Simulating Stimulating Interfaces Applications in Adsorption and Catalysis

Simulating Stimulating InterfacesApplications in Adsorption and Catalysis

C. Heath Turner and Xian WangDepartment of Chemical and Biological Engineering

The University of Alabama

Kah Chun LauDepartment of Chemistry, George Washington University

Brett I. DunlapCode 6189, Naval Research Laboratory, Washington D. C.

Financial Support Provided by the Office of Naval Research

Solid Oxide Fuel Cells

Performance Characteristics…• Mainly for stationary applications with an output from 100 W to 2 MW.

• They typically operate at temperatures between 700 and 1,000°C.

• Efficiency can be as high as 90% (when the off-gas is used to fire a secondary gas turbine).

• Due to the high operating temperature, no need for expensive catalyst.

• SOFC are not poisoned by CO and this makes them highly fuel-flexible. So far they have been operated on methane, propane, butane, fermentation gas, gasified biomass, etc.

• Thermal expansion demands a uniform and slow heating process at startup (typically, 8 hours or more).

…we will focus on the cathode interface

SIMULATION SIZES and METHODS

TIME (s)

LENGTH(m)

Classical Methods

Mesoscale Methods

Continuum Methods

10-10 10-710-9 10-8 10-6 10-5 10-310-4

10-16

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

Semi-Empirical Methods

Ab Initio Methods

Kinetic Monte Carlo

Understanding the Performance of Solid-Oxide Fuel Cells

Determining how fuel cell materials respond at the atomic level to the global operation dynamics, and locally, due to interconnected micro or nanostructures, is a looming challenge.

Many variables to consider…

…how are they all correlated?…how is SOFC performance affected?

• Temperature

• Partial Pressure of the Gases

• Bias Voltage

• Geometry/Surface Area

• Cathode/Anode Materials

• Electrolyte Material, Dopant Level

Difficult to isolate experimentally, but given an appropriate model, simulations can lend some help

THE MODEL• We focus on the cathode-side of the electrolyte interface.

the anode side and the associated reactions are ignored

• The electrolyte is yttrium-stabilized zirconia (YSZ) the dopant level can vary, which affects the oxygen vacancy fraction

• The oxygen partial pressure can vary (PO2) this affects the O2 adsorption rate

• The temperature (T) can vary this affects the O2 adsorption/desorption equilibrium, the elementary

chemical kinetics, and the ionic diffusivity in the YSZ

• The bias voltage can vary this affects the oxygen incorporationreactions at the SOFC interface

• Current can be measured by monitoring the flux of ions through the YSZ.

• The electric double-layer can be incorporated into the model.

• Concentration profiles, surface coverage, and electrochemical information can be extracted.

Z0 Z1 ... Zi ... ZN

Cat

hod

e x

y

z

Anode

O2- FluxO2 (g)

Present WorkVappl- +

Zr4+

Y3+

O2-

Oxide-ion vacancyUnitCell

THE MODEL

• Structure corresponds to YSZ (100) surface of the bulk cubic fluorite (Fm3m) crystal…thermodynamically stable phase of zirconia at high T.

• A fixed Fm3m lattice parameter of 5.14 Å for 9 mol % YSZ is assumed.

• The YZr and Zr ions are fixed during the oxide ion vacancy migration.

• Other thermally, chemically, or electrically induced chemical or morphological changes are not included.

• YSZ: conducts only oxygen ions, electronic insulator.

• Neglect electrode details…assume electrode/YSZ TPB accounts for 1% of total surface area (used to normalize the calculated current).

O2 adsorption

O2 dissociation to O+O

O+O association to O2

O/O2 diffusion

Transfer of O in/outof the YSZ

Diffusion of O through the YSZ

CURRENTCURRENT

Structural Details

K. C. Lau, C. H. Turner, B. I. Dunlap, Solid State Ionics 179, 1912 (2008).

Default Simulation Parameters:• PO2 = 0.30 atm

• T = 1073 K• V = -0.50 V• relative permittivity = 40• D = ~10 nm• Area = ~32 nm2

• 9 mol % YSZ

Kinetic Monte Carlo Simulations

Electrostatic Interactions

Gas Adsorption

Bulk YSZ

• Total potential (VT) = electrode (Ve) + space-charge (Vsc)• Ve = electric potential from electrode (evenly distributed along YSZ)• Vsc = local space-charge (due to distribution of charges within YSZ)

K. C. Lau, C. H. Turner, B. I. Dunlap, Solid State Ionics 179, 1912 (2008).

• Poisson equation of electrostatics: 3D 1D• “Parallel Plate Capacitor”

• Assume uniform charge distribution within each plane and use Gauss’ law.

