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Getting started with electrochemistry
in polymer electrolyte membrane fuel cells (PEMFC):
Francois Lapicque
Laboratoire des Sciences du Génie Chimique, CNRS –ENSIC, Nancy
• Background of electrochemical phenomena in FC
• Features of electrochemical reactions
• Transport and transfer
• Available electrochemical methods for their investigation
Presented by:
Dr Bradley Ladewig
[email protected]
Electrochemistry in membrane fuel cells
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Operation principle of membrane fuel cells
H2
PEMFC
Anode
Membrane
Cathode
H2 + ½ O2
H2O + DH
H2
H+ + 2e
½ O2 + 2e + 4 H+
O2/air
H2O
Charge
eg. Engine
Electron flux in the external circuit
Methanol
DMFC
CH3OH + 3/2 O2
CO2 + 2 H2O + DH
CO2 + 6H+ + 6e
Anode CH3OH + H2O
Membrane
Cathode 3/2 O2 + 6e + 6 H+
3 H2O
O2/air
Charge
eg. Engine
Electron flux in the external circuit
Electrochemistry in membrane fuel cells
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Specific
features
of réaction
electrochemical
reactions
Particularités
de la
électrochimique
Heterogeneous process involving the exchange of charges
Current :
Electrons
Charge
transfer
Transfer to the electrode
Current: Ions
Adsorption
(Chemical Processes)
Desorption
Transport
Electrochemistry in membrane fuel cells
Anode:
A
B+e
Cathode:
C+e
D
3
Specific features of electrochemical reactions (C’td)
Faraday’s law
Existence of several reactions
A + ne e - → B
ne FrA
i
e
I  ne FN A
I ne FN A
i 
 ne FrA
A
A
Current yield
Consequences
Ohmic drop : linked to Joule effect
Ohm’s law
i   s grad  s
To be minimised
• Reduce the electrode gap
• Improve the electrical conductivity of the medium
Electrochemistry in membrane fuel cells
4
Split view of a polymer electrolyte membrane fuel cell
H2
Feed
H2
O2
Outlet
O2
External
plate
Bipolar
plate
Membrane-electrode
assembly
Backing
PEMFC:
Electrolyte = Conducting polymer
• Reduce the membrane thickness
• Improve the electrical connections
Electrochemistry in membrane fuel cells
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Electrochemistry in membrane fuel cells
6
Electrodes and membrane
Pt-Ru catalyst deposited on XC-72
X. Xue et al. Electrochem. Comm. 8 (2006) 1280
Cathode
Anode
Backing
Active
layer
Carbone 30 nm
Platinum 2 nm
Membrane
=
Hydrated
Conducting
gel
Backing
Active
layer
50-150 mm
Electrochemistry in membrane fuel cells
Carbon materials
- conducting
- hydrophobic
20 mm
300 mm
7
Diffusion
to Pt
Cathode
O2 transport
by convection
and diffusion
Electrons
Liquid
water
Formation?
Membrane
Anode
Migration H+
½ O2
+ 2 H+
+ 2e
H2O
Heat
(excessive) Drying
Diffusion
to Pt
H2 transport
by convection
and diffusion
Electroosmosis
(H2O)
H2
2H+
+ 2e
Electrons
Diffusion
of H2O
Water
Feed ?
Heat
Water management
Electrochemistry in membrane fuel cells
Flooding
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- DIFFUSION
DIFFUSEUR
: (180
µm)
LAYER
(backing)
matriceporous
poreusestructure
en
Graphite
graphite
(Toray paper)
(e.g.
Toray paper)
+
agent (PTFE)
+ hydrophobic
agent hydrophobe
(PTFE)
- ELECTRODE : (50 µm)
mince
couche
en matériau
Thin
layer
of carbon
carboné(Vulcan
(VulcanXC-72R
XC-72R)
Materials
+ particules
platinum particles
+
de platine
- MEMBRANE : (125 µm)
échangeuse
de protons
(Proton
exchanging)
(Nafion)
e.g.
Nafion
Electrochemistry in membrane fuel cells
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Ohmic behaviour of PEMFC’s
Importance
of hydration
* Other resistance sources :
• Electrodes
• Backings
• Bipolar plates
• Electrical connectors
• Current leads
Conductivité (S m-1)
* Membrane resistance
Nafion 117 (Wöhr, 2000)
30
20
10
0
0
10
20
30
Nombre  : n(H2O)/site sulfonate
R < 0.3 W cm2
Electrochemistry in membrane fuel cells
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Calculation of the membrane resistance
Ohm’s law:
I
Area S
I
Thickness e
i   s grad  s
1-D model
Demonstrate :
D 1 e
R

