Non-equilibrium steady states of electrolyte interfaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910289447878656 |
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| author | Bier, Markus |
| author_facet | Bier, Markus |
| contents | The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14126 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-equilibrium steady states of electrolyte interfaces Bier, Markus Soft Condensed Matter Mesoscale and Nanoscale Physics Chemical Physics The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions. |
| title | Non-equilibrium steady states of electrolyte interfaces |
| topic | Soft Condensed Matter Mesoscale and Nanoscale Physics Chemical Physics |
| url | https://arxiv.org/abs/2309.14126 |