Mass transfer limiting current

Zone III the E vs ln(l — j/ji ) logarithmic curve corresponds to concentration polarization, which results from the limiting value ji of the mass transfer limiting current density for the reactive species and reaction products to and/or from the electrode active sites an increase inji from 1.4 to 2.2 Acm leads to a further... 

At the mass-transfer limited current density (i/i = 1) always the dimer yield vanishes and it approaches its respective highest value, which depends—but not linearly—on the styrene concentration at vanishing current densities. This result can be formalized by assuming the coupling reaction [Eq. (42b)] and the solvolysis [Eq. (42c)] of the primary radical cation as a heterogeneous reaction of adsorbed reactants. Under this condition, one obtains the expression for the dimer yield,... 

This expression for concentration is the starting point for the development cf the Levich equation for the mass-transfer-limited current to a disk electrode. 

The steady-state mass-transfer-limited current density for a rotating disk (see Section 11.6) can be expressed as... 

The rotating disk electrode, described in Section 11.6, has the advantage that the fluid flow is well defined emd that the system is compact and simple to use. The rotation of the disk imposes a centrifugal flow that in turn causes a radially uniform flow toward the disk. If the reaction on the disk is mass-transfer controlled, the associated current density is imiform, which greatly simplifies the mathematical description. As discussed in sections 5.6.1 and 8.1.3, the current distribution below the mass-transfer-limited current is not uniform. The distribution of current and potential associated with the disk geometry has been demonstrated to cause a frequency dispersion in impedance results. The rotating disk is therefore ideally suited for experiments in which the disk rotation speed is modulated while im-der the mass-transfer limited condition. Such experiments yield another t)q)e of impedance known as the electrohydrodynamic impedance, discussed in Chapter 15. 

The concentration profile expected for a system at one-half of the mass-transfer-limited current and for a concentration perturbation of 20 percent at the interface (see equation (11.44)) is presented in Figure 11.5 with dimensionless time as a parameter. At the higher frequency, the propagation of the disturbance away from... 

The rotating cylinder is a popular tool for electrochemical research because it is convenient to use and both the primary and mass-transfer-limited current distributions are uniform.A schematic representation of the rotating cylinder is presented in Figure 11.12. At very low rotation speeds, the fluid flows in concentric circles around the rotating cylinder, satisfying a no-slip condition at the rotating inner cylinder and at the stationary outer cylinder. Since there is no velocity component in the radial direction, there is no convective enhancement to mass transfer. 

Figure 11.12 Schematic representation of a rotating cylinder electrode a) entire cylinder used as working electrode. This geometry provides a uniform current and potential distribution at and below the mass-transfer-limited current, b) band-shape cylindrical coupon used as a working electrode. This geometry is useful for studies conducted at the open-circuit condition.

The three-term convective-diffusion model provides the most accurate solution to the one-dimensional convective-diffusion equation for a rotating disk electrode. The one-dimensional convective-diffusion equation applies strictly, however, to the mass-transfer-limited plateau where the concentration of the mass-transfer-limiting species at the surface can be assumed to be both uniform and equal to zero. As described elsewhere, the concentration of reacting species is not uniform along the disk surface for currents below the mass-transfer-limited current, and the resulting nonuniform convective transport to the disk influences the impedance response. ... 

P. K. Shukla and M. E. Orazem, "Hydrodynamics and Mass-Transfer-Limited Current Distribution for a Submerged Stationary Hemispherical Electrode under Jet Impingement," Electrochimica Acta, 49 (2004) 2901-2908. 

M. Durbha and M. E. Orazem, "Current Distribution on a Rotating Disk Electrode Below the Mass-Transfer Limited Current Correction for Finite Schmidt Number and Determination of Surface Charge Distribution," Journal of The Electrochemical Society, 145 (1998) 1940-1949. 

The limiting current density is an important parameter for the analysis of mass transfer controlled electrochemical processes and represents the maximum possible reaction rate for a given bulk reactant concentration and fluid flow pattern. During anodic metal dissolution, a mass transfer limiting current does not exist because the surface concentration of the dissolving ion (e.g., Cu + when the anode is composed of copper metal) increases with increasing current density, eventually leading to salt precipitation that blocks the electrode surface. 

One can now substitute various mass transfer/limiting current density correlations for (such as Equation [26.82]) in order to relate with the electrolyte flow conditions. 

FIGURE 26.21 Primary, secondary, and mass transfer limited current distributions on a rotating disk electrode of radius r . 

Relations between surface and bulk concentrations are obtained if one considers the mass transfer limiting currents for all the 4 species - A, A-, D and D+. Thus... 

The effect of the size of the colloidal particle on the rate is also explainable in a similar manner. For spherical particles for a given amount of the catalyst, the surface area A will increase with size by the surface to volume ratio A 1/r. Since the mass-transfer limited current imax is directly proportional to the area, an inverse dependence of i on the colloidal radius would be expected at constant pH. Experimental data on H2 yields at various pH, with different relay species, catalyst size, etc. reported for various sacrificial H2-evolving systems are all explainable in terms of above discussions. 

Mass transport in MREF is a combination of steady state and non-steady state diffusion processes. The mass transfer limited current density (i,) is related to the reactant concentration gradient (Cb-Cs) and to the diffusion layer thickness (8) by Nemst using the following equation ... 

One approach to achieve these goals employs three-dimensional electrodes [4, 116, 117] where the mass transfer-limiting current, for metal ion removal is given by... 

On applying phase transfer agents, electrochemical reactions in liquid/ liquid systems can attain industrial importance. Overall mass transfer limiting currents have been found to be the linear sum of three effects ... 

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