Introduction to Basic Electrochemistry for Fuel Cells and ... · PDF fileIntroduction to Basic Electrochemistry for ... ♦Reaction mechanisms and kinetics limitations ... potential

1 2nd Joint European Summer School for FC & H2 Technology-Heraklion-September 2012

GDR n°3339Piles A Combustible, Systèmes

Introduction to Basic Electrochemistry for

Fuel Cells and Electrolysis

Claude LAMY, Professor

Institut Européen des Membranes, CNRS - GDR n°3339 (PACS),

University of Montpellier 2,2 Place Eugène Bataillon, 34095 Montpellier, France,

E-mail: [email protected]



Introduction♦ Thermodynamics and theoretical energy efficiency♦ Reaction mechanisms and kinetics limitations

The Polymer Electrolyte Fuel Cell♦ Principle of a Polymer Electrolyte Fuel Cell ♦ Cell components (membrane, catalysts, etc.) ♦ Survey of various applications of PEFC

The Direct Methanol Fuel Cell

♦ Reaction mechanisms and kinetics limitations♦ The fuel crossover problem

Conclusions



C.F. Schönbein, W.R. Grove, Philosophical Magazine, (1839)

1801 : Discovery of the Volta Cell1839 : Birth of Georges Leclanché1859 : Gaston Planté discovered the Pb/PbO2 battery1867 : Invention of the Leclanché cell

H2 + ½ O2 → H2O + electricity (+ heat)with ∆G°r = - 237 kJ/mole ; ∆H°r = - 286 kJ/mole

It looks like the reverse of water electrolysis : H2O + electricity → H2 + ½ O2

Electrical Energy :We = - ∆∆∆∆G° ≈≈≈≈ 118 MJ/kg ≈≈≈≈ 33 kWh/kg

Standard e.m.f. : E ° = - ∆∆∆∆G/nF = 1.229 VTheoretical efficiency : εεεε = ∆∆∆∆G/∆∆∆∆H = 83% (25°C)

The Hydrogen/Oxygen Fuel Cell



H2/O2 Fuel Cell

Water electrolysis

j = I/S = n F v i (A/cm 2)

E / V(SHE)

Eelectrolysis = 2,1 V

EFC = 0,7 V

H2O →→→→ O2H2 →→→→ 2 H+

2 H+ →→→→ H2 O2 →→→→ H2O

Overall efficiency (1.23/2.1)x(0.7/1.23 )

= 0.7/2.1 ≈ 33%

Electrolysis efficiency 1.23/2.1 ≈ 59%

Fuel Cell efficiency0.7/1.23 ≈ 57%

Practical energy efficiency of water electrolysis and fuel cells



Leclanché CellZn/MnO2

Internal Combustion Engine: Heat (Q 1, T1)

Fuel CellH2/O2 (air)

BatteryPb/PbO2

FuelTank

Oxidant Heat (Q)

Electricity

Electricity (W e)

Mechanical work (W m)

Heat(Q2, T2)

Thermal Engine (Carnot)εεεεr = Wm/(-∆H) = (Q1-Q2)/Q1

= 1 – Q2/Q1 = 1 – T2/T1

e.g. εεεε = 1 – T2/T1 ≈ 30 to 45 %Practical efficiency ≈ 18 to 30 %

Electrochemical Sourceεεεε = We/(-∆H) = ∆G/∆H

≈ 80 to 97 %Practical efficiency ≈ 40 to 60 %

Energetic Efficiency

Electricity (W e)

Electricity (W e)

FuelTank

Oxidant

How does work a fuel cell : it is an electrochemica l device which transforms directly the combustion energy of a fuel (- ∆G) into electricity (and heat) Comparison with other electric source and Internal Combustion Engine (ICE)



Thermodynamic Relations

A key variable in Electrochemistry: the Electrochemical Potential

Definition Thermodynamic relations

♦ Equilibrium between 2 charged phases α and β♦ Nernst potential ♦ The Standard Hydrogen Electrode (SHE)

Theoretical energy efficiency ♦ Under standard conditions (j = 0) ♦ As a function of temperature



Definition of the Electrochemical potentialConsider a charged phase α containing different species (i) : solvent

molecules (H2O), chemical species Ai of charge zi (zi = 0 for a neutral species, zi > 0 for a cation, < 0 for an anion).

The Electrochemical Potential of one mole of species (i) in phase αis the total work to bring species (i) from a standard reference point (with no interaction), usually Infinity (∞), to the bulk phase α :

