Effect of Nanopore Wall Geometry on Electrical Double-Layer Charging Dynamics

TL;DR

This paper investigates how varying pore wall geometry affects the charging dynamics of electric double layers in supercapacitors, revealing that sloped walls can improve both charging speed and energy storage.

Contribution

It introduces a perturbation analysis of the Poisson-Nernst-Planck equations for varying pore geometries, providing a scalable framework linking pore shape to electrochemical performance.

Findings

Sloped pore walls induce additional ionic flux.

Theoretical predictions match numerical simulations closely.

Modified circuit models capture geometric effects effectively.

Abstract

Confinement strongly influences electrochemical systems, where structural control has enabled advances in nanofluidics, sensing, and energy storage. In electric double-layer capacitors (EDLCs), or supercapacitors, energy density is governed by the accessible surface area of porous electrodes. Continuum models, built on first-principles transport equations, have provided critical insight into electrolyte dynamics under confinement but have largely focused on pores with straight walls. In such geometries, a fundamental trade-off emerges: wider pores charge faster but store less energy, while narrower pores store more charge but charge slowly. Here, we apply perturbation analysis to the Poisson-Nernst-Planck (PNP) equations for a single pore of gradually varying radius, focusing on the small potential and slender aspect ratio regime. Our analysis reveals that sloped pore walls induce an additional ionic flux, enabling simultaneous acceleration of charging and enhancement of charge storage. The theoretical predictions closely agree with direct numerical simulations while reducing computational cost by 5-6 orders of magnitude. We further propose a modified effective circuit representation that captures geometric variation along the pore and demonstrate how the framework can be integrated into pore-network models. This work establishes a scalable approach to link pore geometry with double-layer dynamics and offers new design principles for optimizing supercapacitor performance.