Modeling of Current Distribution on Smooth and Columnar Platinum Structures

Abstract

Studying the growth and stability of anisotropic or isotropic disordered surfaces in electrodeposition is of importance in catalytic electrochemistry. In some cases, the metallic nature of the electrode defines the topography and roughness, which are also controlled by the experimental time and applied external potential. Because of the experimental restrictions in conventional electrochemical techniques and ex situ electron microscopies, a theoretical model of the surface geometry could aid in understanding the electrodeposition process and current distributions. In spite of applying a complex theory such as dynamic scaling method or perturbation theories, the resolution of mixed mass-/charge-transfer equations (tertiary distribution) for the electrodeposition process would give reliable information. One of the main problems with this type of distribution is the mathematics when solving the spatial n-dimensional differential equations. Use of a primary current distribution is proposed here to simplify the differential equations; however it limits wide application of the first assumption. Distributions of concentration profile, current density, and electrode potential are presented here as a function of the distance normal to the surface for the cases of smooth and rough platinum growth. In the particular case of columnar surfaces, cycloid curves are used to model the electrode, from which the concentration profile is presented in a parameterized form after solving a first-type curvilinear integral. The concentration contour results in a combination of a trigonometric inverse function and a linear distribution leading to a negative concavity curve. The calculation of the current density and electrode potential contours also show trigonometric shapes exhibiting forbidden imaginary values only at the minimal values of the trochoid curve.

Current, Concentration and Overpotential Distributions on Columnar Structured Electrodes in a 2D PEMFC Model

“…The calculation of the surface roughness considering the full‐monolayer premise yields a value of about 50 using the carbon monoxide oxidative desorption method [22] . The electrochemical response of the columnar platinum electrode was also described previously [23] but for no carbon supported electrodes. Ex situ STM images are also shown in the topographic mode (Figure 2) to calculate the mean separation and height of the platinum columns.…”

“…In this case, the mass balance equation at early stages of the PEMFC, Equation (3) has to be converted using the parametric curvilinear profile of the trochoid surface [23] [Eqs. (21a,b)]. …”

“…[7] However, when a periodicity or regular tendency is observed as this columnar profile, another modelling is possible. We have shown [23] that curvilinear periodic curves (as trochoids or cycloids) are useful to mimic these surfaces, i. e. points in a plane running along a single line direction without slipping. Thus, the mass balance equations are going to be parameterized using planar trigonometric functions.…”