Thermodynamics and Of Low Temperature Fuel Cells

Frano Barbir

Professor, FESB, Split, Croatia

Joint European Summer School for and Technology Prof. Dr. Frano Barbir

energy partners

What is fuel cell? Fuel cell is an electrochemical energy converter.

It converts chemical energy of fuel (H 2) directly into electricity. Fuel cell is like a battery but with constant fuel and oxidant supply.

heat

_ hydrogen

FUELBATTERY CELL DC electricity +

water Fuel cell history Christian Schönbein Invention of fuel cell (17991868): Prof. of Phys. and Chem. in Basel, first observation of fuel cell effect (Dec. 1838, Phil. Mag.)

William Robert Grove (1811 –1896): Welsh lawyer turned scientist, demonstration of fuel cell (Jan. 1839, Phil. Mag.)

1839 Fuel cell history Invention of fuel cell Scientific curiosity

Friedrich Wilhelm Ostwald (18531932, Nobel prize 1909): founder of “Physical ”, provided much of the theoretical understanding of how fuel cells operate

1839 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  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. 122125, 1894. Fuel cell history Invention of fuel cell Scientific curiosity

Reinvention

1839 1939 Fuel cell history Invention of fuel cell Scientific curiosity

Reinvention Industrial curiosity

1839 1939 1960’s Fuel cell history Invention of fuel cell Scientific curiosity

Reinvention Industrial curiosity

Space program

1839 1939 1960’s PEM Fuel Cells used in Gemini program Apollo program used alkaline fuel cells Space Shuttle uses alkaline fuel cells Renewed interest in PEM fuel cells

First PEM Fuel Cell 1960s Gemini Space Program Grubb and Niedrach (GE)

Courtesy of UTC Fuel Cells Fuel cell history Invention of fuel cell Scientific curiosity

Reinvention Industrial curiosity

Space program

Entrepreneural phase

1839 1939 1960’s 1990’s Fuel cell history Invention of fuel cell Scientific curiosity

Reinvention Industrial curiosity

Space program

Entrepreneural phase

Birth of new industry

1839 1939 1960’s 1990’s Fuel Cell Applications DemonstrationsDemonstrations

Automobiles Buses Scooters Bicycles Golfcarts Distributed power generation Cogeneration Back up power Portable power Space Airplanes Locomotives Boats Underwater 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 What is fuel cell? Fuel cell is an electrochemical energy converter.

It converts chemical energy of fuel (H 2) directly into electricity. Fuel cell is like a battery but with constant fuel and oxidant supply.

hydrogen

electrolyteFUEL CELL

oxygen electrode

water What is fuel cell? Fuel cell is an electrochemical energy converter.

It converts chemical energy of fuel (H 2) directly into electricity.

electrode hydrogen

electrolyte

oxygen electrode

water Types of fuel cells (based on electrolyte)

Alkaline

Acid polymer membrane or Polymer Electrolyte Membrane PEM or Proton Exchange Membrane

Phosphoric acid

Molten carbonate

Solid oxide

/Air fuel cell is not a fuel cell Direct methanol fuel cell is PEM fuel cell Reactions in fuel cells load

e-

depleted fuel and depleted oxidant and product gases out product gases out

H - O 2 OH 2 AFC 65220 °C H2O H2O

H2 H+ O2 PEMFC 60 80 °C PAFC 205 °C H2O

H2 = O2 (CO) CO 3 MCFC CO 2 650 °C CO 2 H2O (CO) H = O 2 O 2 SOFC (CH ) 6001000 °C 4 H2O

fuel in oxidant in

anodeelectrolyte cathode Types of fuel cells (based on electrolyte)

Alkaline

Acid polymer membrane or Polymer Electrolyte Membrane PEM or Proton Exchange Membrane

Phosphoric acid

Molten carbonate

Solid oxide Why PEM Fuel Cells?

