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General Introduction to Fuel Cell Electrochemistry
Frano Barbir
Joint European Summer School for Fuel Cell and Hydrogen Technology
Frano Barbir
Professor, FESB, University of Split, Croatia
FESB = Faculty (School) of electrical engineering,
mechanical engineering and naval architecture
heat
What is fuel cell?What is fuel cell?Fuel cell is an electrochemical energy converter.
It converts chemical energy of fuel (H2) directly into electricity.
Fuel cell is like a battery but with constant fuel and oxidant supply.
hydrogen
DC electricity
_
+
BATTERYoxygen
water
FUEL CELL
Invention of fuel cell
Fuel cell historyFuel cell historyChristian Schönbein (1799-1868):Prof. of Phys. and Chem. in Basel, first observation of fuel cell effect (Dec. 1838, Phil. Mag.)
William Robert Grove
1839
(1811 –1896):Welsh lawyer turned scientist, demonstration of fuel cell (Jan. 1839, Phil. Mag.)
Invention of fuel cell
Scientific curiosity
Friedrich Wilhelm Ostwald (1853-1932, Nobel prize 1909): founder of “Physical Chemistry”, provided much of the theoretical
Fuel cell historyFuel cell history
1839
provided much of the theoretical understanding of how fuel cells operate
Friedrich Wilhelm Ostwald – visionary ideas:
“I do not know whether all of us realise fully what an
imperfect thing is the most essential source of power
which we are using in our highly developed engineering
– the steam engine”
Energy conversion in combustion engines
limited by Carnot efficiency limited by Carnot efficiency
unacceptable levels of atmospheric pollution
vs.
Energy conversion in fuel cells
direct generation of electricity
highly efficient, silent, no pollution
Transition would be technical revolution
Prediction: practical realization could take a long time!
Source: Z. Elektrochemie, Vol. 1, p. 122-125, 1894.
Invention of fuel cell
Reinvention
Scientific curiosity
Fuel cell historyFuel cell history
1839 1939
Industrial curiosity
Invention of fuel cell
Reinvention
Scientific curiosity
Fuel cell historyFuel cell history
1960’s1839 1939
Space program
Industrial curiosity
Invention of fuel cell
Reinvention
Scientific curiosity
Fuel cell historyFuel cell history
Space program
1960’s1839 1939
PEM Fuel Cells used in Gemini program
Apollo program used alkaline fuel cells
Space Shuttle uses alkaline fuel cellsSpace Shuttle uses alkaline fuel cells
Renewed interest in PEM fuel cells
Courtesy of UTC Fuel Cells
First PEM Fuel CellGrubb and Niedrach (GE) Gemini Space Program
1960s
Space program
Industrial curiosity
Invention of fuel cell
Reinvention
Scientific curiosity
Fuel cell historyFuel cell history
Space program
1990’s
Entrepreneural phase
1960’s1839 1939
Space program
Industrial curiosity
Invention of fuel cell
Reinvention
Scientific curiosity
Fuel cell historyFuel cell history
Space program
1990’s
Entrepreneural phase
1960’s1839 1939
Birth of new industry
$120
$100
$80
$60
Re-birth of new industry ??
Birth of new industry - Ballard stock
1996 1998 2000 20102008200620042002
$60
$40
$20 Not a very successful birth of new industry ??
AutomobilesBusesScootersBicyclesGolf-cartsDistributed power generationCogenerationBack-up power
Fuel Cell Applications Fuel Cell Applications -- DemonstrationsDemonstrations
Back-up powerPortable powerSpaceAirplanesLocomotivesBoatsUnderwater vehicles
Why fuel cells
Promise of high efficiency
Promise of low or zero emissions
Run on hydrogen/fuel may be produced from indigenous sources/issue of national security
Simple/promise of low cost
No moving parts/promise of long life
Modular
Quiet
electrodehydrogen
What is fuel cell?What is fuel cell?Fuel cell is an electrochemical energy converter.
It converts chemical energy of fuel (H2) directly into electricity.
Fuel cell is like a battery but with constant fuel and oxidant supply.
electrolyte
electrode
hydrogen
oxygen
water
FUEL CELL
electrodehydrogen
What is fuel cell?What is fuel cell?Fuel cell is an electrochemical energy converter.
It converts chemical energy of fuel (H2) directly into electricity.
electrolyte
electrode
hydrogen
oxygen
water
Types of fuel cellsTypes of fuel cells(based on electrolyte)
Alkaline
Acid polymer membraneor Polymer Electrolyte Membrane or Proton Exchange Membrane
PEM
Phosphoric acid
Molten carbonate
Solid oxide
- Zinc/Air fuel cell is not a fuel cell- Direct methanol fuel cell is PEM fuel cell
Reactions in fuel cells
H2 O2H+
H2 O2
H2OOH-
H2O
depleted oxidant and
product gases out
depleted fuel and
product gases out
load
e-
AFC
PEMFC
65-220 °C
60-80 °CH2 O2
H2OH+
H2O2
H2O
CO3=
H2 O2
H2OO=
CO2
CO2
oxidant infuel in
anode cathodeelectrolyte
PEMFCPAFC
MCFC
SOFC
(CO)
(CO)
(CH4)
60-80 °C205 °C
650 °C
600-1000 °C
Types of fuel cellsTypes of fuel cells(based on electrolyte)
Alkaline
Acid polymer membraneor Polymer Electrolyte Membrane or Proton Exchange Membrane
PEM
Phosphoric acid
Molten carbonate
Solid oxide
Why PEM Fuel Cells?Why PEM Fuel Cells?
