Mass transport and current

It follows from Equation 6.12 that the current depends on the surface concentrations of O and R, i.e. on the potential of the working electrode, but the current is, for obvious reasons, also dependent on the transport of O and R to and from the electrode surface. It is intuitively understood that the transport of a substrate to the electrode surface, and of intermediates and products away from the electrode surface, has to be effective in order to achieve a high rate of conversion. In this sense, an electrochemical reaction is similar to any other chemical surface process. In a typical laboratory electrolysis cell, the necessary transport is accomplished by magnetic stirring. How exactly the fluid flow achieved by stirring and the diffusion in and out of the stationary layer close to the electrode surface may be described in mathematical terms is usually of no concern the mass transport just has to be effective. The situation is quite different when an electrochemical method is to be used for kinetics and mechanism studies. Kinetics and mechanism studies are, as a rule, based on the comparison of experimental results with theoretical predictions based on a given set of rate laws and, for this reason, it is of the utmost importance that the mass transport is well defined and calculable. Since the intention here is simply to introduce the different contributions to mass transport in electrochemistry, rather than to present a full mathematical account of the transport phenomena met in various electrochemical methods, we shall consider transport in only one dimension, the x-coordinate, normal to a planar electrode surface (see also Chapter 5). 

The flux of the species O, /0(x, t), is described in terms of the three components that constitute the Nernst-Planck equation (Equation 6.14). The parameters are defined below. 

The first two terms describe the contributions to the mass transport that are the result of forces that act on the species O. The first term is the diffusion component, which relates to the forces that act on O in the concentration gradient close to an electrode. (Do is the diffusion coefficient of O, C0(x, t) is the concentration of the species O at the distance x and the time t and thus 3Cq(x, t)/dx is the concentration gradient.) The second term is the migration 

Fick s first and second laws (Equations 6.15 and 6.18), together with Equation 6.17, the Nernst equation (Equation 6.7) and the Butler-Volmer equation (Equation 6.12), constitute the basis for the mathematical description of a simple electron transfer process, such as that in Equation 6.6, under conditions where the mass transport is limited to linear semi-infinite diffusion, i.e. diffusion to and from a planar working electrode. The term semi-infinite indicates that the electrode is considered to be a non-permeable boundary and that the distance between the electrode surface and the wall of the cell is larger than the thickness, 5, of the diffusion layer defined as Equation 6.19 [1, 33]  

By introduction of a typical value for D0, 10 r cm2 s 1, it is seen that the value of 8 after, for example, 5 seconds amounts to 0.1 mm. At times larger than 10-20 seconds, natural convection begins to interfere and the assumption of linear diffusion as the only means of mass transport is no longer strictly valid. At times larger than approximately 1 minute, the deviations from pure diffusion are so serious and unpredictable that the current observed experimentally cannot be related to a practical theoretical model. 

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Lla. Landau. U., LBL-2702 Ph.D. thesis. University of California, Berkeley, January 1976. Lib. Landau, U., and Tobias, C. W., Mass Transport and Current Distribution in Channel Type Electrolyzers in the Laminar and Turbulent Flow Regimes, Ext. Abstr., No. 266, Electrochemical Society Meeting, Washington D.C., May 1976, 663. 

We will now discuss how the relationship between potential, mass transport and current manifests itself experimentally in some situations typically met in electroanalytical chemistry. In Sections 6.7.1-6.7.3, we discuss the response curves for two families of electroanalytical methods that are conducted under conditions where linear semi-infinite diffusion to/from planar working electrodes prevail. These are chronoamperometry and double... 

Despite its beneficial effects on electroanalytical techniques, which include avoiding electrode passivation, enhancing mass transport and current intensity, and the ability to modify process kinetics, US assistance has not yet gained widespread acceptance in routine analytical laboratories [132,133]. 

We can consider for simplicity that at the steady-state of the process, mass transport and current generation occurs only along the y-axis ... 

Furthermore, the use of EMM will widen the range of materials application for electronic industries, MEMS, etc. The role of convective mass transport and current distribution in surface finish and shape evolution is very important. Effective EMM process can be achieved by optimal combination of the process parametric conditions. In order to achieve the effective and highly precise material machining of the order of microns, the predominant process variables of the EMM system will have to be optimally controlled. 