Simple

Quick startup

Fast response

High efficiency

High power density (kW/kg and kW/l)

Zero emissions PEM Fuel Cell Basic Components

porous electrode

proton exchange membrane catalyst layer porous electrode Porous electrode structure Gas diffusion layer surface (carbon fiber paper)

80 m PEM Fuel Cell Basic Components

porous electrode

proton exchange membrane

catalyst porous layer electrode

MEA – Membrane Electrode Assembly MEA CrossSection

cell frame / bipolar plate

current collector / gas diffusion layer

Pt-catalyst polymer membrane

Pt-catalyst

current collector / gas diffusion layer

cell frame / bipolar plate PEM Fuel Cell: How does it work?

electrode membrane electrode

Carbon support

Porous Membrane electrode structure How does it work? external load

collector collector electrode membrane electrode plate plate oxygen feed

O2

2e -

2H + H → 2H + + 2e - + - 2 1/2O 2 + 2H + 2e → H2O

Carbon support

Porous Membrane H H O electrode 2 2 structure hydrogen feed Platinum PEM Fuel Cell Basic Principle external load

collector electrode membrane electrode electrode membrane electrode plate oxygen feed oxygen feed

O2 O2

- 2e 2e - 2H + 2H + bipolar collector H → 2H + + 2e – 2 plate

+ – ½O 2 + 2H + 2e → H2O

H2 H2O H2 H2O hydrogen feed hydrogen feed FUEL CELL STACK end plate bus plate bi-polar collector plates coolant in oxidant in hydrogen out

anode membrane cathode

hydrogen in oxidant + water out coolant out

tie rod Actual fuel cell stacks

Teledyne Ballard

Honda

Hydrogenics UTC Fuel Cells Fuel cell needs supporting equipment/balanceequipment/balanceofofplantplant

load

DC/ DC pressure hydrogen tank regulator gorivni članak exhaust compressor pressure regulator heat exchanger/ M humidifier water pump heat exchanger battery fan M M

©2002 by Frano Barbir. Actual fuel cell system

pressure regulator DC/DC inverter hydrogen tank

heat exchangers compressor

bat tery el. motor fuel cell stack

water tank humidifier

water pump

©2002 by Frano Barbir. Understand the difference between:

Single cell

Stack

load

DC/ DC pressure hydrogen tank regulator System gorivni članak exhaust compressor pressure regulator heat exchanger/ M humidifier water pump heat exchanger battery fan M M Fuel Cell Theory ThermodynamicsThermodynamics

Basic reactions

Hydrogen side: anode – hydrogen oxidation Oxygen side: cathode – oxygen reduction

Mnemonic: red uction of oxygen on cat hode: redcat

– + Anode reaction: H2 →→→ 2e + 2H oxidation

– + Cathode reaction: ½O 2 + 2e + 2H →→→ H2O reduction

Overall reaction: H2 + ½O 2 →→→ H2O

Same as combustion of hydrogen Heat of Formation

Combustion of hydrogen is an exothermic reaction – heat is generated

H2 + ½O 2 →→→ H2O + heat How much heat?

From the tables:

Heat of formation: H = (h f)H2O – (h f)H2 – ½(h f)O2 = – 286 – 0 – 0 = – 286 kJ/mol means difference between products and reactants mol is a measure of quantity 1 mol of hydrogen contains 2 grams of hydrogen (2.0159 to be more precise) 1 mol of oxygen contains 32 grams of oxygen 1 mol contains 6.022 x 10 23 (Avogadro’s number) Chemistry can be confusing!!!

Don’t forget – fuel cell is an electro chemical device

Enthalpy = heat of formation Negative heat means heat is released →→→ exothermic reaction Forget about plus and minus →→→ use common sense Of course that combustion of hydrogen and oxygen produces heat. How much heat? →→→ 286 kJ/mol

This enthalpy of hydrogen combustion reaction is also called: Hydrogen Heating Value (or to be more precise Higher Heating Value) obviously – how much heat we can get from hydrogen

Important note: all chemical tables refer to 25ºC.

