theory and application of porous electrodes in fuel cell
TRANSCRIPT
Theory and Application of Porous Electrodes in Fuel Cell Characterization
Dr. Norbert Wagner DLR, Institut für Technische Thermodynamik, Stuttgart
Kronach Impedance Days 2009 "Hermann Göhr" Kloster Banz, May, 27th – 29th , 2009
Presentation outline
IntroductionExamples of porous (technical) electrodes
Theory and models of porous electrodesImpedance models
Application of Göhr‘s porous electrode modelEIS measured at PEFCEIS measured during oxygen reduction on silver in alkaline solution
OutlookExperimental set up for EIS applied for stack measurements
Why porous electrodes?
•Enlargement
of active
electrode
surface•Lowering
of overvoltage
at same
current
input
(electrolyzer) or
output
(fuel
cell)•Increasing
of power density
(galvanic
cells)
•Increasing
of storage
capacity
(supercaps)•Lowering
catalyst
loading
by
increasing
active
surface
-100
-80
-60
-40
-20
0
20
40
60
80
100
-80 -55 -30 -5 20 45 70
Overvoltage / mV
Cur
rent
den
sity
/ m
Acm
-2 i0 = 1 mAcm-2
i0 = 10 mAcm-2
b = 25 mV/decade
HER
HOR
Butler-Volmer equation
for
hydrogen
oxydation
(HOR)
and hydrogen
evolution
reaction
(HER)
η1
η2
i = 100 mAcm-2
Fuel cell overvoltage and current density / voltage characteristic
Cathode
d +(r )P
oten
tial
Current density (Current/Surface)
0, Cathode
ct,C
d +(r )
ct,AAnode
Cell Voltage (UC )
Hydrogen Oxidation Reaction (HOR):
H2 = RT/2F i/i*
Oxygen Reduction Reaction (ORR):
O2/air = RT/[(1-)2F] [ln i - ln i*]
Ohmic loss
= iR
Transport limitation (diffusion)
d = -
RT/2F ln (1 - i/ilim )
Fuel cell voltage
UC = U0 - ct,H2 - ct,O2/air - d -
U0
0Cathode
Field of application of porous electrodesBatteries
and supercaps
Process
fluids
Hydro- gen
GDE
Packed
bed
cathodeMembrane
Auxiliary
supply
Current
collector
Water purification
and treatment
(Bio)-Organic
synthesis
Fuel
Cells
O22H
O22H O ,membranereaction layerdiffusion layer
flow field/current collector
electrons
l c i o ee e tr cal p w r
r t np o o s
a h danode c t o e
NaCl
Cl2
H2 O
NaOH, H2
Cl-Na+
OH-+ -
Electrolysis
(Water, NaCl, etc.)
Current I
U/I - Characteristicof a Fuel Cell
Cel
l vo
ltag
e U
Potential excitation signal - E(t)Cu
rrent respo
nse signal- I(t)
Electrochemical Impedance Spectroscopy: Application to Fuel Cells
Schematic diagram of the U-i characteristic of PEFC and Electrochemical Impedance Measurements
Cel
l vol
tage
Current density
Ruhespannung (ohne Stromfluß)i
AnodeUR acAn
)(
iCathodeUR ac
Cath
)(
iCellUR cd
Cell
)(
i
U(Cell)
U-i measured
i
n
U n
U = iRM
Cathodic Overvoltage
Anodic Overvoltage
PEFC: Schematic Diagram (cross section)
SEM picture of PTFE/C powder
Multi-layer Gas Diffusion Electrodes with different porous layers
Carbon-PTFE
Layer(Dry
sprayed)
Ag-PTFE Layer(Rolled
Layer)
Authors Reference Model and systemJ. -P Candy, P Fouilloux, M. Keddam, H. Takenouti
Electrochim. Acta, 26(1981) 1029 Ni in alkaline solution
R. De Levie Electrochim. Acta, 8(1963) 751 Transmission line model, J.S. Newman and C.W. Tobias J. Electrochem. Soc., 109(1962) 1183 Steady-stateJ. Giner, C. Hunter J. Electrochem. Soc., 116(1969) 1124 Flooded-agglomerate model, Pt-GDE, OCR in