I
 S
Calculate R for Nafion 112, 115 et 117
with S=100 cm2 and =0.1 S cm-1
Calculate the ohmic drop
for current density at 0.1, 0.3 et 1 A cm-2
Electrochemistry in membrane fuel cells
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Time constant of a capacitor and a resistor in series
C
Calculation of the equivalent complex impedance
1  jRC
Z  R.
1  R 2 C 2 2
R
Time constant: RC
C: double layer capacitance (see above). 30 µF cm-2
Calculation of the time constant in two cases:
Flat electrode plane, S=100 cm2
Electrode of PEMFC, S=100 cm2, g=200
Electrochemistry in membrane fuel cells
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Thermodynamics and theoretical yields of PEMFC’s
Uth, thermoneutral voltage
Uth = - DH / nF
Urev, reversible voltage
Urev = - DG / nF
Theoretical yield hth
hth = DG / DH
n
PEMFC
DMFC
2
6
DH (kJ/mol)
-285.83
-726.51
DG (kJ/mol)
-237.13
-703.35
Uth (V)
1.481
1.229
Urev (V)
1.229
1.215
hth
83.0%
96.8%
Electrochemistry in membrane fuel cells
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Variations with temperature
Variations with pressure
1
 U 0 
.DS

 
ne F
 T  P
1
 U 0 
.DV

 
ne F
 P  T
 E

 T

 E00

 P

0
0

1
 
.DS 0

ne F
P

1
 
.DV0

ne F
T
Present case: Water formation from O2 and H2
P
1
1
U 0 (T , P)  U 0 (298.15,1Atm) 
DV .dP 

2F 1 Atm
2F
T
 DS.dT
298.15
1/ 2
RT  PH 2 PO2 
U 0  1.229  0.00085.T  298.15 
ln 

2 F  PH 2O 
Electrochemistry in membrane fuel cells
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FC cell voltage at zero current: the real case
E0, Zero current voltage << Voltage predicted by the thermodynamics. Why ?
Usually, E0 = 0.9 - 1.04 V
1- Oxygen reduction: slow process
H2O2 is an inetermediate, with E(H2O2 /H2O)=0.68 V
2- Presence of Pt oxides, shift of the equilibrium potential
3- Existence of an internal current caused by hydrogen diffusion through the membrane
followed by combustion at the cathode H2 + ½ O2
H 2O
Internal current density (cross over), in = proport. Flux of H2 diffusion
Potential variation proport. to Ln(in)
Electrochemistry in membrane fuel cells
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Kinetics of electrochemical processes
Butler-Volmer’s model
Model assumptions:
A+e
B
• Reversible reaction
• One electron exchanged
• Overall process controlled by charge transfer rate
Development of the model: theory of the activated complex between A et B
Expression for the current density i versus the overpotential h= E - E0
Exchange current
density
Charge transfer coefficient
  F 
 (1   ) F 
i  i0 exp 
h   exp  
h 
RT