µiα = chemical potential; F = Faraday = NNNNeo = 96485 C

Φ = inner potential; Ψ = outer potential; Χ = surface potential

µα

i

ααααi

α

iN,P,Tiαα

i χ with F z )N/G( µµj

++++ΨΨΨΨ====ΦΦΦΦΦΦΦΦ++++====∂∂∂∂∆∆∆∆∂∂∂∂====

A i

µα

i

µiα

χααααPhase α Ψα∞

++

+

+ +

+

+

--

-

- -

+

+

+

+

-+ -

∑∑∑∑

∑∑∑∑

====ΧΧΧΧ

====ΨΨΨΨ

i3iro

iii

ii ro

i

r εε π4

r.p N

r εε π4q

rr



Equilibrium at the electrode-electrolyte Interface

0 distance to electrode x

Inner potential Φ

ΦM

ΦS

E = ΦM - ΦS

αααα β

Si

S

i

S

i

Mi

M

i

M

i F z F z ΦΦΦΦ++++========ΦΦΦΦ++++==== µµµµ

0 - i.e. µµµµµβ

iα

iiβ

iα

i ========∆∆∆∆====

F z / ) - - E iM

i

S

iSM µµ(====ΦΦΦΦΦΦΦΦ====

E: electrode potential; [A i]: activity

A izA + n i e- ←→←→←→←→ B i

zB with µµµµi = µµµµio + RT Ln[A i] and n i = zi

A - ziB

→→→→ E = ΦM – ΦS = (µAS - µB

S + µeM)/nF

E = (µAo - µB

o)/nF +RT/nF Ln([A]/[B]) + µeM/F

E = EoA/B +RT/nF Ln([A]/[B]) + µe

M/F

which looks like a Nernst law, but E is not directly measu rable

µµµSB

Mei

SA n ====++++



Only the potential difference between 2 electrodes, the potential of each is defined by 2 electrochemical systems in equilibrium, is measurable :

A1zA1 + n1 e- ←→←→←→←→ B1

zB1 and A 2zA2 + n2 e- ←→←→←→←→ B2

zB2

Eeq = E2 – E1 = EoA2/B2 – Eo

A1/B1 + RT/nF Ln([A 2] [B 1]/[B 2] [A 1])

since the electron chemical potential (µeM/F) cancels out with the same

metal (Cu) as connecting leads at the extremity of the measuring device.

This corresponds to the overall chemical reaction :

a2 A2zA2 + b1 B1

zB1 ←→←→←→←→ a1 A1zA1 + b2 B2

zB2

with equilibrium constant Ke = ([A1]a1[B2]b2/ [A2]a2[B1]b1) = exp(- ∆Gr/RT)where the reaction free energy is related to the chemical potentials:

(j = products, i = reactants)

so that: Eeq = E2 – E1 = - ∆Gr / nF or

∑∑∑∑∑∑∑∑ ∆∆∆∆∆∆∆∆====∆∆∆∆i

iij

jjr µ N - µ N G

0 G E nF G reqr ====∆∆∆∆====++++∆∆∆∆



Important remarks : Activity and Fugacity

For an electrolytic solution the activity [Ai] of species (i) is related to its concentration Ci = Ni/V (Ni moles in solution of volume V) by:

[Ai] = γi Ci where γi is the activity coefficient(γi → 0 if Ci → 0 ∼ ideal solution)

For a gaseous phase the fugacity of a gaseous species (i) is related to its partial pressure through its chemical potential µµµµi = µµµµi

o + RT Ln (f i /Po) where Po is the pressure of a reference state (Po = 1 bar usually) and f i is proportional to the partial pressure pi, i.e. f i = γi p iwith an activity coefficient γi → 0 if pi → 0 ∼ ideal gas)

In the following, activity and fugacity will be assimilated to concentration and partial pressure, respectively.



Thermodynamic Relations∆G < 0 for spontaneous reaction ; Ecell = Ec – Ea

∆G = - S∆T + V∆P + Σ µi ∆Ni with µi = µio + RT Ln[Ai]

Then : We = - nF Ecell = ∆FT + P ∆V = ∆GT,P = ∆H – T ∆S

For an half cell whose electrode potential is controlled by an electrochemical reaction :

Ai + ni e- ←→←→←→←→ Bi with µi = µio + RT Ln[Ai]

Eeq = EoA/B + (RT/nF) Ln ([Ai] / [Bi]) with

EoA/B = (µA

o - µBo ) / nF = - ∆Go/nF (standard state)

one may define a standard Redox potential EoA/B in the

potential scale of the Standard Hydrogen Electrode (SHE). The Redox potential of all electrochemical systems can

thus be classified in the SHE scale (electrochemical series).



2 H+ + 2 e- ←→←→←→←→ H2 Pt/H2 (p=1 bar) / ([H +]=1), 25°CA i + n i e- ←→←→←→←→ B i____________________

A i + n i/2 H2 ←→←→←→←→ B i + n i H+ with ∆Gr < 0 or > 0

which gives:

Thus Eeq = EoA/B + (RT/nF) Ln ([Ai] / [Bi]) ≈≈≈≈ Nernst law

E Fn - )µ 2/n µ( - µ n µ µ Nj - µ N G eqio

2HiiAoHiiB

jj

iiir ====++++++++====∆∆∆∆∆∆∆∆====∆∆∆∆ ++++∑∑∑∑∑∑∑∑

definition by T 0 F/)µ 1/2 - µ( E since

nF/)µ - µ( F/)µ 1/2 - µ( - nF/)µ - µ( E- E Eo

2HoHSHE

BAo

2HoHBASHEA/Beq

∀∀∀∀========

============

++++

++++

Reference electrode: the Standard Hydrogen Electrode (SHE)

Alkali

0.50.340 1 1.23

SHE

-0.76

Zn2+/Zn Cu2+/Cu

-1 E/V

O2/H2O

0.77

Fe3+/Fe2+ Halogen≈≈ ≈≈ ≈≈ ≈≈



Reference electrodes:

Standard Hydrogen Electrode (SHE) Saturated Calomel Electrode (SCE)

1 M H2SO4

H2 gaspH2 = 1 bar

Pt wire

Pt/Pt foil

Platinum wire

Hg

Hg2Cl2

Frit

KClsaturated solution

KClcrystals

Porous Glass Frit

Platinum wire

Hg

Hg2Cl2

Frit

KClsaturated solution

KClcrystals

Porous Glass Frit



Scheme of a 3-electrode cell for electrochemical measurements with the potential control of the working electrode by a

potentiostat

Cooling water

Working electrode

Reference electrode

Luggin capillary

Salt bridge



Electrochemical half-cell reactions:H2 —–> 2 H+ + 2 e-

1/2 O2 + 2 H+ + 2 e- —–> H2O

Overall reaction : H2 + ½ O2 —–> H2O Then :

Eeq = - ∆Gr/nF = -∆Go/2F + (RT/2F) Ln[(pH2) (pO2

)½ / pH 2O]

Eeq = Eo + (RT/2F) Ln[(pH2) (pO2

)½ / pH 2O]

with Eo = -∆Go/2F is the standard cell voltage, i.e. Eo = 1.229 V at 25°C,

where pH2, pO2

, and pH 2O are the partial pressure of hydrogen, oxygen and

water, respectively.

