Theory and Application of Porous Electrodes in Fuel Cell Characterization

Dr. Norbert Wagner DLR, Institut für Technische Thermodynamik, Stuttgart

Kronach Impedance Days 2009 "Hermann Göhr" Kloster Banz, May, 27th – 29th , 2009

Presentation outline

IntroductionExamples of porous (technical) electrodes

Theory and models of porous electrodesImpedance models

Application of Göhr‘s porous electrode modelEIS measured at PEFCEIS measured during oxygen reduction on silver in alkaline solution

OutlookExperimental set up for EIS applied for stack measurements

Why porous electrodes?

•Enlargement

of active

electrode

surface•Lowering

of overvoltage

at same

current

input

(electrolyzer) or

output

(fuel

cell)•Increasing

of power density

(galvanic

cells)

•Increasing

of storage

capacity

(supercaps)•Lowering

catalyst

loading

by

increasing

active

surface

-100

-80

-60

-40

-20

0

20

40

60

80

100

-80 -55 -30 -5 20 45 70

Overvoltage / mV

Cur

rent

den

sity

/ m

Acm

-2 i0 = 1 mAcm-2

i0 = 10 mAcm-2

b = 25 mV/decade

HER

HOR

Butler-Volmer equation

for

hydrogen

oxydation

(HOR)

and hydrogen

evolution

reaction

(HER)

η1

η2

i = 100 mAcm-2

Fuel cell overvoltage and current density / voltage characteristic

Cathode

d +(r )P

oten

tial

Current density (Current/Surface)

0, Cathode

ct,C

d +(r )

ct,AAnode

Cell Voltage (UC )

Hydrogen Oxidation Reaction (HOR):

H2 = RT/2F i/i*

Oxygen Reduction Reaction (ORR):

O2/air = RT/[(1-)2F] [ln i - ln i*]

Ohmic loss

= iR

Transport limitation (diffusion)

d = -

RT/2F ln (1 - i/ilim )

Fuel cell voltage

UC = U0 - ct,H2 - ct,O2/air - d -

U0

0Cathode

Field of application of porous electrodesBatteries

and supercaps

Process

fluids

Hydro- gen

GDE

Packed

bed

cathodeMembrane

Auxiliary

supply

Current

collector

Water purification

and treatment

(Bio)-Organic

synthesis

Fuel

Cells

O22H

O22H O ,membranereaction layerdiffusion layer

flow field/current collector

electrons

l c i o ee e tr cal p w r

r t np o o s

a h danode c t o e

NaCl

Cl2

H2 O

NaOH, H2

Cl-Na+

OH-+ -

Electrolysis

(Water, NaCl, etc.)

Current I

U/I - Characteristicof a Fuel Cell

Cel

l vo

ltag

e U

Potential excitation signal - E(t)Cu

rrent respo

nse signal- I(t)

Electrochemical Impedance Spectroscopy: Application to Fuel Cells

Schematic diagram of the U-i characteristic of PEFC and Electrochemical Impedance Measurements

Cel

l vol

tage

Current density

Ruhespannung (ohne Stromfluß)i

AnodeUR acAn

)(

iCathodeUR ac

Cath

)(

iCellUR cd

Cell

)(

i

U(Cell)

U-i measured

i

n

U n

U = iRM

Cathodic Overvoltage

Anodic Overvoltage

PEFC: Schematic Diagram (cross section)

SEM picture of PTFE/C powder

Multi-layer Gas Diffusion Electrodes with different porous layers

Carbon-PTFE

Layer(Dry

sprayed)

Ag-PTFE Layer(Rolled

Layer)

Authors Reference Model and systemJ. -P Candy, P Fouilloux, M. Keddam, H. Takenouti