• The effective field influences the migration of the ions (when moving to neighboring plate, only)

• Eeff = E0 + 0.5(q)VT

Kinetic Monte Carlo Simulation: Reaction Events

41% coverage 47% coverage

PO2 = 0.21 atmT = 800 K

= - 0.60 V

0

10

20

30

40

50

0.08 0.09 0.10

Vacancy Fraction

An

gst

rom

s

I = 107 mA/cm2 I = 35 mA/cm2

VO˙˙ PROFILE

PO2 = 0.21 atmT = 800 K

= - 0.40 V

Reaction Steps in the KMC Mechanism:• Adsorption of O2(g): O2(g) + (*) → O2* k1• Desorption of O2*: O2* → (*) + O2(g) k2• Diffusion of O2*: O2* → O2* k3• Dissociation of O2*: O2* → O-* + O-* k4• Dimerization of O-*: O-* + O-* → O2* k5• Diffusion of O-*: O-* → O-* k6• Incorporation of O-*: O-* + VO˙˙→ O- - k7• Diffusion of VO˙˙: VO˙˙ → VO˙˙ k8

i i

ii r

rP

i ir

numberrandomt

)ln(

Choose an event proportional to the rate of the event:

Increment the clock by t:

0

1

2

3

4

5

6

7

8

9

0.04 0.06 0.08 0.10 0.12 0.14

Vacancy Fraction

Le

ng

th (

nm

)

-50

-25

0

25

50

-1 0 1Voltage (V)

Cu

rrent

(mA

/cm2)

• Kinetic parameters taken from previous experiments and calculations.

V = -1.0, T = 1073 K, 9% YSZ

0.01

0.1

1

10

100

1000

0.000001 0.0001 0.01 1 100

Partial Pressure O2 (atm)C

urre

nt (

mA

/cm

2 )

V = -0.50, T = 1073 K, 9% YSZ

0.01

0.1

1

10

100

0.00001 0.0001 0.001 0.01 0.1 1

Partial Pressure O2 (atm)

Cur

rent

(m

A/c

m2 )

RESULTS

• Is the current affected by the O2 partial pressure?

• Is the trend consistent with experimental observations?

• Is the same trend observed at LOWER voltages?

Kinetic Monte Carlo Simulation of a Solid-Oxide Fuel Cell

K. C. Lau, C. H. Turner, B. I. Dunlap, Chem Phys Lett (2009), accepted.

Kinetic Monte Carlo Simulation of a Solid-Oxide Fuel Cell

V = -1.0, PO2 = 0.30, T = 1073 K

50

100

150

200

250

20 40 60 80 100 120 140 160 180Relative Permittivity

Cur

rent

(m

A/c

m2)

12% YSZ9% YSZ6% YSZ

RESULTS

V = -0.5, PO2=0.30, T = 1073 K

0

5

10

15

20

25

30

35

20 40 60 80 100 120 140 160 180Relative Permittivity

Cur

rent

(m

A/c

m2 )

12% YSZ9% YSZ6% YSZ

• Is the current affected by the relative permittivity of the electrolyte?

• Does the Y-dopant level strongly affect the current?

• Is this consistent with the experiments?

• Is the same trend observed at lower voltages?

Kinetic Monte Carlo Simulation of a Solid-Oxide Fuel CellRESULTS

• What is happening at the atomic level at the cathode interface?

…concentration profiles of the individual species can give us some insight.

0.8

1.0

1.2

1.4

1.6

10 20 30 40 50

Rel

ativ

e V

acan

cy C

on

cen

trat

ion

BULK YSZ

INTERFACE

V = -1.0

V = -0.8

V = -0.6

V = -0.4

V = -0.2

V = -0.0

Electric Double-Layer

0.6

0.8

1.0

1.2

10 20 30 40 50

Re

lati

ve

Va

ca

nc

y C

on

ce

ntr

ati

on

BULK YSZINTERFACE

V = 1.0

V = 0.8

V = 0.6

V = 0.4

V = 0.2

V = 0.0


…concentration profiles are consistent when the voltage is reversed.


