Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified stern layer

摘要

Finite element analysis of electric double layer capacitors using a transientnonlinear Nernst-Planck-Poisson (NPP) model and Nernst-Planck-Poisson-modifiedStern layer (NPPMS) model are presented in 1D and 2D. The NPP model providedunrealistic ion concentrations for high electrode surface potential. The NPPMS modeluses a modified Stern layer to account for finite ion size, resulting in realistic ionconcentrations even at high surface potential.The finite element solution algorithm uses the Newton-Raphson method to solvethe nonlinear problem and the alpha family approximation for time integration to solvethe NPP and NPPMS models for transient cases. Cubic Hermite elements are used forinterfacing the modified Stern and diffuse layers in 1D while serendipity elements areused for the same in 2D. Effects of the surface potential and bulk molarity on the electric potential and ionconcentrations are studied. The ability of the models to predict energy storage capacity isinvestigated and the predicted solutions from the 1D NPP and NPPMS models arecompared for various cases. It is observed that NPPMS model provided realistic andcorrect results for low and high values of surface potential.Furthermore, the 1D NPPMS model is extended into 2D. The pore structure onthe electrode surface, the electrode surface area and its geometry are important factors indetermining the performance of the electric double layer capacitor. Thus 2D modelscontaining a porous electrode are modeled and analyzed for understanding of thebehavior of the electric double layer capacitor. The effect of pore radius and pore depthon the predicted electric potential, ion concentrations, surface charge density, surfaceenergy density, and charging time are discussed using the 2D Nernst-Planck-PoissonmodifiedStern layer (NPPMS) model.