Electrochemical reactions overpotential

Overpential and Tafel equation. In Eqn (2.28), the term of E is called the overpotential (77), that is, 7 = F —F , which is used to measure the reversibility of the electrochemical reaction. Overpotential is the driving force of the electrode reaction the larger the overpotential, the faster the electrode reaction rate would be. From Bulter—Volmer Eqn (2.28a), it can be seen that when this overpotential is negative enough. 

So far, uncatalysed electrochemical processes have had to compete with catalytic organic processes. There is considerable scope for a specific catalyst to be developed for specific organic electrochemical reactions. This implies reduced overpotential and acceleration of slow chemical rather than relatively fast charge-transfer steps (Jansson, 1984). Electrocatalysis... 

The usual Tafel evaluation yielded a transfer coefficient a = 0.52 and a rate constant k of 4x 10 cm s at the standard potential of the MV /MV couple. This k value corresponds to a moderately fast electrochemical reaction. In this electrode-kinetic treatment the changes in the rate of electron transfer with pH were attributed only to the changes in the overpotential. A more exact treatment should also take into account the electrostatic effect on the rate of reaction which also changes with pH. 

In general, the physical state of the electrodes used in electrochemical processes is the solid state (monolithic or particulate). The material of which the electrode is composed may actually participate in the electrochemical reactions, being consumed by or deposited from the solution, or it may be inert and merely provide an interface at which the reactions may occur. There are three properties which all types of electrodes must possess if the power requirements of the process are to be minimized (i) the electrodes should be able to conduct electricity well, i.e., they should be made of good conductors (ii) the overpotentials at the electrodes should be low and (iii) the electrodes should not become passivated, by which it is meant that they should not react to form on their surfaces any compound that inhibits the desired electrochemical reaction. Some additional desirable requirements for a satisfactory performance of the cell are that the electrodes should be amenable to being manufactured or prepared easily that they should be resistant to corrosion by the elements within the cell that they should be mechanically strong and that they should be of low cost. Electrodes are usually mounted vertically, and in some cases horizontally only in some rare special cases are they mounted in an inclined manner. 

This energy is consumed to overcome the overpotentials of the electrode reactions (rja, rjc), the IR drop in the external circuit and electrolyte, and it might partly be converted into the free energy, AG, of stable products (if any) of the endoergic electrochemical reaction ... 

The classical electrochemical methods are based on the simultaneous measurement of current and electrode potential. In simple cases the measured current is proportional to the rate of an electrochemical reaction. However, generally the concentrations of the reacting species at the interface are different from those in the bulk, since they are depleted or accumulated during the course of the reaction. So one must determine the interfacial concentrations. There axe two principal ways of doing this. In the first class of methods one of the two variables, either the potential or the current, is kept constant or varied in a simple manner, the other variable is measured, and the surface concentrations are calculated by solving the transport equations under the conditions applied. In the simplest variant the overpotential or the current is stepped from zero to a constant value the transient of the other variable is recorded and extrapolated back to the time at which the step was applied, when the interfacial concentrations were not yet depleted. In the other class of method the transport of the reacting species is enhanced by convection. If the geometry of the system is sufficiently simple, the mass transport equations can be solved, and the surface concentrations calculated. 

Butler27 and Volmer28 advanced Tafel s equation by relating overpotentials to activation barriers. The quantitative relationship between current and overpotential is called the Butler-Volmer equation (eqn (32)), and is valid for electrochemical reactions that are rate limited by charge transfer. 

Electrochemistry is in many aspects directly comparable to the concepts known in heterogeneous catalysis. In electrochemistry, the main driving force for the electrochemical reaction is the difference between the electrode potential and the standard potential (E — E°), also called the overpotential. Large overpotentials, however, reduce the efficiency of the electrochemical process. Electrode optimization, therefore, aims to maximize the rate constant k, which is determined by the catalytic properties of the electrode surface, to maximize the surface area A, and, by minimization of transport losses, to result in maximum concentration of the reactants. 

Steady-State Kinetics, There are two electrochemical methods for determination of the steady-state rate of an electrochemical reaction at the mixed potential. In the first method (the intercept method) the rate is determined as the current coordinate of the intersection of the high overpotential polarization curves for the partial cathodic and anodic processes, measured from the rest potential. In the second method (the low-overpotential method) the rate is determined from the low-overpotential polarization data for partial cathodic and anodic processes, measured from the mixed potential. The first method was illustrated in Figures 8.3 and 8.4. The second method is discussed briefly here. Typical current—potential curves in the vicinity of the mixed potential for the electroless copper deposition (average of six trials) are shown in Figure 8.13. The rate of deposition may be calculated from these curves using the Le Roy equation (29,30) ... 

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... 