alkaline solutionK. Mund, F.v. Sturm Electrochim. Acta, 20(1975) 463 HOR on Ni in alkaline
solutionS. Sunde, Electrochim. Acta, 42(1997) 2637 Composites, SOFCP. Björnbom Electrochim. Acta, 32(1987) 115 Steady state modelR. Holze, W. Vielstich J. Electrochem. Soc., 131(1984) 2298 OCR in alkaline
solutionT.E. Springer, I.D. Raistrick J. Electrochem. Soc., 136(1989) 1594 Flooded-agglomerate and thin film model,
differential element of a pore wallH. Göhr Poster ISE Erlangen, 1983 Homogeneous porous model, Pb
in sulfphuric
acid
G. Paasch, K. Micka, P. Gersdorf Electrochim. Acta, 38(1993) 2653 Macrohomogeneous
porous electrode modelW. Scheider J. Phys. Chem., 79(1975) 127 Model with pore branchingS. Srinivasan, H. D. Hurwitz, J. O'M Bockris J. Chem. Phys., 46(1967) 3108 Thin
film modelM. Kramer, M. Tomkiewicz J. Electrochem. Soc. 131(1984) Stochastic approach with interpenetrating
networkA. Winsel, E. Bashtavelova J. Power Sources, 73(1998) 242 Agglomerate-of-spheres modelM. Tomkiewicz, B. Aurian-Blajeni J. Electrochem. Soc. 135(1988) 2743 True effective medium approachH. Keiser, K.D. Beccu, M.A. Gutjahr Electrochim. Acta, 21(1976) 539 Various geometries of single pore, Ni-GDE
Brief Overview of Porous electrode models and Applications
R = electrolyte resistance inside the pore per unit lengthC = interface capacitance per unit length
Simple pore model of interface charging RC-transmission line of a flooded pore
RCiCi
RiZ
coth)(
imag
inar
y pa
rt /
real part /
0
-3
-2
-2.5
-1
-1.5
-0.5
-1 -0.5 0 0.5 1 1.5 2
C=500mFPore
Nyqusit representation of Impedance of RC- transmission line, model of a flooded pore
R
C
R = 3 Ω C = 0.5 F
RCiCi
RiZ
coth)(
R0 R0
= R/3 = δL/3πr2
δ
= specific
electrolyte
resistancer = pore
radius
L = pore
lenght
Lr
100 mHz
Simple pore model with faradaic processes in pores RC-transmission line of a flooded pore
ct
c = interface capacitance per unit lengthrct = interface charge transfer resistance per unit lenght (Faraday impedance y2 )
r = electrolyte resistance inside the pore per unit length
Nyqusit representation of porous electrode impedance with faradaic impedance element
imag
inar
y pa
rt /
real part /
0
-3
-2
-2.5
-1
-1.5
-0.5
-0.5 0 0.5 1 1.5 2 2.5
C=500mFC+Rpor(3 Ohm)C//R(1.5 Ohm)
r
c rct
r = 3 c = 500 mFrct
= 1.5
Generalization of RC-transmission line of a flooded pore
Thin-film model of a porous electrode
Thin-film model and agglomerate plus thin-film model of a porous electrode
I.D. Raistrick, Electrochim. Acta, 35(1990) 1579
Theory of Agglomerated Electrodes
metal side
electrolyte sideionic current
Gas (backing) side
electrolyte sideionic current
M. Eikerling, A.A. Kornyshev, E. Lust, J. Electrochem. Soc., 152 (2005) E24
Hierarchical model (Cantor-block model)
ll
l/al/alz
lz/az
n = 0
n = 1
ll
l/al/alz
lz/azn = 2
R
C
(a2/az)R
Caaz)
(a2/az)2R
Caaz)2
(a2/az)2R
R
C
(a2/az)R
Caaz)
(a2/az)2R
Caaz)2
(a2/az)2R
n = 0
n = 1
n = 2
R
C
(a2/az)R
Caaz)
(a2/az)2R
Caaz)2
(a2/az)2R
R
C
(a2/az)R
Caaz)
(a2/az)2R
Caaz)2
(a2/az)2R
n = 0
n = 1n = 1
n = 2n = 2
S.H. Liu, Phys. Rev. Letters, 55(1985) 5289T.Kaplan, L.J.Gray, and S.H.Liu, Phys. Rev. B 35 (1987) 5379
μsL μ 2 2
z
μ2 2
z(1)μ
2 2z
(2)μ
(3)μ
/11
/11
/11
...
