Charging dynamics of electric double layer capacitors including beyond-mean-field electrostatic correlations
Year: 2025
Type: article
Abstract: Electric double layer (EDL) formation underlies the functioning of supercapacitors and several other electrochemical technologies. Here we study how the EDL formation near two flat blocking electrodes separated by $2L$ is affected by beyond-mean-field Coulombic interactions, which can be substantial for electrolytes of high salt concentration or with multivalent ions. Our model combines the Nernst-Planck and Bazant-Storey-Kornyshev (BSK) equations; the latter is a modified Poisson equation with a correlation length ${\ensuremath{\ell}}_{c}$. In response to a voltage step, the system charges exponentially with a characteristic timescale $\ensuremath{\tau}$ that depends nonmonotonically on ${\ensuremath{\ell}}_{c}$. For small ${\ensuremath{\ell}}_{c}, \ensuremath{\tau}$ is given by the BSK capacitance times a dilute electrolyte's resistance, in line with Zhao [Phys. Rev. E 84, 051504 (2011)]; here $\ensuremath{\tau}$ decreases with increasing ${\ensuremath{\ell}}_{c}$. Increasing the correlation length beyond ${\ensuremath{\ell}}_{c}\ensuremath{\approx}{L}^{2/3}{\ensuremath{\lambda}}_{D}^{1/3}$, with ${\ensuremath{\lambda}}_{D}$ the Debye length, $\ensuremath{\tau}$ reaches a minimum, rises as $\ensuremath{\tau}\ensuremath{\propto}{\ensuremath{\lambda}}_{D}{\ensuremath{\ell}}_{c}/D$, and plateaus at $\ensuremath{\tau}=4{L}^{2}/({\ensuremath{\pi}}^{2}D)$. Our results imply that strongly correlated, strongly confined electrolytes---such as ionic liquids in the surface force balance apparatus---move slower than predicted so far.
Source: Physical review. E
DOI: 10.1103/1c8c-zjf7
Authors: David Fertig, Mathijs Janssen
Institution: Norwegian University of Life Sciences
Language: English
Subfield: Physical and Theoretical Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: green
Funder: Norges Forskningsråd
OpenAlex ID: W4412970079