Electrochim. Acta, 26(1981) 1029 Ni in alkaline solution

R. De Levie Electrochim. Acta, 8(1963) 751 Transmission line model, J.S. Newman and C.W. Tobias J. Electrochem. Soc., 109(1962) 1183 Steady-stateJ. Giner, C. Hunter J. Electrochem. Soc., 116(1969) 1124 Flooded-agglomerate model, Pt-GDE, OCR in

alkaline solutionK. Mund, F.v. Sturm Electrochim. Acta, 20(1975) 463 HOR on Ni in alkaline

solutionS. Sunde, Electrochim. Acta, 42(1997) 2637 Composites, SOFCP. Björnbom Electrochim. Acta, 32(1987) 115 Steady state modelR. Holze, W. Vielstich J. Electrochem. Soc., 131(1984) 2298 OCR in alkaline

solutionT.E. Springer, I.D. Raistrick J. Electrochem. Soc., 136(1989) 1594 Flooded-agglomerate and thin film model,

differential element of a pore wallH. Göhr Poster ISE Erlangen, 1983 Homogeneous porous model, Pb

in sulfphuric

acid

G. Paasch, K. Micka, P. Gersdorf Electrochim. Acta, 38(1993) 2653 Macrohomogeneous

porous electrode modelW. Scheider J. Phys. Chem., 79(1975) 127 Model with pore branchingS. Srinivasan, H. D. Hurwitz, J. O'M Bockris J. Chem. Phys., 46(1967) 3108 Thin

film modelM. Kramer, M. Tomkiewicz J. Electrochem. Soc. 131(1984) Stochastic approach with interpenetrating

networkA. Winsel, E. Bashtavelova J. Power Sources, 73(1998) 242 Agglomerate-of-spheres modelM. Tomkiewicz, B. Aurian-Blajeni J. Electrochem. Soc. 135(1988) 2743 True effective medium approachH. Keiser, K.D. Beccu, M.A. Gutjahr Electrochim. Acta, 21(1976) 539 Various geometries of single pore, Ni-GDE

Brief Overview of Porous electrode models and Applications

R = electrolyte resistance inside the pore per unit lengthC = interface capacitance per unit length

Simple pore model of interface charging RC-transmission line of a flooded pore

RCiCi

RiZ

coth)(

imag

inar

y pa

rt /

real part /

0

-3

-2

-2.5

-1

-1.5

-0.5

-1 -0.5 0 0.5 1 1.5 2

C=500mFPore

Nyqusit representation of Impedance of RC- transmission line, model of a flooded pore

R

C

R = 3 Ω C = 0.5 F

RCiCi

RiZ

coth)(

R0 R0

= R/3 = δL/3πr2

δ

= specific

electrolyte

resistancer = pore

radius

L = pore

lenght

Lr

100 mHz

Simple pore model with faradaic processes in pores RC-transmission line of a flooded pore

ct

c = interface capacitance per unit lengthrct = interface charge transfer resistance per unit lenght (Faraday impedance y2 )

r = electrolyte resistance inside the pore per unit length

Nyqusit representation of porous electrode impedance with faradaic impedance element

imag

inar

y pa

rt /

real part /

0

-3

-2

-2.5

-1

-1.5

-0.5

-0.5 0 0.5 1 1.5 2 2.5

C=500mFC+Rpor(3 Ohm)C//R(1.5 Ohm)

r

c rct

r = 3 c = 500 mFrct

= 1.5

Generalization of RC-transmission line of a flooded pore

Thin-film model of a porous electrode

Thin-film model and agglomerate plus thin-film model of a porous electrode

I.D. Raistrick, Electrochim. Acta, 35(1990) 1579

Theory of Agglomerated Electrodes

metal side

electrolyte sideionic current

Gas (backing) side

electrolyte sideionic current

M. Eikerling, A.A. Kornyshev, E. Lust, J. Electrochem. Soc., 152 (2005) E24

Hierarchical model (Cantor-block model)

ll

l/al/alz

lz/az

n = 0

n = 1

ll

l/al/alz

lz/azn = 2

R

C

(a2/az)R

Caaz)

(a2/az)2R

Caaz)2

(a2/az)2R

R

C

(a2/az)R

Caaz)

(a2/az)2R

Caaz)2

(a2/az)2R

n = 0

n = 1

n = 2

R

C

(a2/az)R

Caaz)

(a2/az)2R

Caaz)2

(a2/az)2R

R

C

(a2/az)R

Caaz)

(a2/az)2R

Caaz)2

(a2/az)2R

n = 0

n = 1n = 1

n = 2n = 2

S.H. Liu, Phys. Rev. Letters, 55(1985) 5289T.Kaplan, L.J.Gray, and S.H.Liu, Phys. Rev. B 35 (1987) 5379

μsL μ 2 2

z

μ2 2

z(1)μ

2 2z

(2)μ

(3)μ

/11

/11

/11

...