  RT 
Electrochemistry in membrane fuel cells
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Kinetics of electrochemical processes (C’td)
400
Example
 = 0.5, i0 variable
350
10 A/m2
Current density (A/m2)
300
250
Exponential part
(irreversible) : Tafel
200
150
100
1 A/m2
Linear part
50
0
-50 -0.3
Tafel’s law for
h large enough
-100
h=a+blog(i)
-150
-200
-0.2
-0.1
0
0.1
0.3
0.2
Overpotential (V)
Electrochemistry in membrane fuel cells
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Electrode reactions: Hydrogen oxidation
Platinum : Excellent catalyst
« Easy reaction »
Volmer-Tafel’s model :
2 Pt + H2
2H2O + 2PtH)ads
2 PtH)ads
2Pt + 2H3O+ + 2e
 
 CH

2
2
F
i  i 0  0 exp
h  1
RT
 CH

2
Current
density
Slow process
Fast process
h
h + 30 mV
i
10 i
Overpotential
Electrochemistry in membrane fuel cells
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Electrode reactions: Oxygen reduction
Platinum : One of the less worse catalysts
Overall slow reaction
Kinetics and mechanism : Pt or PtO2 ?
* Potential < 0.8 V (High cd)
Pt + O2
PtO2)ads + H+ + e
PtO2H)ads + 3 H+ + 3e
h
h + 120 mV
PtO2)ads
PtO2H)ads
2H2O + Pt
i
h + 60 mV
i
Fast
10 i
* Potential > 0.8 V (Low cd)
h
Fast process
Slow process
10 i
Electrochemistry in membrane fuel cells
PtO2
19
Charge transfer resistance , Ract
Ract
h h 1 1


 .
I
Si S i
h
T=60°C
S=100 cm2
i=0.5 A/cm2
 F 
i  i0 exp 
h   i0 exp b h 
 RT 
Ract 
1
S .b.i
b=17.4 V-1 (56 mV/decade)
and Ract = 1.13 mW
C
Calculation of the time constant Ract.C
Ract
Electrochemistry in membrane fuel cells
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Kinetics of electrochemical processes (C’td)
Case of high current densities: mass transfer can become rate-controlling
Electrode
CAb
i
Electrolytic
medium
CAS
Existence of an additional
overpotential
 C Ab 
RT

