application of electrochemical impedance spectroscopy...
TRANSCRIPT
Application of Electrochemical Impedance Spectroscopy for Fuel Cell Characterization
Dr. Norbert Wagner DLR, Institut für Technische Thermodynamik, Stuttgart
Kronach Impedance Days 2010 Kloster Banz, April, 14th – 16th , 2010
Presentation outline
Introduction and motivationExamples of porous (technical) electrodes
Theory and models of porous gas diffusion 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
Electrochemical kinetic and electrode structure
-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
Increasing power output (P=I·U) at constant cell voltage (overvoltage) by:
•
enlargement of active electrode surface using porous electrodes (electrode structure)
•
increasing i0
(electrode material with high catalytic activity)
I= Surface·i= Surface·i0
·exp{(αRT/zF)η}
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.)
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
Schematic representation of main types of fuel cells
AFC80 °C
PEM80 °C
PAFC200 °C
MCFC650 °C
SOFC1000 °C
O2
H2
AlkalineFC
PhosphoricAcidFC
MoltenCarbonate
FC
SolidOxide
FC
PolymerElectrolyt
MembraneFC
H2
OH-
H+ H+
CO3- O2
-
O H O2 2
H H O2 2
O H O2 2
H H OCO CO
2 2
2
H H OCO CO
2 2
2
CO O2 2 O2Current
Load
Oxidant
Anode
Temperature
Charge carrierin electrolyte
Cathode
Fuel gas
Measuring methods used for fuel cell and fuel cell components characterization : in-situ und ex-situ methods
In-situ measuring methodsCurrent-voltage characteristic (U(i))Electrochemical Impedance Spectroscopy (EIS)
Local and time resolvedCyclic Voltammetry (CV)Current interruption (CI))Chronopotentiometry (CP) und Chronoamperometry (CA)Current density distribution
Ex-situ measuring methods used for fuel cell and fuel cell components characterization
Scanning electron microscopy (SEM) and Transmission electron microscopy (TEM)Energy dispersive X-ray spectroscopy (EDS)X-ray photoelectron spectroscopy (XPS) X-Ray Diffraction (XRD)Thermal gravimetric analysis (TGA) Porosimetry (Hg-Porosimetry)Measurement of the specific surface area (BET-measurement)Determination of gas permeability
Electrochemical Impedance Spectroscopy: Application to Fuel Cells
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
The Metal-Electrolyte Interface
The Metal-Electrolyte Interface
Double layer
capacity
(Cdl
)+ -
The Metal-Electrolyte Interface
Double layer
capacity
(Cdl
)
Faraday-Impedance
(ZF
)
Impedance spectra of a simple electrochemical system (ZF =Rct ): Nyquist representation
Imaginary part /
Real part /
0
-8
-6
-4
-2
2
103 7
Rct
=10
Cdl
=1 mF
Rel
=1
2fmax
=max
=1/Cdl
Rct
Rel Rel
+Rct
fmax
=15.9 Hz
Rct
Impedance spectra of a simple electrochemical system (ZF =Rct ): Bode representation
Rel
=1Rct
=10
Cdl
=1 mF
2fmax
=(1/Rct
Cdl
)(1+Rct
/Rel
)1/2
at =2f=1: ZC
=1/Cdl (------)
PhaseImpedance /
Frequency / Hz
0
20
40
60
80
1
2
5
10
10m 100m 1 10 100 1K 10K
Rel
+Rct
Rel
Rct
fmax
=52.8 Hz
Rel
Schematic representation of different steps during electrochemical reaction as a function of distance
from electrode surface
Redbulk
Mass transport
n e-
Oxad*
Redad*
Charge transfer
Ox* Ox* Oxbulk
Red* Red*
Mass transport
Chem. reaction
Chem. reaction
Adsorption
Ads. Des.
Des.
Electrode Double layer Reaction layer Diffusion layer
Ox + ne- ↔ Red
Multi-layer Gas Diffusion Electrodes with different porous layers
Carbon-PTFE
Layer(Dry
sprayed)
Ag-PTFE Layer(Rolled
Layer)
SEM micrograph of a cross section of SOFC
Anode
Electrolyte
Cathode
SEM micrograph of a porous silver membrane
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
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
Simple pore model with faradaic
processes in pores
RC-transmission line of a flooded pore
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
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 ZZ
p s
*
Z ZZ
p 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*
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
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
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
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
Diffusion
RM
Charge transfer
of ORR
O
V=597 mV; i=400 mAcm-2
V=497 mV; i=530 mAcm-2
V=397 mV; i=660 mAcm-2
+
V=317 mV; i=760 mAcm-2
Charge transfer
of HOR
N. Wagner, K.A. Friedrich, Dynamic Operational Conditions. In: J. Garche, C. Dyer, P. Moseley, Z. Ogumi, D. Rand and B. Scrosati, editors.
Encyclopedia of Electrochemical
Power Sources, Vol. 2. Amsterdam: Elsevier, 2009, pp. 912-930
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
EC
EA
EM
EDiff.
Cdl,a
RM
RA
Cdl,c
RC
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
Evaluation of EIS measured during ORR Equivalent circuit and Rct = f(i)
200
400
600
800
-500 -400 -300 -200 -100current/mA
R / m
N
1
2
3
4
5
6
1 170.8 m2 5.521 ms-1/2
19.38 s-1
3 61.37 mF
942.8 m 4 1
309.9 m 3.18 m
5 508.6 m6 73.35 nH
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
Experimental EIS set-up for stack measurements