That means that both reactants and products are at 25 ºC. Heat of combustion – heating value

1 mol of H O (l) 1 mol of H 2 + ½ mol of O 2 2 18 g of H O (l) 2 g of H 2 + 16 g of O 2 2 T = 25 °C (298.15 K) T = 25 °C (298.15 K)

PV = GRT or PV = N RT Heat = 286 kJ Heat of combustion – heating value

1 mol H 2 + x mol O 2 1 mol of H 2O (g) + (x ½) mol O 2 2 g of H 2 + 32x g of O 2 18 g of H 2O (g) T = 25 °C (298.15 K) T = 25 °C (298.15 K)

PV = GRT or PV = N RT Heat = 241 kJ Heat of combustion – heating value

Saturation pressure at 25°C:

Psat = 3.169 kPa

Maximum water content in air(oxygen) at saturation:

mol H 2O/mol O 2 = P H2O /P O2 = 3.169/(101.3 – 3.169) = 0,0323

1 mol of H 2O (g) + (x ½) mol O 2 x – ½ >>>= 1/0.0323 = 31 18 g of H 2O (g) T = 25 °C (298.15 K) X >>> = 31.5

1 mol H2 + 32 mol O2 Heat = 241 kJ Higher and lower heating value

Liquid water produced: 286 kJ/mol Higher heating value

Water vapor produced: 241 kJ/mol Lower heating value

The difference is: 45 kJ/mol Heat of evaporation

45 kJ/mol = 2.5 kJ/g = 2500 kJ/kg 18 g/mol

Why do we care about heating value? There is no combustion in fuel cell!

We use heating value as a measure of energy going into the fuel cell:

mol/s x kJ/mol = kJ/s = kW Beauty of SI system! In a fuel cell both heat and electricity are generated.

But how much electricity?

Can all heat be converted into useful work (electricity)?

Remember 2 nd law of thermodynamics? Remember entropy?

For mechanical processes: W = Q TS

For chemical reactions: G = H T S

G = Gibbs free energy

means difference between products and reactants

G = 237.2 kJ/mol (at 25ºC) Theoretical cell voltage

Electrical work = charge x voltage Electrical power = current x voltage

Mechanical work = distance x force Mechanical power = flow rate x pressure

Charge = 2 XX 6.022x10 23 1.602x10 19

electrons/ of H 2 molecules/mol Coulombs/electron

Faraday’s constant 96,485 C/electron mol Coulomb = Amper .second

Electrical work = G = – 2FE

– G 237,200 E = voltage = = = 1.23 V (at 25ºC) 2F 2x96.485

J/mol Ws/mol = = V Beauty of SI system! C/mol As/mol More thermodynamics – effect of temperature

G = H T S

means difference between products and reactants

hf (J/mol) s (J/mol,K)

H2 0 130.59 O2 0 205.14 H2O (l) –285,838 70.05 H2O (g) –241,827 188.83

(at 25ºC) H = (h f)H2O – (h f)H2 – ½(h f)O2 = – 286 – 0 – 0 = – 286 kJ/mol

S = (s) H2O – (s) H2 – ½(s) O2 = 70.05 – 130.59 – ½x205.14 = – 163.11 J/mol,K

T T h = f(T) 1 h === h +++ c dT sT === s298.15 +++ cpdT s = f(T) T 298.15 ∫∫∫ p ∫∫∫ T 298.15 298.15 Cp = f(T) G = f(T) Cp = f(T)

43.00 H O(g) 41.00 2 39.00 37.00 35.00 O2 33.00 31.00 H2 29.00 SpecificSpecific heatheat (J/mol,K) (J/mol,K) 27.00 25.00 273 373 473 573 673 773 873 973 1073 Temperature (K)

Dashed lines: equations from Larminie&Dicks pp.392393 Solid lines: equations from Fuel Cell Handbook H and G as a function of temperature

350

300

250

200

G G G (kJ/mol) (kJ/mol) 150 H (l)

dH orordH dH dG dG (kJ/mol) (kJ/mol) 100 G (l) H or H H (g) 50 G (g) 0 0 200 400 600 800 1000 1200 temperature (C) Theoretical cell voltage – function of temperature

1.3 1.25 liquid water 1.2 water vapor 1.15 1.1 1.05 1

Cell Potential (V) (V) Potential Potential Cell Cell 0.95 0.9 0.85 0.8 0 200 400 600 800 1000 1200 temperature (C) Theoretical Fuel Cell Efficiency

Efficiency of any process Ein Eout

E ηηη = out Eout < E in Ein Edeg

Fuel cell (ideal) efficiency H G G 237.2 ηηη = = = 0.83 fc H 286.0 G < H Q = T S G Remember: = 1.23 V 2F H By analogy: = 1.48 V thermoneutral voltage 2F 1.23 V Fuel cell (ideal) efficiency ηηη = = 0.83 fc 1.48 V Sometimes the lower heating value is used to express the efficiency

In internal combustion engines the products leave at a temperature above 100ºC – product water is steam indeed. Therefore, the heat of condensation cannot be utilized, and because of that the lower heating value is used to calculate the engine efficiency.