Simple
Quick start-up
Fast response
High efficiency
High power density (kW/kg and kW/l)
Zero emissions
PEM Fuel Cell Basic ComponentsPEM Fuel Cell Basic Components
protonexchangemembrane
porouselectrode
porouselectrode
catalystlayer
Porous electrode structureGas diffusion layer surface(carbon fiber paper)
80 µµµµm
protonexchangemembrane
porouselectrode
PEM Fuel Cell Basic ComponentsPEM Fuel Cell Basic Components
porouselectrode
catalystlayer
MEA – Membrane Electrode Assembly
cell frame / bipolar plate
Pt-catalyst
current collector /
gas diffusion layer
MEA Cross-Section
current collector /
gas diffusion layer
cell frame / bipolar plate
Pt-catalyst
polymer membrane
PEM Fuel Cell: How does it work?PEM Fuel Cell: How does it work?
membraneelectrode electrode
MembranePorous
electrode
structure
Carbonsupport
Platinum
2H+
collector
plate
collector
plate
2e-
O2
oxygen feed
How does it work?How does it work?
membraneelectrode electrode
external load
2H+
1/2O2 + 2H+ + 2e- → H2O
H2OH2
hydrogen feed
H2 → 2H+ + 2e-
MembranePorous
electrode
structure
Carbonsupport
Platinum
electrode membrane electrode
oxygen feed
collector
plate
O2
external load
2e-
electrode membrane electrode
oxygen feed
O2
PEM Fuel Cell - Basic Principle
2H+
H2 → 2H+ + 2e–
H2
2e-
H2O
hydrogen feed
bi-polarcollector
plate
2H+
H2 H2O
hydrogen feed
2e-
½O2 + 2H+ + 2e– → H2O
end plate
oxidant inhydrogen out
bus plate
bi-polar collector plates
anode
coolant in
FUEL CELL STACKFUEL CELL STACK
oxidant + water outhydrogen in
tie rod
membrane
anode
cathode
coolant out
Actual fuel cell stacksActual fuel cell stacks
BallardTeledyne
UTC Fuel Cells
Honda
Hydrogenics
exhaust
pressureregulator
compressor
load
DC/DC
hydrogen tankgorivni članak
Fuel cell needs supporting equipment/balanceFuel cell needs supporting equipment/balance--ofof--plantplant
pressureregulator
compressor
heatexchanger
waterpump
MM
M
fan
heat exchanger/humidifier
battery
©2002 by Frano Barbir.
compressor
battery
heat exchangers
hydrogen tankpressureregulator DC/DC inverter
Actual fuel cell systemActual fuel cell system
fuel cell stack
battery
humidifierwater tank
water pump
el. motor
©2002 by Frano Barbir.
Understand the difference between:Understand the difference between:
Single cell
StackStack
Systemexhaust
pressureregulator
pressureregulator
compressor
heatexchanger
waterpump
load
MM
M
DC/DC
hydrogen tank
fan
gorivni članak
heat exchanger/humidifier
battery
Fuel Cell Theory Fuel Cell Theory -- ThermodynamicsThermodynamics
Hydrogen side: anode – hydrogen oxidationOxygen side: cathode – oxygen reduction
Mnemonic: reduction of oxygen on cathode: red-cat
Basic reactions
Anode reaction: H2 →→→→ 2e– + 2H+ oxidation
Cathode reaction: ½O2 + 2e– + 2H+ →→→→ H2O reduction
Overall reaction: H2 + ½O2 →→→→ H2O
Same as combustion of hydrogen
Combustion of hydrogen is an exothermic reaction – heat is generated
How much heat?
H2 + ½O2 →→→→ H2O + heat
From the tables:Heat of formation: ∆∆∆∆H = (h ) – (h ) – ½(h ) = – 286 – 0 – 0 = – 286 kJ/mol
Heat of Formation
∆∆∆∆ means difference between products and reactants
Heat of formation: ∆∆∆∆H = (hf)H2O – (hf)H2 – ½(hf)O2 = – 286 – 0 – 0 = – 286 kJ/mol
mol is a measure of quantity1 mol of hydrogen contains 2 grams of hydrogen (2.0159 to be more precise)1 mol of oxygen contains 32 grams of oxygen1 mol contains 6.022 x 1023 molecules (Avogadro’s number)
In a fuel cell both heat and electricity are generated.
But how much electricity?
Can all heat be converted into useful work (electricity)?
Remember 2nd law of thermodynamics?Remember entropy?
