a virtual li/s battery: modeling, simulation and computer-aided development david n. fronczek 1,2,3...

A virtual Li/S battery: Modeling, simulation and computer-aided development

David N. Fronczek1,2,3 and Wolfgang G. Bessler1,2,4

1German Aerospace Center (DLR) 2Helmholtz Institute Ulm (HIU)3Lawrence Berkeley National Laboratory (LBNL)4From 09/2012: Offenburg University of Applied Sciences

> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 •


• Introduction

• Fundamentals of Li/S batteries

• Modeling approach

• Simulation results

• Outlook & Summary

www.DLR.de • Chart 2

DLR – The German Aerospace Center

Locations and employees

- ~8000 employees across 33 institutes and facilities at13 sites.

- Offices in Brussels, Paris and Washington.

- DLR Institute of Technical Thermodynamics: R&D activity of Electrochemical Energy Technology since 1986

n Cologne

n Oberpfaffenhofen

Braunschweig n

n Göttingen

Berlin n

n Bonn

n Neustrelitz

Weilheim n

Bremen n n Trauen

n Dortmund

Lampoldshausen n

Hamburg n

Stuttgart n

> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 • www.DLR.de • Chart 3

http://www.dlr.de/tt/en/

http://www.dlr.de/tt/en/

Electrochemical Energy Technology

Head: Prof. K. Andreas Friedrich

PersonnelAbout 60 employees 5 research areas

- SOFC – Günter Schiller - PEFC – Erich Gülzow - Batteries – Norbert Wagner- Modeling – Wolfgang Bessler- Electrochemical systems – Josef Kallo

Budget 2011~ 8 M€ (without operation cost of large test facilities)About 50 % third-party funding


Modeling and simulation of lithium batteries

LiFePO4 batteries:Electrochemistry and impedance

Li+e–

-Understanding and optimization of physicochemical behavior

Thermal management and runaway risk

-Understanding and optimization of thermal and safety behavior

Lithium-sulfur cells:Redox chemistry and transport

-Analysis of cycling propertiesand chemical reversibility

Lithium-air cells:Multi-phase chemistry and reversibility

- Improvement of porous air electrode

Lithium-ion technology Post lithium-ion cells


http://upload.wikimedia.org/wikipedia/commons/2/22/Cyclooctasulfur-gate-3D-balls.png


Helmholtz Institute Ulm forElectrochemical Energy Storage

• Center of Excellence for research in electrochemical energy storage

• Started in Jan. 2011

• New building on University Ulm campusfor 80 scientists (2013)

• DLR battery modeling activities are integrated into HIU


http://www.hiu.kit.edu/

http://www.hiu.kit.edu/



• Introduction






www.DLR.de • Chart 8 > Lithium/Sulfur Batteries: An Elementary Modeling Approach > D. N. Fronczek • ModVal 9 > April 2, 2012

Lithium/sulfur batteries – properties and potentials

Li-Ionhigh E

Pb Li-Ionhigh P

Li/S Li-air

10 100 1000 10000

Specific energy / Wh/kg

gasoline(50 % of theoretical max.)

10 100 1 000 10 000Specific Energy / Wh/kg

Y. Mikhaylik et al., Sion Power Corp., ECS presentation, 2009.

USABC targetsLi/S (2009)

Rate Cap.

Lower T

Power Density

Specific Power

Recharge Time

Specific Energy

Energy density

Upper T

Cycle life


http://upload.wikimedia.org/wikipedia/commons/3/34/Benzinkanister_5_Liter_blau_DSC7174_copy.jpg














www.DLR.de • Chart 9> Lithium/Sulfur Batteries: An Elementary Modeling Approach > D. N. Fronczek • ModVal 9 > April 2, 2012

Lithium/sulfur battery – layout

Global reaction: S8 + 16 Li 8 Li⇄ 2S + 3400 kJ/mol

Complex chemistry, complex multi-phase behavior!

PositiveElectrode

Negative ElectrodeSeparator

Lithium(metal)

Sulfur / Carbon matrix Organic Electrolyte

Li+ Li0

Dis

ch

arg

e

Ch

arg

e

S8

Li2S8

Li2S4

Li2S2

Li2S

S82−

S62−

S42−

S22−

S2−

Li2S6

Cur

rent

col

lect

or

Cur

rent

col

lect

or



• Introduction







Computational domain

• Modeling framework: DENIS (detailed electrochemistry and numerical impedance simulation)*

• 1D continuum model, 15 mesh points

• 169 algebraic and differential equations (standard model)

y

PositiveElectrode

Separator NegativeElectrode


*W. G. Bessler, S. Gewies, M. Vogler, A new framework for physically based modeling of solid oxide fuel cells, Electrochimica Acta 53 (2007) 1782-1800.


Governing equations

• Electrochemistry (evaluated by CANTERA†):

Rates of production and relation to current

Modified Arrhenius rate expressions

• Transport in the liquid electrolyte: diluted solution theory

Nernst-Planck-eq.