Hydrogen higher heating value: 286 kJ/mol Hydrogen lower heating value: 241 kJ/mol G 237.2 η ======0.83 Efficiency based on higher heating value: H 286.0 G 237.2 Efficiency based on lower heating value: η ======0.98 H 241.0 (case of condensing boilers)

Remember: V η === cell HHV G/2F = 1.23 V Efficiency is also: 1.482 H /2F = 1.482 V HHV V H /2F = 1.254 V η === cell LHV LHV 1.254 Maximum efficiency for mechanical systems

Qin TH Carnot efficiency or Wout Efficiency of Carnot engine TC Wout < Q in W T Qdeg ηηη = out = 1 – C Qin TH

Carnot efficiency is the maximum efficiency any process/engine taking place between the two temperatures can have.

However, from any practical point of view the Carnot efficiency is meaningless!

An engine operating with Carnot efficiency would produce zero power! Carnot efficiency

Max efficiency = 1 – Tc/T h

0.9 Efficiency at 0.8 max. power = 1 – Tc/T h 0.7 0.6 0.5 0.4 efficiency efficiency 0.3 0.2 0.1 0 0 20 40 60 80 100 120 power Similarity between Carnot efficiency and fuel cell ideal efficiency

An engine operating with Carnot efficiency would produce zero power!

A fuel cell operating with ideal efficiency would produce zero power!

E = – G is maximum cell voltage 2F

Maximum voltage is achieved when there is no current.

Power = current x voltage Difference between Carnot efficiency and fuel cell ideal efficiency

0.9 0.8 Carnot 0.7 0.6 fuel cell 0.5

0.4 0.3 efficiencyefficiency limit limit 0.2 0.1 0 0 200 400 600 800 1000 1200 temperature (C) Ideal cell Voltage at different temperature and pressure

G = H T S

G H TS G H TS === −−− At 25ºC === 1.23 V === 1.482 V === 0.252 V nF nF nF nF nF nF

ET = 1.482 – 0.000845T Note: H and S are f(T)

For T<373K E T ≈≈≈ 1.482 – 0.000845T

All of the above considerations were at ambient pressure P = 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 = V mdP

For an ideal gas:

PV m = RT

– dG = RT dP P P – G = – G0 + RT ln P0

Fuel cell reaction: H2 + ½ O 2 →→→ H2O Nernst Equation

 0.5  0.5 − G − G0 RT PH2 ⋅PO2  P ⋅⋅⋅P    RT H O2 = + ln E === E +++ ln 2  nF nF nF  P  P 0   H2O nF P    H2O  Summary

Ideal fuel cell voltage

E0 = E 1atm,298.15K = 1.23 V 0.5 RT  P ⋅⋅⋅PO  E === 1.482 −−− 0.000845T +++ ln H2 2  P,T 2F  P   H2O  0.5  P ⋅⋅⋅PO  E === 1.482 −−− 0.000845T +++ 0.0000431T ln H2 2  P,T  P   H2O  Caution: valid only for low temperatures

This is voltage at 0 current So called open circuit voltage (OCV) Ideal Cell voltage: 1.23 V (H 2/O 2 at 25ºC, 1 atm)

Function of temperature, pressure and concentration of reactants: At 80ºC: 1.186 V Air instead of O2: 1.174 V

Actual voltage is always lower! 0.97 Ideal Cell voltage: 1.23 V (H 2/O 2 at 25ºC, 1 atm)

Function of temperature, pressure and concentration of reactants: At 80ºC: 1.186 V Air instead of O2: 1.174 V

Actual voltage is always lower! 0.970.950.900.800.700.600.50 1.174 0.97 voltage

0 current Relationship between current and voltage

ButlerVolmer equation

 − αF(E − Er ) (1− α)F(E − Er ) i = i0 exp  − exp    RT   RT 

i0 = exchange current density ααα = charge transfer coefficient F = Faraday’s constant R = gas constant T = temperature E = potential

