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

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.