Mass-transport-limited current density

The expression for the mass-transport-limiting current density may be employed together with the Nemst equation to deduce the complete current-potential response in a solution containing only oxidized or reduced species... 

One consequence of the foregoing analysis, which may at first seem somewhat surprising, is that the activation-controlled current density determined by proper correction for mass transport, can actually be much larger than the mass-transport-limited current density This follows directly from Eq. SOD. If we substitute m = ili in this equation, we can write... 

The need to enhance the rate of mass transport is obvious. Looking again at Eq. 3A we note that the measured current density becomes equal to the activation-controlled current density if the latter is small compared to the mass-transport-limited current density. 

The mass-transport-limited current density for oxygen reduction is independent of the kinetic parameters for this reaction rather it depends on factors such as the concentration and the diffusion coefficient of oxygen in the medium. It depends oh the rate of flow of the liquid in a pipe or around a sailing ship or a structure immersed in a river. 

Clearly, the smaller of the two currents is dominant. The mass-transport-limited current density can be written in the form... 

We alluded to the Nernst diffusion layer thickness 5, in the first chapter. It relates to the mass-transport limited current density through the equation... 

For the former group, the allowed level of impurity is relatively easy to assess. It should be several orders of magnitude less than the concentration of the material being studied, and the mass-transport-limited current density at which the impurity can react should be smaller than the smallest current we wish to observe. 

The effect of rotation rate was studied in the range of 2,000 to 5,000 rpm, which represents a 90% (= 2.5" ) increase in the rate of mass transport to a RCE. The effect of rotation rate on the deposition process is shown in Fig. 10. As the concentration of WO is increased tenfold, from 0.04 to 0.40 M, the current density increases by a factor of only two. The limiting current density, calculated on the basis of the concentration of WO4 in solution, is much higher than the partial current densities for deposition of this metal, so one would not expect a 40% increase of the rate of deposition of W with the increase of the rate of mass transport, as foimd experimentally. The explanation of these unexpected observations lies in the formation of the mixed-metal complex, as shown in Eq. (33). The concentration of this complex is low, and its rate of formation is also expected to be low. From the dependence of the partial current density for W deposition shown in Fig. 10a, the activation-controlled and the mass transport-limited current densities can be estimated, using the Levich equation, as applied to RCE experiments, namely... 

Limiting current density (commonly the mass-transport-limited current density)... 

A typical expression for the mass transport limiting current density (J ) resulting from the interdiffusion of 0 and N2 in a porous air electrode is given by ... 

Moreover, at very high overpotentials, the electron transfer is very fast, so Co O. Then the mass transport limited-current density is given by ... 

Mass-Limiting Current Density We previously examined ohmic limiting current density. Now we consider the case of mass transfer hmiting current density U. At the mass transport limiting current density, the rate of mass transport to the reactant surface is insufficient to promote the rate of consumption required for reaction. In this case, the local concentration of reactant will be reduced to zero, which, from Eq. (4.84), must also reduce the cell voltage to zero. Assuming the surface concentration Cr) is zero at the limiting state (//)... 

Example 4.11 Determine Concentration Polarization Given the anodic mass-transport-limited current density is 15 A/cm and the cathode mass-transport-limited enrrent density is 2.5 A/cm, determine the anode and cathode concentration polarization at 0.1 and 1.0 A/cm. Assume the B factor is 0.045 V on both electrodes and Eq. (4.88) is appropriate and is determined from curve-fit of several polarization enrves. 

In Example 5.8, we solved for the mass transport limiting current density of an electrode based on the resistance to gas-phase transport only. In the PEFC and some other fuel cells, a thin layer of liquid or ionomer may cover portions of the catalyst surface, resulting in an additional film resistance. Symbolically show this simation to form a more precise model of mass transfer limited current density at an electrode. Ignore convective effects and Knudsen diffusion in this problem. 

Linear sweep voltammetry (LSV) is often used to study the intrinsic kinetics of the catalyst provided the total current is actually a fraction of the mass transport limited current density. The concentration of the electrolyte can also impact the measurement unless the reaction kinetics is zeroth order in either the soluble species or the electrolyte concentration. 

The mass-transport-limited current density for oxygen reduction is independent of the kinetic parameters for this reaction rather, it depends on factors such as the... 

The case of mass transport limitation has been discussed before. This leads to a mass-transport-limited current density, independent of potential. But a limited current density could also be observed when the limitation is kinetic. This can happen when the metal ion exists in solution as a complex, although the electroactive species participating in the charge-transfer step is the free ion. An example of such a situation is the deposition of Cu from a solution containing copper pyrophosphate. A chemical step, the rate of which is independent of potential, is followed by an electrochemical step, as shown by the next two equations... 

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