Cathodic under transport control

Mixed potential systems with the cathodic partial process under transport control and the anodic partial process under activation control is typical of many corrosion systems. For the cathodic partial process to be under transport control. Equation 44 must be unity or larger. This occurs when the absolute value of the difference between the equilibrium electrode potential of the cathodic partial process and the corrosion is on the order of one volt. This condition prevails for most metals of interest in corrosion studies if oxygen... 

Although most corrosion systems can be described by the limiting models presented above, there are instances where control of the corrosion system is a combination of both types, viz., activation controlled anodic partial process with two cathodic partial processes - one under activation control and another under transport control. Examples are iron corrosion in acid solution with inorganic contaminants (, 18) and oxygen ( ). The corrosion current density in such systems is... 

The results of the error analysis indicate that the error of the corrosion-rate determination can be considerable, even for small values of /corrA/j if Ih ratio is high. That is, the often used assumption that the mass-transport effect is negligible when the corrosion current density is a small fraction of the limiting current density (//// 1) is not justifiable for the general case. However, at low b jb ratios the conventional data evaluation methods can be used with acceptable errors for any value of i corr A/ At bjb = 0.25, the error for the corrosion current density is less than about 5 %, and at balb = Q.5, the maximum error is 25%. As discussed in Section IV.l(ii), the b jb ratio of many corrosion reactions is small therefore, this classical electrochemical technique may be applicable, without correction for the mass-transport effect, for many practical systems even when the system is near or under cathodic mass-transport control. 

This sensor principle is based on the electrochemical reduction of oxygen at the cathode. For a typical working electrode potential setting of —0.6 V vs. Ag/AgCV 0.1 M KCl, the following cathodic reaction occurs under transport-controlled conditions ... 

As discussed earlier, it is generally observed that reductant oxidation occurs under kinetic control at least over the potential range of interest to electroless deposition. This indicates that the kinetics, or more specifically, the equivalent partial current densities for this reaction, should be the same for any catalytically active feature. On the other hand, it is well established that the O2 electroreduction reaction may proceed under conditions of diffusion control at a few hundred millivolts potential cathodic of the EIX value for this reaction even for relatively smooth electrocatalysts. This is particularly true for the classic Pd initiation catalyst used for electroless deposition, and is probably also likely for freshly-electrolessly-deposited catalysts such as Ni-P, Co-P and Cu. Thus, when O2 reduction becomes diffusion controlled at a large feature, i.e., one whose dimensions exceed the O2 diffusion layer thickness, the transport of O2 occurs under planar diffusion conditions (except for feature edges). 

Equation (10.27) indicates that the charge transfer becomes the rate-limiting step under the condition when kcr (kS[ + ) The term in large brackets is a function of transport control of the photocurrent. If the electrode potential is sufficiently negative in a cathodic reaction at a p -type semiconductor, CT (kSI + kbr) and interfacial charge transfer control is lost. Eventually, control passes to transport within the semiconductor (although it is affected by recombination). 

It is useful now to describe the origins of the shape of the anodic and cathodic E-log i behaviors shown in Fig. 2. Note that the anodic reaction is linear on the E-log i plot because it is charge transfer controlled and follows Tafel behavior discussed in Chapter 2. The cathodic reaction is under mixed mass transport control (charge transfer control at low overpotential and mass transport control at high overpotential) and can be described by Eq. (1), which... 

Figure 2 Evans diagram illustrating the influence of solution velocity on corrosion rate for a cathodic reaction under mixed charge transfer-mass transport control. The anodic reaction shown is charge transfer controlled.

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. 

In a related study, Walsh et al. [14] examined the performance of a reactor divided by a DuPont Nafion 417 membrane for the removal of copper. The cathode was a 5 cm X 5 cm X1.2 cm piece of RVC operated under mass transport controlled conditions in a 0.5 M Na2S04 solution (pH 2) containing low levels (<100 ppm) of CUSO4. A lead - 6% antimony anode was used along with a 0.5 M Na2S04 solution as the anolyte. 

Figure 11. Illustration of two alternative designs for the rotating cylinder Hull (RCH) cell, which allows the study of non-uniform current distribution on the cathode, under controlled mass-transport conditions. A anode, C cathode, IC insulating cylinder. Reproduced from Ref. 150 with kind permission of Springer Science and Business Media, and with permission from Ref. 95, Copyright (1996) The Electrochemical Society.

A very low frequency or scan rate may be required to obtain Rp defined by Eq 34 under circumstances where reactions are mass transport limited, as indicated by Eq 32. Here, a 1 of 0.1 cm and D = 10" cm /sec requires that a frequency below 0.1 mHz be implemented to obtain Rp from IZ( )I at the zero frequency limit. Hence, a common experimental problem in the case of diffusion controlled electrochemical reactions is that extremely low frequency (or scan rates) are required to complete the measurement of Rp. In the case where Rp is dominated by contributions from mass transport such that Eq 33 applies, the Stem approximation of Eqs 25 and 26 must be modified to account for a Tafel slope for either the anodic or cathodic reaction under diffusion controlled conditions (i.e., Pa or Pa = oo). In fact, Eq 19 becomes invalid. 

During the treatment of dilute solutions, the cathodic deposition of metal is often under mass transport control, either initially or during longer batchprocessing times (section 2.5.2), In such cases, it was seen in Chapter 2 that the maximum duty of the reactor may be expressed in terms of the limiting current (which is proportional to the rate of metal deposition). From the definition of the mass transport coefficient ... 

Reduction (cathodic) partial current density Oxidation (anodic) partial current density Limiting current density (under mass transport control due to diffusion or convective diffusion)... 

Many of the commercial probes are based on a Clark-type electrode (Fig. 12.15) which effectively responds to oxygen via its cathodic reduction under mass-transport control (section 12.4). The medical applications for dissolved oxygen include the following ... 

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