Therefore by increasing the pressure of reactants (H2 and O2) and decreasing the pressure of the product (water) one can increase the cell voltage. The variation of Eeq with T is contained mainly in the entropic term, i.e.∆Sr

o = nF (dEo/dT) : temperature coefficient.

Nernst equation for the H 2/O2 system



Thermodynamics of Hydrogen Oxidation

H2 —–> 2 H+ + 2 e- acid mediumAnode

H2 + 2 OH- —–> 2 H2O + 2 e- alkaline medium

1/2 O2 + 2 H+ + 2 e- —–> H2O acid mediumCathode

1/2 O2 + H2O + 2 e- —–> 2 OH- alkaline mediumH2 + 1/2 O2 —–> H2O overall reaction

with ∆G° = - 237 kJ and ∆H° = - 286 kJ/mole H2 (standard state)

Energy efficiency under standard conditions: εrcell = ∆G° / ∆H° = 0.829

Volt1,23 2x96500

10237x

nFG E - E E

3aceq ========∆∆∆∆−−−−========

°°°°−−−−++++°°°°

kWhr/kg 33 32.9 3600x2237x

3600xM

W 103Ge ≈≈≈≈========∆∆∆∆−−−−====

°°°°



Reversible energy efficiency (I = 0)

83% 286237

H

S T 1

HG

H)(

E F n

H)(W

eqecellr ==

∆∆−=

∆∆=

∆−=

∆−=ε

For a Fuel Cell working under standard conditions (25°C, 1 bar) :

43% C)(350 623C)(80 353

- 1 TT 1

Q

Q 1

H)(W

1

2

1

2rthermalr =

°°=−=−=

∆−=ε

For a Thermal Engine, such as an ICE, working between an hot source Q1 at 350°C and a cold source Q 2 at 80°C :



Thermodynamic data for the H2/O2 combustion reaction (kJ/mol) as a function of temperature

Physical state of water

T/K ∆H ∆G EeqEfficiency (ε=∆G/∆H)

Standard state 298 -285.83 -237.17 1.229 0.830

Liquid 328 -284.88 -232.32 1.203 0.816

Liquid 348 -284.25 -229.14 1.187 0.806

Liquid 368 -283.61 -225.99 1.171 0.797

Gaseous 298 -241.82 -228.58 1.185 0.945Gaseous 400 -242.84 -223.90 1.160 0.922Gaseous 500 -243.82 -219.05 1.135 0.898Gaseous 600 -244.75 -214.01 1.109 0.874Gaseous 700 -245.62 -208.81 1.082 0.850Gaseous 800 -246.42 -203.50 1.055 0.826Gaseous 900 -247.16 -198.09 1.027 0.801Gaseous 1000 -247.82 -192.60 0.998 0.777



Thermodynamic data for the H2/O2 combustion reaction (kJ/mol): H2 + 1/2 O2 —–> H2O

In the liquid state of water (273 K < T < 373 K) :

∆H = ∆G + T ∆S = ∆HHHV = ∆HLHV + ∆QCond

so that in the standard state (T = 298.15 K, p =1 bar) :∆QCond = ∆HHHV – ∆HLHV = - 285.8 + 241.8 = - 44 kJ/mol

εrHHV = ∆∆∆∆G° / ∆∆∆∆H°HHV = 237/286 = 0.83

In the gaseous state of water (T > 373 K) :

∆H = ∆G + T ∆S = ∆HLHV

so that at e.g. T = 400 K (≈≈≈≈ 127°C, p =1 bar) :∆H = ∆HLHV = - 242.84 kJ/mol

εrLHV = ∆∆∆∆G° / ∆∆∆∆H°LHV = 224/243 = 0.92

HHV = High Heating Value ; LHV = Low Heating Value ; ∆∆∆∆QCond = Heat of Condensation



Theoretical energy efficiency (FC vs. Carnot)

0,00

0,10

0,20

0,30

0,40

0,50

0,60

0,70

0,80

0,90

1,00

300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500Hot source temperature / K

The

oret

ical

effi

cien

cy

FC efficiency

Carnot efficiency

εεεεcell = εεεεCarnot 80°C ≈≈≈≈ 0,72 at T ≈≈≈≈ 1250 K (977°C)

εεεεcell = εεεεCarnot 25°C ≈≈≈≈ 0,74 at T ≈≈≈≈ 1150 K (877°C)

εεεε Cellεεεε Carnot (T cold = 25°C)εεεε Carnot (T cold = 80°C)

Linear (εεεε Cell)Polynomial (εεεε Carnot (T cold = 25°C)Polynomial (εεεε Carnot (T cold = 80°C)