hd 
ln 
(1   ) F  C As 
The overpotential is the sum of the charge transfer overpotential (Butler Volmer)
and the concentration overpotential hd
More complex relationship between i and h
Electrochemistry in membrane fuel cells
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Kinetics of electrochemical processes (C’td)
hd: depends on mass transfer rate (diffusion and convection)
When h tends to infinite, CAs = 0 and i tends to iL, limiting current density
iL=96 A/m2
Example :  = 0.5
100
Current density (A/m2)
80
100 A/m2
60
10 A/m2
40
20
1 A/m2
0
-20 -0.3
-0.2
-0.1
0
0.1
0.2
0.3
-40
-60
-80
-100
Overpotential (V)
Electrochemistry in membrane fuel cells
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Control by mass transfer phenomena in FC’s
The involved phenomena
Gas
Convection (bipolar plates, backing)
Diffusion (backing, active layers)
Knudsen diffusion (active layers)
Sharper problems
For dilute reacting gases
(air, reforming hydrogen)
Water Transport through the membrane
Problems raised by liquid water:
Flow hindrance in the various parts: lower transfer rates
i(lim) = 0.5 – 2 A cm-2
Electrochemistry in membrane fuel cells
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Cell voltage
U c  E0 a  E0c  h a  h c  h da  h dc  Re I
Usual reactors
Cathode c
Anode a
E0,a
ha+hda
Ea
Ohmic
drop
For usual
electrochemical reactors
Separator
Ec
hc+hdc
E0,c
Fuel cells
U c  E0a  E0c ha  hc hda  hdc  Re I
Electrochemistry in membrane fuel cells
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Available voltage in PEMFC’s
Cell voltage (V)
Revrsible voltage Urev = -DG/2F
Urev
Hydrogen cross-over,
PtO2, H2O2 etc.
Zero current voltage
Electrochemical
activation
Ohmic drop
Diffusion control
Zone 1
Zone 2
Zone 3
Current density (A/cm2)
Electrochemistry in membrane fuel cells
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Example of i-E curves
Experimental data
0.8
Cell voltage / V
0.7
Exp. 2
Exp. 3
Humid H2
Exp. 5
0.6
Exp. 6
0.5
Exp. 7
0.4
0.3
Dry air
Humid
air
0.2
0.1
0
2
4
6
Current / A
Electrochemistry in membrane fuel cells
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10
26
Dynamics of diffusion processes
Transient Fick’s law, 1-D
C
 C
 D 2
t
x
2
Characteristic time
td 
2
D
, characteristic dimension
Thickness of the Nernst’s film
Thickness of the electrode?
10 µm
D, diffusion coefficient
10-10 m2/s (in liquids or in the gel)
t d  1s
Electrochemistry in membrane fuel cells
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Technology of electrochemical cells
Electrical connection with monopolar electrodes
I
Uc
+ - + - + - + - + Series
I
I
Uc
Parallel
I
5 x Uc
I
4xI
Selection of the connection:
* Significance of energy losses in the E-converter
* Avoid too large currents and low voltages!!
Electrochemistry in membrane fuel cells
Uc
28
Electrochemical methods for FC investigations
Current
Fuel cell
Voltage
Current
Voltage
In most cases:
No reference electrodes
Steady-state techniques
Fixed current
Low-rate scanning (of potential or current)
Transient methods
High-rate scanning
Impedance spectroscopy
Current step
Interpretation
Frequency range: 50 kHz – 10 mHz
Estimation of the ohmic drop
Electrochemistry in membrane fuel cells
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Impedance spectroscopy
• Principle
Courant
Current
u(t )  u  Du cos t 
i(t)  i  Di cos t  
i+Di
u+Du
Tension
Voltage
Z
û cos ( t)
î cos ( t  )
Complex variable
– Varying the frequency (10kHz to 10mHz)
– Plotting data: Nyquist (-Z’’ vs. Z’), or
– Bode (|Z] and  vs. 
– Modelling using equivalent circuits or various
balances
Electrochemistry in membrane fuel cells
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Response of the electrodes
25
Equivalent electrical circuit
- Z" (ohm .cm ²)
20
Rm
15
Q
Ract
Tension
10
5
<1 Hz
100 Hz
0
0
5
10
15
Z' (ohm .cm ²)
Electrochemistry in membrane fuel cells
5 kHz
20
25
10 mHz
31
Equivalent electrical circuit: a simple case
1  jRt C
Z  Rm  Rt .
1  Rt2C 2 2
Rm
C
Rt
Tension
-Z ’’
 infinite
=0
=1/(RtC)
Z = Rm
Z = R p = R m + Rt
Z’
Rm
Electrochemistry in membrane fuel cells
Rt
Rp
32
Electrochemical impedance: equivalent circuit
ZCPE,a
ZCPE,c
RΩ
Rct,a
Tilted loop
in most cases:
CPE
Rct,c
FCO39
0.02
Diffusion
0.01
Z" (ohm)
In most cases,
only one loop
can be observed.
W diff,c
Rs (ohmic)
0
Rt (charge
transfer)
Rp (polarisation)

-0.01
0
0.02
0.04
Z' (ohm)
Electrochemistry in membrane fuel cells
0.06
0.08
33
Some fuel cell references
• Larminie, J. and Dicks, A. (2000) Fuel Cell Systems
Explained, Wiley, England.
• Vielstich W (2003) Handbook of Fuel Cells (4
volumes), Wiley, England.
• Grove, W. (1839) On voltaic series and the
combination of gases by platinum, Philosophical
Magazine Series 3 14:127 – 130.
• Fuel Cell Today www.fuelcelltoday.com [funded by
Johnson Matthey, worlds largest producer of
Platinum, including that used by Mr Grove, producer
of catalyst and MEAs]
Electrochemistry in membrane fuel cells
34