∆∆For mechanical processes: W = Q - T∆∆∆∆S
For chemical reactions: ∆∆∆∆G = ∆∆∆∆H - T ∆∆∆∆S
∆∆∆∆G = Gibbs free energy
∆∆∆∆ means difference between products and reactants
∆∆∆∆G = 237.2 kJ/mol (at 25ºC)
Electrical work = charge x voltage
Mechanical work = distance x force
Charge =
Electrical power = current x voltage
Mechanical power = flow rate x pressure
electrons/molecule of H2 molecules/mol Coulombs/electron
2 6.022x1023 1.602x10-19X X
Faraday’s constant
Theoretical cell voltage
∆∆∆∆G = – 2FE
E = voltage
Faraday’s constant
96,485 C/electron mol
Electrical work =
= – ∆∆∆∆G 2F
= 237,2002x96.485
= 1.23
J/mol Ws/molC/mol As/mol
Coulomb = Amper.second
= = V
V
Beauty of SI system!
(at 25ºC)
Theoretical cell voltage – function of temperature
1.05
1.1
1.15
1.2
1.25
1.3C
ell
Po
ten
tial
(V
)liquid water
water vapor
0.8
0.85
0.9
0.95
1
0 200 400 600 800 1000 1200
temperature (C)
Cel
l P
ote
nti
al (
V)
Efficiency of any process
Fuel cell (ideal) efficiency
Theoretical Fuel Cell Efficiency
Ein Eout
Edeg
Eout < Einηηηη =
Eout
Ein
∆∆∆∆H ∆∆∆∆G∆∆∆∆G 237.2
∆∆∆∆H ∆∆∆∆G
Q = T ∆∆∆∆S∆∆∆∆G < ∆∆∆∆H
ηηηηfc = ∆∆∆∆G
∆∆∆∆H
237.2
286.0= = 0.83
Remember:∆∆∆∆G
2F= 1.23 V
∆∆∆∆H
2F= 1.48 VBy analogy: thermoneutral voltage
Fuel cell (ideal) efficiency ηηηηfc = = 0.831.23 V
1.48 V
Ideal cell Voltage at different temperature and pressure
∆∆∆∆G = ∆∆∆∆H - T ∆∆∆∆S
nF
ST
nF
H
nF
G ∆∆∆−−−−==== At 25ºC V231
nF
G.====
∆V4821
nF
H.====
∆V2520
nF
ST.====
∆
ET = 1.482 – 0.000845T Note: ∆∆∆∆H and ∆∆∆∆S are f(T)
For T<373K ET ≈≈≈≈ 1.482 – 0.000845TFor T<373K ET ≈≈≈≈ 1.482 – 0.000845T
All of the above considerations were at ambient pressureP = 1 atm, P = 101.3 kPa; P = 1.013 bar, P = 14.698 psi; P = 0 psig
Does the ideal voltage change with pressure?
Unfortunately – yes!
A little bit of basic thermodynamics
– dG = VmdP
For an ideal gas:
PVm = RT
– dG = RT dPP
– G = – G0 + RT ln PP0
Fuel cell reaction: H2 + ½ O2 →→→→ H2O
⋅⋅⋅⋅++++====
OH
50OH
0P
2
22
P
PP
nF
RTEE
.
ln
Nernst Equation
⋅+
∆−=
∆−
OH
50
2O2H0
2P
PP
nF
RT
nF
G
nF
G .
ln
Summary
E0 = E1atm,298.15K = 1.23 V
Ideal fuel cell voltage
⋅⋅⋅⋅++++−−−−====
OH
50OH
TP
2
22
P
PP
F2
RTT00084504821E
.
, ln..
⋅⋅⋅⋅
++++−−−−====50
OH 22PP
T00004310T00084504821E.
ln...
This is voltage at 0 currentSo called open circuit voltage (OCV)
⋅⋅⋅⋅++++−−−−====
OH
OHTP
2
22
P
PPT00004310T00084504821E , ln...
Caution: valid only for low temperatures
Ideal Cell voltage: 1.23 V
Function of temperature, pressure and concentration of reactants:At 80ºC: 1.186 VAir instead of O2: 1.174 V
Actual voltage is always lower!
0.97
(H2/O2 at 25ºC, 1 atm)
0.97
Ideal Cell voltage: 1.23 V
Function of temperature, pressure and concentration of reactants:At 80ºC: 1.186 VAir instead of O2: 1.174 V
Actual voltage is always lower!
