An Elementary Kinetic Model for the LSCF and LSCF-CGO Electrodes of Solid Oxide Cells: Impact of Operating Conditions and Degradation on the Electrode Response

An elementary kinetic model was developed to predict the electrochemical response of porous LSCF and LSCF-CGO electrodes. The model was validated thanks to experiments performed on symmetrical cells using a three-electrode setup. After the model calibration on polarization curves, it has been shown that the model is able to simulate accurately the experimental impedance diagram at OCP and under polarization without additional fitting. Moreover, the evolution of the electrode polarization resistance with the oxygen partial pressure is well reproduced by the model. The electrodes reaction mechanism was thoroughly analyzed and it has been shown that the transition from the bulk path to the surface path depends on the temperature, the polarization and the oxygen partial pressure. The rate-determining steps for the LSCF electrode have been identified at OCP as function of the oxygen partial pressure. Finally, a sensitivity analysis has been performed to study the impact of LSCF demixing on the electrode performances. For a given decomposition, it has been highlighted that the surface passivation would be more impacting than the decrease of the ionic conductivity. Moreover, the impact of the LSCF decomposition would be more detrimental for the electrode performances evaluated in electrolysis mode. List of symbols Roman Symbols: {C}_dl^surface Surface double layer capacitance (F m ⁻² ) {C}_dl^CGO/LSCF Double layer capacitance at the LSCF/CGO interface (F m ⁻² ) {C}_{{O}_o^x}^max Maximum concentration of neutral oxygen atoms in LSCF (mol m ⁻³ ) {C}_{{V}_o^··} Vacancies concentration in LSCF (mol m ⁻³ ) {C}_{{V}_o^··}^eq Vacancies concentration in LSCF at equilibrium (mol m ⁻³ ) {D}_chem Bulk oxygen chemical diffusion coefficient in LSCF (m ² s ⁻¹ ) {D}_i^eff Effective diffusion for the i-th species (m ² s ⁻¹ ) {D}_{{V}_O^••} Oxygen vancancies self-diffusion coefficient (m ² s ⁻¹ ) {D}_{k,{O}₂} Knudsen diffusion coefficient (m ² s ⁻¹ ) {D}_{{O}₂,{N}₂} Molecular diffusion coefficient (m ² s ⁻¹ ) {D}_{{O}⁻−{s}_LSCF} Diffusion coefficient of the oxygen ad-ions (m ² s ⁻¹ ) {D}_{O−{s}_LSCF} Diffusion coefficient of the oxygen ad-atoms (m ² s ⁻¹ ) {D}_{{O}₂−{s}_LSCF} Diffusion coefficient of the oxygen ad-molecules (m ² s ⁻¹ ) E Local electrode potential (V) {E}_act,i Activation energy for the i-th species (kJ mol ⁻¹ ) F Faraday’s constant (C mol ⁻¹ ) {F}_Tot^inlet Total inlet gas flow rate (mol s ⁻¹ ) {h}^· Hole defect in LSCF (–) {\overset{⃗}{i}}_io/e’ Ionic current density in CGO/Electronic current density in LSCF (A m ⁻² ) {K}_eⁱ Thermodynamic equilibrium constant for the i-th species (–) {k}₊ Forward reaction kinetic constants for R1 for the LSCF ^(*) or LSCF-CGO ^(**) electrode ^(*) (mol m ⁻¹ s ⁻¹ ) or ^(**) (mol m ⁻² s ⁻¹ ) {k}_ox^LSCF/gas Forward