# Geometrically Induced Acceleration for Charging Dynamics of Electrical Double-Layers in a Nanopore with Sloped Walls

## TL;DR

This paper shows how sloped walls in nanopores can speed up charging while improving energy storage in supercapacitors.

## Contribution

The study introduces a new theoretical framework linking pore geometry to double-layer dynamics, enabling faster and more efficient supercapacitor designs.

## Key findings

- Sloped pore walls induce additional ionic flux, accelerating charging and enhancing charge storage.
- Theoretical predictions align closely with simulations while reducing computational cost by 5–6 orders of magnitude.
- A modified circuit model captures geometric variations and can be integrated into pore-network models.

## 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.