(H2/O2 at 25ºC, 1 atm)
0.97 1.1740.950.900.800.700.600.500.97
current
volt
ag
e
0.97
1.174
0
0.950.900.800.700.600.50
Relationship between current and voltage
Butler-Volmer equation
( ) ( ) ( )
−α−−
−α−=
RT
EEF1
RT
EEFii rr0 expexp
i0 = exchange current densityαααα = charge transfer coefficientF = Faraday’s constantF = Faraday’s constantR = gas constantT = temperatureE = potentialEr = reversible potential
Factors affecting the exchange current densityCatalyst
Roughness/actual surface area
Temperature
Reactants concentration
Pressure
−−
=
γ
Crefr
ccref
T
T
RT
E
P
PLaii 1
00 exp
ref
refr
ccTRTP00
i0ref = exchange current density at reference conditions (T,P) in A/cm2 Pt surface
ac = catalyst specific area (for Pt theoretically: 2,400 cm2/mgpractically: 600-1,000 cm2/mgin electrode: 420-700 cm2/mg
Lc = catalyst loading (today 0.3 to 0.5 mg/cm2)Ec = activation energy (66 kJ/mol)R = universal gas constant (8.314 J/molK)γγγγ = pressure coefficient (0.5 to 1.0)
αααα = charge transfer coefficient
αααα ≅≅≅≅ 1Notes: in some literature nαααα is used instead of αααα
n = 2 for the anode and n = 4 for the cathodeLarminie&Dicks suggest ααααa = 0.5 and ααααc = 0.1 to 0.5 Newman specifies αααα in a range between 0.2 and 2.0
αααα is an empirical factorit should be distinguished from a symmetry factor ββββββββ may be used for single-step reaction with n=1 ββββ may be used for single-step reaction with n=1 ββββRd + ββββOx = 1 or ββββOx = 1 – ββββRd
for metallic surfaces ββββ ≅≅≅≅ 0.5
ααααRd + ααααOx ≠≠≠≠ 1ααααRd + ααααOx = n/νννν
n = number of electrons involvedνννν = number of times the rate-determining step must occur for
the overall reaction to occur once*
*E. Gileadi, Electrode kinetics for Chemists, Chemical Engineeris and Material Scientists,
VCH Publishers, New York, 1993
Relationship between current and voltage
Butler-Volmer equation
( ) ( ) ( )
−α−−
−α−=
RT
EEF1
RT
EEFii rr0 expexp
αααα = charge transfer coefficient
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii rOxrRd0 expexp
(E – Er) = overpotential
On the fuel cell anode:
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii rOxrRd0 expexp
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii araaOxaraaRd
0a
,,,, expexp
Er,a = 0 definition of zero potential – hydrogen electrode
(Ea – Er,a) > 0
negative sign means current is leaving the electrode – oxidation reaction
( )
−α−=
RT
EEFii araaOx
0a
,,exp
(E – Er) = overpotential
On the fuel cell anode:
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii rOxrRd0 expexp
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii araaOxaraaRd
0a
,,,, expexp
Er,a = 0 definition of zero potential – hydrogen electrode
(Ea – Er,a) > 0
negative sign means current is leaving the electrode – oxidation reaction
( )
−α−=
RT
EEFii araaOx
0a
,,exp
On the fuel cell cathode:
Er,c = 1.23 V
(E – E ) < 0
( ) ( )
−α−
−α−=
RT
EEF
RT
EEFii crccOxcrccRd
0c
,,,, expexp
(Ec – Er,c) < 0
( )
−α−=
RT
EEFii crccRd
c0c
,,
, exp
Types of losses in fuel cell:
Activation losses (activation polarization)
Resistive (Ohmic) losses
Mass transfer losses (concentration polarization)
Internal current and fuel crossover
Activation polarization losses
Tafel equation: ∆∆∆∆Vact = a + b . log(i) (empirical)
α=∆
0i
i
F
RTV ln
∆α=
RT
VFii 0 exp
i = current density (mA/cm2)i0 = exchange current density (mA/cm2)R = universal gas constant = 8.314 J/molT = temperature of the process (K)T = temperature of the process (K)α = charge transfer coefficientn = number of electrons involved (2)F = Faraday’s constant = 96,485 C
( ) ( )iF
RTi
F
RTV 0 lnln
α+
α−=∆
( ) ( )00 iF
RT32i
F
RTa log.ln
α−=
α−=
F
RT32bα
= . Tafel slope
Activation polarization losses
α=∆
0i
i
F
RTV ln
∆∆∆∆Vact = a + b . log(i)
0
0.2
0.4
0.6
0.8
1
1.2
po
ten
tia
l lo
ss
(V
)
i0a
slope = b
log scale
For αααα = 1, T = 333 K ⇒⇒⇒⇒ b = 0.066 V/dec
0
0.2
0.4
0.6
0.8
1
1.2
0 500 1000 1500 2000
current density (mA/cm²)
po
ten
tial
lo
ss (
V)
0
