28 July 2003 Interfacial transport theory for electrochemical phenomena with application to electric double layer
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Modeling ionic diffusion in electrolytes requires the simultaneous solution of the Nernst-Planck (electro-diffusion) equation and Gauss' law. Unfortunately, the Nernst-Planck equation is not applicable in the ionic double layer that forms at an electrode/electrolyte interface. Furthermore, the large gradients of the electric potential in the double layer can cause numerical instabilities. The double layer is usually modeled using the Gouy-Chapman theory, a steady state solution, which predicts an exponential decay of the electric potential and ion concentration in the direction normal to the electrode. In the present paper we present a novel theory in which the Gouy-Chapman equation, a three-dimensional theory, is replaced by an interface (2-D) theory of the double layer. The effects of the double layer are then modeled as boundary conditions applied to the Nernst-Planck equation and Gauss' law. Interfacial equations are derived for the species mass balances, the conservation of charge, Gauss's law, and the quasi-static form of Faraday's law. Each of these physical principles is derived for both a regular (or single) interface and a double interface representing an electric double layer. The standard interfacial variables are augmented with an electric charge, electric potential, electric field, electric polarization, and electric displacement, whereas conventional electrostatics includes only interfacial charge.
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James Boyd, James Boyd, Muralidar Ambati, Muralidar Ambati, } "Interfacial transport theory for electrochemical phenomena with application to electric double layer", Proc. SPIE 5051, Smart Structures and Materials 2003: Electroactive Polymer Actuators and Devices (EAPAD), (28 July 2003); doi: 10.1117/12.484367; https://doi.org/10.1117/12.484367

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