• Can we model the frequency-response characteristics of the fuel cell?

…apply an alternating bias voltage.

As the frequency increases, the electric double-layer begins to diminish…the voltage frequency becomes larger than the dynamics of the charge accumulation.

0.0

0.5

1.0

1.5

2.0

2.5

1.00E+03 1.00E+05 1.00E+07 1.00E+09 1.00E+11

Am

plit

ud

e R

ati

o

current

(A/cm2)

effective voltage(V)

-90

-60

-30

0

30

1.00E+03 1.00E+05 1.00E+07 1.00E+09 1.00E+11

Applied Voltage Frequency

Ph

as

e A

ng

le

effective voltage

current

-2.5

-1.5

-0.5

0.5

1.5

2.5

simulation data…


(a)

(b)

(c)

Rp

Cdl

Re

Element Freedom Value Error Error %Rp Free(? 1.501E8 3.7752E6 2.5151Cdl Free(? 7.282E-15 1.7872E-16 2.4543Re Free(? 2.0242E6 52052 2.5715

Chi-Squared: 0.018252Weighted Sum of Squares: 0.4563

Data File: D:\fuel_cells\newcode-data\t1073-50\1.datCircuit Model File: D:\fuel_cells\newcode-data\t1073-20v05\3r2c.mdlMode: Run Fitting / Freq. Range (0.001 - 1000000000)Maximum Iterations: 100Optimization Iterations: 0Type of Fitting: ComplexType of Weighting: Calc-Modulus

(c)

0 10 20 30 40

-40

-30

-20

-10

0

Z'

Z''

FitResult

(cm2)

(cm2)

0 10 20 30 40

-40

-30

-20

-10

0

Z'

Z''

FitResult

(cm2)

(cm2)

Z'

Z''

103 104 105 106 107 108 10910-1

100

101

102

Frequency (Hz)

|Z|

FitResult

103 104 105 106 107 108 109

-75

-50

-25

0

Frequency (Hz)

the

ta

(cm2)

(degree)

103 104 105 106 107 108 10910-1

100

101

102

Frequency (Hz)

|Z|

FitResult

103 104 105 106 107 108 109

-75

-50

-25

0

Frequency (Hz)

the

ta

(cm2)

(degree)

Double-layer capacitance (Cdl)Polarization resistance (Rp)Electrolyte resistance (Re)


(b)

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.00.51.01.52.02.53.03.5

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

)||

(D

eg

ree

)

Vcal

Log (Hz)

J T=873K T=973K T=1073K T=1173K T=1273K

J (A

/cm

2 )

T=873K T=973K T=1073K T=1173K T=1273K

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.0

0.3

0.6

0.9

1.2

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

)||

(D

egre

e)

Vcal

Log (Hz)

J d=20a d=30a d=40a d=50a d=60a

J (A

/cm

2 )

d=20a d=30a d=40a d=50a d=60a

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.0

0.2

0.4

0.6

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

) |

| (D

egre

e)

Vcal

Log (Hz)

J P

O2=0.05atm

PO2

=0.30atm

PO2

=1.00atm

J (A

/cm

2 )

P

O2=0.05atm

PO2

=0.30atm

PO2

=1.00atm

Fitted voltage Vcal, current density J, and phase angle shift


(a)

(b)

(c)

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.00.51.01.52.02.53.03.5

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

)||

(D

eg

ree

)

Vcal

Log (Hz)

J T=873K T=973K T=1073K T=1173K T=1273K

J (A

/cm

2 )

T=873K T=973K T=1073K T=1173K T=1273K

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.0

0.3

0.6

0.9

1.2

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

)||

(D

egre

e)

Vcal

Log (Hz)

J d=20a d=30a d=40a d=50a d=60a

J (A

/cm

2 )

d=20a d=30a d=40a d=50a d=60a

-0.50

-0.45

-0.40

-0.35

-0.30

-0.25

0.0

0.2

0.4

0.6

2 3 4 5 6 7 8 9 10

0

20

40

60

80

Vca

l (V

) |

| (D

egre

e)

