Current density calculation films

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

In other words, it now includes the term t] = Ed — E which represents the difference between the two expressions, Eqs. (11.1) and (11.2), above. The factor av+ represents, again, the activity value of the cation being deposited (i.e., cation in the film or layer of the bath at the cathode face). Thus tj is the overpotential (deposition factor). It is the extra potential needed to maintain the deposition going at a given desired rate suitable to the nature and properties of the cathode film. In practice, then, calculating the metal deposition potential by the above means that the practitioner must know the values of av+ and 17 for a fixed plating condition, including bath parameters, such as current density and temperature, as well as ionic parameters, such as concentration, valence, and mobility. 

The concentration polarization occurring in electrodialysis, that is, the concentration profiles at the membrane surface can be calculated by a mass balance taking into account all fluxes in the boundary layer and the hydrodynamic conditions in the flow channel between the membranes. To a first approximation the salt concentration at the membrane surface can be calculated and related to the current density by applying the so-called Nernst film model, which assumes that the bulk solution between the laminar boundary layers has a uniform concentration, whereas the concentration in the boundary layers changes over the thickness of the boundary layer. However, the concentration at the membrane surface and the boundary layer thickness are constant along the flow channel from the cell entrance to the exit. In a practical electrodialysis stack there will be entrance and exit effects and concentration... 

The calculated pH of the sample at —1300 mV is 10.5 which is higher than the value of 8.3 obtained in CeCl3 solution at a peak value of — 1170 mV. The lower pH in CeCb solution is evidence of inhibition of the cathodic reaction by CeCl3. The polarization curve obtained after 64 h shows a further reduction in current density, which suggests the presence of surface film responsible for inhibition of the cathodic reaction. 

In 1902, Klupathy [72] derived this equation for the Wehnelt interrupter. He compared his calculation with experimental data. For a nominal current density of about 0.6 A/mm2, he measured gas film formation times of 4 ms (the frequency of operation of the Wehnelt interrupter). His conclusion was that, based on the experimentally measured formation times, the joule heating inside the electrolyte cannot account for the gas film formation for the geometries he considered. More recently, Guilpin [45] and Fascio [32] showed, for different geometries than those considered by Klupathy, that the measured gas film formation times axe of a similar order of magnitude as the one predicted by Equation (4.4). 

The processes in real corroding systems are obviously more complicated than represented by this model. Useful quantitative calculation of the distribution of current density, and hence corrosion rate along the surface, based on the polarization curves for the anodic and cathodic reactions and on the geometry of the anodic and cathodic sites is very complex. In principle, computer-based techniques can be used if exact polarization curves and the geometry of the anodic and cathodic areas are available. For most industrially important situations, this information is not available. Also, time-dependent factors, such as film formation, make quantitative calculations of long-time corrosion rates very uncertain. The theory underlying these calculations, however, has been useful in interpreting observations in research and in industrial situations. 

Influence of hydrogen on the deposition process was evidenced in electrolytes containing boric acid. In such electrolytes, application of very negative potentials caused, simultaneously, Co reduction as well as evolution of hydrogen. Film thicknesses obtained by the RBS technique were used to determine the cobalt average current density icobait, which was then compared with the average total current density i,olai, calculated from the measured deposition current (7). 

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