0.0001 0.001 0.01 0.1 1 10 100 1000 10000
current density (mA/cm²)
Resistive losses
Ohmic law: ∆∆∆∆V = I.R = i.Ri
I = current (Amps)R = resistance (Ohms)i = current density (A/cm2)Ri = aerial resistance (Ohm-cm2)
A
dR ρ==== ρ = resistivity (Ohm-cm)
d = distance, length (cm)A = cross sectional area (cm2)
Ri = R.A
0
0.2
0.4
0.6
0.8
1
1.2
0 500 1000 1500 2000
current density (mA/cm²)
po
ten
tial
loss (
V)
Resistance through:Membrane (ionic)ElectrodesBi-polar platesInterfacial contacts
electrode membrane electrode
oxygen feed
collector
plate
O2
external load
electrode membrane electrode
O2
2e-
V
bus
plate
Resistive losses
2H+
H2 H2O
hydrogen feed
bi-polarcollector
plate
2H+
H2 H2O
hydrogen feed
2e-
½O2 + 2H+ + 2e– → H2O
2e-
H2 → 2H+ + 2e–
Concentration polarization or mass transport losses
Po
iLi
P ii
PPP
L
00 −−−−====
L0 i
i1
P
P−−−−====
−−−−====
====ii
i
F2
RT
P
P
F2
RTV
L
L0 lnln∆
−−−−−−−−====
Li
i1
F2
RTV ln∆or
0
0.2
0.4
0.6
0.8
1
1.2
0 500 1000 1500 2000
current density (mA/cm²)
po
ten
tia
l lo
ss (
V) theoretical
more realistic
⋅=∆d
icVconc exp
Fick’s First Law of Diffusion:(((( ))))
ACCD
N SB
δ−−−−⋅⋅⋅⋅
====
N = flow rate, mol/sD = diffusion coefficient, cm2/sCB = bulk concentration, mol/cm3
CS = concentration at catalyst surface, mol/cm3
δ= diffusion path, thickness of diffusion layer, cm
A = active area, cm2
nF
IN ====
====
S
B
C
C
nF
RTV ln∆Voltage gain/loss
(Nernst equation)
Alternative way to express concentration polarization
A = active area, cm2
(((( ))))δ
SB CCDnFi
−−−−⋅⋅⋅⋅⋅⋅⋅⋅====
δB
LCDnF
i⋅⋅⋅⋅⋅⋅⋅⋅
====
LB
S
i
i1
C
C−−−−====
−=∆
L
L
ii
i
nF
RTV ln
Voltage loss due to concentration polarization:
Limiting current CS = 0
0.6
0.8
1
1.2p
ote
nti
al l
oss
(V
)
Voltage losses compared
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
po
ten
tial
lo
ss (
V)
activation
resistiveconcentration
Actual fuel cell voltage
concresactPTcell VVVEV ∆∆∆ −−−−−−−−−−−−==== ,
(((( )))) (((( )))) (((( )))) (((( ))))caconcanconcrescaactanactPTcell VVVVVEV ∆∆∆∆∆ −−−−−−−−−−−−−−−−−−−−==== ,
Losses occur on both anode and cathode:
−+⋅−
α−=
Li
0PTcell
i
i1
nF
RTRi
i
i
F
RTEV lnln,
0.8
0.2
0.4
0.6
Cathode solid phase potential
Anode overpotential
Ecell
E
DL DLCL CL
membrane1 A/cm2
po
ten
tial (V
)
0
0.2
-0.4
-0.2
Anode solid phase potential
Anode overpotential
Cathode overpotential
electrolyte phase potential
Eloss
Eeq
po
ten
tial (V
)
0 50 150100nominal cell thickness (µµµµm)
0.6
0.8
1
1.2ce
ll p
ote
nti
al (
V)
Fuel cell polarization curve
activation losses
resistance losses
theoretical (ideal) voltage
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
cell
po
ten
tial
(V
)
mass transport lossesresulting V vs. i curve
©2002 by Frano Barbir.
0.6
0.7
0.8
0.9
1p
ow
er
den
sit
y (
W/c
m²)
Power density vs. current density
Power density = V.i (W/cm2 or mW/cm2)
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000
current density (mA/cm²)
po
wer
den
sit
y (
W/c
m²)
©2002 by Frano Barbir.
0.5
0.6
0.7
0.8
0.9
1
cell
po
ten
tial
(V)
Cell potential vs. power density
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
power density (W/cm²)
cell
po
ten
tial
(V)
©2002 by Frano Barbir.
2e-
O2
e- loss
Internal currents and fuel crossover
2H+
1/2O2 + 2H+ + 2e- → H2O
H2OH2
H2 → 2H+ + 2e-
H2 loss
©2002 by Frano Barbir.
Hydrogen consumption in fuel cell
Faraday’s law:
I = nFN(Amps = Amp-second/mol x mol/s) nF
IN ====
Hydrogen consumption in fuel cell: NH2 = I/(2F)
mol/s
Oxygen consumption in fuel cell: NO2 = ½ NH2 = I/(4F)
Water generation in fuel cell: NH2O = I/(2F)
©2002 by Frano Barbir.
Both internal currents and hydrogen crossover mean loss of current:
Iloss = 2FNloss
This means that even at 0 external current there is hydrogen consumption.
+
α−=
0
lossPTcell
i
ii
F
RTEV ln,
Internal currents and fuel crossover
0.900
0.920
0.940
0.960
0.980
1.000
1.020
0 2 4 6 8 10 12
current density (mA/cm2)
ce
ll p
ote
nti
al
(V)
iloss = 1 mA/cm2
iloss = 2 mA/cm2
iloss = 4 mA/cm2
iloss = 8 mA/cm2
©2002 by Frano Barbir.
