Influence of the Number of Dimensions in the Impedance Spectroscopy Simulation of a YSZ Electrolyte

Ouba, Ana Kaori de Oliveira; Chinelatto, Adilson Luiz; Borcezi, Janaina Semanech; Neitzel, Ivo; Chinelatto, Adriana Scoton Antonio

doi:10.1590/1980-5373-MR-2022-0259

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Articles • Mat. Res. 25 • 2022 • https://doi.org/10.1590/1980-5373-MR-2022-0259 copy

Influence of the Number of Dimensions in the Impedance Spectroscopy Simulation of a YSZ Electrolyte

Authorship SCIMAGO INSTITUTIONS RANKINGS

The use of computer simulation to predict the behavior of devices and materials allows for the acceleration of system operation and reduces costs, as it eliminates the need to build prototypes for testing. This work proposes the construction of 3 models with different complexities to simulate the electrical behavior of a solid electrolyte fuel cell. Experimental data were compared with simulation data. The experimental data were obtained from the production of a solid YSZ by tape casting, sintered at 1550 °C. The material was characterized using impedance spectroscopy in atmospheric air. From the experimental data, a computer simulation was conducted by using commercial code (COMSOL Multiphysics v.5.4). The construction of the model was developed to 1D, 2D axisymmetric and 3D dimensions to simulate an electrolyte to use in cylindrical planar SOFC. Nyquist Impedance graphics were plotted for the three geometries in comparison with the experimental value. No variation was observed between the curves obtained by the different geometries for the same interface. In other words, the interface complexity did not interfere in the result obtained for the same experimental data. We concluded that the 1D model is ideal to predict the influence of operational parameters because it is simpler and saves analysis time, maintaining the reliability and accuracy of the results.

Keywords:
Impedance spectroscopy; solid oxide fuel cell; electrolyte; simulation model

Dimension	Axis	Region	Analysis
1D	z	Electrolyte	Reagent flow
		Electrolyte	Reagent concentration
		TPB sites	Reagent concentration
			Temperatures
			Electrical and electrochemical potentials
2D	y-z	Electrolyte	Reagent flow
	x-z	Electrolyte	Reagent concentration and products
		TPB sites
		Gas diffusion region
		Gas diffusion region	Temperatures
		Canals	Temperatures
		Canals	Electric and ionic potentials
3D	x-y-z	Electrolyte	Reagent flow
		Electrolyte	Charge losses
		TPB sites	Charge losses
		TPB sites	Reagent concentration and products
		Gas diffusion region
		Canals
			Temperatures
			Heat removal
			Electric and ionic potentials

Description of geometric parameters	1D model	2D model	3D model
Electrolyte thickness	1.5 x 10^-4 m	1.5 x 10^-4 m	1.5 x 10^-4 m
Thickness of platinum electrodes	1.0 x 10^-4 m	1.0 x 10^-4 m	1.0 x 10^-4 m
Electrolyte radius	-	6.0 x 10^-3 m	6.0 x 10^-3 m
Radius of platinum electrodes	-	3.6 x 10^-3 m	3.6 x 10^-3 m
Electrolyte diameter	-	-	1.2 x 10^-2 m
Diameter of platinum electrodes	-	-	7.2 x 10^-3 m

