Shape Optimization of Supercapacitor Electrode to Maximize Charge Storage

Abstract

This work proposes a shape optimization approach for electrode morphology to maximize charge storage in supercapacitors. The ionic distributions and electric potential are modeled by the steady-state Poisson–Nernst–Planck system. Shape sensitivity analysis is performed to derive the Eulerian derivative in both volumetric and boundary expressions. An optimal electrode morphology is obtained through gradient flow algorithms. The steady-state Poisson–Nernst–Planck system is efficiently solved by the Gummel fixed-point scheme with finite-element discretization, in which exponential coefficients with large variation are tackled with inverse averaging techniques. Extensive numerical experiments are performed to demonstrate the effectiveness of the proposed optimization model and corresponding numerical methods in enhancing charge storage in supercapacitors. It is expected that the proposed shape optimization approach provides a promising tool in the design of electrode morphology from a perspective of charge storage enhancement.