# AMaSiS 2021 - Abstract

**Vágner, Petr**

*Generalized Nernst--Planck--Poisson model of solid oxide YSZ I LSM I O_2 electrode interface*

Weierstrass Institute, Germany

A nanoscale-continuum generalized Nernst-Planck-Poisson model describing transport of oxide ions O^{2−} in the face-centered cubic yttria-stabilized zirconia (YSZ) was formulated in the framework of non-equilibrium thermodynamics [1] and investigated in [6]. The model was resolved numerically in the 1D half cell geometry and it accounted for the experimentally observed capacitance of a blocking YSZ I Au I O_2 electrode [5]. The nanoscale-continuum model of bulk YSZ was further endowed with triple phase boundary (TPB) reaction mechanism of lanthanum strontium manganite (LSM), oxygen; i.e. YSZ(s) I LSM(s) I O_2(g), electrode. The generalized mass action law kinetics [3] was employed to model the TPB reaction mechanism which included adsorption of the bulk O^{2−} ions, electron-transfer reaction, adsorption of gaseous oxygen and drift-diffusional equilibrium of the LSM electrons. We found that the scaling of the reactions rates w.r.t. mass densities was necessary to qualitatively match the dependencies on the O_2 partial pressure observed in the experiments. Moreover, the robust formulation of the reaction kinetics [4] allowed to show that assumption of the shared TPB lattice sites -- unlike the separate sites model -- rendered the oxygen adsorption in accordance with the measurements in the low frequency region of the impedance spectra. Finally, the drift-diffusion equilibrium of electrons introduced the jump of the electrochemical potential of electrons between the surface and the LSM bulk in to the chemical affinity. Since the jump which was realized outside the simulation domain, it was assumed to be proportional to the difference of the electrostatic potential due to the space-charge layer in the YSZ. This resulted into a non-local boundary condition and was instrumental in the fitting of cyclic voltammetry measurements. The fitted dataset spans temperatures from 700°C to 850°C. The numerical solution of the coupled drift-diffusion system with the non-local boundary condition was provided by the finite volume solve based one the Voronoi cells [2].

**Acknowledgments:** This work was supported by German Research Foundation, DFG project no. FU 316/14-1, and by Czech Science Foundation, GAČR project no. 19-14244J.

**References**

[1] W. Dreyer. et.al., Entropy, 20(12):939, 12 2018.

[2] J. Fuhrmann. VoronoiFVM.jl - Solver for coupled nonlinear partial differential equations based on the Voronoi finite volume method. https://github.com/j-fu/VoronoiFVM.jl, 2019-2021.

'[3] M. Grmela, Physica D: Nonlinear Phenomena, 241(10):976-986, 2012.

[4] V. Miloš . et.al., WIAS Preprint, (2797), 2020.

[5] J. E. ten Elshof, Journal of Materials Chemistry, 11(10):2564?2571, 2001.

[6] P. Vágner. et.al., Journal of Solid State Electrochemistry, 23(10):2907?2926, 2019.