Electrochemical reaction rates

The two dashed lines in the upper left hand corner of the Evans diagram represent the electrochemical potential vs electrochemical reaction rate (expressed as current density) for the oxidation and the reduction form of the hydrogen reaction. At point A the two are equal, ie, at equiUbrium, and the potential is therefore the equiUbrium potential, for the specific conditions involved. Note that the reaction kinetics are linear on these axes. The change in potential for each decade of log current density is referred to as the Tafel slope (12). Electrochemical reactions often exhibit this behavior and a common Tafel slope for the analysis of corrosion problems is 100 millivolts per decade of log current (1). A more detailed treatment of Tafel slopes can be found elsewhere (4,13,14). 

Conway, B. E. The Temperature and Potential Dependence of Electrochemical Reaction Rates, and the Real Form of the Tafel Equation 16... 

The fuel utilized in the fuel cell is mainly hydrogen since its electrochemical reaction rate is much faster than other fuels. Methanol and formic add can directly partidpate in the electrochemical reaction, but their reaction rates are an order of magnitude lower than hydrogen. Therefore, hydrogen is usually produced from other fuels by using a separate fiiel proeessor and subsequently supplied to the fuel cell. 

Alexander N. Frumkin pointed out in 1932 that an electrochemical reaction occnrring at different potentials can be regarded as an ideal set of chemical reactions of the same type, and suggested that the Brpnsted relation be nsed to explain the potential dependence of electrochemical reaction rates. On the basis of Eqs. (14.6) and (14.11), the relation for the activation energy becomes... 

Let / be the potential at the point where the reacting particle had been prior to the reaction, or where a product particle just generated by the reaction would be. This potential (which is referred to the potential in the bulk solution) has a value similar to potentials /2 or )/j, respectively, and gives rise to two effects important for the electrochemical reaction rates. 

Electrochemical reaction rates are also influenced by substances which, although not involved in the reaction, are readily adsorbed on the electrode surface (reaction products, accidental contaminants, or special additives). Most often this influence comes about when the foreign species I by adsorbing on the electrode partly block the surface, depress the adsorption of reactant species j, and thus lower the reaction rate. On a homogeneous surface and with adsorption following the Langmuir isotherm, a factor 10, will appear in the kinetic equation which is the surface fraction free of foreign species 1 ... 

In 1930, Max Volmer and Tibor Erdey-Griiz used the concept of a slow discharge step for cathodic hydrogen evolntion (slow discharge theory). According to these ideas, the potential dependence of electrochemical reaction rate constants is described by Eq. (6.5). Since hydrogen ions are involved in the slow step A, the reaction rate will be proportional to their concentration. Thus, the overall kinetic equation can be written as... 

It is very difficult in view of the vast amount of experimental data to draw general conclusions that would hold for different, let alone all electrocatalytic systems. The crystallographic orientation of the surface undoubtedly has some specific influence on adsorption processes and on the electrochemical reaction rates, but this influence is rather small. It can merely be asserted that the presence of a particular surface orientation is not the decisive factor for high catalytic activity of a given electrode surface. 

Controlling of the Electrochemical Reaction Rate by Electrode Potential and Cell Current... 

The electrochemical reaction rate and thus the speed of production in the cell are proportional to the cell current. The current density - the cell current divided by the electrode area - is dependent on the potential of the working electrode. 

The properties and composition of the CL in PEM fuel cells play a key role in determining the electrochemical reaction rate and power output of the system. Other factors, such as the preparation and treatment methods, can also affect catalyst layer performance. Therefore, optimization of the catalyst layer with respect to all these factors is a major goal in fuel cell development. For example, an optimal catalyst layer design is required to improve catalyst... 

The catalyst layer is composed of multiple components, primarily Nafion ion-omer and carbon-supported catalyst particles. The composition governs the macro- and mesostructures of the CL, which in turn have a significant influence on the effective properties of the CL and consequently the overall fuel cell performance. There is a trade-off between ionomer and catalyst loadings for optimum performance. For example, increased Nafion ionomer confenf can improve proton conduction, but the porous channels for reactanf gas fransfer and water removal are reduced. On the other hand, increased Pt loading can enhance the electrochemical reaction rate, and also increase the catalyst layer thickness. 