Er = reversible potential

ααα≅≅≅ 1 Note: in some literature n ααα is used instead of ααα n = 2 for the anode and n = 4 for the cathode

Larminie&Dicks suggest αααa = 0.5 and αααc = 0.1 to 0.5 Newman specifies ααα in a range between 0.2 and 2.0 Factors affecting the exchange current density Catalyst Roughness/actual surface area Temperature Reactants concentration Pressure γ  P   E  T  i = irefa L  r  exp − C 1−  0 0 c c  ref      Pr   RT  Tref 

ref 2 i0 = exchange current density at reference conditions (T,P) in A/cm Pt surface 2 ac = catalyst specific area (for Pt theoretically: 2,400 cm /mg practically: 6001,000 cm 2/mg in electrode: 420700 cm 2/mg 2 Lc = catalyst loading (today 0.3 to 0.5 mg/cm ) Ec = activation energy (66 kJ/mol) R = universal gas constant (8.314 J/molK) γγγ = pressure coefficient (0.5 to 1.0)  − αF(E − Er ) (1− α)F(E − Er ) i = i0 exp  − exp    RT   RT 

(E – Er) = overpotential

On the fuel cell anode:

 − αaF(Ea −Er,a ) (1− αa )F(Ea −Er,a ) ia = i0,a exp  − exp    RT   RT 

Er,a = 0 definition of zero potential – hydrogen electrode

(E a –Er,a ) > 0

(1− αa )F(Ea − Er,a ) ia = −i0,a exp   RT 

negative sign means current is leaving the electrode – oxidation reaction On the fuel cell cathode:

 − αcF(Ec − Er,c ) (1− αc )F(Ec − Er,c ) ic = i0,c exp  − exp    RT   RT 

Er,c = 1.23 V

(E c – Er,c ) < 0

− αcF(Ec − Er,c ) ic = i0,c exp   RT  Types of losses in fuel cell: Activation losses (activation polarization) Resistive (Ohmic) losses transfer losses (concentration polarization) Internal current and fuel crossover Activation polarization losses

. Tafel equation: Vact = a + b log (i) (empirical)

RT  i   αFV  V = ln  i = i0 exp     RT  αF  i0  i = current density (mA/cm 2) 2 i0 = exchange current density (mA/cm ) R = universal gas constant = 8.314 J/mol T = temperature of the process (K) α = charge transfer coefficient n = number of electrons involved (2) F = Faraday’s constant = 96,485 C RT RT V = − ln()i + ln()i αF 0 αF

RT RT RT a = − ln()i = −2.3 log()i b = 2.3 Tafel slope αF 0 αF 0 αF Activation polarization losses log scale 1.2 RT  i  V = ln  1 αF  i   0  0.8

. 0.6 Vact = a + b log (i) 0.4 pe = b potential loss (V) slo

0.2 For ααα = 1, T = 333 K ⇒⇒⇒ b = 0.066 V/dec a i0 0 1.2 0.0001 0.001 0.01 0.1 1 10 100 1000 10000 current density (mA/cm²) 1

0.8

0.6

0.4 potential potential loss (V)

0.2

0 0 500 1000 1500 2000 current density (mA/cm²) Resistive losses

. . Ohmic law: V = I R = i Ri

I = current (Amps) d R = resistance (Ohms) R === ρ ρ = resistivity (Ohmcm) i = current density (A/cm 2) A d = distance, length (cm) 2 2 A = cross sectional area (cm ) Ri = aerial resistance (Ohmcm ) . Ri = R A

1.2

1 Resistance through: Membrane (ionic) 0.8

Electrodes 0.6 Bipolar plates 0.4 Interfacial contacts potential loss (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) Resistive losses V

external load bus collector plate plate electrode membrane electrode electrode membrane electrode oxygen feed

O2 O2

- 2e - 2H + 2e 2H +

bipolar collector H → 2H + + 2e – 2 plate

+ – ½O 2 + 2H + 2e → H2O

H2 H2O H2 H2O hydrogen feed hydrogen feed Concentration polarization or mass transport losses