Kinetics Relations

A typical kinetics law in Electrochemistry: the Butler-Volmer equation

Kinetics of a simple electrochemical reaction

The Butler-Volmer law ♦ Establishment of the Butler-Volmer law ♦ Mass transfer limitations ♦ Cell voltage vs. current density curves♦ Energy efficiency under working conditions (j ≠ 0)



mass transfer

mass transfer

Electrolyte

I ions

electron transfer

I

Kinetic relations for a simple electrochemical reaction : A i + n i e- ←→←→←→←→ B i

I = dQ/dt = nF ( dNA/dt) = nF ( dNB/dt)

I = nF v with the reaction rate v = ( dNA/dt)

I < 0 for a reduction reaction ; I > 0 for an oxidati on reaction

Reaction mechanism



AizA

B izB

Kinetics of a charge transfer reaction (heterogeneous reaction) : A i

zA + n i e- ←→←→←→←→ B izB

Activation barrier for an electrochemical reaction (K is the decrease in activation energy due to the electrode catalyst)

0 I 0 E nF G G ≠≠≠≠⇒⇒⇒⇒≠≠≠≠++++∆∆∆∆====∆∆∆∆aa v nF I (anodic) reaction oxidation : 0 I 0 G ====≥≥≥≥⇒⇒⇒⇒≥≥≥≥∆∆∆∆

cc v nF - I (cathodic) reaction reduction :0 I 0 G ====≤≤≤≤⇒⇒⇒⇒≤≤≤≤∆∆∆∆



Expression of the reaction rates with the Arrhenius law

E nF α G G with )RT/Gexp(- C S k C S T)(E,k v cccelecA

oc

elecAcc ++++∆∆∆∆====∆∆∆∆∆∆∆∆======== ++++++++++++

E nF )α -(1 - G G with )RT/Gexp(- C S k C S T)(E,k v aaaelecB

oa

elecBaa

++++++++++++ ∆∆∆∆====∆∆∆∆∆∆∆∆========where αααα is the charge transfer coefficient (0 < αααα < 1), i.e. the fraction of electrical energy which activates the reduction reaction (A → B), and (1- αααα) nFE activating the oxidation reaction (B → A). Thus:

[[[[ ]]]] ]RT/nFEα-exp[ )RT/G-exp(C k-]RT/nFE)α-1exp[( )RT/G-exp(C k nFS/Ij celecA

oca

elecB

oa

++++++++ ∆∆∆∆∆∆∆∆========

At equilibrium va = vc and j = 0, so that ja = -jc, E = Eeq and Cielec = Ci

o :

Then Eeq=EoA/B + RT/nF Ln(CA

o/CBo) with Eo

A/B = exp(-∆Go/RT) ≈≈≈≈ Nernst law

and jo = nF (k co)1-αααα (ka

o)αααα (CAo)1-αααα (CB

o)αααα = nF k so (CA

o)1-αααα (CBo)αααα

Out of equilibrium j = ja - jc ≠ 0. Dividing j by jo one obtains:j(η) = jo [(CB

elec/CBo) exp(1-α)(nF/RT)η - (CA

elec/CAo) exp-α(nF/RT)η] or

j(η) = jo [exp(1- αααα)(nF/RT)η – exp- αααα(nF/RT)η] (no mass transfer limitation)

)RT/nFEα-exp( )RT/G-exp(CnFk ]RT/nFE)α-1exp[( )RTG-exp(CknFj-j j eqo

coA

oceq

oa

oB

oaoca

++++++++ ∆∆∆∆====∆∆∆∆============

Butler-Volmer law with ηηηη = E - Eeq the overvoltage and j o the exchange current density



Expression of the Butler-Volmer law in some limitin g cases

Very often α = ½ so that j(η) = 2 jo sh[(nF/2RT) η] ∼∼∼∼ hyperbolic sinus curveIf α = 0 or 1 then j(η) = jo [exp(nF/RT η) - 1] or j(η) = jo [1 - exp(nF/RT) η]

For |η| << RT/nF (≈ 25/n mV at 25°C) then j(η) = jo (nF/RT) η = η/Rt or η = Rt j with Rt = RT/nFjo the charge transfer resistance (∼∼∼∼ Ohm’s law )

For η >> RT/nF then j(η) = jo exp[(1- α )nF/RT η] or η = RT/(1-α)nF Ln(j/jo) and for η << - RT/nF then j(η) = - jo exp[- α nF/RT η] or η = -RT/αnF Ln(-j/jo)i.e. η = a ± b log |j| ∼∼∼∼ Tafel law with the Tafel slopes bi = 2.3 RT/αinF in V dec-1

For the Hydrogen Oxidation Reaction (HOR) the exchange current density is very high (jo ≈ 1 mA cm-2) so that the reaction is reversible and the Ohm’s law does apply (linear relationship between overvoltage and current density)

For the Oxygen Reduction Reaction (ORR) the exchange current density is small (jo ≈ 1 µA cm-2 ) so that the reaction is irreversible (one may neglect the reverse reaction, i.e. water oxidation) and one may write:j(η) = - jo exp(-α nF/RT η) or ηc

act = - RT/ααααcnF Ln(|j|/j o) ∼∼∼∼ activation overvoltage



Mass transfer limitations : concentration overvolta ge

The reaction kinetics can be controlled by the mass transfer (diffusion, migration, convection) of the reacting species inside the electrolytic phase, so that the current density is proportional to the mass flux density Ji of species (i): ji = |zi|F Ji with Ji = 1/S ∆Ni/∆t = Ci vi (vi is the velocity).