RZ R
N a aj
N a aj
N a aj
j
mZZe
metalelectrolyte pores
porous layer
Zs1 ZsnZsi
ZpnZpiZp1
Zq1 Zqi Zqn
H. Göhr
in Electrochemical Applications/97, www.zahner.de
Cylindrical homogeneous porous electrode model (H. Göhr) I
Cylindrical homogeneous porous electrode model (H. Göhr) IIIons (H+, OH -,..)
I I
Por
e
Ele
ctro
de, p
orou
s lay
er
Electrolyte Zq
Zp ZS
Zo
Zn
Current (e-)
qsp ZZZ )(Z* =Z ZZ Z
p s
p s
( )Z#
=
C = cosh S = sinhZ ZZp s
*
Z ZZp s
*
P = q0
= v = sp
p
ZZZ
ZZ o
* Z ZZ
p s*
qn
= ZZn
* s = = 1-p ZZ Z
s
p s
C C p s S p q s q
S q q C q qn o
n o n o
( ) ( )( ) ( )
1 21
2 2
Z = Z#+Z*
Porous electrode model with faradaic impedance
Simulation of Impedance Spectra using Porous Electrode Model
(Rct
||Cdl
“+“Rel,por
)+RM
+L Rct
= 50 mCdl
= 50 mF RM
= 3m L = 20 nH
Rel,por
= 0 m Ω 10mΩ 20 mΩ 30mΩ
imag
inar
y pa
rt / m
real part / m
0
-20
20
10 20 30 40 50 60
pore 0mpore 10mpore 20mpore 30m
|Z| / m
frequency / Hz
5
10
20
15
50
100m 1 3 10 100 1K 10K 100K
pore 0mpore 10mpore 20mpore 30m
frequency / Hz
|phase| / 0
0
15
30
45
60
75
90
100m 1 3 10 100 1K 10K 100K
pore 0mpore 10mpore 20mpore 30m
Electrochemical Impedance Spectroscopy: Experimental Set-up
Electrochemical
workstation
PEFC
Flow
contollerPressure
regulator
Humidifier
Bode diagram of measured EIS at different cell voltages (current densities) I
|Z| /
frequency / Hz
|phase| / 0
0
15
30
45
60
75
90
10m
30m
100m
300m
1
3
10m 100m 1 3 10 100 1K 10K 100K
OCV 1024 mV952 mV901 mV871 mV841 mV807 mV777 mV747 mV717 mV
Bode diagram of measured EIS at different cell voltages (current densities) II
Phase oImpedance / m
Frequency / Hz
0
20
40
60
80
10
20
15
30
50
10m 100m 1 10 100 1K 10K 100K
O
E=597 mV; i=400 mAcm-2
E=497 mV; i=530 mAcm-2
E=397 mV; i=660 mAcm-2
+
E=317 mV; i=760 mAcm-2
Bode diagram of measured EIS at different cell voltages (current densities) III
Phaseo
Impedance /
Frequency / Hz
0
20
40
60
80
10m
30m
100m
300m
1
3
10m 100m 1 10 100 1K 10K 100K
O
E=1024 mV; I=0 mA
E=841 mV; I=1025 mA
E=597 mV; I=9023 mA+
E=317 mV; I=17510 mA
Common Equivalent Circuit for Fuel Cells
Cdl,a
RM
Rct,a
Cdl,c
Rct,c
Common Equivalent Circuit for Fuel Cells
Cdl,a
RM
Rct,a
Cdl,c
Rct,cZdiff
Diffusion of O2
Common Equivalent Circuit for Fuel Cells
Cdl,a
RM
Rct,a
Cdl,c
Rct,c ZdiffZdiff
Diffusion of H2
EIS at Polymer Fuel Cells (PEFC): Common equivalent circuit and boundary case
Cdl,a
RM
Rct,a
Porous electrode with pore electrolyte resistance (Rpor ) and surface layer resistance (RS )
Cdl,c
Rct,c
CN
RN
Cdl,a
RM
Rct,a
Cdl,c
Rct,c
Equivalent
circuit
of the PEFC: anode and cathode
simulated
without
pores, without
diffusion
(valid
for
example
at lower
current
densities)