Fuel cell efficiency4821
Vcell
.====η HHV
Efficiency = Electricity out
Hydrogen in=
I.V
N.HHHV
=I.V
F2
IN ====
I.HHHV/(2F)
Vcell
1.482=
Cell potential vs. power densityefficiency
0.5
0.6
0.7
0.8
0.9
1
cell
po
ten
tial
(V)
cell
eff
icie
ncy
(HH
V)
0.7
0.6
0.5
0.4
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
power density (W/cm²)
cell
po
ten
tial
(V)
cell
eff
icie
ncy
(HH
V)
0.3
0.2
Fuel cell efficiency4821
Vcell
.====η HHV
Efficiency = Electricity out
Hydrogen in=
I.V
N.HHHV
=I.V
F2
IN ====
I.HHHV/(2F)
Vcell
1.482=
Hydrogen in = hydrogen converted into current + hydrogen loss
II++++ iVIV
F2
IIN loss++++====
loss
cell
loss
cell
ii
i
4821
V
II
I
4821
V
++++====
++++====
..η⇒⇒⇒⇒
electrolyte
electrode
electrode
hydrogen in
oxygen in
hydrogen out
oxygen outelectrolyte
electrode
electrode
hydrogen in
oxygen in
hydrogen out
oxygen out
In some cases excess hydrogen is fed into the fuel cell – some H2 is wasted
fucellV
η=η4821.
hydrogen consumed
hydrogen suppliedηηηηfu =
Fuel cell efficiency vs. power density
0.5
0.6
0.7
0.8
0.9
1ef
fici
en
cy (
HH
V)
not counting crossover & internal current losses
0
0.1
0.2
0.3
0.4
0.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
power density (W/cm²)
effi
cien
cy (
HH
V)
Additional slides
0.6
0.8
1
1.2c
ell
po
ten
tia
l (V
)Tafel = 77 mV/dec
Tafel = 66 mV/dec
Tafel = 55 mV/dec
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
0.8
1
1.2c
ell
po
ten
tia
l (V
)io = 0.0003 mA/cm²
io = 0.003 mA/cm²
io = 0.03 mA/cm²
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
0.2
0.4
0.6
0.8
1
1.2
ce
ll p
ote
nti
al
(V)
ix = 0 mA/cm²
ix = 2 mA/cm²
ix = 20 mA/cm²
1.2ix = 0 mA/cm²
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
0
0.2
0 500 1000 1500 2000
current density (mA/cm²)
0.6
0.7
0.8
0.9
1
1.1
0 20 40 60 80 100
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
ix = 2 mA/cm²
ix = 20 mA/cm²
0.8
1
1.2c
ell
po
ten
tia
l (V
)
R = 0.1 Ohm-cm²
R = 0.15 Ohm-cm²
R = 0.2 Ohm-cm²
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
0.8
1
1.2c
ell
po
ten
tia
l (V
)iL = 1200 mA/cm²
iL = 1600 mA/cm²
iL = 2000 mA/cm²
−+⋅−
+α
−=L
i
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
0.8
1
1.2c
ell
po
ten
tia
l (V
)
P = 300 kPa
P = 200 kPa
P = 101.3 kPa
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
Operating pressure
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
+α
−==
==3P0
loss3PT3Pcell
i
ii
F
RTEV
,
,, ln
( ) ( ) ( )loss3P03T3Pcell iiF1
RTi
F1
RTP
F4
RTEV +
⋅−
⋅++= == lnlnln ,,
( ) ( ) ( )iiRT
iRT
PRT
EV +−++= lnlnln( ) ( ) ( )loss1P01T1Pcell iiF1
RTi
F1
RTP
F4
RTEV +
⋅−
⋅++= == lnlnln ,,
+
=− ==1
3
F
RT
1
3
F4
RTVV 1Pcell3Pcell lnln,,
Vcell,P=3 – Vcell,P=1 = 0.039 V (at 60º)
0.6
0.8
1
1.2c
ell
po
ten
tia
l (V
)air
oxygen
−+⋅−
+
α−=
Li
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
Air vs. oxygen
0
0.2
0.4
0.6
0 500 1000 1500 2000
current density (mA/cm²)
ce
ll p
ote
nti
al
(V)
V0560210
1
F
RT
210
1
F4
RTVV 1Pcell3Pcell .
.ln
.ln,, ====
++++
====−−−− ========
Evidence of Mass Transport Losses
Source: T.P. Ralph and M.P. Hogarth, Platinum Metals Review, Vol. 46, No. 1, pp. 3-14, 2002
Constant currentConstant voltageConstant resistanceConstant powerVariable power
0.6
0.7
0.8
0.9
1
ce
ll p
ote
nti
al
(Vo
lts
)V OP1
OP2
R=2ΩΩΩΩcm2 1 0.5
w=1W/cm2
0
0.1
0.2
0.3
0.4
0.5
0.6
0 200 400 600 800 1000 1200 1400 1600 1800 2000
current density (mA/cm2)
ce
ll p
ote
nti
al
(Vo
lts
)V OP1
0.2
w=1W/cm
0.8
0.6
0.4
0.2
Operational conditions.
Operating pressure
Flow rates of reactants
Operating temperature
Humidity of reactants
What else can affect the polarization curve?