Ji can be expressed by the Nernst-Planck equation :

In the following we will neglect the contribution of the migration currentjim = |zi| Fui Ci EEEE = |zi| λi Ci EEEE = κi EEEE and the convection current jicv = |zi|F Ci vi

ext

so that we will only consider the diffusion process (Fick’s laws ) of species (i):

with Di = diffusion coefficient; ui = ziFDi/RT = electric mobility; λi = Fui = molar conductivity; Κi = |zi| λi Ci = ionic conductivity;

EEEE = - ∇Φ = electrical field

extiiii

iii

extiii

iii vC CD

RTFz

- CD- vC µRT

DC - J

rrrrrr++++ΦΦΦΦ∇∇∇∇∇∇∇∇====++++∇∇∇∇====

on)conservati mass law 2 s(Fick' C D Jdiv - t

CJ Fz j and law) 1 s(Fick' C D - J

ndii

di

i

dii

di

stii

di

≈≈≈≈∆∆∆∆========∂∂∂∂

∂∂∂∂====∇∇∇∇====

r

rrrr



)δ x (0 (0)C xδ

)0(C - C (0)C x )x/C( )x(C and

δ

)0(C - C )x/C( to leading 0 x/)t,x(C D t/)t,x(C

x/C D Fz j and 0 t/C ,x/C D - J

iiio

i0xii

iioi

2i

2ii

0xiiidiiii

di

≤≤≤≤≤≤≤≤++++====++++∂∂∂∂∂∂∂∂====

====∂∂∂∂∂∂∂∂====∂∂∂∂∂∂∂∂====∂∂∂∂∂∂∂∂

∂∂∂∂∂∂∂∂±±±±========∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂∂====

====

====

Resolution of Fick’s equations (in the approximation of a semi-infinite linear diffusion, under steady state conditions):

Cio

xδ

Ci(x)

Ci(0)

00

Electrode distance

Electrode Electrolyte

δ = thickness of the

diffusion layer



For the electrochemical reaction, A i + n i e- ←→←→←→←→ B i, the rate of which is controlled only by diffusion, the current density can be written as:

ljl = |jid| = nF Di |cio – ci(0)| / δ, with n = zA – zB

with ci(0) the concentration at the electrode surface.For high rate, i.e. high current densities, all the reacting species

arriving at the electrode surface are immediately consumed and their activity (concentration) becomes 0. Thus the concentration gradient reaches a maximum value, leading to a limiting current density:

jli = nF Di cio / δwith Di (in m2/s or cm2/s) the diffusion coefficient of species (i), cio its concentration in the bulk of electrolyte and δ the thickness of the diffusion layer (in the approximation of a semi-infinite linear diffusion).

Mass transfer limitations : concentration overvolta ge



For a very fast transfer reaction, only limited by mass transfer, the Nernst equation does apply at the surface, leading to concentration overvoltages:

Eeq = EoA/B + (RT/nF) Ln (cA(0)/cAo / cB(0)/cBo) = E1/2 + (RT/nF) Ln[(j-jlc)/(jla-j)]

(equation of a Polarographic Wave assuming the same diffusion coefficients)

anode theat jj

1lnFn

RTη

ala

conca

−−−−====

cathode theat jj

1lnFn

RTη

clc

concc

−−−−====

By doing the ratio of j with jli one may obtain:ljl/jli = [cio – ci(0)] / cio = 1 - ci(0)/cio = 1 - pi(0)/pio

The superficial concentration (or partial pressure for gaseous species) is :ci(0)/cio = pi(0)/pio = 1 - ljl / jli

Mass transfer limitations: concentration overvoltag e Mass transfer limitations : concentration overvolta ge



E(j) curves limited by mass transfer (diffusion)

0,00,20,40,60,81,01,21,4

00,

20,

40,

60,

81

1,2

1,4

Cur

rent

den

sity

/ A

cm

-2

Cell voltage / V

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

0 0,2 0,4 0,6 0,8 1 1,2 1,4

Current density / A cm -2C

ell v

olta

ge /

V

Tafel slope bc = 60 mV/dec.

Limiting current jlc = 1.4 A/cm2



The cell voltage vs. current density characteristics for the H2/O2 fuel cell, taking into account charge transfer overvoltages, concentration overvoltages and ohmic drop can thus be written as:

E(j) = Ec(j) – Ea(j) – Rej = Eeq – (|ηηηηaact(j)| + |ηηηηa

conc (j)| + |ηηηηcact(j)| + |ηηηηC

conc (j)|) – Rej

jRj

j1

j

j1ln

nFRT

j

jjln

nFα

RTE)j(E e

ll2oo

eqca

ca −

−×

−+

×+=

Cell voltage vs. current density E(j) curves



IjI = n F v i = n F(1/S) dN i/dt

j/mA

cm

-2

300

≈ 0.8 V

≈ 0.3 V

E eq ( ) ≈ 1.21 V

100

η a η c200

CH 3OH

CHCH 33OHOHH2HH22 O 2OO 22

PtPtPtPt -Ru50 -50

PtPt --RuRu5050 --5050

Pt -Ru80 -20

PtPt --RuRu8080 --2020Pt -Ru -

XPtPt --RuRu --XX

E = Ec – Ea ≈≈≈≈ 0.8 V

≈ 0.3 V

Eeq(CH3OH) ≈ 1.21 V

η a η c

H2

PtPtPtPt -Ru50 -50

PtPt --RuRu5050 --5050

Pt -Ru80 -20

PtPt --RuRu8080 --2020Pt -Ru - XPtPt --RuRu --- X

O2CH3OH

0.5 1.23E/V vs. RHE00

EcEa

Current density vs. electrode potential for electrochemical reactions involved in fuel cells



