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Introduction to SOFC Technologies

Fundamentals of Electro-Chemistry, Electrochemical Kinetics &

Solid State Chemistry

Robert Mücke

Forschungszentrum Jülich GmbH, Institute of Energy and Climate Research(IEK-1: Materials Synthesis and Processing)

Joint European Summer School for Fuel Cell and Hydrogen TechnologyViterbo, ItalyAugust 22nd 2011

2 Robert Mücke, Joint European Summer School for Fuel Cell and Hydrogen Technology

1. Introduction• electrochemical cells • thermodynamic potentials

2. The Driving Force• 1.+2. law of thermodynamics• chemical potentials • Nernst‘s potential • open cell voltage

3. Drawing a Current• i-V characteristics • ohmic losses • polarisation• electrochemical impedance spectroscopy

4. Operation of SOFCs• operation field • degradation

Contents


1. IntroductionElectrochemical Cells

Electrochemical Cells

Galvanic CellsElectrolytic Cells

Substance producers

not carried out spontaneously (free

energy change ΔΔΔΔG>0)

Energy producers

carried out spontaneously (free

energy change ΔΔΔΔG<0)

Batteries Fuel Cells

Electrodes contain fuel(being dissociated)

Fuel separately added


Electrochemical Cells - Principle

anode electrolyte cathode

e–

I–

I+

or

electrical work(input or output)

IX → e– + I+ + X

I– + Y → e– + IYor

electronation/oxidation

ionconduction

de-electronation/reduction

e– + I+ + Y → IY

e– + IX → I– + Xor

IX + Y → IY+ X

(simplified)overall cell reaction

SOFC:X= –

Y = fuelI = ½ O2I–= O2–

Li-Ion (e.g.)X= C

Y = Li1-xCoO2I = LiI+= Li+


Electrolytic cells

Electrical work is used for splitting a HI solution (e.g. I=O2)

positive negative


Galvanic Celle.g. SOFC

positivenegative


Chemical vs. Electrochemical Reactions

Chemical Reaction Electro-chemical reaction

Activation thermal electric

Intermediates formed

collision of reactants separated electron / ion transfer

Electrons directly released and taken during reaction

continuously transferred from anode to cathode in external circuit

Products anywhere in reacting system

at the 2 electrode/electrolyte interfaces

Additional degree of freedom: Electrical field(supplied voltage / current load)


Repetition of Basic Principle

electrolyte

cathode

anode

oxidation

reduction

L.G.J. de Haart, IEF-3, FZJ

fuel

air / O2

user


Umolecular energy

F = U –TSmolecular energy minus environmentenergy

H = U + pVmolecular energy plus energy of constrained room

G = U +pV–TS

molecular energy plus energy of constrained room minus environment energy

+ p Vp V = work needed to get a certain pressure + volume

Thermodynamic PotentialsInternal Energy, Entropy, Enthalpy, Free Energy


Umolecular energy

F = U –TSmolecular energy minus environmentenergy

H = U + pVmolecular energy plus energy of constrained room

G = U +pV–TS

molecular energy plus energy of constrained room minus environment energy

+ p V

– T S

p V = work needed to get a certain pressure + volume

–T S = energy provided from the environment limits the system work

300K

QH

QCW

600K

0 K

water wheel analogy

Thermodynamic PotentialsInternal Energy, Entropy, Enthalpy, Free Energy


+

-

Anode side

= 0.21 bar

~ 10–21 bar

Ucell

Cathode side

2. The Driving ForceThe Chemical Potential

1 O2

4 e–

2 O2–

Assuming homogenous temperature

Chemical potential

Current flow

Power (if no losses)

Open cell voltage

~1 V


The Ideal SOFCFirst Law of Thermodynamics

Fuel cellT, p

totalreactants’enthalpy

> 0

totalproducts’enthalpy

< 0

Qreleased heatQ < 0

W

delivered workW < 0

energies that are transferred into the system are positive,ones that are released are negative

Conservation of energy:

Energy of fuel isdecreased


Reaction Enthalpies for SOFC Fuels(Direct Oxidation)

H2 + ½O2 → H2O

CO + ½O2 → CO2

CH4 + 2O2 → 2 H2O+CO2

reaction enthalpies from Singhal & Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, Oxford 2003, p.61

–242 kJ/mol

–283 kJ/mol

–802 kJ/mol

at standard conditions(25°C, 1bar)

binding energy(enthalpy)


The Ideal, Reversible SOFCSecond Law of Thermodynamics

energies that are transferred into the system are positive,ones that are released are negative

