Identification of reaction ratedetermining steps at SOFC electrodes

Identification of reaction rate-determining steps at SOFC electrodes using State-Space Modelling Michel Prestat ETH-Zürich Institute for Nonmetallic Materials Head: Prof. L. J. Gauckler ETH - Ceramics http: //ceramics. ethz. ch

Solid Oxide Fuel Cell (SOFC) O 2 reduction O 2 ½O 2 + 2 e- D O 2 - O 2 e- O 2 mechanism? rate-limiting steps? cathode electrolyte O 2 - fuel oxidation O 2 - O 2 anode e- H 2 H 2 O H 2 + O 2 - D H 2 O + 2 e. H 2 O mechanism? rate-limiting steps? overall: H 2 + ½O 2 → H 2 O ETH - Ceramics http: //ceramics. ethz. ch

Outline Electrochemical Impedance Spectroscopy and State-Space Modelling Oxygen reduction at electronic conducting SOFC cathodes Oxygen reduction at mixed conducting SOFC cathodes ETH - Ceramics http: //ceramics. ethz. ch

Impedance spectroscopy Principle of impedance spectroscopy Small amplitude (5 -10 m. V) input signal → Linearization Current (A) steady-state operating point ~ I= 1 Z(jω) ~ E Admittance Transfer Function ~ E Potential (V) Z = impedance complex ( j 2 = -1) frequency dependant ( ω = 2π f ) ETH - Ceramics http: //ceramics. ethz. ch

EIS spectra and equivalent circuits Im (Z) Re (Z) experimental EIS spectra R -6 f= Im (Z) 1 2π RC Im (Z) /Ω f (Hz) C -4 103 102 -2 104 Re (Z) R 10 1 0 R 0 2 4 6 8 10 12 Re (Z) / Ω C 2 Im (Z) Re (Z) R 1 C 2 Im (Z) R 1 R 2+R 3 ETH - Ceramics Re (Z) R 1 R 2 C 3 R 3 How to interpret the experimental equivalent circuit ? ? http: //ceramics. ethz. ch

State-Space Model calculating the faradaic impedance: electrochemical system Kads O 2(g) D Oads D O 2 - E (input) electrode potential Kb Kdes Kf K = model parameters (Kads, Kdes, Kf , Kb …) IF (output) faradaic current q = state variable (Oads concentration) State-Space Model dq = f (q , E , K) ® state equation dt IF = g (q , E , K) ® output equation ETH - Ceramics http: //ceramics. ethz. ch

State-Space Modelling time domain . linearization Laplace transform . θ = Kads(1 - θ)2 +. . . θ = Aθ +B E IF = -Kf θ e-f. E + … IF = Cθ +D E ZF(jω) varying ω Im(ZF) state-space model* frequency domain * * ** ** * Re(ZF) I . θ=0 E Simulink®: easy implementation of the model. Matlab®: state-space calculations and computing steady-state analysis ETH - Ceramics http: //ceramics. ethz. ch

Oxygen reduction at electronic conducting SOFC cathodes ETH - Ceramics http: //ceramics. ethz. ch

Electronic conducting cathodes O 2 Oads electrode O 2 e- Oads x O 2 - ( Oo ) No O 2 -reduction through the bulk of the electrode. Electrode = electron supplier Typical material: Lax. Sr 1 -x. Mny. O 3 (LSM). ETH - Ceramics electrolyte triple phase boundary (tpb) x. . Electrolyte = O 2 - conductor (Vo and Oo) Typically YSZ (Y 2 O 3 - Zr. O 2) http: //ceramics. ethz. ch

Oxygen reduction reaction models O 2 Oads reservoir O 2 Oads θ 3 θeq diffusion layer Diffusion processes 2 nd Fick‘s law: → Finite difference approach to estimate time and space derivatives O 2 Oads θ 1 x O 2 - ( Oo ) tpb electrolyte → state variable θ (θ 1, θ 2, θ 3) = vector θ 1 ≤ θ 2 ≤ θ 3 ETH - Ceramics http: //ceramics. ethz. ch

Model implementation in Simulink® Block diagrams: as many as compartments in the diffusion layer. in-port out-port θ 1 θ 2 θ 3 (2) θ 2 θ 1 (3) IF E input ETH - Ceramics tpb (1) output http: //ceramics. ethz. ch

Model Implementation in Simulink® Block diagram n° 2 Kads p. O 2 Kdes u 2 1 Kdif/4 + + + - θ 2 state variable - in-ports 1/3 + θ 3 2/3 + θ 1 θ 2 ETH - Ceramics out-port to block diagrams (1) and (3) http: //ceramics. ethz. ch