A Quantitative Version of the Dependence of the Electrochemical Reaction Rate on Overpotential ... 

In section B-C, the fraction of the current used to charge the interfacial region to the designated overpotential is progressively reduced and more and more of the current flowing between electrode and solution is due to electrons that cross the interfacial region and take part in the electrochemical reaction. By C, all the electrons (for i, at T),) are being used in the electrode reaction which then, from a simplistic point of view, should continue to flow at a constant rate independent of time. 

When one examines the rate of an electrochemical reaction and how it varies with overpotential, it is often found that equations such as (7.150) and (7.150a) (which depend on a Langmuir assumption as to the implied isotherm) are obeyed, and there is no need to modify the kinetic equations to allow for a special isotherm. 

However, electrochemical reactions generally occur at t RT/F. Such reactions are called irreversible and the physical occurrences that govern the degree of overpotential that has to be developed to make a given i flow depend on the chemical physics of the interface—the work function of the electrode and the bond strength of its surface atoms, etc.82 (Chapter 9). 

As has been made abundantly clear in Section 7.2.3, when an electrode reaction is controlled by interfacial reactions—not by transport to the electrode in the solution or (as in semiconductors) within the electrodes—the electrochemical reaction rale depends exponentially on the overpotential. Thus, regarding the approximate equations ... 

How many times higher than the exchange current density does the limiting current density for the electrochemical reaction ox(soln) + e = red(soln) have to be to assume that the reaction is activation controlled at an overpotential of -300 mV (Take p = 0.5 and T= 298 K.) (Gokjovic)... 

The current density for an overall electrochemical reaction (A + 2e - C) was measured as a function of the overpotential listed in Table P.l. Develop the mechanism of the reaction and find the rate-determining step, assuming a symmetry factor of 0.5. 

In the case of very fast electrochemical reactions, it can be assumed that an overpotential is caused only by slow transport of reacting particles from the bulk of the solution toward the electrode surface and that the activation overpotential is negligible. What is the error of that approximation for the electrochemical... 

Fig. 8.5. In electrochemical reactions involving one or more adsorbed reaction intermediates (sometimes involved in the rate-determining step), the steady-state concentration of the intermediate changes with the potential. However, each intermediate has a time constant to reach the surface coverage corresponding to a given overpotential. The downside of too low a pulse time, or too fast a sweep rate, is that the intermediate concentration does not relax to its appropriate concentration in time. The Tafel slope (sometimes a significant mechanism indicator) may then differ from that calculated for the assumed path and rate-determining step.

The overpotentia] measured at a current density of 10-5 A/cm2 was +0.236 V. The decay of the overpotential with the cut off of the current was observed as listed Table P.l. Calculate the double-layer capacitance, the exchange current density, and the transfer coefficient for the electrochemical reaction. (Kim)... 

Marcus stressed that only harmonic modes U = were involved in the ion-solvent interactions and went further than Weiss in formulating a simple equation for the rate of adiabatic electron transfer, taking the case of an isotopic reaction so that the AG° term was eliminated. Under this condition and using Eq. (9.32), the current density (or electrochemical reaction rate) at a given overpotential t], in the cathodic direction (T] is negative) is... 

Correspondingly, a typical value for AG°/ES [cf Eq. (9.3)] is 0.5 so that (0r /3 In i) = (2RT/1.5F) = 1.3(RT/F). Although observed values of this coefficient vary from RT/4F to 2RT/F, and sometimes above this, the figure for the majority of electrochemical reactions is very near 2RT/F and thus the formation of the rate— overpotential relation to which this Weiss-Marcus harmonic energy variation theory gives rise is not consistent with experiment (Fig. 9.26). 

It is an experimental fact that whenever mass transfer limitations are excluded, the rate of charge transfer for a given electrochemical reaction varies exponentially with the so-called overpotential rj, which is the potential difference between the equilibrium potential F0 and the actual electrode potential E (t) = E — Ed). Since for the electrode reaction Eq. (1) there exists a forward and back reaction, both of which are changed by the applied overpotential in exponential fashion but in an opposite sense, one obtains as the effective total current density the difference between anodic and cathodic partial current densities according to the generalized Butler-Volmer equation ... 

In electrode kinetic studies, reactant concentrations are, in general, in the millimolar range and double layer contributions for such low ionic concentrations may become very important. If excess of inert or supporting electrolyte is used, the relative variation in the ionic concentration at the double layer due to the electrochemical reaction is at a minimum at high concentration of an inert z z electrolyte, most of the interfacial potential drop corresponds to the Helmholtz inner layer and variations of A02 with electrode potential are small (Fig. 3). In addition, use of supporting electrolyte prevents the migration of electroactive ionic species from becoming important and also reduces the ohmic overpotential. 

---