Electric potential and surface oxygen ion density for planar, spherical and cylindrical metal oxide grains

Abstract

In this article, the mathematical model presented by Barami and Ghafarinia (Sensors and Actuators B: Chemical 293 (2019) 31–40) for metal oxide grains is discussed. The nonlinear governing model, which is a Poisson-Boltzmann-type equation, is solved by a simple and efficient method. Analytical expressions for the electrical potential and oxygen ion density within the planar, cylindrical and spherical metal oxide grains are expressed in terms of the absolute value of the electric potential and grain thickness. In addition, an investigation of the effects of parameters such as grain diameter, grain thickness, and uniform distribution of single donors on the performance. The validity of the derived analytical expression is established by direct comparison with computer-generated numerical simulations in addition to previously available limiting cases’ results (low and high oxygen adsorption on the grain).