The electrochemical reaction rate for the anodic etching of Si in HF was very rapid. This is confirmed by the electrochemical impedance diagram of Fig. 7 that shows a real component equal to 150 cm, and is the result of the high reactivity of the transient bare —Si sites that appear under anodic current. The detailed mechanism of the transformation was investigated by FIS, which revealed quite an unusual inductive loop, which is shown in Fig. 7. Such a diagram was obtained by modeling the reaction kinetics based... 

The current density (or electrochemical reaction rate) that signifies the rate of electric charge flow (e.g., electrons leaving the metal to go to ions in an adjacent layer in solution) is given by, for example, Eq. (7.7) by putting the constant terms kT/h andexp(-AG0 t) together as k ... 

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

One other effect that deals with the structure of the interface and how it affects electrochemical reaction rates can be mentioned. As explained in Cliapter 6, some ions (usually anions) chemisorb on the electrode, bending back their solvation sheaths so that the ion itself comes into contact with the electrode surface and forms valence bonds with it. Such effects are potential dependent, and since the adsorption will tend to block the electrode surface, it will change the dependence of log i on Aty assumed earlier [Eq. (7.7)]. Such effects are particularly important in organoelectrochemistiy (see Cliapter 11) where the reactants themselves may adsorb in contact with the electrode as a function of potential and complicate the theory of the dependence of the rate of reaction (or current density, i) on potential... 

The only test of a satisfactorily purified solution is constancy of the electrochemical reaction rate upon an increase in the degree of purification. Solution purification in electrode kinetics is expensive and time consuming. Each system should be... 

Measuring the Electrochemical Reaction Rate as a Function of Potential (at Constant Concentration and Temperature)... 

Electrochemical Reaction Rates as a Function of the System Pressure... 

The Equations. It is possible to view the effects of pressure on electrochemical reaction rates in two ways. On the one hand, the partial pressure of a gaseous reactant (e.g 02) takes its place in kinetic equations and has an effect on the reaction rate similar to that of the concentration of an ionic reactant. 

Using a relation such as 7.229, one might write a general relation for an electrochemical reaction rate as... 

In interfacial electrochemical reaction rates given by the Butler—Volmcr equation (7.24), the current density, or rate of reaction per unit area, is zero at zero oveipotential (equilibrium), but significant net currents are observed if the potential of the working electrode is displaced from the reversible potential by only 1 mV. In the case of rate-controlling nucleation, however, there is no detectable current until the oveipotential exceeds a few millivolts, after which (at, say, 7 mV), the reaction rate suddenly undergoes an explosive increase. 

Our chapter has two broad themes. In the first, we will consider some aspects of quantum states relevant to electrochemical systems. In the second, the theme will be the penetration of the barrier and the relation of the current density (the electrochemical reaction rate) to the electric potential across the interface. This concerns a quantum mechanical interpretation of Talel s experimental work of 1905, which led (1924-1930) to the Butler-Volmer equation. 

Arrhenius law17 for the variation of the velocity of reactions with temperature was followed in 1905 by Tafel s equation for the variation of the electrochemical reaction rate with potential. The two laws may be compared ... 

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... 

It is usual to relate electrochemical reaction rates and currents to the unit surface, thus obtaining surface-specific reaction rates and current densities i as a measure of electrochemical reaction rates ... 

In recent years, considerable effort has gone into the development of a new class of electrochemical devices called chemically modified electrodes. While conventional electrodes are typified by generally nonspecific electrochemical behavior, i.e., they serve primarily as sites for heterogeneous electron transfer, the redox (reduction-oxidation) characteristics of chemically modified electrodes may be tailored to enhance desired redox processes over others. Thus, the chemical modification of an electrode surface can lead to a wide variety of effects including the retardation or acceleration of electrochemical reaction rates, protection of electrodes, electro-optical phenomena, and enhancement of electroanalytical specificity and sensitivity. As a result of the importance of these effects, a relatively new field of research has developed in which the... 

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