Fuel cellT, p

totalreactants’entropy

> 0

released heat(reversible)

Q < 0

reversible work

totalproducts’entropy

Ideal reversible system:

Entropy of reactants isdecreased


The Ideal, Reversible SOFCUsable Work

Putting first & second law of thermodynamics together:


Entropy (S)

Measure of disorder, non-usable energy

Standard state conditionsPartial pressures of gases involved: 0.1 MPaConcentrations of aqueous solutions: 1 MTemperature of 25 C (298 K)

Entropy increases (S ), if:• degrees of freedom (f ) • solid liquid gas• T• number of particles (n) • number of soluted phases

During chemical reaction:changes dS measured from heat transfer δQ at certain temperature T


Recation Entropies for SOFC Fuels(Direct Oxidation)

H2 + ½O2 → H2O

CO + ½O2 → CO2

CH4 + 2O2 → 2 H2O+CO2

reaction entropies from Singhal & Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, Oxford 2003, p.61

–44.3

–86.4

–5.13

1 mol + ½ mol → 1 mol


1 mol + 2 mol → 2 mol + 1 mol

at standard conditions(25°C, 1bar)

(800°C, 1bar)

usablebinding energy

–242

–283

–802

binding energy

[J/(mol K)] [kJ/mol] [kJ/mol]

–195

–192

–797


The Ideal, Reversible SOFCThermal Efficiency

from first & second law of thermodynamics:

theoretical efficiency decreaseswith temperature (in contrast to thermal engines)

efficieny:


0%

20%

40%

60%

80%

100%

0 200 400 600 800 1000

Operating temperature [°C]

Eff

icie

ncy

Carnot cycle (against 25°C)

endoreversible Carnot cycle

reversible oxidation H2

reversible oxidation CO

reversible oxidation CH4

Comparison with Thermal Engines

[kJ/mol]

H2 CO CH4

ΔrH

ΔrS

reaction enthalpies / entropies from Singhal & Kendall 2003, p.61, (reversible oxidation of fuels)

CH4

H2

CO

H2 + ½O2 → H2O

CO + ½O2 → CO2

CH4 + 2O2 →2 H2O+CO2


Reversible Cell Voltage(Gibbs Potential)

2H+ + 2e–

½O2H2OO2–

2 e–

anode electrolyte cathode

2 e–

O2–H2

work

fuel H2 CO CH4

nel 2 2 8

Current

electrons per fuel molecule

Power (if no losses occur)

Reversible voltageuse of tabulated values only valid for standard conditions and negligible fuel utilisation (mixing of fuel+products is irreversible)

fuel H2 CO CH4

nel 2 2 8

U

also termed (standard) Gibbs potentialdoes not include any ohmic etc. losses

open circuit voltage


Pressure Dependence (Nernst Equation)

Pressure depending entropy (ideal gas)

Cell voltage without losses (Nernst potential):

Reaction entropy difference after integration yields

p0with equilibrium constant K

pj

vj

Terming: Nernst potential is the electromotoric force (EMF)UNernst(i = 0 A/cm²) = Open Cell Voltage = Open Circuit Voltage (OCV) = UOCV


Cell Voltage vs. Temperature and Pressure

reaction entropies from Singhal & Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, Oxford 2003, p.61

p = overallpressure

CH4: reactantsand products:almost same volume


Example of Nernst Potential

H2 + ½O2 → H2O


vj

Slightly rewritten form of Nernst potential:


0.8

0.9

1.0

1.1

1.2

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Wasserstoffpartialdruck / bar

Off

ene

Zel

lsp

ann

un

g (O

CV

) vs

Lu

ft /

Vo

lt

900 °C

850 °C800 °C

750 °C700 °C

650 °C600 °C

Wasserdampf-partialdruck

0,03 bar

A,OH

A,H½

K,O0OCV

2

22

p

ppln

F2RT

UU +=OHO½H 222 →+

open

cell

volta

ge(O

CV

) vs

air,

V

hydrogen partial pressure, bar

water vaporpressure0.03 bar

Example of Nernst PotentialpH2, Different Temperatures


Example of Nernst Potentialvs. Fuel Utilisation (Uf)

(excess of air)

Singhal & Kendall, High Temperature Solid Oxide Fuel Cells, Elsevier, Oxford 2003, p.65

Higher fuel utilisation leads to mixing of gases (additional ΔS>0) and changesof gas concentration (partial pressures)


pO2 Form from Nernst Potential

H2 + ½O2 → H2O H2 + ½O2

Keq→←

Equilibrium coefficient of reaction (anode side)

Relationship to Gibbs standard energy:

Use for overall fuel cell reaction in Nernst equation:

superscript A: anode sidesuperscript C: cathode side


3. Drawing a Currentno current, i = 0 with current load, i > 0

- -


Experimental Setup


OCV

Vol

tage

, U

[V]

0

Nernst potential (EMF)

gas consumption

ohmic losses

polarisation losses

: overpotentials

actual cell voltage

Current density, i [A/cm²]

Drawing a Current – Overpotentials


Drawing a Current – Overpotentials

OCV


Vol

tage

, U

[V]

0

gas consumption

ohmic losses

polarisation losses

: overpotentials

activationoverpotential

ohmic range

concentrationoverpotential

Nernst potential (EMF)


Ohmic Losses(also Ohmic Polarisation)

Ω

indexACE

ΩΩ

σ


Vol

tage

, U [

V]

0

Nernst potential

ohmic range

if Nernst potential is constant over Δi (low or constant Uf only!)

Nernst potential (emf)

Otherwise


anode supported cell (ASC)(800°C)

electrolyte supported cell (ESC)(850°C)

thickness ASR[mΩ cm²]

% total ASR

thickness[μm]

ASR[mΩ cm²]

% total ASR

Anode ~50 ~25% 310 32%

Electrolyte 50 25% 500 53%

Cathode ~150 ~50% 140 15%

Ohmic LossesAn Practical Example

electrolyte support

cathode

anode

anodesupport


Comparison of Measured i-V curvesASC vs. ESC

ASC = anode supported cellESC = electrolyte supported cellspecifications: see last slide

ASR~0.2 Ω cm²

ASR~0.95 Ω cm²

Better ion-conducting materials for ESCsgive now upto i = 0.8 A/cm² at 0.7 V

0.7


Potential of Thinner ASC ElectrolyteASRs

even more obvious in linear scale


Potential of Thinner ASC ElectrolyteCurrent Densities Results (I)

(La0.58Sr0.4Fe0.2Co0.8O3- )


Potential of Thinner ASC ElectrolyteCurrent Densities Results (II)

Han, PhD Thesis, 2010


Real LifeContact Layers / Contacting

Cr alloyinterconnect steel

Cr O2 3

(Cr,Mn) O3 4

MnOx

cathode contact layer

cathode current collector

~10 m cm²Ω}

~120 μm

~50 μm

~10 μm

~0,02 S/cm

~10 S/cm

~100 S/cm

thicknessmaterialsconduct.

materials ASR

~1-4 μm

~0,1 m cm²Ω

~0,1 m cm²Ω

~50 S/cm ~0,1 m cm²Ω

+ contact potentials + contacting area + longitudinal resistance

Interconnect

Interconnect

Cell

~1-3 mm

Currently dominating issue!upto 50% performance loss forhigh performance ASC due to contacting


O2- O2- O2- O2-

O2 N2

Concentration Polarisation(or Concentration Overpotential)

Definition:is the resistance in mass transfer of the electroactive speciesto or from the electrodes (diffusion/permeation limit, cell starves)

O2- O2- O2- O2-

H2 H2O

binary diffusivity

anode cathode


Activation PolarisationAnode Side

surface diffusion (?)

or ?

Nickel

Electrolyte

H2 (internal reforming)

fuel adsorption

TPB

anodic reaction (model)

O2–

2e–

VO••


Activation PolarisationAnode Side

surface diffusion (?)

or (after all, these are just models)

Nickel

Electrolyte

H2 (internal reforming)

fuel adsorption

TPB

anodic reaction (model)

O2–

2e–

VO••

(Tafel equation)


Activation PolarisationCathode Side

catalyst without ionic conductivity(only electronic)

catalyst with high ionic conductivitymixed ionic electronic conductor (MIEC)


Mixed Ionic Electronic ConductorCathodes

direct tp

b

reaction

O2(g)

O x(a

d)

O2-

VÖ

Ox(ad)

Ogb

Ox(ad)

O2(g)

VÖ VÖ

O2(g)

Ox(ad)

gasdiffusion

surf

ace

diff

usio

n

volu

me

diff

uion

grai

n bo

unda

ry d

iffus

ion

YSZ

(Ln,A)MTO3+δδδδ

VÖh+

(h+)

e-

VÖ

1 μm

micropores

e-/h+-(surface)

conductivity of electrolyte

h+h+

h+

(h+)

h+

(h+)

h+


ηα−−ηα= AcAas

OHrH,0 RT

nFexp

RTnF

expppjj222H

AK , ηη

Butler-Volmer equation

ηα−−ηα= Acs

OHrH,0Aa

sOH

rH,0 RT

nFexpppj

RTnF

expppjj222H222H

−+ += jjj

process of charge transfer (no diffusion limit)