Im(ZF) / W -0. 6 Modelling results O 2 Oads -0. 4 R 1 electrode O 2 -0. 2 rds = charge transfer rds = rate-determining step(s) Oads 0 2 2. 5 Im(ZF) / W -0. 6 Re(ZF) / W 3 3. 5 O 2 - electrolyte O 2 C 2 Oads -0. 4 R 1 -0. 2 R 2 electrode O 2 Oads rds = adsorption and charge transfer 0 2 2. 5 Re(ZF) / W 3 3. 5 O 2 - Im(ZF) / W -0. 6 electrolyte O 2 Oads -0. 4 electrode O 2 -0. 2 Oads 45° rds = diffusion and charge transfer 0 2 2. 5 Re(ZF) / W 3 3. 5 O 2 - Im(ZF) / W -0. 6 electrolyte O 2 Oads -0. 4 electrode O 2 -0. 2 Oads rds = adsorption, diffusion and charge transfer 0 2 ETH - Ceramics 2. 5 Re(ZF) / W 3 3. 5 O 2 - electrolyte http: //ceramics. ethz. ch

Modelling results Im(ZF) / W -0. 6 O 2 C 2 Oads -0. 4 R 1 -0. 2 R 2 electrode O 2 Oads rds = adsorption and charge transfer 0 2 2. 5 Re(ZF) / W 3 3. 5 O 2 - electrolyte charge transfer rate constants (potential dependant) R 1 and R 2 are not independant adsorption/desorption rate constants → Necessity of a modelling approach to comprehensively interpret experimental impedance even for relatively simple reaction models ETH - Ceramics http: //ceramics. ethz. ch

Experimental reference potentiostat electrode (DC) working electrode frequency response analyzer counter (AC) electrode ~ E+E ~ I+I CDL -3 CF ZTOT = RΩ R 1 R 2 ZF ETH - Ceramics Im (ZTOT) / Ω CDL high CDL moderate CDL=0 (ZF) -2 -1 0 0 1 2 3 4 5 Re (ZTOT) / Ω http: //ceramics. ethz. ch

Experimental porous ~10 -30 mm „real“ electrodes dense ~100 nm -1 mm Geometrically well-defined electrodes microstructured ~20 mm -100 mm top view ETH - Ceramics http: //ceramics. ethz. ch

Comparison modelling - experiments Example of the LSM/YSZ interface La 0. 85 Sr 0. 15 Mn. O 3 @ 800°C I =170 m. A. cm-2 in air. One unique vector (Kads, Kdes Kdif, kf) has to describe at least 4 different impedance spectra Zexp → practical identification - (RΩ, CDL) O 2 Oads electrode O 2 Oads electrolyte O 2 - rds = adsorption, diffusion and charge transfer ETH - Ceramics http: //ceramics. ethz. ch

Oxygen reduction at mixed ionic-electronic conducting SOFC cathodes ETH - Ceramics http: //ceramics. ethz. ch

Mixed ionic-electronic electrodes (MIEC) O 2 Current (A) Oads O 2 - Intermediate T° (500 -800°C) ideal electrode LSCF Oads O 2 - LSM electrolyte Typical material: La 0. 6 Sr 0. 4 Co 0. 2 Fe 0. 8 O 3 -δ (LSCF). Competition between two reaction pathways for O 2 reduction: surface and bulk. → the fastest pathway is rate-determining Eeq Potential (V) Why is LSCF a better electrocatalyst than LSM for oxygen reduction? → the rate-detemining pathway influences the microstructure of the electrode ETH - Ceramics http: //ceramics. ethz. ch

Mixed ionic-electronic electrodes surface pathway is rate-limiting: → porous electrodes, large tpb top view bulk and surface pathways are rate-limiting: → Optimization of microstructure (a, b) b a bulk pathway is rate-limiting: → thin dense electrodes, large electrolyte coverage, low tpb. ETH - Ceramics http: //ceramics. ethz. ch

gwd electrodes Model system: geometrically well-defined (gwd) electrodes O 2 LSCF electrode S d d CGO electrolyte tpb O 2 - S and ltpb constant S=0. 25 cm 2, ltpb= 2 cm O 2 - d is varied d ~ 100 nm - 1 µm → Zsim (E, p. O 2, d) ETH - Ceramics http: //ceramics. ethz. ch

Experimental gwd LSCF layers are prepared by pulsed laser deposition: dense, crack-free. LSCF electrode S CGO electrolyte tpb LSCF 300 nm CGO → Zexp (E, p. O 2, d) = Zsim (E, p. O 2, d) ? ETH - Ceramics http: //ceramics. ethz. ch

Summary · electrochemical reactions yield complex impedance behavior Þ necessity of a modelling approach (analytical or numerical) Þ use of geometrically well-defined electrodes · State-Space Modelling (with modern computation tools) enables to simulate the electrochemical behavior of multistep reactions Þ faradaic impedance Þ I-U curves Þ electroactive species concentration profiles ETH - Ceramics http: //ceramics. ethz. ch

Outlook · SOFC electrode reactions with mixed conductors · Single gas chamber SOFC · State-Space Modelling of entire cells: - with ionic conducting electrolyte (YSZ) - with mixed ionic-electronic conducting electrolyte (Gd. O-Ce. O 2) · SSM approach can be applied to any other field of electrochemistry Þ PEM-FC, batteries, corrosion, electrodeposition… ETH - Ceramics http: //ceramics. ethz. ch

