Reaction rate, in terms of current

The data discussed in Figs. 20 through 24 represent the type of data in a polarization curve combinations of potential and applied current density. Figure 26 shows a complete polarization curve for the iron in acid systems for which the Evans diagram is shown in Fig. 25. The Evans lines are included as dotted lines in the figure. The difference between the Evans diagram and the polarization curve is that the polarization curve data display applied current densities, whereas the Evans diagram displays the reaction rates in terms of current densities. 

We now examine the mathematical representation of electrochemical reaction rates in terms of current, rate constant, and electrode potential. The velocity tJ of a chemical reaction may be written as... 

This ionic molar flux will be deflned in details in Chapter 4. The reaction rate in terms of current density t given by eq. (3.8) is valid for one-step reaction. Hence, the controlling reaction may be part of a series of reaction steps, but the slowest reaction step is the rate-controlling. For any reaction, eq. (3.8) can be approximated by letting x = oaFri/RT and y = (1 — a) zFrj/RT. Expanding the exponential functions according to Taylor s series yields... 

Thus far, these models cannot really be used, because no theory is able to yield the reaction rate in terms of physically measurable quantities. Because of this, the reaction term currently accounts for all interactions and effects that are not explicitly known. These more recent theories should therefore be viewed as an attempt to give understand the phenomena rather than predict or simulate it. However, it is evident from these studies that more physical information is needed before these models can realistically simulate the complete range of complicated behavior exhibited by real deposition systems. For instance, not only the average value of the zeta-potential of the interacting surfaces will have to be measured but also the distribution of the zeta-potential around the mean value. Particles approaching the collector surface or already on it, also interact specifically or hydrodynamically with the particles flowing in their vicinity [100, 101], In this case a many-body problem arises, whose numerical... 

These partial reactions proceed with equal reaction rates when the metal is freely corroding. In order to express the reaction rates in terms of a current, the conversion per time is multiplied by the Faraday constant according to the following equation ... 

The corrosion reaction may also be represented on a polarisation diagram (Fig. 10.4). The diagram shows how the rates of the anodic and cathodic reactions (both expressed in terms of current flow, I) vary with electrode potential, E. Thus at , the net rate of the anodic reaction is zero and it increases as the potential becomes more positive. At the net rate of the cathodic reaction is zero and it increases as the potential becomes more negative. (To be able to represent the anodic and cathodic reaction rates on the same axis, the modulus of the current has been drawn.) The two reaction rates are electrically equivalent at E , the corrosion potential, and the... 

Rate of Electrochemical Reaction in Terms of Current. In this part of the derivation we start with a definition of the rate of reaction and the definition of the electric current. The rate of the reduction reaction v, reaction (6.6) from left to right, is defined as the number of moles m of Ox reacting per second and per unit area of the electrode surface ... 

Equations (6.18) and (6.20) give the reaction rates of the general electrochemical reaction (6.6) in terms of current density. 

Current-Potential Relationship for Partial Reactions, Partial i = /(A(/)) functions can be derived by joining equations expressing the rate of electrochemical reactions in terms of current [Eqs. (6.18) and (6.20)] and equations expressing the rate constant as a function of potential [Eqs. (6.31) and (6.32)]. Thus, the cathodic partial current density i is obtained from Eqs. (6.18) and (6.31) to yield... 

Interaction Between Partial Reactions. The original mixed-p)otential theory assumes that the two partial reactions are independent of each other (1). In some cases this is a valid assumption, as was shown earlier in this chapter. However, it was shown later that the partial reactions are not always independent of each other. For example, Schoenberg (13) has shown that the methylene glycol anion (the formaldehyde in an alkaline solution), the reducing agent in electroless copper deposition, enters the first coordination sphere of the copper tartrate complex and thus influences the rate of the cathodic partial reaction. Ohno and Haruyama (37) showed the presence of interference in partial reactions for electroless deposition of Cu, Co, and Ni in terms of current-potential curves. 

In electrodics, the reaction rate is expressed in terms of current density i (Section 7.2.1). Thus one would expect, by analogy, the electrochemical order of the reaction to be given by an expression similar to (7.145) which should result from the Butler-Volmer expression ... 