−− +↔+ e2OHOH 22

2

Butler-Volmer Equation


cathodicanodictotal

η

+j

j

−+ += jjj

−j

ηα−−ηα= AcAas

OHrH,0 RT

nFexp

RTnF

expppjj222H

Butler-Volmer Equation

Tafelregion

−ηα= Aas

OHrH,0 RT

nFexpppjj

222H


Contribution of Different Polarisations

0 3.02.52.01.51.00.5

cathodeactivation

anodeactivation

ohmic


Model calculation for ASC 800°C

S.H. Chan et al., Journal of Power Sources, 93 (2001), 130-140


Electrochemical Impedance Spectroscopy (EIS)

I. Finke, IEF-3, FZJ


Phase Angles



Z´´

Z´

10 mHz

1 Hz1 kHz

100 kHz

impedance spectrum (Nyquist-Plot)

≈ 1 μm

cathode

electrolyte

+ + + + + + +- - - - - - -

Equivalent Circuits and Impedance Spectra

O2–

h+h+ ½ O2(g)

A. Weber, IWE, Karlsruhe

anodecathode electrolyte

RΩ,AnRΩ,catRΩ,El

Rpol,anCpol,an

Rpol,catCpol,cat

simplified equivalent circuit

R0 = RΩ,Cat + RΩ,An + RΩ,El

Rpol,catCpol,cat

Rpol,anCpol,an

ohmiclosses

cathode + anodepolarisations

simplified reaction on tri phase boundary

Rpol,catCpol,cat


Equivalent Circuit Elements

Frequently used:

• Charge transfer R

• Double layer capacitance CZ'

–Z''

parallel

• Diffusion processes Warburg (W)

Z'

–Z''

Z'

–Z''

• real processes:constant phase element Qinstead of C

Q parallel with R

• Coupled reactions anddiffusion

Gerischer (G)

Z'

–Z''


Multiple Equivalent Circuitsfor Simulating Results

Z'

–Z''

All three equivalent circuits are possible!


Getting OCV and CurrentCharacteristics Simultaneously

reference electrode:• to determine the potential drop / overpotentialat the working electrode• as close as possible to the working electrode as possible to avoid Ohmic contributionsdraw

current

reference electrode


3 Electrode Setup


Potentiostat


EIS Example withDistribution of Relaxation Times

Leonide et. al, Journal of The Electrochemical Society, 155, B36-B41 (2008)

Nyquist-Plot

Equivalent Circuit

Distribution of Relaxation Times

ASC/800°C

54 Robert Mücke, Joint European Summer School for Fuel Cell and Hydrogen TechnologyLeonide et. al, Journal of The Electrochemical Society, 155, B36-B41 (2008)

Cathode p(O2) Anode p(H2O)

EIS Example withDistribution of Relaxation Times


OCVU

00

Stromdichte / A/cm²

Zel

lspa

nnun

g /

V

Leis

tung

sdic

hte

/ W

/cm

²

Pmax

cell

volta

ge, V

current density, A/cm²

pow

er d

ensi

ty, W

/cm

²

4. OperationOperating Field of SOFCs

p = U · i

0.6V


OCVU

00


Zel

lspa

nnun

g /

V

Leis

tung

sdic

hte

/ W

/cm

²

0.6V

Pmax

cell

volta

ge, V


pow

er d

ensi

ty, W

/cm

²

fuel cells are not operated at pmax!

