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Author: Müller, Rüdiger × End date: 2019 × Start date: 2010 × Has files: Yes × Type: Text × Subject: Butler-Volmer × WGL Institute: WIAS ×

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    A new perspective on the electron transfer: Recovering the Butler-Volmer equation in non-equilibrium thermodynamics
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger
    Understanding and correct mathematical description of electron transfer reaction is a central question in electrochemistry. Typically the electron transfer reactions are described by the Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Since in the classical form, the validity of the Butler-Volmer equation is limited to some simple electrochemical systems, many attempts have been made to generalize the Butler-Volmer equation. Based on non-equilibrium thermodynamics we have recently derived a reduced model for the electrode-electrolyte interface. This reduced model includes surface reactions and adsorption but does not resolve the charge layer at the interface. Instead it is locally electroneutral and consistently incorporates all features of the double layer into a set of interface conditions. In the context of this reduced model we are able to derive a general Butler-Volmer equation. We discuss the application of the new Butler-Volmer equations to different scenarios like electron transfer reactions at metal electrodes, the intercalation process in lithium-iron-phosphate electrodes and adsorption processes. We illustrate the theory by an example of electroplating.
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    Rational modeling of electrochemical double-layers and derivation of Butler-Volmer equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dreyer, Wolfgang; Guhlke, Clemens; Müller, Rüdiger
    We derive the boundary conditions for the contact between an electrolyte and a solid electrode. At first we revisit the thermodynamic consistent complete model that resolves the actual electrodeelectrolyte interface and its adjacent boundary layers. The width of these layers is controlled by the Debye length that is typically very small, leading to strongly different length scales in the system. We apply the method of asymptotic analysis to derive a simpler reduced model that does not resolve the boundary layers but instead incorporates the electrochemical properties of the layers into a set of new boundary conditions. This approach fully determines the relation of bulk quantities to the boundary conditions of the reduced model. In particular, the Butler-Volmer equations for electrochemical reactions, which are still under discussion in the literature, are rational consequences of our approach. For illustration and to compare with the literature, we consider a simple generic reaction.