Po P P i 0 RT  P0  RT  iL  P === P0 −−− i === 1−−− V === ln === ln  P i P i     L 0 L 2F  P  2F  iL −−−i  RT  i  or V === −−− ln1−−−  i iL 2F  iL 

1.2

1 theoretical 0.8

0.6 more realistic

0.4 potential (V) loss  i  0.2 Vconc = c ⋅exp   d  0 0 500 1000 1500 2000 current density (mA/cm²) Alternative way to express concentration polarization

Voltage gain/loss RT  CB  V === ln  (Nernst equation) nF  CS  N = flow rate, mol/s D = diffusion coefficient, cm 2/s D⋅⋅⋅(((CB −−− CS ))) Fick’s First Law of Diffusion: N === A C = bulk concentration, mol/cm 3 δ B CS = concentration at I catalyst surface, mol/cm 3 N === δ= diffusion path, thickness nF of diffusion layer, cm A = active area, cm 2 nF⋅⋅⋅D⋅⋅⋅(((C −−− C ))) i === B S δ

nF⋅⋅⋅D⋅⋅⋅C Limiting current C = 0 i === B S L δ

C i S === 1−−− CB iL RT  i  V = ln L  Voltage loss due to concentration polarization:   nF  i − iL  Voltage losses compared

1.2

1

0.8

0.6 activation 0.4

potential potential potential loss loss (V) (V) concentration 0.2 resistive

0 0 500 1000 1500 2000 current density (mA/cm²) Actual fuel cell voltage

Vcell === ET,P −−− Vact −−− Vres −−− Vconc

Losses occur on both anode and cathode:

Vcell === ET,P −−− (((Vact )))an −−− (((Vact )))ca −−− Vres −−− (((Vconc )))an −−− (((Vconc )))ca

RT  i  RT  i      Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL  0.8 Cathode solid phase potential 1 A/cm2 membrane 0.6 DL CL CL DL 0.4

Ecell 0.2 Anode overpotential Eeq Anode solid phase potential 0 potential (V) (V) potentialpotential 0.2 electrolyte phase potential Eloss Cathode overpotential 0.4

0 50 100 150 nominal cell thickness ( m) Fuel cell polarization curve

1.2 theoretical (ideal) voltage

1 activation losses

0.8 resistance losses 0.6

0.4 mass transport

cellcell potential potential (V) (V) resulting V vs. i curve losses 0.2

0 0 500 1000 1500 2000 current density (mA/cm²)

©2002 by Frano Barbir. Power density vs. current density

Power density = V .i (W/cm 2 or mW/cm 2)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3

power density (W/cm²) (W/cm²) power power density density 0.2 0.1 0 0 500 1000 1500 2000 current density (mA/cm²)

©2002 by Frano Barbir. Cell potential vs. power density

1 0.9 0.8 0.7 0.6 0.5 0.4

cellcell potential potential (V) (V) 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 power density (W/cm²)

©2002 by Frano Barbir. Internal currents and fuel crossover

O2 e- loss 2e -

2H + + - H2 → 2H + 2e + - 1/2O 2 + 2H + 2e → H2O

H2 loss

H2 H2O

©2002 by Frano Barbir. Hydrogen consumption in fuel cell

Faraday’s law: I I = nFN N === mol/s (Amps = Ampsecond/mol x mol/s) nF

Hydrogen consumption in fuel cell: N H2 = I/(2F)

Oxygen consumption in fuel cell: N O2 = ½ N H2 = I/(4F)

Water generation in fuel cell: N H2O = I/(2F)

©2002 by Frano Barbir. Internal currents and fuel crossover

Both internal currents and hydrogen crossover mean loss of current:

Iloss = 2FN loss

This means that even at 0 external current there is hydrogen consumption.

