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
Authors: Effori E. , Laurencin J. , Silva E. Da Rosa , Hubert M. , David T. , Petitjean M. , Geneste G. , Dessemond L. , Siebert E. 
Published: March 2021

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

d
l

surface

Surface double layer capacitance
(F m−2)

C

d
l

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

c
h
e
m

Bulk oxygen chemical diffusion coefficient in LSCF
(m2 s−1)

D

i

e
f
f

Effective diffusion for the i-th species
(m2 s−1)

D

V

O

•
•

Oxygen vancancies self-diffusion coefficient
(m2 s−1)

D

k
,

O

2

Knudsen diffusion coefficient
(m2 s−1)

D

O

2

,

N

2

Molecular diffusion coefficient
(m2 s−1)

D

O

−

−

s

L
S
C
F

Diffusion coefficient of the oxygen ad-ions
(m2 s−1)

D

O
−

s

L
S
C
F

Diffusion coefficient of the oxygen ad-atoms
(m2 s−1)

D

O

2

−

s

L
S
C
F

Diffusion coefficient of the oxygen ad-molecules
(m2 s−1)

E

Local electrode potential
(V)

E

a
c
t
,
i

Activation energy for the i-th species
(kJ mol−1)

F

Faraday’s constant
(C mol−1)

F

T
o
t

i
n
l
e
t

Total inlet gas flow rate
(mol s−1)

h

·

Hole defect in LSCF
(–)

i
⃗

io
/
e
’

Ionic current density in CGO/Electronic current density in LSCF
(A m−2)

K

e

i

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
(m3 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
(mol2 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
(–)

N
⃗

i

Molar flux of the i-th species
(mol·m−2·s−1)

O

o

x

(
L
S
C
F
)

Oxygen atom in the LSCF lattice
(–)

O

o

x

(
C
G
O
)

Oxygen atom in the CGO lattice
(–)

O

−

−

s

L
S
C
F

Oxygen ad-ion on LSCF surface
(–)

O
−

s

L
S
C
F

Oxygen ad-atom on LSCF surface
(–)

O

2

−

s

L
S
C
F

Oxygen ad-molecule on LSCF surface
(–)

O

2

Gaseous oxygen molecule
(–)

P

O

2

Oxygen partial pressure
(atm)

P

t

Total pressure
(atm)

r
¯

p
o
r
e
s

Mean pore radius
(m)

R

universal gas constant
(J mol−1 K−1)

R

s

Serial resistance
Ω cm2

R

p

Polarization resistance
Ω cm2

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

e
l
.

Electrode surface
(cm2)

T

Absolute temperature
(K)

V

i

Fuller’s volume for the i-th species
(–)

V

o

·
·

(
L
S
C
F
)

Oxygen vacancy in the LSCF lattice
(–)

V

o

·
·

(
C
G
O
)

Oxygen vacancy in the CGO lattice
(–)

y

i

Molar fraction of species i-th species
(–)

Greek Symbols:

α

R
i

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

L
S
C
F

Free sites on the LSCF surface
(–)

θ

O

−

−

s

L
S
C
F

e
q

Coverage rate of oxygen ions on LSCF at equilibrium
(–)

θ

O
−

s

L
S
C
F

e
q

Coverage rate of oxygen atoms on LSCF at equilibrium
(–)

θ

O

2

−

s

L
S
C
F

e
q

Coverage rate of oxygen molecules on LSCF at equilibrium
(–)

θ

s

L
S
C
F

e
q

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)

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

e
f
f

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
(–)