Macroscopic modelling of degradation phenomena in fuel cells · Macroscopic modelling of degradation phenomena in fuel cells Andrei Kulikovsky Research Centre Juelich Institute of

Mitg

lied

der H

elm

holtz

-Gem

eins

chaf

t

Macroscopic modelling of degradationphenomena in fuel cells

Andrei Kulikovsky

Research Centre JuelichInstitute of Energy and Climate Research, IEK-3

2nd European Summer School, Iraklion, September 2012

Institute of Energy and Climate Research (IEK-3) 1

Outline

• Introduction

• Poisoning wave along the feed channel

• Carbon corrosion in PEM fuel cells

• Ruthenium corrosion in DMFCs

• Poisoning wave in the catalyst layer: Cr deposition in SOFC

• Conclusions

0 0.2 0.4 0.6 0.8 10

50

100

150

200

OR

R ra

te /

A cm

-3

1 2 3Degradation wave

4

5l*

Gas

-diff

usio

n la

yer

/ tx l


What is wrong with our cells?

Key aging problems are in catalyst layers (agglomeration, dissolution, corrosion etc)


General aging models?

Can we develop general models of cell aging,not specifying microscopic mechanisms?

Yes, we can!


Quasi-2D cell modeling

x

zcathode channel

cathode GDL

CCLmembrane

inle

t

outle

t

inle

t

outle

t

anode channel

anode GDL

ACL

air

fuel

In the MEA, the dominant transport is through-plane; in the channels, it is along the channel.

Quasi-2D models.


Quasi-2D equations

0lim

ln ln 1/ /ref ref

j jb j c c j c c

h

*

æ öæ ö ÷ç÷ç ÷÷ çç= - - ÷÷ çç ÷÷ ç÷ç ÷çè ø è ø

0 c jvz nFh

¶= -

¶

cell ocV V RJh= - -

Voltage loss on the cathode side

Mass conservation in the channel(plug flow)

Cell voltage


Solutions:

/1 1

ln 1 1z L

jJ

ll l

æ öæ ö÷ ÷ç ç= - - -÷ ÷ç ç÷ ÷÷ ÷ç çè øè ø

/

0

11

z Lc

c l

æ ö÷ç= - ÷ç ÷÷çè ø

Normalized distance along the channel0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

0

c

c

Normalized distance along the channel0.0 0.2 0.4 0.6 0.8 1.0

0

1

2

3

jJ

The lower stoich, the larger local current at the inlet


Model and experiment of Kućernak’s group

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

Cur

rent

/ A

0 0.2 0.4 0.6 0.8 1

0

1

2

3

4

5

2.0691.2021.0114

Lambda

502010 sccm

Inlet Outlet

Raw data

Model (lines) and experiment

A.A.Kulikovsky, A.Kucernak and A.A.KornyshevElectrochim. Acta 50 (2005) 1323.

( )( )/

0 1 1ln 1 1

z LjJ

ll l

= - - -


Suppose that there exists a critical current density

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

critj

wl

0t 1t

nt

/z LInlet Outlet

11

w

w

z z

L z

w

j Lf

J L z l l

--æ ö æ ö÷ ÷ç ç÷= ⋅ - ÷ç ç÷ ÷ç ÷ç÷ç - è øè ø

11 11

1

w

w

z z

z

w

jf

J z l l

--æ ö æ ö÷ ÷ç ç÷= ⋅ - ÷ç ç÷ ÷ç ÷ç÷ç - è øè ø

The length of the domain subject to degradation is obtained from

( )w w critj z l j+ =


Equation of wave motion

( ) ( )( )( )

1 ln (1 ) / ( )

ln 1 1/w crit w

w

z j z f Jl l

l

- -=

-

w w

d

z l

t t¶

=¶

This is an equation of degradation wave motion. Tau_d is the characteristic time of degradation, determined by the microscopic nature of the degradation.

Just a simple algebra…


The law of wave motion

1 exp ln( )expwz a a té ù= - -ë û

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

critj

wl

0t 1t

nt

j

/z L

slow phase

Wavefront position vs. time

Inlet Outlet

It seems that typically 1a

(0) / crita j j=

where

( )ln 1 1/d

tt

t l-=

Time is scaled according to


Degradation wave: overpotential

0 5 1012

10

8

6

4

bh

t

slow phase

(time)

A.A.Kulikovsky, H. Scharmann and K.Wippermann Electrochem. Comm 6 (2004) 75.