It should be emphasised that when convection is present in a system, it is an important form of mass transport, and current densities 3-100 times greater than the steady state diffusion limited value are common. 

The effect of turbulence-promoting meshes on mass transport and current distribution [22, 35, 38] computational flow modeling [40]. 

Several research groups have shown that under batch conditions and constant current, the current efficiency declines with substrate conversion as the contaminant concentration falls and the kinetics shift away from current control towards mass transport control [1,10]. Between the extremes of mass transport and current control, a general rate equation can be written with fractional kinetic order, the values of m and n changing with the experimental conditions [14] ... 

For quasi-reversible systems the limiting current is controlled by both mass transport and charge transfer ... 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

It was shown in Section 1.8 that in addition to ion migration, diffusion and convection fluxes are a substantial part of mass transport during current flow through electrolyte solutions, securing a mass balance in the system. In the present chapter these processes are discussed in more detail. 

Ohmic losses AEohmic originate from (i) membrane resistance, (ii) resistance of CLs and diffusion layers, and (iii) contact resistance between the flow field plates. Although it is common practice to split current-voltage characteristics of an MEA into three regions— kinetic (low currents), ohmic (intermediate currents), and mass transport (high currents) [Winter and Brodd, 2004]—implicit separation of vt Afiohmic is not always straightforward, and thus studies of size and... 

The above brief analysis underlines that the porous structure of the carbon substrate and the presence of an ionomer impose limitations on the application of porous and thin-layer RDEs to studies of the size effect. Unless measurements are carried out at very low currents, corrections for mass transport and ohmic limitations within the CL [Gloaguen et ah, 1998 Antoine et ah, 1998] must be performed, otherwise evaluation of kinetic parameters may be erroneous. This is relevant for the ORR, and even more so for the much faster HOR, especially if the measurements are performed at high overpotentials and with relatively thick CLs. Impurities, which are often present in technical carbons, must also be considered, given the high purity requirements in electrocatalytic measurements in aqueous electrolytes at room temperature and for samples with small surface area. 

For small K, i.e., K = 0.5 in Fig. 17, the response of the equilibrium to the depletion of species Red] in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced flux to the UME, causing... 

Therefore, criteria in the selection of an electrode reaction for mass-transfer studies are (1) sufficient difference between the standard electrode potential of the reaction that serves as a source or sink for mass transport and that of the succeeding reaction (e.g., hydrogen evolution following copper deposition in acidified solution), and (2) a sufficiently low surface overpotential and rate of increase of surface overpotential with current density, so that, as the current is increased, the potential will not reach the level required by the succeeding electrode process (e.g., H2 evolution) before the development of the limiting-current plateau is complete. 

Equation (2.161) expresses the relative contributions of mass transport and kinetics to the observed current and is one expression of the Koutccky- Levich equation. 

Little is known about the mechanisms that cause the three other current extrema ]2 to J4. The kinetic and diffusional contributions of the characteristic currents Ji to J4 show a different concentration dependence. While the diffusion current is found to be roughly proportional to Cp, the kinetic current shows an exponent of 2 < <2.5 [Ha3]. No dependence of the characteristic currents to ]4 on doping kind and density is observed. This indicates again that to ]4 depend on mass transport and reaction kinetics rather than on charge supply. For n-type electrodes, of course, strong illumination is necessary in order to generate a sufficient number of minority carriers to support the currents. 

There are a few electrochemical techniques in which the working electrode is moved with respect to the solution (i.e. either the solution is agitated or the electrode is vibrated or rotated). Under these conditions, the thickness of the diffusion layer decreases so that the concentration gradient increases. Since the rate of the mass transport to an electrode is proportional to the concentration gradient (Chapter 1, Section 4.2.2), the thinning of the diffusion layer leads to an increase of the mass transport, and hence to an increase of the faradaic currents. 

The Magnitude of the Current Rates of Electron Transfer, Mass Transport, and their Implications... 

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