RT  i + i   loss  Vcell = ET,P − ln  αF  i0 

1.020 iloss = 1 mA/cm2 1.000 iloss = 2 mA/cm2 iloss = 4 mA/cm2 0.980 iloss = 8 mA/cm2 0.960

0.940 cell potential (V) 0.920

0.900 0 2 4 6 8 10 12 current density (mA/cm2)

©2002 by Frano Barbir. V Fuel cell efficiency η === cell HHV 1.482

. . Electricity out I V I V Vcell Efficiency = = = = Hydrogen in . . N HHHV I HHHV /(2F) 1.482 I N === 2F efficiency Cell potential vs. power density

0.7 1 0.6 0.9 0.8 0.5 0.7 0.4 0.6 0.5 0.3 0.4 cell efficiency (HHV) (HHV) efficiency efficiency cellcell

0.2 cellcell potential potential (V) (V) 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 power density (W/cm²) V Fuel cell efficiency η === cell HHV 1.482

. . Electricity out I V I V Vcell Efficiency = = = = Hydrogen in . . N HHHV I HHHV /(2F) 1.482 I N === 2F Hydrogen in = hydrogen converted into current + hydrogen loss I+++ I V I V i N === loss ⇒⇒⇒ η === cell === cell 2F 1.482 I+++ Iloss 1.482 i +++ iloss

In some cases excess hydrogen is fed into the fuel cell – some H 2 is wasted hydrogen in hydrogen out V electrode cell η = ηfu electrolyte 1.482 oxygen in oxygen out electrode hydrogen consumed ηηη = fu hydrogen supplied Fuel cell efficiency vs. power density

1 0.9 0.8 0.7 0.6 0.5 0.4

efficiency (HHV) (HHV) efficiency efficiency 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 power density (W/cm²) Additional slides RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 Tafel = 77 mV/dec 1 Tafel = 66 mV/dec Tafel = 55 mV/dec 0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 io = 0.0003 mA/cm² 1 io = 0.003 mA/cm² io = 0.03 mA/cm² 0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 ix = 0 mA/cm² 1 ix = 2 mA/cm² ix = 20 mA/cm² 0.8

0.6

0.4 cell potential (V) 1.2 0.2 ix = 0 mA/cm² 1.1 ix = 2 mA/cm² 0 ix = 20 mA/cm² 0 500 10001 1500 2000 current density (mA/cm²) 0.9

0.8 cell potential (V) 0.7

0.6 0 20 40 60 80 100 current density (mA/cm²) RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 R = 0.1 Ohmcm² 1 R = 0.15 Ohmcm² R = 0.2 Ohmcm² 0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) RT  i +++ i  RT  i   loss    Vcell === ET,P −−− ln  −−−i⋅⋅⋅Ri +++ ln1−−−  αnF  i0  nF  iL 

1.2 iL = 1200 mA/cm² 1 iL = 1600 mA/cm² iL = 2000 mA/cm² 0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) Operating pressure RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 P = 300 kPa 1 P = 200 kPa P = 101.3 kPa 0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) RT  i +++ i  V = E − ln loss  cell,P===3 == T,P===3 −−   αnF  i0,P===3  RT RT RT V === E +++ ln((()(P )))+++ ln((()(i )))−−− ln((()(i +++ i ))) cell,P===3 T 4F 3 0.5⋅⋅⋅2F 0,P===3 0.5⋅⋅⋅2F loss RT RT RT V === E +++ ln(((P )))+++ ln(((i )))−−− ln(((i +++ i ))) cell,P===1 T 4F 1 0.5 ⋅⋅⋅2F 0,P===1 0.5⋅⋅⋅2F loss

RT  3  RT  3  Vcell,P===3 −−− Vcell,P===1 === ln  +++ ln  4F  1 F  1

Vcell,P=3 –Vcell,P=1 = 0.039 V (at 60º) Air vs. oxygen RT  i + i  RT  i   loss    Vcell = ET,P − ln  − i ⋅Ri + ln1−  αF  i0  nF  iL 

1.2 air 1 oxygen

0.8

0.6

0.4 cellcell potentialpotential (V) (V) 0.2

0 0 500 1000 1500 2000 current density (mA/cm²) RT  1  RT  1  Vcell,P===3 −−− Vcell,P===1 === ln  +++ ln  === 0.056V 4F  0.21 F  0.21

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 current Constant voltage Constant resistance Constant power Variable power R=2 cm 2 1 1 0.5

0.9 0.8

0.7 OP2 0.6 w=1W/cm 2 OP1 V 0.5 0.8 0.4 0.2 0.3 0.6 cellcell potentialpotential (Volts) (Volts) 0.2 0.4 0.1 0.2

0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 current density (mA/cm2) What else can affect the polarization curve?