Cathode overpotential vs. time


PEFC lifetime experiment from PSI


PEFC flooding (ZSW and Fraunhofer ISE)

Scholta, Lehnert, Grünerbel, Jörissen

Air inlet

Outlet


Some lessons

It seems that fuel cell never dies uniformly: some areas are more stressed and they die first. Then, the “stressing spot” shifts to a new position and it starts killing a new domain. In the stack, the process is facilitated by the fixed total current.

Stressing factors: (i) high local current, (ii) high local temperature, (iii) high local overpotential. These factors induce numerous microscopic aging processes.

We could imagine radial waves propagating from the circular spot, or 2D waves. However, the mechanism of propagation remains the same.

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5


C.A.Reiser, L.Bregoli, T.W.Patterson, J.S.Yi, J.D.Yang, M.L.Perry, T.D.Jarvi. ESSL 8 (2005) A273

Anode inlet Anode outlet

Cell “reversal”

0.5eqcrE V=1.23eq

oxE V=

eqc Eh j= -F -

metal electrolyte OCV


Carbon corrosion in PEM fuel cells

Experiment

F

coxh

1.23 V

- 1.23 V

aoxh

ccrh

0.5 V

ahyh


Model

A

CN-domain R-domain

Hydrogen oxidation Oxygen reduction

Oxygen reduction Carbon corrosion

x

y


Membrane potential

2 2

2 20

x y

¶ F ¶ F+ =

¶ ¶x

y A

CN-domain R-domain

2

2

1

a c

m m c a

mm m m m m

y y j jy y l ly

s ss

s s s

¶F ¶F-

æ ö¶ F ¶ ¶F ¶ ¶ -÷ç= » =÷ç ÷÷ç¶ ¶è ø¶

Where we have used Ohm’s law: mjy

s¶F

= -¶


Membrane potential

2 2

2 20

x y

¶ F ¶ F+ =

¶ ¶

2

2

a c

m m

j jlx s

¶ F -=

¶

Ok, instead of

we get

22

2a cj j

xe

¶ F= -

¶

, , m

m c

x jjlx

L b bsF

F= = =

Introducing dimensionless vars

we obtain

where

ml

Le =


What is epsilon?

22

2372.5 10

1010

ml

Le

--

æ öæ ö ⋅ ÷÷ çç ÷÷= = çç ÷÷ çç ÷ ÷ç çè ø è ø

Thus, at leading order we can set epsilon = 0 and the Poisson equation

simplifies to

a cj j=

2D Laplace equation is reduced to a much simpler algebraic equation!

For j^a and j^c we can write Butler-Volmer-like equations. For concen-trations we take a step function.

2 2

2 20

x y

¶ F ¶ F+ =

¶ ¶

22

2a cj j

xe

¶ F= -

¶

a cj j=


Currents

( ) ( ) 0a a c chy ox ox crj j j j- - - =

No current in the external circuit


An example: HOR current

2 sinh hyBVhy hy

hy

j jb

h*æ ö÷ç ÷ç= ÷ç ÷÷çè ø

lim

1 1na BVhy hy hy

f

j j j= +

lim2 ref

hy hy

b reh

fy

FD c

l jj =

011 tanh

2nx x

fs

æ æ öö- ÷÷ç ç ÷÷= -ç ç ÷÷ç ç ÷÷ç çè è øø

a eqhy c hyEh j= -F -

(Crude approximation for HOR…)


Concentrations and currents

0 1 2 3 4 5 6 7 8 9 10Distance along the channel / cm

-0.6

-0.4

-0.2

0

Phi

/ V

0

0.2

0.4

0.6

0.8

1

Con

cent

ratio

n / c

ref

oxc

hyc


0

0.5

1

1.5

2

j cat

hode

/ A

cm

-2

coxj

ccrj

Anode concentrations and Phi “Cathode” currents

F

Prescribed step functions for hydrogen and oxygen concentrations and the solution for Phi. Our approximation fails in a narrow yellow zone.

ORR and CCR current densities on the cathode side.


More currents


0

0.5

1

1.5

2

2.5

j ano

de /

A c

m-2

“Anode” currents

ahyj

aoxj

0 1 2 3 4 5 6 7 8 9 10Distance

0

0.5

1

1.5

2

j x m

embr

ane

/ A c

m-2

a chy oxj j-a cox crj j-

In-plane current

x¶F¶

large

HOR and ORR currents on the anode side. Note the peak of HOR, something is happening there.