0,000

0,200

0,400

0,600

0,800

1,000

1,200

0 0,25 0,5 0,75 1 1,25 1,5

j/A cm -2

E/ V

Ohmic losses R e jCharge transfer

overvoltage

Eeq = 1.23 V

Mass transferovervoltage

0,7

0,4 0,9

Po = 0,175 W/cm2 P/Po=1,6 P/Po= 3,6 P/Po= 6

Cell voltage vs. current

density E(j) curves j0 = 10-8 ; Re = 0,15 ; j l = 1,3

j0 = 10-6 ; Re = 0,10 ; j l = 2,2j0 = 10-6 ; Re = 0,15 ; j l = 1,4

j0 = 10-8 ; Re = 0,30 ; j l = 1,2

E(j) = Ec(j) – Ea(j) – Re j = Eeq – (|η|η|η|ηc(j) |||| + |η|η|η|ηa(j) |||| + Re j)



Eeq Eeq Eeq )jeR )j(cη )j(aη( Eeq jeR )j(Ea )j(Ec )j(E −−+=⟨++−=−−−+=

Energy efficiency under working conditions (j ≠ 0)

n

nexpjm

j ε and % 57

1.230.7

eqE

)jeR (j)cη (j)aη( 1 eqE

E(j) ε FE ==≈=

++−==

FEcellr

exp

eq

eqexpcell εεε

n

n

EE(j)

H)(

E F n

H)(

E(j) F n ε ××××××××====××××××××

∆∆∆∆−−−−====

∆∆∆∆−−−−====

ηa = E-(j) – E-eq with ηa > 0 (fuel oxidation)

ηc = E+(j) – E+eq with ηc < 0 (oxygen reduction)

Re = electrolyte and interface resistance

εεεεcell = 0.83 x 0.57 x 0.99 ≈≈≈≈ 47% and εεεεCHP ≈≈≈≈ 85 to 95%



The Polymer Electrolyte Fuel Cell (PEFC)

♦ Principle of a Polymer Electrolyte Fuel Cell

♦ Cell components (membrane, catalysts, etc.)



2 H+

I4 OH

Anodic catalyst

Cathodiccatalyst

H2O

½ O2

2e-

2e-

PEM

H2

2e-

+ We

Overall reaction: H 2 + ½ O2 →→→→ H2O with ∆G < 0

Schematic representation of a PEFC elementary cell



Schematic representation of a PEFC elementary cell

End Plate

BipolarPlate End Plate

Bipolarplate

Teflon ® gasket

MEA

Polymer Electrolyte Fuel Cell (PEFC)



Schematic representation of the Membrane Electrode Assembly (MEA)

AnodeVent

CathodeVent

AnodeFeed, H2

CathodeFeed, O2

0.5 to 0.9 V

Gas DiffusionBacking

Proton Exchange Membrane (≈≈≈≈ 100 µm)

CatalystlayerH+

Membrane Electrode Assembly (MEA)Thickness e ≈≈≈≈ 5 mm

Thickness e ≈≈≈≈ 500 µm

(10 µm)

(200 µm)

, Alcohol



jo = 10-8 A cm -2; Re = 0,15 ΩΩΩΩ cm 2; j l = 1,3 A cm -2


0,000

0,200

0,400

0,600

0,800

1,000

1,200

0 0,25 0,5 0,75 1,0 1,25 1,5Current density j/A cm -2

Ohmic drop R e j

Charge transfer activation

Mass transferactivation

0,7

Eeq = 1,23 V

0,4

Cel

l vol

tage

E/V

Cell voltage E(j) = E +(j) – E–(j) - Re j

Influence of the membrane specific resistance (Re = e/σ) on the cell voltage-current density characteristics E(j)



E(j) characteristics of a PEFC elementary cell with different membranes : Dow (e = 125 µm) ; o Nafion® 115 (e = 125 µm) ; ∆ Nafion® 117 (e = 175 µm)

After K. Prater (Ballard), J. Power Sources, 29 (19 90) 239

Current density (j/A cm -2)

Cel

l vol

tage

(E/V

)

Specific resistance (R e = e / σσσσ)e.g. for Nafion ® 115 :

0.0125 cm / 0.125 S cm -1

≈≈≈≈ 0.1 ΩΩΩΩ cm 2

><><><><

DUPONT NAFION®

O

CF2

CF

O

CF2CF2CF2CFCF2CF2

H+

CF2

S=OO=

O

CF2

– CF3

––

Dow



j0 = 10-6 A cm -2 ; Re = 0,10 ΩΩΩΩ cm 2 ; j l = 2,2 A cm -2

j0 = 10-6 A cm -2 ; Re = 0,15 ΩΩΩΩ cm 2 ; j l = 1,4 A cm -2

0,000

0,200

0,400

0,600

0,800

1,000

1,200

0 0,25 0,5 0,75 1,0 1,25 1,5

Current density j/A cm -2

Cel

l vol

tage

E/ V

Ohmic losses R e jCharge transfer

overvoltage

Eeq = 1.23 V

Mass transferovervoltage

0,7

0,4 0,9

Cell voltage E(j) = E +(j) – E–(j) - Re j

Influence of the mass transfer limitations (limiting current density jl) on the cell voltage-current density characteristics E(j)



Current density / mA cm -2

Cell voltage vs. current density curves for an H 2/air FC with MEAs using three different types of carbon cathode GDL (80°C, 0.22 mg cm −2 Pt loading) : () microporous layer-coated and 30 wt.% FEP-impregna ted; () 30 wt.% FEP-impregnated; ( ) 10 wt.% FEP-impregnated.