Heat transfer
Fluid mechanics
Fluid mechanics/chemistry
PsychrometryHumidity of reactants PsychrometryThermodynamics of moist gases
We must know some basics!
We must know fuel cell inner working!
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltage
+
∆−
∆−=
OH
50O2H
PT
2
2
P
PP
nF
RT
nF
ST
nF
HE
.
, ln
( )50OHPT 22PPT00004310T00084504821E .
, ln... +−=
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membrane
T. Sakai, et al., J. Electrochem. Soc., Vol. 133, No. 1, pp. 88-92, 1986
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membraneFaster kinetics – Reduced activation losses (exchange current density)
−−
=
γ
ref
C
refr
rcc
ref00
T
T1
RT
E
P
PLaii exp
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membraneReduced activation losses (exchange current density)Improved conductivity of materials
T.A. Zawodzinski, Jr., C. Lopez, R. Jestel, J. Valerio, and
S. Gottesfeld, J. Electrochem. Soc. 140, 1981, 1993
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membraneReduced activation losses (exchange current density)Improved conductivity of materialsMass transport properties (diffusion coefficients)
( ) ( )21b
11Ta/
( ) ( ) 51
ji
125jcic
31jcic
jcic
effij
M
1
M
1TTpp
TT
T
p
aD ./
,,/
,,
,,
ε
+
=
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membraneReduced activation losses (exchange current density)Improved conductivity of materialsMass transport properties (diffusion coefficients)Tightly related to relative humidity of the reactant gases
0
0.2
0.4
0.6
0.8
wa
ter
co
nte
nt in
air
(g
/g)
50 60 70 80 90 temperature (°C)
atm. 200 kPa 300 kPa
What effect does the operating temperature have on fuel cell performance?
Reduced theoretical voltageMore hydrogen permeation through the membraneReduced activation losses (exchange current density)Improved conductivity of materialsMass transport properties (diffusion coefficients) Tightly related to relative humidity of the reactant gasesStack compression
Endplate
Tie Rods
Spring Washers
Positive Terminal
Negat ive Terminal
Reversible Cells
Fluid Manifold
Effect of operating temperature on fuel cell performance
Current density @0.6 V
Q. Yan, H. Toghiani, H. Causey. Steady state and dynamic performance of proton
exchange membrane fuel cells (PEMFCs) under various operating conditions and load
changes, Journal of Power Sources, 2006
Effect of operating temperature Effect of operating temperature -- 1010--cell stackcell stack
0.8
0.9
1 ce
ll p
ote
ntia
l50°C 60°C 70°C
NG2000 10-cell
308 kPa
H2/air
1.5/2.5
0.5
0.6
0.7
ce
ll p
ote
ntia
l
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 current density (A/cm²)
0.8
0.9
1
1.1
Performance Curve: Freeze Tolerant Test50% Propylene Glycol & 50% DI-water
Com m ents :
Date:03-26-99Cell #:5 x 10-074Test Stand #:5Com p./ele.(in.):
H2/Air s toic:1.2/2.0Tem p.(deg. C):see legendPressure (PSIG):30
Mem brane:P-01598(10006284)Active area(cm 2):Res .(ohm s-cm 2):.Current Dens ity(m A/cm 2):
energy partners confidential
Freeze tolerance testFreeze tolerance test
0.3
0.4
0.5
0.6
0.7
0 200 400 600 800 1000 1200
Current Density (mA/cm2)
60 C 50 C 40 C 30 C 20 C 10 C 5 C 0 C -10 C
T
Definition of Operating Temperature
cell surface (where)cell inside (where and how)heating padcoolant incoolant outreactants out
Tpad
Tcout
Operation with thermal pad
Operating temperature
Tcell Tcell
Tcout <=> Tcin
Operation with coolant
Q = mc.cp
.(Tcout – Tcin).
Q = heat to be removedfrom the fuel cell;Tpad
Tcin
TairoutTcell < Tpad
Tcell > Tair,out
Tcell > Tcout if Tcout > Tcin
Tcell < Tcin if Tcout < Tcin
from the fuel cell;function of design ofinside the fuel cell andoperational conditions
©2002 by Frano Barbir.
Q = ŪA.∆∆∆∆Tm
also:
What else can affect the polarization curve?