These differences are expected to be zero; however, they are not. Peak manifests an in—plane current at the interface.


0 1 2 3 4 5 6 7 8 9 10

0

0.01

0.02

j cat

hode

/ A

cm

-2

Oxygen on the anode due to crossover

0 1 2 3 4 5 6 7 8 9 10-0.3

-0.2

-0.1

0

Phi

/ V

0

0.2

0.4

0.6

0.8

1

Con

cent

ratio

n / c

ref

oxc

hyccoxj

ccrj

“Cathode” currents

The interface is much wider now, as the currents are much lower. Note large shift of Phi gradient position with respect to concentration gradient.

Very similar to the previous case; however, the gradients are smaller.


Currents

0 1 2 3 4 5 6 7 8 9 100

0.01

0.02

0.03

j ano

de /

A c

m-2

ahyj

aoxj

0 1 2 3 4 5 6 7 8 9 100

0.01

0.02

0.03

j x m

embr

ane

/ A c

m-2

a chy oxj j-a cox crj j-

“Anode” currents “In-plane” current

Peak of in—plane current at the interface gets wider.


Experiment: T.W.Patterson, R.M.Darling, ESSL 9 (2006) A183

1

2345

6


Experiment 2anode

cath1

2345

6


N/R interface: Virtual fuel cell

A.A.Kulikovsky J. Electrochem. Soc. (2011)

0 1 2 3 4 5 6 7 8 9 100

0.01

0.02

0.03

j x membrane / A cm-2


N/R interface: proton trajectory

cathode

anode


How could we block reversal?

• Simple solution is to apply external potential to the cell; this is what companies are doing.

• More exotic solution is the membrane with anisotropic conductivity. If proton conductivity along the y—axis is small, the virtual fuel cell cannot form and no reversal could happen.


DMFC with methanol starvation

0

0.5

1

Met

h. c

once

ntra

tion


-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Pot

entia

ls /

V

inle

t

outle

t

O2

CH3OH

cell voltage

xy

MOR CCR

ORR ORR

ccj

acj

Mc

F


Methanol starvation: Environment for Ru corrosion

Distance along the channel / cm0 2 4 6 8 10

-0.2

0.0

0.2

0.4

0.6

0.8

Ove

rpot

entia

l / V

Oxygen

Methanol

Carbon

Ruthenium

(a)

(a)

The same model leads to balance of currents produced on the anode and the cathode sides. From this balance we get the shape of Phi, currents and overpotentials for all reactions.

The shaded domain suffers from carbon corrosion and Ru dissolution on the anode side.

2Ru Ru 2e+ - +


The effect of depleted domain length

Fraction of methanol-depleted domain0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.1

0.2

0.3

0.4

0.5

Pot

entia

l / V

0.6

0.7

100 mA cm-2

Ru

CarbonVcell


Degradation wave in the catalyst layer

2 sinhj

cx

e h¶

= -¶

jxh¶

= -¶

Charge

Ohm’s law

0c

D j jx

¶= -

¶Mass transport


Current conversion with transport loss

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0

2

4

6

8

10

/ tx l GDLMem

j

reacR

Poor feed transport Poor ionic transport

h c

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

0

500

1000

Rat

e of

con

vers

ion

/ A c

m-3

reacR

j

/ tx lMem GDL

h

c

Flooded PEMFC cathode DMFC anode, SOFC cathode

1

0

nFDcl

j* =0

tbljs

* =

l* l*


Polarization curves

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

0

2

4

6

8

10

00 2 ln

D

jb

jh

æ ö÷ç= ÷ç ÷çè ø

21 /D refj i nFDc c*=

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

0

500

1000

Rat

e of

con

vers

ion

/ A c

m-3

00 2 ln

jb

jsh

æ ö÷ç= ÷ç ÷çè ø

12 /t refj i bc cs s*=

This case is of largest interest for DMFC, SOFC and HT-PEMFC


Cr poisoning of the CCL in SOFC

( )2 3 2 2 2 23

Cr O (s) + O (g) + 2H O 2CrO OH (g)2

( ) - 2-2 2 3 22CrO OH (g) + 6e 3O + Cr O (s) + 2H O(g)

On the BP surface

In the FL, electro-chemical process!