RZ R

N a aj

N a aj

N a aj

j

mZZe

metalelectrolyte pores

porous layer

Zs1 ZsnZsi

ZpnZpiZp1

Zq1 Zqi Zqn

H. Göhr

in Electrochemical Applications/97, www.zahner.de

Cylindrical homogeneous porous electrode model (H. Göhr) I

Cylindrical homogeneous porous electrode model (H. Göhr) IIIons (H+, OH -,..)

I I

Por

e

Ele

ctro

de, p

orou

s lay

er

Electrolyte Zq

Zp ZS

Zo

Zn

Current (e-)

qsp ZZZ )(Z* =Z ZZ Z

p s

p s

( )Z#

=

C = cosh S = sinhZ ZZp s

*

Z ZZp s

*

P = q0

= v = sp

p

ZZZ

ZZ o

* Z ZZ

p s*

qn

= ZZn

* s = = 1-p ZZ Z

s

p s

C C p s S p q s q

S q q C q qn o

n o n o

( ) ( )( ) ( )

1 21

2 2

Z = Z#+Z*

Porous electrode model with faradaic impedance

Simulation of Impedance Spectra using Porous Electrode Model

(Rct

||Cdl

“+“Rel,por

)+RM

+L Rct

= 50 mCdl

= 50 mF RM

= 3m L = 20 nH

Rel,por

= 0 m Ω 10mΩ 20 mΩ 30mΩ

imag

inar

y pa

rt / m

real part / m

0

-20

20

10 20 30 40 50 60

pore 0mpore 10mpore 20mpore 30m

|Z| / m

frequency / Hz

5

10

20

15

50

100m 1 3 10 100 1K 10K 100K

pore 0mpore 10mpore 20mpore 30m

frequency / Hz

|phase| / 0

0

15

30

45

60

75

90

100m 1 3 10 100 1K 10K 100K

pore 0mpore 10mpore 20mpore 30m

Electrochemical Impedance Spectroscopy: Experimental Set-up

Electrochemical

workstation

PEFC

Flow

contollerPressure

regulator

Humidifier

Bode diagram of measured EIS at different cell voltages (current densities) I

|Z| /

frequency / Hz

|phase| / 0

0

15

30

45

60

75

90

10m

30m

100m

300m

1

3

10m 100m 1 3 10 100 1K 10K 100K

OCV 1024 mV952 mV901 mV871 mV841 mV807 mV777 mV747 mV717 mV

Bode diagram of measured EIS at different cell voltages (current densities) II

Phase oImpedance / m

Frequency / Hz

0

20

40

60

80

10

20

15

30

50

10m 100m 1 10 100 1K 10K 100K

O

E=597 mV; i=400 mAcm-2

E=497 mV; i=530 mAcm-2

E=397 mV; i=660 mAcm-2

+

E=317 mV; i=760 mAcm-2

Bode diagram of measured EIS at different cell voltages (current densities) III

Phaseo

Impedance /

Frequency / Hz

0

20

40

60

80

10m

30m

100m

300m

1

3

10m 100m 1 10 100 1K 10K 100K

O

E=1024 mV; I=0 mA

E=841 mV; I=1025 mA

E=597 mV; I=9023 mA+

E=317 mV; I=17510 mA

Common Equivalent Circuit for Fuel Cells

Cdl,a

RM

Rct,a

Cdl,c

Rct,c

Common Equivalent Circuit for Fuel Cells

Cdl,a

RM

Rct,a

Cdl,c

Rct,cZdiff

Diffusion of O2

Common Equivalent Circuit for Fuel Cells

Cdl,a

RM

Rct,a

Cdl,c

Rct,c ZdiffZdiff

Diffusion of H2

EIS at Polymer Fuel Cells (PEFC): Common equivalent circuit and boundary case

Cdl,a

RM

Rct,a

Porous electrode with pore electrolyte resistance (Rpor ) and surface layer resistance (RS )