Operational conditions.

Operating pressure Fluid mechanics Flow rates of reactants Fluid mechanics /chemistry Operating temperature Heat transfer Humidity of reactants Psychrometry Thermodynamics of moist gases

We must know some basics!

We must know fuel cell inner working! 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 polarization Ohmic (resistive losses) Concentration polarization or mass transport losses Internal currents and reactants crossover

Resulting polarization curve: RT  i +++ i  RT  i   loss    Vcell === ET,P −−− ln  −−−i⋅⋅⋅Ri +++ ln1−−−  αnF  i0  nF  iL 

Effect of operating pressure Effect of oxygen vs. air

V Fuel cell efficiency: η === cell 1.482 PEM Specific Issues – Water transport, gas diffusion PEM Fuel Cell: Membrane/Electrode Processes + - + - H2 → 2H + 2 e e 2H + 1/2O2 + 2 e → H2O

Hydrogen

Oxygen e e e e Electron e e e

Platinum +

Carbon +

+ Polymer + Electrolyte + +

Functional Group

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 λλλ = 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

Nafion conductivity: ~0.1 S/cm

1/conductivity = resistivity = 10 Ohm-cm

Nafion 115 thickness: 5 mils = 0.0127 cm

Resistance = 10 Ohm-cm x 0.0127 cm = 0.127 Ohm-cm 2

At 1 A/cm 2 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 • 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 Cell Resistance and Performance: PEM Thickness Effects

1.0 • Electro-osmotic Increasing )

2 drag removes 0.8 Membrane Thickness water from the

0.6 anode side.

(Neat With thicker Oxygen 0.4 membranes, Cathodes) back diffusion

oror CELLCELL VOLTAGEVOLTAGE (V) (V) 0.2 of water is HFHF RESISTANCERESISTANCE (ohm(ohm cm cm difficult - the 0.0 Fg 3, TF69,109,74,117 Ox's anode side loses 0.0 0.5 1.0 1.5 2.0 2.5 3.0 2 CURRENT DENSITY (A/cm ) water content.

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 mol mol .cm cm 2/s x mol/cm 3atm = or cm .s.atm cm 2. s.atm

3 For ideal gas: Pv m = RT; at standard conditions v m = 0.024 m /mol 3 vm = 24,060 cm /mol cm 3. cm cm 3. cm 1 atm = 75 cmHg = 10 10 barrers cm 2. s.atm cm 2. s.cmHg

Example: -11 . -1 -1 -1 Pm = 1.5x10 mol cm s atm -7 2 1.5x10 -11 mol .cm -1s-1atm -1 x 24,060 cm 3/mol = DH2 = 6.65x10 cm /s -5 3 = 3.6x10 -7 cm 3. cm .cm -2. s-1atm -1= SH2 = 2.2x10 mol/cm atm = 3.6x10 -7 cm 3. cm .cm -2. s-1atm -1/75 cmHg/atm = = 4.8x10 -9 cm 3. cm .cm -2. s-1cm -1Hg = 48 Barrers Permeation rate , N (mol/s)

. . N = P m A P/d . 3 3 N = I/nF NV = N 24060 (cm /mol) = 0.125 ×I cm /s

. . 3 i = I/A = nF Pm P/d NV = 7.5 cm /min/Amp Example: -11 . -1 -1 -1 -7 Pm = 1.5x10 mol cm s atm N = 2.94x10 mol/s A = 100 cm 2 I = nFN = 0.057 A d = 51 m = 0.0051 cm P = 1 atm (partial pressure) i = I/A = 0.00057 A/cm 2 = 0.57 mA/cm 2

5.00E-06

Additional variable (complication) 4.00E-06

3.00E-06 -2602/T DH2 = f(T) = 0.0041e 2.00E-06

diffusivity(cm²/s) 1.00E-06

0.00E+00 0 20 40 60 80 100 120 temperature (°C) Permeation of gases through Nafion

Source: T. Sakai, et al., J. Electrochem. Soc ., Vol. 133, No. 1, pp. 88-92, 1986