Operating Field of SOFCs


OCVU


Zel

lspa

nnun

g /

V

Nut

zung

sgra

d /

%

konstante Brenngas- und Luftdurchflüßen

Brenngasnutzung

Sauerstoffnutzung

Fu

oxu

100

50

80

cell

volta

ge, V


effic

ienc

y, %

constant fuel and air flow

fuel utilization

air utilization

Operating Field of SOFCsEfficiency

00


OCVU

00


Zel

lspa

nnun

g /

V

constant fuel and air flow

fuel utilisation%80uF =

constant fuel and air utilisation

cell

volta

ge, V


Constant Fuel/Air Flow vs. Utilisation


00


Zel

lspa

nnun

g /

V

cell or electrode areaoxidant: air or oxygen

fuel compositionair and fuel flow rates

air and fuel utilisationtemperature

cellR linear region

maxP V7.0P

cell

volta

ge, V


Summary of Factors that InfluenceElectrochemical Performance


00


Sta

cksp

annu

ng/

V

cell or electrode areaoxidant: air or oxygen

fuel compositionair and fuel flow rates

air and fuel utilisationtemperature distribution

maxP V7.0P

amount of cells in stack

air / fuel inair/ fuel outmax / min / medium

temperaturecellR linear region

stac

kvo

ltage

, V


Summary of Factors that InfluenceElectrochemical Performance in a Stack


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

cell

volta

ge /

V

current density / A/cm2

single cell M0611 / 16 cm²

temperature: 800 °Coxidant: 1000 ml/min air

fuel: H2 H2Oml/min ml/min %1000 31 31000 333 33750 250 33

1000 1000 50500 500 50

1000 4000 80500 2000 80300 1200 80

Single Cell Performance for SelectedH2/H2O ratios at 800°C


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2. T H2 H2O Ar CH4 Luft

°C ml/min ml/min ml/min ml/min ml/min802 1000 30.0 -- -- 1000797 500 500.0 -- -- 1000800 125 560.0 35 280 1000804 235 470.0 60 235 1000

cell

volta

ge /

V

current density / A/cm2

Single Cell Performance for SelectedH2/H2O/CH4 ratios at 800°C


electrolyte

fuel

fuel electrode(anode)

−− +→+ e2OHOH 22

2−− +→+ e2COOCO 2

2

reforming

O2- O2- O2- O2-

224 H3COOHCH +→+

shift reaction222 HCOOHCO +→+

Internal Reforming


Gradual Reforming

M. Mogensen, RisoeChanges in gas composition(additional to fuel consumption)

65 Robert Mücke, LargeSOFC Summer School, Ancona, 2009

0 50 100 150 200 250 300 350

Temperatur / °C

Brenngasnutzung 70 %Laufzeit 320 hEbene 8

Ofentemperatur 800°CStrom 179,3 A (-dichte 0,5 A/cm²)Spannung 7,36 V Leistung 1,32 kW

CH4

4,35 l/minH

20,5 l/min

H2O 8,71 l/min

Luft 200 l/min

Bre

nnga

s ei

n

Luft

ein

Position / mm

650 675 700 725 750 775 800 825 850

Temperature Distribution in200x200mm Cells

fuel: methane; fuel utilization: 70%

air

in

fuel

in


Overall Efficiency

thermodynamic efficiency(laws of thermodynamics)

electrochemical efficiency(all polarisations)

fuel utilisation

total electrical efficiency

(up to 60% achieved)


Electrical Net Efficiency, Based on Natural Gas Fuel

Basis: Siemens 100 kW system

Gas Input

cellvoltage650 mV

100%

62.5%

52.5% 50.4%46.9%

fuelutil.84%

BoPeffic.96%

invertereffic.93%

celleffic.62,5%

improvement of cell properties

0%

10%

20%

30%

40%

50%

60%

70%

80%

600 650 700 750 800 850 900

cell voltage [mV]

el. n

etef

fici

ency

El. net efficiency as a functionof cell voltage

61.3%

improvement of cell performance

all efficiencies optimised 67.8%

optimised: 81,7% 90% 96% 96%

Net efficiency ηηηηel = ηηηηz × uF × ηηηηp × ηηηηInv = ηηηηstack × ηηηηp × ηηηηInv

(cell efficiency × fuel utilisation × BoP efficiency × inverter efficiency)

L. Blum, IEK-3


Sources of Degradation

Cr poisoning / cathode change cathode activation + ohmic

coking (occupation of TPBs) anode activation

contact loss ohmic

cathode / electrolyte reaction ohmic + cathode activation

coarsening of anode microstructure anode activation

Sorted by approx. relevance


Measurement of Degradation

A. Mai, Hexis

better to measure ASR instead of ΔV, however, requires i-V cures taken at intervals


Acknowledgements

Special thanks for graphics and results are due to

Prof. E. Ivers-Tiffée • Dr. A. Weber • A. Leonide (IWE/KIT)Dr. A. Mai (Hexis)

Prof. M. Mogensen (Risoe National Lab.)

Prof. Ludger Blum • Dr. Martin Bram • Dr. Izaak C. Finke •Dr. V.A.C. Haanappel • Dr. L.G.J. de Haart • Dr. Natividat Jordan-Escalona •

Dr. Norbert H. Menzler • Dr. Sven Uhlenbruck (all FZJ)

The fuel cell project team under Dr. Robert Steinberger-Wilckens.

The SOFC group of IEK-1 in Jülich under Dr. H.-P. Buchkremer(and fomerly Prof. Dr. D. Stöver).

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