Node or sub-node	Equation used	Formula	Ref
Electrolyte	Ohm's Law with charge balance	$\nabla \cdot i_{l} = Q_{l}$	Daneshvar et al.²⁵25 Daneshvar K, Fantino A, Cristiani C, Dotelli G, Pelosato R, Santarelli M. Multi-physics simulation of a circular-planar anode-supported solid oxide fuel cell. In: COMSOL Conference; 2012; Milan. Proceedings. Grenoble: COMSOL; 2012.
Electrolyte	Ohm's Law with charge balance	$i_{l} = - σ_{l} \nabla Φ_{l}$
Isolation	Boundary condition	$i_{k} \cdot n = 0$	COMSOL¹⁴14 COMSOL Application Gallery. Current density distribution in a solid oxide fuel cell [Internet]. Grenoble: COMSOL Multiphysics; 2022 [cited 2022 May 29]. Available from: https://br.comsol.com/model/current-density-distribution-in-a-solid-oxide-fuel-cell-514 https://br.comsol.com/model/current-dens...
Initial values	Boundary condition	$Φ_{s} = 0$	COMSOL¹⁴14 COMSOL Application Gallery. Current density distribution in a solid oxide fuel cell [Internet]. Grenoble: COMSOL Multiphysics; 2022 [cited 2022 May 29]. Available from: https://br.comsol.com/model/current-density-distribution-in-a-solid-oxide-fuel-cell-514 https://br.comsol.com/model/current-dens...
Initial values	Boundary condition	$Φ_{l} = 0$
Porous electrode	Ohm's Law with charge balance	$\nabla \cdot i_{s} = Q_{s}$	Singhal and Kendal²⁶26 Singhal SC, Kendal K. High temperature and solid oxide fuel cells: fundamentals, design and applications. 1st ed. USA: Elsevier Science; 2003.
Porous electrode	Ohm's Law with charge balance	$i_{s} = - σ_{s} \nabla Φ_{s}$
Reaction at the porous electrode	Butler-Volmer Kinetics	$i_{l o c, m} = i_{0} (\exp (\frac{α_{a} F η}{R T}) - \exp (\frac{- α_{c} F η}{R T}))$	Singhal and Kendal²⁶26 Singhal SC, Kendal K. High temperature and solid oxide fuel cells: fundamentals, design and applications. 1st ed. USA: Elsevier Science; 2003.
Electrical double layer capacitance	Boundary condition	$i_{d l} = 0$	COMSOL¹⁴14 COMSOL Application Gallery. Current density distribution in a solid oxide fuel cell [Internet]. Grenoble: COMSOL Multiphysics; 2022 [cited 2022 May 29]. Available from: https://br.comsol.com/model/current-density-distribution-in-a-solid-oxide-fuel-cell-514 https://br.comsol.com/model/current-dens...
Electrical double layer capacitance	Boundary condition	$C_{d l} \neq 0$
Electrolyte potential	Boundary condition	$Φ_{l} = Φ_{l, b n d} = 0$	COMSOL¹⁴14 COMSOL Application Gallery. Current density distribution in a solid oxide fuel cell [Internet]. Grenoble: COMSOL Multiphysics; 2022 [cited 2022 May 29]. Available from: https://br.comsol.com/model/current-density-distribution-in-a-solid-oxide-fuel-cell-514 https://br.comsol.com/model/current-dens...
Current in the electrode	Boundary condition	$\int_{\partial Ω}^{} i_{s} \cdot n d p = i_{s, a v e r a g e} \int_{\partial Ω}^{} d p$	COMSOL¹⁴14 COMSOL Application Gallery. Current density distribution in a solid oxide fuel cell [Internet]. Grenoble: COMSOL Multiphysics; 2022 [cited 2022 May 29]. Available from: https://br.comsol.com/model/current-density-distribution-in-a-solid-oxide-fuel-cell-514 https://br.comsol.com/model/current-dens...
Harmonic perturbation	$-$	It depends on selected boundary condition	Experimental

Parameter	Symbol	Value	Ref
Platinum conductivity	$k$	3.9 x 10⁴ S/cm	Burkov et al.²⁹29 Burkov AT, Heinrich A, Konstantinov PP, Nakama T, Yagasaki K. Experimental set-up for thermopower and resistivity measurements at 100-1300 K. Meas Sci Technol. 2001;12(3):264-72.
YSZ conductivity	$σ$	1.8 x 10^-4 S/cm	Experimental
Temperature	T	973 K	Experimental
Equilibrium potential	$E_{e q}$	0.95 V	Choi et al.³⁰30 Choi D-W, Ohashi M, Lozano CA, Vanzee JW, Aungkavattana P, Shimpalee S. Sulfur diffusion of hydrogen sulfide contaminants to cathode in a micro-tubular solid oxide fuel cell. Electrochim Acta. 2019;321(20):134713.
Anodic transfer coefficient	$α_{a}$	3.5	Dickinson³¹31 Dickinson E. Electrochemical impedance spectroscopy: experiment, model, and app [Internet]. Grenoble: COMSOL Multiphysics; 2017 [cited 2022 May 29]. Available from: https://br.comsol.com/blogs/electrochemical-impedance-spectroscopy-experiment-model-and-app/ https://br.comsol.com/blogs/electrochemi...
Cathodic transfer coefficient	$α_{c}$	0.5	Andersson et al.³²32 Andersson M, Paradis H, Yuan J, Sundén B. Three dimensional modeling of an solid oxide fuel cell coupling charge transfer phenomena with transport processes and heat generation. Electrochim Acta. 2013;109(30):881-93.
Average current density of the electrode	$i_{a v g}$	-0,05 x 10^-6 A/cm²	Experimental
Perturbation amplitude	$Δ i_{a v g}$	0.9 A/cm²	Experimental
Exchange current density	$i_{0}$	4 x 10^-3 A/m²	Okamoto et al.³³33 Okamoto H, Kawamura G, Kudo T. Study of oxygen adsorption on platinum through observation of exchange current in a solid electrolyte concentration cell. Electrochim Acta. 1983;28(3):379-82.
Double layer capacitance	$C_{d l}$	0.01 F/m²	Ge et al.²⁷27 Ge X, Fu C, Chan SH. Double layer capacitance of anode/solid-electrolyte interfaces. Phys Chem Chem Phys. 2011;13(33):15134-42.

	YSZ - Atmospheric air
$T (° C)$	350	400	450	500	550	600	650	700
$R (Ω)$	1695.0	483.3	145.2	52.1	23.1	12.5	7.9	5.2
$σ (S / c m)$	$5.8 x 10^{- 5}$	$2.0 x 10^{- 4}$	$6.8 x 10^{- 4}$	$1.9 x 10^{- 3}$	$4.3 x 10^{- 3}$	$7.9 x 10^{- 3}$	$1.3 x 10^{- 2}$	$1.8 x 10^{- 2}$

Geometry	Number of freedom degrees	Solution Time
1D	44	25 s
2D	938	41 s
3D	76886	499 s

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