Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential
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| Format: | Preprint |
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2025
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| _version_ | 1866908609904902144 |
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| author | Aslyamov, Timur Esposito, Massimiliano Janssen, Mathijs |
| author_facet | Aslyamov, Timur Esposito, Massimiliano Janssen, Mathijs |
| contents | Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly-applied potential, close to the equilibrium potential $Ψ^\text{eq}$ at which there is no net Faradaic charge transfer. Specifically, we solve the coupled Poisson-Nernst-Planck and Frumkin-Butler-Volmer equations by asymptotic approximations, using the pore's small inverse aspect ratio as the small parameter. In the early-time limit, the reaction-diffusion equations yield an extended Faradaic transmission line model that includes a voltage source, $Ψ_\text{eq}$, biasing the Faradaic reactions, captured by the resistance $R_F$. In the long-time limit, the model exhibits a nontrivial potential of zero charge, $Ψ_\text{pzc} = Ψ_\text{eq}[1 - \hat{Z}(0)/R_F]$, where $\hat{Z}(0)$ is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to experimentally measure the Faradaic contribution to $Ψ_\text{pzc}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_21336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential Aslyamov, Timur Esposito, Massimiliano Janssen, Mathijs Statistical Mechanics Soft Condensed Matter Chemical Physics Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly-applied potential, close to the equilibrium potential $Ψ^\text{eq}$ at which there is no net Faradaic charge transfer. Specifically, we solve the coupled Poisson-Nernst-Planck and Frumkin-Butler-Volmer equations by asymptotic approximations, using the pore's small inverse aspect ratio as the small parameter. In the early-time limit, the reaction-diffusion equations yield an extended Faradaic transmission line model that includes a voltage source, $Ψ_\text{eq}$, biasing the Faradaic reactions, captured by the resistance $R_F$. In the long-time limit, the model exhibits a nontrivial potential of zero charge, $Ψ_\text{pzc} = Ψ_\text{eq}[1 - \hat{Z}(0)/R_F]$, where $\hat{Z}(0)$ is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to experimentally measure the Faradaic contribution to $Ψ_\text{pzc}$. |
| title | Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential |
| topic | Statistical Mechanics Soft Condensed Matter Chemical Physics |
| url | https://arxiv.org/abs/2510.21336 |