Cdl,c

Rct,c

CN

RN

Cdl,a

RM

Rct,a

Cdl,c

Rct,c

Equivalent

circuit

of the PEFC: anode and cathode

simulated

without

pores, without

diffusion

(valid

for

example

at lower

current

densities)

Bode diagramm of the EIS, measured at the PEFC at 80°C, symmetrical gas supply of the cell

Phase oImpedance /

Frequency / Hz

0

20

40

60

80

10m

100m

1

10

10m 100m 1 10 100 1K 10K 100K

O2 /O2 H2 /H2

EIS at Polymer Fuel Cells (PEFC): Contributions to the cell impedance at different current densities

0

0.04

0.08

0.12

0.16

0.2

0 100 200 300 400 500 600 700

Current density /mAcm-2

Cel

l im

peda

nce

/Ohm

0

0.2

0.4

0.6

0.8

0 200 400 600Current density /mAcm-2

Cell

impe

danc

e /O

hm

Evaluation of the U-i characteristics from EIS

100

300

500

700

900

1100

0 200 400 600 800

Current density /mAcm-2

Cel

l vol

tage

/mV

measured

curve: Un

= f(in

)calculated

curve: Un

= in

Rn

(without

integration) calculated

curve

using

method

II: Un

= an

i2n

+bn

in

+cnx calculated

curve

using

method

I: Un

= an

in

+bn

RU

In n

Integration method

I:

U UU

I

U

II I

n n n n n n

112 1 1

( ) ( )

Integration method

II:

U a I b I cn n n n n n 2 with:

aR R

I Inn n

n n

1

12 ( )

b R a In n n n

1 12

c U a I b In n n n n n

1 12

1

EIS at Polymer Fuel Cells (PEFC): Contributions to the overal U-i characteristic determined by EIS

200300400500600700800900

10001100

0 100 200 300 400 500 600 700 800

Current density / mAcm-2

Cel

l vol

tage

/ mV

E0

EK

EA

EM

EDiff.

Cdl,a

RM

RA

Cdl,c

RK

CN

RN

Evaluation of EIS with the porous electrode model I

I

I

I

00.020.040.060.080.1

0 200 400 600 800

Current density /mAcm-2R

p,a;

Rct

,a; R

por,a

/Ohm

21

21

,

,

,,,

tanh

)(

act

apor

actaporap

RR

RRR

Porous electrode resistance (Rp, a ), charge transfer resistance (Rct, a ) and electrolyte resistance (Rpor, a ) in the pore of the anode at different current densities

Evaluation of EIS with the porous electrode model i-V characteristic and current dependency of pore electrolyte resistance

of the anode and cathode

Rel,por,Anode♦

Rel,por,Kathode

0

5

10

15

20

25

30

35

40

0 2 4 6 8 10 12 14 16 18

Current / A

Pore

ele

ctro

lyte

resi

stan

ce /

mO

hm

0

200

400

600

800

1000

1200

Cell

volta

ge /

mV

Impedance Measurements during Oxygen Reduction Reaction (ORR) in 10 N NaOH, on Silver Electrodes

at Different Current Densities

10m 100m 1 3 10 100 1K 10K 100K

500m

1

2

1.5

5

|Z| /

0

15

30

45

60

75

90|phase| / o

frequency / Hz

45 mA40 mA

35 mA30 mA

25 mA20 mA

15 mA

10 mA

5 mA

100 mA95 mA90 mA85 mA80 mA75 mA70 mA65 mA60 mA55 mA50 mA

1 2 3 4 5

0

-4

-2

Z' /

Z'' /

-50

5 mA

10 mA

15 mA20 mA

100 mA

i / mA

Outlook

Further improvement of porous electrode models

Combination and extension of existent and new models

Application of EiS to segmented cells

Experimental validation of models usingPEFC and DMFC electrodes with different porous structureGas Diffusion Electrodes (GDE) for Oxygen Consumption Reaction (OCR) in alkaline solution using different gas compositions