reaction kinetic constants for R2 (m ³ mol ⁻¹ s ⁻¹ ) {k}_ox^TPBls Forward reaction kinetic constants for R3 for the LSCF ^(*) or LSCF-CGO ^(**) electrode ^(*) (m s ⁻¹ ) or ^(**) (s ⁻¹ ) {k}_deion Forward reaction kinetic constants for R4 (s ⁻¹ ) {k}_ass Forward reaction kinetic constants for R5 (mol ² m ⁻¹ s ⁻¹ ) {k}_des Forward reaction kinetic constants for R6 (s ⁻¹ ) ℓ Electrode thickness (μm) ℓ _CGO Electrolyte thickness (μm) {M}_i Molar mass for the i-th species (g mol ⁻¹ ) m Reaction order (–) {\overset{⃗}{N}}_i Molar flux of the i-th species (mol·m ⁻² ·s ⁻¹ ) {O}_o^x(LSCF) Oxygen atom in the LSCF lattice (–) {O}_o^x(CGO) Oxygen atom in the CGO lattice (–) {O}⁻−{s}_LSCF Oxygen ad-ion on LSCF surface (–) O−{s}_LSCF Oxygen ad-atom on LSCF surface (–) {O}₂−{s}_LSCF Oxygen ad-molecule on LSCF surface (–) O ₂ Gaseous oxygen molecule (–) {P}_{{O}₂} Oxygen partial pressure (atm) {P}_t Total pressure (atm) {\overset{¯}{r}}_pores Mean pore radius (m) R universal gas constant (J mol ⁻¹ K ⁻¹ ) {R}_s Serial resistance Ω cm ² {R}_p Polarization resistance Ω cm ² {s}_LSCF Adsorption site on LSCF surface (–) {S}_p^CGO/LSCF Specific surface area between CGO and LSCF for the LSCF ^(*) or LSCF-CGO ^(**) electrode ^(*) (–) or ^(**) (m ⁻¹ ) {S}_p^LSCF/gas Specific surface area between LSCF and gas phase (m ⁻¹ ) {S}_el. Electrode surface (cm ² ) T Absolute temperature (K) {V}_i Fuller’s volume for the i-th species (–) {V}_o^··(LSCF) Oxygen vacancy in the LSCF lattice (–) {V}_o^··(CGO) Oxygen vacancy in the CGO lattice (–) {y}_(i) Molar fraction of species i-th species (–) Greek Symbols: {α}_Ri^ox/red Charge transfer coefficient for oxidation or reduction for the reaction Ri (–) Γ Surface density of available sites on LSCF (mol m ⁻² ) ε _X Phase volume fraction for the phase X (–) η Overpotential (V) {θ}_{{O}⁻–{s}_LSCF} Coverage of oxygen ions on LSCF (–) {θ}_{O–{s}_LSCF} Coverage of oxygen atoms on LSCF (–) {θ}_{{O}₂₋{s}_LSCF} Coverage of oxygen molecules on LSCF (–) {θ}_{{s}_LSCF} Free sites on the LSCF surface (–) {θ}_{{O}⁻−{s}_LSCF}^eq Coverage rate of oxygen ions on LSCF at equilibrium (–) {θ}_{O−{s}_LSCF}^eq Coverage rate of oxygen atoms on LSCF at equilibrium (–) {θ}_{{O}₂−{s}_LSCF}^eq Coverage rate of oxygen molecules on LSCF at equilibrium (–) {θ}_{{s}_LSCF}^eq Free site on LSCF at equilibrium (–) {ν}_(i) Kinetic rate of chemical/electrochemical reaction (i) in the electrode ^(*) or at the electrolyte interface ^{(**) (*)} (mol m ⁻³ s ⁻¹ ) or ^(**) (mol m ⁻² s ⁻¹ ) {\overset{˜}{μ}}_i Electrochemical potential (J mol ⁻¹ ) {ξ}_TPBls Density of triple phase boundary lengths for the LSCF ^(*) or LSCF-CGO ^(**) electrode ^(*) (m ⁻¹ ) or ^(**) (m ⁻² ) {σ}_{{h}_LSCF^·} Electronic conductivity of LSCF (S m ⁻¹ ) {σ}_{io, CGO} Ionic conductivity of CGO (S m ⁻¹ ) {σ}_i^eff Effective conductivity for th i-th species (S m ⁻¹ ) φ _i Potential (V) χ Surface electrostatic potential (V) τ _X Tortuosity factor for the phase X (–)