# Electrolyte solutions at curved electrodes. I. Mesoscopic approach

## TL;DR

This paper systematically analyzes electrolyte solutions at curved electrodes using the Poisson-Boltzmann approach, revealing how curvature influences capacitance and providing universal and simplified models for different curvature regimes.

## Contribution

It introduces a mesoscopic analysis of electrolyte-electrode interactions considering curvature effects, with new analytic expressions for capacitance behavior at various curvatures.

## Key findings

- Capacitance depends strongly on surface charge at small curvature.
- At large curvature, capacitance behavior becomes independent of surface charge.
- An analytic expression captures the universal behavior at large curvatures.

## Abstract

Within the Poisson-Boltzmann (PB) approach electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance $C$ on the surface charge density $\sigma$ and the ionic strength $I$ are examined as function of the wall curvature. The surface charge density has a strong effect on the capacitance for small curvatures whereas for large curvatures the behavior becomes independent of $\sigma$. An expansion for small curvatures gives rise to capacitance coefficients which depend only on a single parameter, allowing for a convenient analysis. The universal behavior at large curvatures can be captured by an analytic expression.