, 830 determination, 832 of ideal gas, 936 interactions, 835 of organic adsorption. 975 and work function, 835... 

Chronopotentiometry, galvanostatic transients, 1411 as analytical technique, 1411 activation overpotential, 1411 Clavilier, and single crystals, 1095 Cluster formation energy of, 1304 and Frumkin isotherm, 1197 Cobalt-nickel plating, 1375 Cold combustion, definition, 1041 Cole-Cole plot, impedance, 1129, 1135 Colloidal particles, 880, 882 and differential capacity, 880 Complex impedance, 1135 Computer simulation, 1160 of adsorption processes, 965 and overall reaction, 1259 and rate determining step, 1260... 

Now, it is necessary to define a new and central term. It is called the overpotential, t. It refers to the departure of the potential of the electrode from its equilibrium value, A e. By making T negative, one can push excess electrons into the electrode and provoke a net exiting of electrons from metal to solution one can provoke the entry of electrons. Suppose we impose (using the outside power source) a shift (1)) in the electrode potential from the equilibrium value in a negative direction. The new interfacial potential is to be A< >. Then, the definition of overpotential is... 

In words, the overpotential is a deviation of the Galvani potential of the electrode from the value it has when the rate of charge flow across its interface with the solution is equal in each direction for the reaction concerned (i.e., Mz+. + ze M). The definition given in Eq. (7.14) is general, although it is necessary to define the electrode reaction concerned, the solution composition, etc., because the value of the thermodynamic A e is different for each electrode reaction, concentration of reactant, and temperature. 

For large absolute values of q, only that component of the electrode process favoured by the direction of the overpotential need be considered, i.e. the back reaction can be neglected. From the definitions of rc and ia we have... 

These relationships can be combined to give an expression for the net current density (j), which by definition is equal to j — jc in terms of the activation overpotential (substitute rj + AEe = AE), which is referred to as the Butler-Volmer equation ... 

The method which seems theoretically most nearly sound is that of Bowden and Ridcal.4 These authors measured the quantity of electricity which had to be passed in order to build up a definite overvoltage on a metal surface. There is reason to believe that this quantity, i.e. the number of ions per square centimetre for each millivolt of overpotential is independent or nearly so of the nature of the metal therefore the true area of the nietal surface is proportional to the quantity of electricity needed to build up a given overpotential. It was first assumed that the real area of a mercury surface was equal to the apparent area with this assumption the real area of various smooth or polished metals appeared... 

Consider now what happens at equilibrium. The overpotential is, by definition, zero and so is the net current density. This leads to... 

This definition of overpotenlial is phenomenological and is always valid, irrespective of the reasons for the deviation of the potential from its reversible value. The overpotential is always defined with respect to a specific reaction, for which the reversible potential is known. When more than one reaction can occur simultaneously on the same sdectrode, there is a different overpotential with respect to each reaction, for any value of the measured potential. Tliis situation is encountered most commonly during the corrosion of metals. When iron fOOrrodes, for example, in a neutral solution, the overpotential may be... 

Equation 3IE represents the rate of an anodic oxidation reaction for which the overpotenlial is, by definition, positive. For a cathodic reduction we write a similar equation with a negative sign in the exponent, and we take the overpotential, by definition, to be negative. In either case the current density increases exponentially with increasing absolute value of the overpotential. 

Now we come to the concept of quasi-equilibrium. If there is a distinct rate-determining step in a reaction sequence, then all other steps before and after it must be effectively at equilibrium. This comes about because the overall rate is, by definition, very slow compared to the rate at which each of the other steps could proceed by itself, and equilibrium in these steps is therefore barely disturbed. To see this better, consider the specific example given earlier for chlorine evolution. Assume, for the sake of argument, that the values of the exchange current density i for steps 8F and 9F are 250 and 1.0 mA/cm, respectively. Assume now that we apply a current density of 0.5 mA/cm. We can calculate the overpotential corresponding to each step in the sequence, using Eq. 6E, namely... 

Me/Me + respectively. This definition supposes that all additional steps involved in reaction (1.1) such as charge transfer, diffiision, and chemical reactions are fast, so that they can be considered to be in thermodynamic equilibrium. Then, as their contribution to the overpotential can be neglected 7/totai Vc Me deposition happens... 

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