Current Singularity on a Disk-Shaped Electrode Particle Surrounded by a Non-Conducting Material

Abstract

In this study, we analyze the electrical problem of an electrochemical cell composed of two parallel electrodes, where one electrode contains a disk-shaped conductive particle surrounded by a nonconductive material. Under the condition of quasi-steady state, the problem is formulated as a Fredholm integral equation. Closed-form analytical solutions are derived for two limiting cases, while the general case is solved numerically. The analysis reveals that the normal component of the electric field, which is proportional to the current density, is nonuniformly distributed over the disk surface and exhibits a square-root singularity at the edge of the conductive disk. The strength of singularity increases as the spacing between the disk-like conductive particle and the counter electrode decreases. A similar singular behavior is expected in the ion flux at the particle edge due to the proportionality between the current density and the flux of electrolyte ions. This result suggests that nonuniform distribution of the normal current density on conductive particles in lithium-ion batteries is expected to develop even though they are in contact not only with the liquid electrolyte but also with surrounding nonconductive materials through multiple interfaces.