After C. Lim, C.Y. Wang, Electrochim. Acta 49 (2004) 4149–4156



Influence of the catalytic properties of electrodes (exchange current density jo) on the cell voltage E(j)

0,000

0,200

0,400

0,600

0,800

1,000

1,200

0 0,25 0,5 0,75 1,0 1,25 1,5Current density j/A cm -2

Cel

l vol

tage

E/V

Ohmic drop R e jCharge transfer

overvoltage

Eeq = 1,23 V

Mass transfer overvoltage

0,7

E(j) = E+(j) - E–(j) - Re j = Eeq – (|η|η|η|ηc(j) |||| + |η|η|η|ηa(j) ||||) - Re j

0,4 0,9





Fuel cell characteristics of a DEFC recorded at 110 °C.Influence of the nature of the bimetallic catalyst (30% loading).

Anode catalyst : 1.5 mg.cm -2 ; Cathode catalyst : 2 mg.cm -2 (40% Pt/XC72 E-TEK)Membrane : Nafion ® 117; Ethanol concentration : 1 M

0 20 40 60 80 100 120 140 160

0100200300400500600700800

PtPt-Sn(80:20)Pt-Ru(80:20)Pt-Mo(80:20)

Cel

l vol

tage

/ m

V


Polarization curves Power density curves

0 20 40 60 80 100 120 140 1600

5

10

15

20

25

30 PtPt-Sn(80:20)Pt-Ru(80:20)Pt-Mo(80:20)

Pow

er d

ensi

ty /

mW

cm

-2


After C. Lamy et al., in ”Catalysis for Sustainable Energy Production”, edited by P. Barbaro and C. Bianchini, Wiley-VCH, Weinheim, 2009, Chap.1, pp. 3-46.



What are their uses ?? Production of electric energy(and eventually heat in CHP systems) in a wide range of power (1 W to about 10 MW) with a similar energy efficiency :

Electric Power Plant (1 to 10 MW) Electric Vehicle (10 to 200 kW) Auxiliary Power Unit (APU from 1 to 100 kW) Aerospace power supply (1 to 50 kW) Household Application (1 to 10 kW) Power supply for portable electronics (1 to 100 W)

Survey of various applications of PEM Fuel Cells



City Bus equipped with a 200 kW FC for the 2008 Olympic Games in Beijing



Fuel CellSystem

(SAFRAN Group)

APU for aircrafts and spacecrafts



Airbus 320 equipped with a PEFC APU as demonstrated by DLR (Germany)



Laptop Computer ~ 10-100 W Cell Phone ~ 1-10 W

Application to portable electronics (1 to 100 W)



The Direct Methanol Fuel Cell (DMFC)

♦ Principle of a Direct Methanol Fuel Cell

♦ Reaction mechanisms and kinetics problems



6e-I

Electrolyte

Ionic conductore.g. a PEM

CathodeAnode

Electronic conductor+ catalyst

Electronic conductor+ catalyst

CH3OH

+ H2OCO2 + 6H++ 6e- 6H+

CO2

6e-+ 6H+ + 3/2O2

Oxygen

(Air)

3H2O

We= 6.1 kWhr/kg A

−−−− 6e-

I

++++

Direct Methanol Fuel Cell



Pt + CH3OH → Pt - CH3OHads

Pt - CH3OHads → Pt - CHOads + 3 H+ + 3 e-

Pt - CHOads → Pt - COads + H+ + e-

Ru + H2O → Ru – OHads + H+ + e-

Pt - COads + Ru – OHads → Pt + Ru + CO2 + H+ + e-

Overall reaction CH 3OH + H2O → CO2 + 6 H+ + 6 e-

Reaction mechanism of the electrocatalytic oxidation of methanol

at platinum-based electrodes



Modification of platinum by Ruthenium using the colloidal method (after Bönnemann et al.)

carbon

Pt-Ru

Pt-Ru alloy

Pt-Ru/XC72

carbone

PtRu

Pt and Ruon the same support

carbon

Pt

Pt+Ru/XC72

Pt and Ru on different supports

carbone

Pt

carbon carbone

Ru

carbon

Pt

Pt

RuRu

Pt/XC72+Ru/XC72

This a complex 6-electron reaction mechanism, which needs the preparation of bimetallic and plur imetallic

electrocatalysts for methanol oxidation catalysts



Pt/XC72Pt+Ru/XC72 Pt/XC72+Ru/XC72Pt-Ru/XC72

0,3 0,4 0,50

20

40

60

80

100

E/V vs. RHE

I/mA

mg

Pt-1

Oxidation of 0.1M methanol (v=5mV s -1)

0,0 0,2 0,4 0,6 0,8 1,0 1,2

0

10

20

30

40

50

Pt/XC72Pt+Ru/XC72Pt/XC72+Ru/XC72Pt-Ru/XC72

I/ m

A m

g P

t-1

E/V vs. RHE

Alloy >>>>PlatinumOn same C particles

On different C particles>>>> >>>>On same

C particles AlloyOn different C particles Platinum>>>> >>>> >>>>

Oxidation of preadsorbed CO (v=50mV s -1)

Evaluation of the electrocatalytic activity of PtRu / C electrodes by cyclic voltammetry (room temperature)



0

20

40

60

80

100

120

140

160

180

0 2 4 6 8 10

Time / hours

MeO

H /

mm

ol

Nafion 117

NEM 1

NEM 6

NEM 20

NEM 21

Permeability to methanol of different Solvay membra nes in comparison with Nafion 117 at room temperature.

