Kinetic and electrochemical model
Creators: name: Strandbakke, Ragnar
name: Småbråten, Didrik
Publisher: name: Zenodo
Year: 2022
Subjects: Proton Ceramic Conductor, kinetic, electrochemical model

description: The deliverable reports on the progress in the development of a kinetic and electrochemical model. Kinetics of the reaction sequence over the electrode are described by atomistic modelling and implemented as input parameters in the electrochemical model. In the electrochemical model, the current-potential relation is given a generic analytical expression adaptable to all applications relying on electrochemical conversion and transport of protons over a solid electrolyte. This model is under development, meaning that it incorporates kinetic parameters, but still needs an analytical solution to incorporate the effect of voltage on the reaction rates. We therefore also derive a semi-analytical solution, where measured resistances at increasing voltage is used to derive a current-voltage relation over the electrode. An atomistic modelling approach using Density Functional Theory (DFT) is being developed for calculating material specific rate parameters, including energy barriers Ea(i) and preexponential factors A0 (i), for migration, diffusion, and (electro)chemical reactions. Significant progress has been made, where we can now readily determine the kinetic parameters for, e.g., bulk and surface diffusion, adsorption, dissociation, and chemical reactions. However, there is still progress to be made on how to properly describe the charge transfer associated with electrochemical conversion, and the plethora of different potentials μ(i), ϕ, etc. The DFT approach is applied to the triple-phase boundaries in the Ni-BZCYO cermet system, which is relevant for hydrogen pumping. This is a well-studied and chemically "simple" model system, which makes it highly suitable for developing and testing the DFT approach. In the electrochemical model, the first step is to define the various energy contributions, how equilibrium is established at Open Cirquit Voltage (OCV), and how chemical equilibrium is shifted by a deviation of the electrostatic potential (Δϕ) from OCV (current (I) is running). The relation between Δϕ and I constitutes the overpotential (η). The η-I relation is given by the limitations acrossthe electrodes‘ (positrode and negatrode) reaction coordinates, given by rate- and diffusion expressions. These expressions will be parameterized by μ(i), A0 (i) and Ea(i) and constitute the polarisation resistance. In order to link IV-relations in real systems - under realistic process conditions - to the IV-relations studied and parameterized over model electrodes with defined geometries, the model must incorporate all charge carriers that contribute to the total current under the given thermal and atmospheric conditions. The model is developed and fitted to impedance measurements under positive, zero and negative bias at high temperatures, symmetrical atmosphere (zero chemical gradient) and low pH2O, where the electrolyte is only partially hydrated. The electrochemical model therefore incorporates transport of protons, oxide ions and electron holes and extract the selectivity for each charge carrier over the assembly of electrodes and electrolyte. Furthermore, the model incorporates the effect of process parameters, allowing the model to be applied also under real process conditions. Here, we present interpretations of how polarisation resistance (Rp) depends on DC bias, and give a general conversion of I-Rp to I-η, enabling a semi-analytical I-U model.