Surface roughness current distributions

There are several explanations for the origin of CPE, such as surface roughness, a distribution of - reaction rates and a nonuniform current distribution. 

For n = 1-e, where 0electrode surface roughness or distribution/accumulation of charge carriers. For n = 0.5 e, where 0< < 0.1, the CPE is related to diffusion, with deviations from Fick s second law. For n = 0 e, where 0inductive energy accumulation. Therefore, the CPE is a generalized element. Several factors can contribute to the CPE surface roughness, varying thickness or composition, non-uniform current distribution, and a distribution of reaction rates (non-homogeneous reaction rates on the electrode surface) [3],... 

Leveling in the Presence of Leveling Agents True Leveling, We first consider the case of uneven current distribution that results in increased roughness of the surface. 

When the primary distribution does not illustrate the current or electric potential distribution well, an additional resistance, that is, the charge transfer electrode resistance, has to be considered. In such cases, we need to account for the electrode kinetics, and the secondary current and potential distributions emerge from the models. For industrial purposes the porous or tortuous electrocatalyst has to be considered as a dynamic system. This means that its porosity shape and density besides the surface roughness and the real geometric area changes all the time. This point makes us think that it... 

Theoretical approaches to current distribution on rough surfaces... 

Metal distribution is determined by the current distribution. For HDI, VLSI, as well as PTH applications, an important determination of current distribution is macroprofile and microprofile. In a macroprofile (Figure 3a), the roughness of the surface is large compared with the thickness of the diffusion layer, and the diffusion layer tends to follow the surface contour. In a microprofile (Figure 3b), the roughness of the surface is small... 

It is recognized that porosity or roughness of the electrode surface could be expected to lead to a frequency dispersion of the interfacial impedance even in the absence of detailed considerations of the current distribution problems as outlined above. 

As pointed out by de Levie, however, the most important weakness in the model is the assumption that the current distribution is normal to the macroscopic surface, that is a neglect of the true current distribution. For a rough surface, the lines of electric force do not converge evenly on the surface. The double layer will therefore be charged unevenly, and the admittance will be time and frequency dependence. 

In general, the impedance of solid electrodes exhibits a more complicated behavior than predicted by the Randles model. Several factors are responsible for this. Firstly, the simple Randles model does not take into account the time constants of adsorption phenomena and the individual reaction steps of the overall charge transfer reaction (Section 5.1). In fact the kinetic impedance may include several time constants, and sometimes one even observes inductive behavior. Secondly, surface roughness or non-uniformly distributed reaction sites lead to a dispersion of the capacitive time constants. As a consequence, in a Nyquist plot the semicircle corresponding to a charge-transfer resistance in parallel to the double-layer capacitance becomes flattened. To account for this effect it has become current practice in corrosion science and engineering to replace the double layer capacitance in the equivalent circuit by a... 

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