Mass transport controlled current density

So far, we have discussed the properties of the limiting current density at the RDE. What about activation or mixed control For a purely activation-controlled process, the current should be independent of rotation rate, or should at least become independent of it beyond a certain rotation rate. Under conditions of mixed control, the activation-and mass-transport-controlled current densities combine to yield the total current density as the sum of reciprocals, namely... 

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 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... 

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)... 

The corrosion engineer concerned with mass transport controlled corrosion is interested in determining the limiting current density for a variety of geometries... 

The objective of the mass transport lab is to explore the effect of controlled hydrodynamics on the rate at which a mass transport controlled electrochemical reaction occurs on a steel electrode in aqueous sodium chloride solution. The experimental results will be compared to those predicted from the Levich equation. The system chosen for this experiment is the cathodic reduction of oxygen at a steel electrode in neutral 0.6 M NaCl solution. The diffusion-limited cathodic current density will be calculated at various rotating disk electrode rotation rates and compared to the cathodic polarization curve generated at the same rotation rate. 

Fig. 1.10 Trend of the percentage of phenol converted to CO2 (open triangle) and to aromatic compounds (open square) during phenol electrolysis in 1M HCIO4 on BDD under (a) current limited control, initial phenol concentration 20mM, current density 5mA cm-2 (b) mass transport control, initial phenol concentration 5 mM, current density 60 mA cm 2...

An alternative way of correcting for mass transport limitation is to replace the concentration term C° in the rate equation by the concentration at the surface, C(s), given by Eq. 13D. The measured current density i is smaller than the activation-controlled current density, because the concentration at the surface is lower than in the bulk. The ratio between the two is given by... 

An alternative method, based on the notion that mass transport and charge transfer occur consecutively, may also be employed. The current density during a transient is related to the activation-controlled current density by... 

X is the dimensionless rate constant given by % = (]2tl7D) k. It is proportional to the activation controlled current density i corrected for mass transport. From Schwarz, Ph.D. Disserta-... 

Dendritic deposits grow under mass transport-controlled electrodeposition conditions. These conditions involve low concentration of electrolyte and high current density. A dendrite is a skeleton of a monocrystal consisting of stem and branches. The shapes of the dendrites are mainly determined by the directions of preferred growth in the lattice. The simplest dendrites consist of the stem and primary branches. The primary branches may develop secondary and tertiary branches. The angles between the stem and the branches, or between different branches, assume certain definite values in accordance with the space lattice. Thus, dendrites can be two dimensional (2D) or three dimensional (3D). 

Mass transport control of electrode reactions can be caused by one of two physical processes. In the first case, the interfacial concentration of the reactant drops to zero, i.e., the electron transfer reaction consumes the species as quickly as it arrives at the interface. In the second case, the interfacial concentration of the product reaches saturation. When these conditions prevail, the rate of mass transport is at its limiting (maximum) value. Limiting current densities, ij and in, for anodic and cathodic partial reactions, respectively, are... 

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