Theory of expansion of porous carbon electrodes in aqueous solutions according to the Donnan model

TL;DR

This paper develops a theoretical model predicting how porous carbon electrodes expand upon charging, showing that the expansion scales with the charge density to the 4/3 power, advancing understanding of electrode mechanics.

Contribution

It introduces a novel theoretical framework for electrode expansion based on the Donnan model, linking charge density to physical expansion in porous carbon electrodes.

Findings

Expansion scales with charge density to the 4/3 power

Provides a simple predictive model for electrode deformation

Enhances understanding of electrode behavior in energy storage

Abstract

The Donnan model describes the electric double layer structure inside carbon micropores and is an essential element of larger-scale models for capacitive porous carbon electrodes for energy storage and water desalination. The Donnan model was not yet developed to describe the expansion of carbon electrodes upon charging. Here we provide a simple theory which predicts that the one-dimensional expansion of a carbon particle scales with electrode charge density according to a 4/3$^\text{rd}$ power.