Unsteady conditions (flooding/drying)
Contaminants
Crossover leaks
Aging (loss of catalyst surface, crossover leaks, change in membrane properties)
Summary
Voltage losses:Activation polarizationOhmic (resistive losses)Concentration polarization or mass transport lossesInternal currents and reactants crossover
+ iRTiiRT
Resulting polarization curve:
4821
Vcell
.====ηFuel cell efficiency:
−+⋅−
+α
−=L
i
0
lossPTcell
i
i1
nF
RTRi
i
ii
F
RTEV lnln,
Effect of operating pressureEffect of oxygen vs. airEffect of operating temperature
PEM Specific Issues – Water transport, gas diffusion
PEM Fuel Cell:
Membrane/Electrode Processes
e-e-
e-
e-
e-e-
Hydrogen
Oxygen
e-
H2 → 2H+ + 2 e- 2H+ + 1/2O2 + 2 e- → H2O
e-
+
+
+ +
+
+
e-e-
e-
Platinum
Carbon
Functional Group
Polymer Electrolyte
e- Electron
Materials Science and Technology Division
Water content and conductivity
Source: T.A. Zawodzinski, et al., J. Electrochem. Soc., Vol. 140, No. 7, pp. A1981-A1985, 1993
λλλλ = water molecules per sulfonate groupλλλλ = water molecules per sulfonate group
Water content and conductivity
Source: T.A. Zawodzinski, et al., J. Electrochem. Soc., Vol. 140, No. 7, pp. A1981-A1985, 1993
Nafion conductivity: ~0.1 S/cm
1/conductivity = resistivity = 10 Ohm-cm
Nafion 115 thickness: 5 mils = 0.0127 cm
Nafion conductivity
Resistance = 10 Ohm-cm x 0.0127 cm = 0.127 Ohm-cm2
At 1 A/cm2 it would cause 0.127 V loss
Nafion conductivity is a function of water content and temperature!
Nafion resistivity – function of membrane thickness?
• unisotropic structure• resistance from the electrodes• thickness of the membrane in the cell different from measured before assembly
Source: F.N. Buchi and G.G. Scherer, J. Electrochem. Soc., Vol. 148, No. 3, pp. A181-A188, 2001
• Electro-osmotic
drag removes
water from the
anode side.
With thicker 0.6
0.8
1.0
HF
RE
SIS
TA
NC
E (
oh
m c
m2)
or
CE
LL
VO
LT
AG
E (
V)
Cell Resistance and Performance:
PEM Thickness Effects
Increasing
Membrane
Thickness
With thicker
membranes,
back diffusion
of water is
difficult - the
anode side loses
water content.
0.0
0.2
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
HF
RE
SIS
TA
NC
E (
oh
m c
m
or
CE
LL
VO
LT
AG
E (
V)
CURRENT DENSITY (A/cm2)
Fg 3, TF69,109,74,117 Ox's
(Neat
Oxygen
Cathodes)
Materials Science and Technology Division
Membrane resistance – function of current density
Source: F.N. Buchi and G.G. Scherer, J. Electrochem. Soc., Vol. 148, No. 3, pp. A181-A188, 2001
Permeation of gases through the membrane
Permeability is a product of diffusivity and solubility:
Pm = D x S
cm2/s x mol/cm3atm =mol
cm.s.atm
For ideal gas: Pvm = RT; at standard conditions vm = 0.024 m3/mol
mol.cm
cm2.s.atmor
For ideal gas: Pvm = RT; at standard conditions vm = 0.024 m3/mol
vm = 24,060 cm3/mol
cm3.cm
cm2.s.atm
cm3.cm
cm2.s.cmHg1 atm = 75 cmHg = 1010 barrers
Example:
DH2 = 6.65x10-7 cm2/s
SH2 = 2.2x10-5mol/cm3atm
Pm = 1.5x10-11mol.cm-1s-1atm-1
1.5x10-11mol.cm-1s-1atm-1 x 24,060 cm3/mol =
= 3.6x10-7 cm3.cm.cm-2.s-1atm-1=
= 3.6x10-7 cm3.cm.cm-2.s-1atm-1/75 cmHg/atm =
= 4.8x10-9 cm3.cm.cm-2.s-1cm-1Hg = 48 Barrers
Permeation rate, N (mol/s)
N = Pm.A.∆P/d
N = I/nF
i = I/A = nF.Pm.∆P/d
Example:
Pm = 1.5x10-11mol.cm-1s-1atm-1
A = 100 cm2
d = 51 µm = 0.0051 cm
N = 2.94x10-7mol/s
I = nFN = 0.057 A
NV = N.24060 (cm3/mol) = 0.125×I cm3/s
NV = 7.5 cm3/min/Amp
d = 51 µm = 0.0051 cm∆P = 1 atm (partial pressure)
I = nFN = 0.057 A
i = I/A = 0.00057 A/cm2 = 0.57 mA/cm2
Additional variable (complication)
DH2 = f(T) = 0.0041e-2602/T
0.00E+00
1.00E-06
2.00E-06
3.00E-06
4.00E-06
5.00E-06
0 20 40 60 80 100 120
temperature (°C)
dif
fusi
vit
y (
cm²/
s)
Permeation of gases through Nafion
Source: T. Sakai, et al., J. Electrochem. Soc., Vol. 133, No. 1, pp. 88-92, 1986
PEM Fuel Cells: Theory and Practice
More information about PEM fuel cells:More information about PEM fuel cells:
Frano Barbir
PEM Fuel Cells: Theory and PracticeElsevier/Academic Press, 2005
ISBN 978-0-12-078142-3
Written as a textbook
for engineering students.
Used at hundreds of universities
Available from:
www.elsevier.com
www.amazon.com
www.barnesandnoble.com
Used at hundreds of universities
In U.S., China, India, Korea, Iran Q
New updated edition coming out 2011!