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

• Analytical expressions for the electric potential for planar, spherical and cylindrical geometries are derived used a simple series method. • The proposed mathematical approach is simple and reliable and can be easily implemented by researchers from various science disciplines. • A study of the effect of various parameters such as grain size, grain shape and doping level is conducted. • Analytical formula for the density of oxygen ion is derived. • The maximum surface potential is determined. 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). [ABSTRACT FROM AUTHOR]