Bode diagramm of the EIS, measured at the PEFC at 80°C, symmetrical gas supply of the cell
Phase oImpedance /
Frequency / Hz
0
20
40
60
80
10m
100m
1
10
10m 100m 1 10 100 1K 10K 100K
O2 /O2 H2 /H2
EIS at Polymer Fuel Cells (PEFC): Contributions to the cell impedance at different current densities
0
0.04
0.08
0.12
0.16
0.2
0 100 200 300 400 500 600 700
Current density /mAcm-2
Cel
l im
peda
nce
/Ohm
0
0.2
0.4
0.6
0.8
0 200 400 600Current density /mAcm-2
Cell
impe
danc
e /O
hm
Evaluation of the U-i characteristics from EIS
100
300
500
700
900
1100
0 200 400 600 800
Current density /mAcm-2
Cel
l vol
tage
/mV
measured
curve: Un
= f(in
)calculated
curve: Un
= in
Rn
(without
integration) calculated
curve
using
method
II: Un
= an
i2n
+bn
in
+cnx calculated
curve
using
method
I: Un
= an
in
+bn
RU
In n
Integration method
I:
U UU
I
U
II I
n n n n n n
112 1 1
( ) ( )
Integration method
II:
U a I b I cn n n n n n 2 with:
aR R
I Inn n
n n
1
12 ( )
b R a In n n n
1 12
c U a I b In n n n n n
1 12
1
EIS at Polymer Fuel Cells (PEFC): Contributions to the overal U-i characteristic determined by EIS
200300400500600700800900
10001100
0 100 200 300 400 500 600 700 800
Current density / mAcm-2
Cel
l vol
tage
/ mV
E0
EK
EA
EM
EDiff.
Cdl,a
RM
RA
Cdl,c
RK
CN
RN
Evaluation of EIS with the porous electrode model I
I
I
I
00.020.040.060.080.1
0 200 400 600 800
Current density /mAcm-2R
p,a;
Rct
,a; R
por,a
/Ohm
21
21
,
,
,,,
tanh
)(
act
apor
actaporap
RR
RRR
Porous electrode resistance (Rp, a ), charge transfer resistance (Rct, a ) and electrolyte resistance (Rpor, a ) in the pore of the anode at different current densities
Evaluation of EIS with the porous electrode model i-V characteristic and current dependency of pore electrolyte resistance
of the anode and cathode
Rel,por,Anode♦
Rel,por,Kathode
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12 14 16 18
Current / A
Pore
ele
ctro
lyte
resi
stan
ce /
mO
hm
0
200
400
600
800
1000
1200
Cell
volta
ge /
mV
Impedance Measurements during Oxygen Reduction Reaction (ORR) in 10 N NaOH, on Silver Electrodes
at Different Current Densities
10m 100m 1 3 10 100 1K 10K 100K
500m
1
2
1.5
5
|Z| /
0
15
30
45
60
75
90|phase| / o
frequency / Hz
45 mA40 mA
35 mA30 mA
25 mA20 mA
15 mA
10 mA
5 mA
100 mA95 mA90 mA85 mA80 mA75 mA70 mA65 mA60 mA55 mA50 mA
1 2 3 4 5
0
-4
-2
Z' /
Z'' /
-50
5 mA
10 mA
15 mA20 mA
100 mA
i / mA
Outlook
Further improvement of porous electrode models
Combination and extension of existent and new models
Application of EiS to segmented cells
Experimental validation of models usingPEFC and DMFC electrodes with different porous structureGas Diffusion Electrodes (GDE) for Oxygen Consumption Reaction (OCR) in alkaline solution using different gas compositions