Effect of the crossover of the fuel through the pol ymer membrane



As a result of the crossover of the fuel to the cathode, the electrode potential Em will be determined by a mixed reaction resulting from the reduction of oxygen and the oxidation of methanol at the same potential Em. As both reactions are quite irreversible, a Tafel behavior is practically always observed. Under these conditions, the current density (jm) and mixed potential (Em) are given by the equations :

and :

where joi and bi are the exchange current density and the Tafel slopes, respectively, for both half-cell reactions.

cb)o

cEmE( -

ocab)o

aEmE(

oam 10 j 10j j

−−−−−−−−

========

oa

oc

ca

ca

ca

oca

oac

m jj

log bb

bb

b bE b E b

E++++

++++++++++++====

This will result in a negative shift, ∆Em, of the mixed potential at the oxygen cathode, as given by the following equation :

with jo’a = 103 joa and ba ≈ bc ≈ 120 mV/decade for both the oxygen reduction (at high current densities) and the methanol oxidation reactions.

mV 18010log2

120jj

logbb

bbE 3

a'o

oa

ca

cam −−−−≈≈≈≈≈≈≈≈

++++====∆∆∆∆ −−−−



Effect of methanol crossover through the membrane

0 50 100 150 200

0,0

0,2

0,4

0,6

0,8

1,0

emf MeOH/O2

Ean MeOH.

Ecat MeOH cross-over

Ean H2.

Ecat H2.

E /V

j / mA cm-2

0 50 100 150 200

0,0

0,2

0,4

0,6

0,8

1,0

emf MeOH/O2

Ean MeOH.

Ecat MeOH cross-over

Ean H2.

Ecat H2.

E /V

j / mA cm-2

Polarization curves of an H 2/O2 PEFC and a DMFC in the presence of methanol at the cathodic compartment : ( ) potential of the PEFC cathode;

(O) potential of the DMFC cathode ; ( ) DMFC cell voltage



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 200 400 600 800 1000j / mA.cm-2

E /

V

0

20

40

60

80

100

120

P /m

W.cm

-2

Pt-Ru (1:1) Pt-Ru (2:1) Pt-Ru (4:1)

Anode 2 mg.cm -2 Pt-Ru / C, Nafion 117, Cathode 2 mg.cm -2 Pt / C, [MeOH] = 2 M, 2 mL/min., P MeOH = 2 bar ; Tcell = 110°C, O 2 = 120 mL/min., P O2

= 2.5 bar ; T MeOH = TO2= 95°C.

E(j) and P(j) curves of a single DMFC with Pt-Ru/C electrodes of different Pt-Ru atomic ratios



TOSHIBA DMFC for portable applications

Applications of DMFC to portable electronics: cell phone, laptop computer, cam recorder, etc.



MCFCMCFC

PAFCPAFC

SOFCSOFC

PEMFCPEMFC

AFCAFC

MiniMiniPACPAC

1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 100kW 1 MW100kW 1 MW

PortablePortable

TransportTransport

MCFCMCFC

PAFCPAFC

SOFCSOFC

PEFC

AFCAFC

MiniMiniPACPAC

1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 100kW 1 MW100kW 1 MW1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 1mW 0.1 W 1W 10 W 100W 1 kW 10 kW 100kW 1 MW100kW 1 MW

PortablePortable

TransportTransportation

Stationary

AerospaceGdR PACEMGdR PACEM

GdR ITSOFC

Bio-fuel Cells

Different kinds of applications of FC

GdR PACEMGdR PACEM



[1] P.W. ATKINS, Physical Chemistry, Oxford Universi ty Press, Oxford, 1995.[2] A.J. BARD, L.R. FAULKNER, Electrochemical Meth ods - Fundamentals and

Applications, John Wiley & Sons, New York, 1980.[3] J. O’M BOCKRIS, S. SRINIVASAN, Fuel Cells : thei r electrochemistry,

McGraw Hill Book Co., New York, 1969.[4] A.J. APPLEBY, F.R. FOULKES, Fuel Cell Handbook, Van Nostrand Rheinhold,

New York, 1989.[5] K. KORDESH, G. SIMADER, Fuel cells and their app lications,

VCH, Weinheim, 1996.[6] K. PRATER, J. Power Sources, 29 (1990) 239.[7] C. LAMY, J.-M. LEGER, J. Phys.IV, Colloque C1, V ol.4 (1994) C1-253.[8] C. LAMY, J.M. LEGER, S. SRINIVASAN, Direct Metha nol Fuel Cells : From

Fundamental Aspects to Technology Development, in " Modern Aspects of Electrochemistry", J. O'M. Bockris, B.E. Conway (Ed s.), Plenum Press, New York, volume 34 (2001) pp. 53-117.

[9] Handbook of Fuel Cells, W. Vielstich, H. Gast eiger, A Lamm (Eds.), Wiley, Chichester (UK), Volume 1, "Fundamentals and Survey of Systems", (2003)pp.323-334. Volume 2 to 6, 2003-2009.

[10] F. BARBIR, PEM Fuel Cells: Theory and Practi ce, Elsevier/Academic Press, 2005.

References



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