Current -overpotential transport control

Equation (14.6) predicts that for constant in and large overpotential r/ the current becomes equal to Bvery large, the current is transport controlled, the surface concentration is negligible, and j = ] nn = Btn 1/2, the limiting current density. This remains true for the scheme of Eq. (14.7) as long as the dissociation... 

A correlation between the spacing of striae and convection downstream of protrusions does not fully describe the process. The initial protrusions arise far from transport control and cannot be attributed to a diffusive instability of the type described in the previous section. Jorne and Lee proposed that striations formed on rotating electrodes by deposition of zinc, copper and silver are generated by an instability that arises only in systems in which the current density at constant overpotential decreases with increasing concentration of metal ion at the interface [59]. 

It is difficult to measure kinetic currents at high overpotentials, since then the reaction is fast and usually transport controlled (see Chapter 13). At small overpotentials only Butler-Volmer behavior is observed, and the deviations predicted by theory were doubted for some time. But they have now been observed beyond doubt, and we will review some relevant experimental results in Chapter 8. 

Instruction Calculate the current density values as a function of overpotential (in a range of -0.200 to 0.200 V) assuming that the reaction is under mass transport control and under mixed mass transport and charge-transfer control determine the error of the approximation and plot i-T) dependencies. (Gokjovic)... 

Why did we introduce this purely experimental material into a chapter that emphasizes theoretical considerations It is because the ability to replicate Tafel s law is the first requirement of any theory in electrode kinetics. It represents a filter that may be used to discard models of electron transfer which predict current-potential relations that are not observed, i.e., do not predict Tafel s law as the behavior of the current overpotential reaction free of control by transport in solution. 

To obtain quantitative expressions for the corrosion current and the corrosion potential, one has to substitute the proper expression for the metal-dissolution- and electronation-current densities. If no oxide films form on the surface of the corroding metal and neither of the current densities is controlled by mass transport, i.e., there is no concentration overpotential, one can insert the Butler-Volmer expression for the deelectronation- and electronation-current densities. Thus,... 

However, in any practical cell, these mass-transport rates have a maximum, corresponding to zero concentration of the reactants or very high concentration of the products on the electrode surface, and this maximum, denoted // (for diffusion-limited current) dictates the actual shape of the current-potential curve at high overpotentials. Under these conditions, the cell operation is mass transport controlled (Fig. 12). 

In his more recent paper, Beck d compares the reaction rates of liquid-phase hydrogenation reactions with electrochemical reductions. The comparison is somewhat arbitrary, as Beck concedes. Thus the electrochemical reduction rates become potential-independent at higher overpotential, and it is this transport-limited current that is used as one half of the comparison. The liquid-phase hydrogenations also appear to be mass-transport controlled. However, given that the conditions, in either case, are reasonable relative to their respective technologies, it is interesting to note that the ratio of electrochemical to gas-phase reaction rates (per unit catalyst area) ranges from 4.5 1 to 20 1. ... 

The overpotential caused by electron transfer is assumed to be limitingly low. Under these conditions, the relationship between potential and current density is given by considering it to consist of the shift in the equilibrium potential due to a change in the concentration of reactants in solution away from that at equilibrium to that caused by the holdup in transport control. 

This expression is known as the Levich equation, and it provides an excellent test that the current is entirely mass transport controlled a plot of /vs should be linear and pass through the origin, and the slope of such a plot may be used to estimate the diffusion coefficient for the electroactive species, e.g. Fig. 4.10. Except when a chemical reaction limits the current density, the Levich equation will describe the rotation rate dependence of the anodic and cathodic limiting currents at high positive and high negative overpotentials respectively. 

Ftg. 2.20 An idealizied strategy fot operation of a three-dimensonal electrode (assuming that the entire electrode operates under mass transport control), (a) Dehnition sketch, (b) Current versus overpotential curve. 

In the assumptions that were made in this chapter up to the beginning of this section, it was assumed that transport of charge carriers to and from the electrode played no part in rate control because it was always plentiful. Thus, in the evolution of hydrogen from acid solutions, the current density in most experimental situations is less than 10 times the limiting diffusion current and for this reason there is a negligible contribution to the overpotential due to an insufficiency of charge carriers. Like water from the tap in a normal city, the rate of supply of carriers is both tremendously important but seldom considered, for there is always plenty available. 

The tertiary current distribution Ohmic factors, charge transfer controlled overpotential effects, and mass transport are considered. Concentration gradients can produce concentration overpotentials. The potential across the electrochemical interface can vary with position on the electrode. 

The Butler-Volmer equation relates the effect of anodic or cathodic overpotential to net anodic or cathodic current density for an electrode reaction under activation control that is, free from mass transport and concentration effects. 

As already shown in Fig. 1, a general feature of electrocatalysis is that the current passing through an electrode-electrolyte interface depends exponentially on overpotential, as described by the Butler-Volmer equation discussed in Sect. 2.4.1, so that logi versus r] U — C/rev) gives straight lines, termed Tafel plots (Fig. 1). On this basis, one would expect an exponential-type dependence of current on overpotential in Fig. 12 (curve labeled 7ac). Such a curve would correspond to pure activation control, that is, to infinitely fast mass-transport rates of reactants and products to and from the two electrodes. 

Additives that increase the deposition overpotential at a given current density, for instance, by altering the Tafel constants, can be considered deposit-leveling additives. Since additives are typically present in very small concentrations, their transport to the electrode is nearly always under diffusion control and sensitive to flow variations. 

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