Many thanks to. . . ETH-Zürich S. Rey-Mermet, Dr. Paul Muralt (EPF-Lausanne, Lab. de Céramique) Dr. J. -F. Koenig (Université de Strasbourg, Lab. d‘éléctrochimie) S. Schlumpf SOFC group of ETH-Zürich ETH - Ceramics http: //ceramics. ethz. ch

END ETH - Ceramics http: //ceramics. ethz. ch

Tentative model for oxygen reduction at LSCF T = 700°C gas phase: O 2 - air - no gas phase diffusion - p. O 2 constant Kads Kdes Oads Dense electrode (LSCF) Kin Kout Slow surface diffusion (negligible) Dense electrode: O 2 Kads D O 2 Electrolyte (CGO) Kf Kb O 2 - triple phase boundary (tpb) gas/electrode/electrolyte ETH - Ceramics O 2 - mixed conducting: e- (h) and O 2 - low potential gradient - well-defined dimension Kdes Oads Kfs Kbs Electrolyte - pure O 2 - conductor O 2 - Competition between surface and bulk pathways http: //ceramics. ethz. ch

Mixed ionic-electronic electrodes Modelling MIEC is still very controversial O 2 Oads O 2 - O 2 electrode Oads O 2 - electrolyte Modelling MIEC is still very controversial - incorpotation of oxygen in the - extension of space charge region - influence of permittivity ETH - Ceramics - influence of permittivity: presence of a displacement current? - is electroneutrality fulfilled? http: //ceramics. ethz. ch

Model Implementation in Simulink® dθads 2 2 = Kads p. O 2(1 -qads) – Kdesqads – Kf(E) qads + Kb(E) (1 -qads) dt IF = Ki [– Kf(E) qads + Kb(E) (1 -qads)] Kads p. O 2 Kdes u 2 1 θads + + θads + - 1 -θads state variable function Kf (E) kf exp(-2 b f E) x + E input kb exp (2 (1 -b) f E) x Ki IF output function Kb (E) ETH - Ceramics http: //ceramics. ethz. ch

Model Implementation in Simulink® dθads 2 2 = Kads p. O 2(1 -qads) – Kdesqads – Kf(E) qads + Kb(E) (1 -qads) dt IF = Ki [– Kf(E) qads + Kb(E) (1 -qads)] Kads p. O 2 Kdes u 2 1 θads + + θads + - 1 -θads integrator function Kf (E) kf exp(-2 b f E) x + E input kb exp (2 (1 -b) f E) x Ki IF output function Kb (E) ETH - Ceramics http: //ceramics. ethz. ch

Alternative approch: modeling the impedance new model reaction model DOOads D OO 2 -2 OO 22 D , D 2 ads state-space modeling experimental impedance Im (Z) faradaic impedance Im (Z) Re (Z) validation of the model assessment of kinetics ETH - Ceramics http: //ceramics. ethz. ch

Model 1 (without surf. diffusion) Dissociative adsorption: Kads O 2(g) + 2 s D 2 Oads Kdes O 2 Charge transfer: electrode Oads Kf(E) Oads + 2 e- D O 2 Kb(E) θads x O 2 - ( Oo ) electrolyte → consecutive reaction steps → state variable θads = scalar → state-space model dθads 2 2 = Kads p. O 2(1 -qads) – Kdesqads – Kf(E) qads + Kb(E) (1 -qads) dt IF = Ki [– Kf(E) qads + Kb(E) (1 -qads)] ETH - Ceramics http: //ceramics. ethz. ch

Numerical approach Kads O 2(g) + 2 s D 2 Oads Kdes Kdif O 2 Oads reservoir O 2 Oads θ 3 θeq Oads " Oads Kf(E) Oads + 2 e- D O 2 Kb(E) Diffusion processes 2 nd Fick‘s law: → Finite difference approach to estimate time and space derivatives diffusion layer O 2 Oads θ 1 x O 2 - ( Oo ) tpb electrolyte → state variable θ (θ 1, θ 2, θ 3) = vector θ 1 ≤ θ 2 ≤ θ 3 ETH - Ceramics http: //ceramics. ethz. ch

Model implementation in Simulink® Block diagram n° 2 Kads p. O 2 Kdes u 2 1 Kdif/4 + + + - 1 s Integrator (θ 2) - in-ports 1/3 + θ 3 2/3 + θ 1 θ 2 ETH - Ceramics out-port to block diagrams (1) and (3) http: //ceramics. ethz. ch

Im(ZF) / W -0. 6 Modelling results O 2 C 2 Oads -0. 4 R 1 -0. 2 R 2 electrode O 2 Oads rds = adsorption and charge transfer 0 2 2. 5 Re(ZF) / W 3 3. 5 O 2 - electrolyte charge transfer rate constants (potential dependant) amount of adsorbed oxygen R 1 and R 2 are not independant adsorption/desorption rate constants → Necessity of a modelling approach to comprehensively interpret experimental impedance ETH - Ceramics http: //ceramics. ethz. ch

Experimental investigation O 2 electrode O 2 - Consequence of parallel pathways electrolyte Intermediate T° SOFC (600 -800°C). Typical material: Lax. Sr 1 -x. Coy. Fe 1 -y. O 3 (LSCF). ETH - Ceramics http: //ceramics. ethz. ch