TY - JOUR A1 - Bier, Markus T1 - Non-equilibrium steady states of electrolyte interfaces T2 - New Journal of Physics N2 - 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. KW - Poisson-Nernst-Planck theory, non-equilibrium steady state, electrolyte interface, Gouy-Chapman model Y1 - 2024 UR - https://opus4.kobv.de/opus4-fhws/frontdoor/index/index/docId/5468 UR - https://doi.org/10.1088/1367-2630/ad19a9 VL - 26 IS - 1 SP - 013008 ER -