Nucleation overpotential — In 1898 Haber showed that different reaction products could be obtained at different -> electrode potentials, using the reduction of nitrobenzene as an example [i]. However, a further forty four years would elapse before the invention of the -> potentiostat by Hickling (1942), which finally made the control of the electrode potential routine [ii]. In the interim, a tradition developed of describing the mechanisms of electrode reactions in terms of current as input and overpotential as output. The culmination of this tradition was Vetters magnum opus of 1961 which summarized much of the theory of - overpotentials [iii]. Today, the use of overpotentials survives only in certain specialist applications, such as in metal plating, where nucleation overpotentials continue to be routinely measured. The relation between the rate of nucleation of bulk crystals and overpotential was first derived in 1931 by -> Erdey-Gruz and... 

For aluminium, the factor is 1.79 and for brass 7.69. The reciprocal of these factors will convert mdd to mpy. Some electrochemical techniques may express corrosion rates in terms of an electrical current. In such cases, the anodic reaction must he known so that Faraday s laws may he used in converting to a mass rate loss. Thus, an exchange current density of 8/iAcm 2 on mild steel will result in a corrosion rate of about 20mdd, i.e. 

A manometric technique was used to measure the rate of pressure rise which in turn is a measure of the rate of formation of volatile products produced during the thermal decomposition of hydrazinium monoperchlorate and hydrazinium diperchlorate. Kinetic expressions were developed, temperature coefficients were determined, and an attempt was made to interpret these in terms of current theories of reaction kinetics. The common rate-controlling step in each case appears to be the decomposition of perchloric acid into active oxidizing species. The reaction rate is proportional to the amount of free perchloric acid or its decomposition products which are present. In addition the temperature coefficients are similar for each oxidizer and are equivalent to that of anhydrous perchloric acid. 

At equilibrium, Eq. (1) is in its dynamic condition, i.e., the rate of forward reaction equals the rate of the reverse reaction. If Eq. (1) departs from equilibrium, i.e., one of the directions of the reaction is faster than the other, then the net fiow of protons and electrons, or current, develops. The anode is defined as the electrode at which the de-electronation reaction occurs and the cathode as the electrode at which the electronation reaction occurs. The rate of the electron transfer reaction can be written in terms of current, which is defined by the movement of electrical charges carried by electrons in an electronic conductor and by ions in an ionic conductor. The more the system is away from equilibrium, the higher the current. As the... 

The rate of the electrochemical reactions is frequently expressed in terms of current density (A/cm ) as... 

Although the first reaction does not pass electric charge across the interface directly, each time it occurs the second reaction must pass two electrons across the interface. Consequently, we can write the rate of reaction (1) in terms of an equivalent current density,... 

Where J equals current, n number of electrons transferred per molecule, F equals Faraday constant and Q is the rate of the reaction expressed in terms of moles per unit time. If the above equation is divided by the surface area the current density can be expressed as follows ... 

So far, we have focused on the formal description of current generation in the catalyst layer and discussed major effects of structure and composition on exchange current density and catalyst utilization. In the remainder of this chapter, we will explore in detail, how electrocatalytic activity interferes with other processes at the catalyst surface (e.g. surface diffusion) and transport in the bulk phases. The key measure of catalyst layer performance is the current density that could be extracted from a cell for a given cell potential. This links the spatially varying concentrations and reaction rates with the global performance, rated in terms of power density and fuel cell efficiency. 

It is easy to relate this current density to the many familiar expression for the rate in terms of moles/cm s. Let the current density be given by the symbol i (current per unit area and time, e.g., A/m /s ) then the number of coulombs which are passing in the time t is given by definition as / t, where i is in A cm and t is in seconds. A constant called the Faraday (which has a value of 96,500 C/mole) is associated with every mole of charge so that if in an electrochemical reaction one passes n electrons in one act of the overall reaction the number of coulombs flowing is nF, or n X 96,500 coulombs per mole every time the reaction occurs once (in the molar sense). 

In electrochemistry we always deal in terms of current density when we want to express our rates. But it is easy, as seen, to convert to the more familiar chemical designation of moles cm s for a heterogeneous reaction rate. 

In the 1920 s, E. MQller and his co-workers made a series of studies on the anodic oxidation of methanol, formaldehyde, and formic acid which represent the first extensive mechanistic investigation of these compounds, although the principles of electrode kinetics had not yet been formulated. Muller did not establish mechanisms for these reactions however, many of his observations have been later confirmed and his studies were among the first with a comparison of polarization curves on several noble metals including platinum, palladium, rhodium, iridium, osmium, rubidium, gold, and silver (cf. Figure 1). As was usual at that time, Muller discussed his results in terms of polarization, rather than in terms of current or reaction rate. 

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