A Poisson-Boltzmann Description for the Double-Layer Capacitance of an Electolytic Cell

TL;DR

This paper employs a Poisson-Boltzmann model to analyze the double-layer capacitance in electrolytic cells, revealing how capacitance shapes vary with voltage, sample thickness, and surface charge, with implications for understanding electrochemical interfaces.

Contribution

It introduces a Poisson-Boltzmann framework for calculating double-layer capacitances in finite systems, incorporating voltage-dependent screening length and analytical solutions.

Findings

Capacitance exhibits bell-like and camel-like shapes depending on voltage.

The model accounts for finite-length effects and surface charge variations.

Debye screening length becomes voltage-dependent in the analysis.

Abstract

A Poisson-Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities exhibit the bell-like and the camel-like shapes as a function of the applied voltage, when the thickness of the sample or the surface charge are varied. The problem is formulated treating the bulk liquid as a member of a grand canonical ensemble in contact with blocking electrodes. As a consequence, an applied voltage dependent Debye's screening length arises as a fundamental length governing the electrical behavior of the system.