Ele

ctro

lyte

Gas

-diff

usio

n la

yer

(cur

rent

col

lect

or)

Functional layer

0 10

Bipo

lar p

late


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

0

500

1000

Rat

e of

con

vers

ion

/ A c

m-3

Model of CL aging

reacR

/ tx l

l*

The shape of overpotential for the parasitic reaction is simply a shifted ORR overpotential.

The rate of CL aging has peak in the conversion domain, which dies first.

h

eqc Eh j= -F -


Degradation wave

0 0.2 0.4 0.6 0.8 10

50

100

150

200

OR

R ra

te /

A c

m-3


4

5l*

Gas

-diff

usio

n la

yer

/ tx l

When the conversion domain is dead, the ORR/poisoning peak shifts toward the GDL and a new domain is subject to aging.


Auxiliary problem: Performance of partially degraded CL

Note a small residual conversion activity of the poisoned domain (inset).

0 0.2 0.4 0.6 0.8 10

10

20

30

40

0

40

80

120

0 0.2 0.4 0.6 0.8 10.001

0.01

0.1

1

jreacR

h

( )i x*

/ tx l

A.A.Kulikovsky, Electrochem. Comm.12 (2010) 1780

0 10 20 30 405

10

15

20

0.20.40.6

0.0 (fresh)

(fully degraded)

0.1

1.0

SOFC

( )0 /t tj l bs

0

bh

Polarization curves for the indicated poisoned fraction of the CL.

GDLEle


DW in the CL: Cr poisoning of SOFC cathode

A.A.Kulikovsky, J. Electrochem. Soc. 158 (2011) B253.

Cathode polarization voltage vs. time for different cell currents, model

0 0.2 0.4 0.6 0.8 1Time / a.u.

10

15

20

Pol

ariz

atio

n vo

ltage

/ b

10

20

40

5

Model

0 10 20 30 405

10

15

20

0.20.40.6

0.0 (fresh)

(fully degraded)

0.1

1.0

SOFC

( )0 /t tj l bs

0

bh


DW in the CL: Cr poisoning of SOFC cathode


Model

0 0.2 0.4 0.6 0.8 1Time / a.u.

10

15

20

Pol

ariz

atio

n vo

ltage

/ b

10

20

40

5

Experiment (Konysheva et al. JES, 154 (2007) B1252)

Model Experiment: half-cell voltage vs. time


Why?


0 0.2 0.4 0.6 0.8 10

50

100

150

2001 2 3 4

5

0 0.2 0.4 0.6 0.8 10

5

10

15

20

OR

R ra

te /

A c

m-3 1 2 3

45

/ tx l / tx l

Low current High current

Conversion runs in a fresh domain. At 40% poisoned fraction, conversion runs in a poisoned domain, i.e., 40%-poisoned CL works almost as bad as fully poisoned.


Cr distribution in the FL

J.A.Schuler, P.Tanasini, A.Hessler-Wyser, C.Comninellis, J. Van herleEleComm, 12 (2010) 1682–1685


Experimental cell voltage vs. time (A.Schuler and J. van Herle, Lausanne Univ.)

Time / hours

Cel

l vol

tage

/ V

450 mA/cm2

600 mA/cm2

750 mA/cm2

300 mA/cm2

0

1lifet j

Model:


0.01 0.1 1 10 100 10000.1

1

10

doub

le T

afel

trans

ition

Tafel

linear

0.01 0.1 1 10 100 10000.01

0.1

1

10

linear double Tafeltrans

ition

Polarization curves

0je0je

0h

10e = 0.1e =

( )02 ln je

( )20ln 2 je

( )02 ln je

0je

A.A.Kulikovsky, Electrochim. Acta 55 (2010) 6391.

20je

To prevent fast Cr deposition, the ionic conductivity of the FL should be large.


Conclusions

• Macroscopic equations suggest the general scenarios of cell performance degradation

• Fuel cell never die uniformly. Some domains of the cell are stressed more and they die first. This simple idea leads to various aging waves in cells.

• In a stack environment, more degradation waves are possible…

0 0.2 0.4 0.6 0.8 10

50

100

150

200

OR

R ra

te /

A cm

-3


4

5l*

Gas

-diff

usio

n la

yer

/ tx l

Documents

Macroscopic modelling of degradation phenomena in fuel cells · Macroscopic modelling of degradation phenomena in fuel cells Andrei Kulikovsky Research Centre Juelich Institute of