One-dimensional partial differential model for asymmetric hybrid supercapacitor

Abstract

Asymmetric hybrid supercapacitors (AHSC) are increasing in popularity due to their high energy density. This paper introduces a partial differential model for an AHSC device. The structure contains nickel hydroxide (Ni(OH)2) film as the positive electrode, activated carbon (AC) as the negative electrode, potassium hydroxide (KOH) aqueous electrolyte, and two Helmholtz layers. Potassium ions (K+) and hydroxyl ions (OH−) move under the influence of the electric field and the concentration gradient. The electrode current of pseudocapacitance is described by Frumkin–Butler–Volmer (FBV) equation. Only OH− ions were assumed to pass through the Helmholtz layer and diffuse into the interlayer of the Ni(OH)2 electrode. An AC electrode with a high specific surface area can adsorb a large number of ions to form an electric double layer (EDL). Electrons, injected OH−, and fixed holes together affect the distribution of the electric field in the positive electrode. Nernst–Planck equation, Poisson equation and modified the Ohm’s law were adopted to describe the concentration fields and electric fields. Finally, the simulation was carried out for conditions of Cyclic Voltammetry and potentiostat discharge. The validity and accuracy of the model were verified by experimental data. The performance indices and physical field variables can be estimated accurately.