Vcal

Log (Hz)

J P

O2=0.05atm

PO2

=0.30atm

PO2

=1.00atm

J (A

/cm

2 )

P

O2=0.05atm

PO2

=0.30atm

PO2

=1.00atm

Fitted voltage Vcal, current density J, and phase angle shift


(a)

(b)

(c)

0 2 4 6 8 70 72 74 76 78 80

1.00

1.02

1.04

1.06

1.08

1.10

1.12

0 2 4 6 8 72 76 800.98

1.00

1.02

1.04

1.06

1.08

1.10

= 873K = 1073K = 1273K

Electric Double-layer

Bulk YSZ

Re

lativ

e V

aca

ncy

Co

nce

ntr

atio

n

Layer Number (along z-axis)

=9.87103Hz

=9.87104Hz

=9.87105Hz

=9.87106Hz

=9.87107Hz

(b)=9.87106 Hz

(a)


Bulk YSZ

4 5 6 7 8 9 10

0.99

1.02

1.05

1.08

1.11

1.14

1.17

1.20

Rel

ativ

e V

acan

cy C

once

ntra

tion

Log (Hz)

d T(K) PO2

(atm) r

40a 1073 0.30 40 20a 1073 0.30 40 60a 1073 0.30 40 40a 873 0.30 40 40a 1273 0.30 40 40a 1073 0.05 40 40a 1073 1.00 40 40a 1073 0.30 20 40a 1073 0.30 60

(c)

The relative oxide-ion vacancy concentrations of the YSZ layers


(a)

(b)

(c)

Rp

Cdl

Re

Element Freedom Value Error Error %Rp Free(? 1.501E8 3.7752E6 2.5151Cdl Free(? 7.282E-15 1.7872E-16 2.4543Re Free(? 2.0242E6 52052 2.5715

Chi-Squared: 0.018252Weighted Sum of Squares: 0.4563

Data File: D:\fuel_cells\newcode-data\t1073-50\1.datCircuit Model File: D:\fuel_cells\newcode-data\t1073-20v05\3r2c.mdlMode: Run Fitting / Freq. Range (0.001 - 1000000000)Maximum Iterations: 100Optimization Iterations: 0Type of Fitting: ComplexType of Weighting: Calc-Modulus

(c)

T (K) Cdl/A(F/cm2) RpA(cm2) ReA(cm2) 873 3.318710-8 806.7 9.258 973 3.431210-8 147.1 2.392 1073 3.433910-8 37.09 0.84092 1173 3.580110-8 11.78 0.35427 1273 3.711410-8 4.266 0.16535

101040 supercellsVo = -0.5 VRelative permittivity of YSZ r = 40PO2=0.3 atm

NZ Cdl/A(F/cm2) RpA(cm2) ReA(cm2) 20 6.650410-8 34.68 0.42522 30 4.528810-8 36.83 0.63526 40 3.433910-8 37.09 0.84092 50 2.7810-8 39.12 1.057 60 2.308110-8 37.24 1.237

T = 1073 KVo = -0.5 VRelative permittivity of YSZ r = 40PO2 = 0.3 atm

PO2 (atm) Cdl/A(F/cm2) RpA(cm2) ReA(cm2) 0.05 2.308110-8 37.24 1.237 0.3 3.433910-8 37.09 0.84092 1.0 3.521810-8 38.69 0.8469

101040 supercellsT = 1073KVo= -0.5 VRelative permittivity of YSZ r = 40

X. Wang, K. C. Lau, C. H. Turner, B. I. Dunlap, J Electrochem Soc (2009), submitted.

Conclusions

• Temperature, dopant fraction, and relative permittivity strongly affect the current density.

• Frequency response analysis shows limiting current behavior and can be used to extract capacitance and resistance data.

• An improved kinetics database is needed to bring the qualitative results closer to experimental values.

• The SOFC model is being further developed, in order to include the anode side of the fuel cell.

• We do not use adjustable parameters…we take parameters from quantum mechanical calculations and experiments, without modification.

Simulating Stimulating Interfaces Applications in Adsorption and Catalysis

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