†D. G. Goodwin et al., Cantera, http://code.google.com/p/cantera, 2001-2012.


http://code.google.com/p/cantera

Governing equations

• Evolution of Phases‡

Production rate derived from chemical source terms

Adaptive active surfaces ( : volume fraction)

• Plus boundary conditions, e.g. electroneutrality

www.DLR.de • Chart 13> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 •

‡J. P. Neidhardt, D. N. Fronczek, T. Jahnke, T. Danner, B. Horstmann, and W. G. Bessler, "A flexible framework for modeling multiple solid, liquid and gaseous phases in batteries and fuel cells," J. Electrochem. Soc., in press (2012)

Electrochemical model

Chemical reactions considered on the positive electrode side:

sulfur reduction precipitationS8(s) ⇌ S8(l)

S8(l) + 2 e− ⇌ S82− 2 Li+ + S8

2− ⇌Li2S8(s)

S82− + 2⁄3 e− ⇌ 4⁄3 S6

2− 2 Li+ + S62− ⇌

Li2S6(s)

S62− + e− ⇌ 3⁄2 S4

2− 2 Li+ + S42− ⇌ Li2S4(s)

S42− + 2 e− ⇌ 2 S2

2− 2 Li+ + S22− ⇌

Li2S2(s)

S22− + 2 e− ⇌ 2 S2− 2 Li+ + S2− ⇌

Li2S(s)

Lithium plating/stripping on the negative electrode side:

Li(s) Li⇌ + + e−

Global reaction: 16 Li + S8 8 Li⇌ 2S + 3400 kJ/mol, EMF = ~2.2 V


* K. Kumaresan, Y. Mikhaylik and R. E. White, J. Electrochem. Soc. 155, A576 (2008)

Lis

t o

f p

aram

eter

s




• Introduction







Simulated experiment

• CC discharge, CCCV charge @ ~1/50 C

0 50 100 150 200

-0.4

-0.2

0.0

0.2

0.4

Time / h

C

urre

nt d

ensi

ty /

A/m

2

0

400

800

1200

1600

2000

Cap

acity

/

Ah/

kgS

ulfu

r



Results: Discharge / charge profile

• Two distinct stages during discharge can be reproduced

• Explanation: Presence of solid S8 (Phase I) or Li2S (Phase II)

• CV charge phase

necessary to re-

cover full capacity

• Asymmetric phase

behavior during

charge/discharge

0 50 100 1502.0

2.2

2.4

2.6

2.8

Time / h

Ce

ll vo

ltag

e /

V

0.0

0.1

0.2

0.3

0.4

0.5

Li2S

Vol

ume

frac

tion

S8(s)

Results: Discharge / charge profilecompared to experiment

Experiment Simulation


0 400 800 1200 16001.5

2.0

2.5

Discharge capacity / Ah/kgSulfur

Cel

l vol

tage

/ V

0 400 800 1200 16001.8

2.0

2.2

2.4

2.6 0.01C 0.1C 1C

Cel

l vol

tage

/ V

Discharge capacity / Ah/kg of S8

*N. Cañas, K. Hirose, N. Wagner, Ş. Sörgel and K. A. Friedrich, "In-situ XRD and electrochemical characterization of cathodes for Li-sulfur batteries“, 2nd Ertl Symposium on Surface and Interface Chemistry, June 24–27 2012, Stuttgart, Germany, Poster.

Results: Cathode composition

• The composition of the cathode varies tremendously during discharge and charge, as phases are formed and consumed

• Discharge and charge are asym-metric processes, introducing hyster-esis into the system


0 50 100 150 200

Vol

ume

frac

tion

Time / h

Carbon

Sulfur

Li2S

Electrolyte

0.4

0.2

0.0

1.0Discharge CC charge CV charge

0.5

Results: Cathode compositioncompared to experiment


*N. Cañas, K. Hirose, N. Wagner, Ş. Sörgel and K. A. Friedrich, "In-situ XRD and electrochemical characterization of cathodes for Li-sulfur batteries“, 2nd Ertl Symposium on Surface and Interface Chemistry, June 24–27 2012, Stuttgart, Germany, Poster.

Li2S [2 2 2]

S8 [2 2 2]

- *


Results: Concentrations

• Species concen-trations are highly time and SOC dependant

• S8 and S2− concen-trations buffered by presence of solid phases

• Current breaks down when electrolyte is depleted of (Poly-) sulfide ions

0 50 100 15010-9

10-6

10-3

100

103

Time / h

Con

cent

ratio

ns /

mol

/l

Li+

S2-

S8(l)

S2-4

S2-6

PF-6

S2-2

S2-8

Discharge ← → Charge


0 100 200 300 4000

100

200

300

400

Im /

Ohm

*cm

2

Re / Ohm*cm2

100 % 99 % 75 % 50 % 25 % 3 %

Results: Impedance

• EIS simulation based on

physicochemical model

(no equivalent circuit)*

• Non-ambivalent

interpretation of results

• Cell performs best when

discharged!


*W. G. Bessler, "Rapid impedance modeling via potential step and current relaxation simulations," J. Electrochem. Soc. 154, B1186-B1191

0 100 200 300 4000

100

200

300

400

Im /

Ohm

*cm

2

Re / Ohm*cm2

100 % 99 % 75 % 50 % 25 % 3 %

Results: Impedancecompared to experiment


*W. G. Bessler, "Rapid impedance modeling via potential step and current relaxation simulations," J. Electrochem. Soc. 154, B1186-B1191

Experiment Simulation



• Introduction






Outlook

Li/S trends:

• Higher sulfur contents

• Engineered nanostructured

materials

• Profound understanding is

paramount to successful

electrode/cell design


*E. J. Cairns, " Beyond Lithium Ion: The Lithium/Sulfur Cell “, Beyond Lithium Ion V Meeting,June 5–7, 2012, Berkeley, CA


Summary

• Li/S model implemented in multi-phase framework

• Prediction of- voltage, current and capacity- concentrations- porosity and volume fractions

• Qualitative explanation of- two distinct stages during discharge- electrochemical impedance

• Toolset established for further investigations,

e.g. of degradation mechanisms

Li

S

0 500 1000 1500

Discharge capacity / Ah/kgSulfur

Ce

ll vo

ltag

e

/ V

Vo

lum

e f

ract

ion

S8Li2S

0.5

0.0

0.25

2.5

2.4

2.3




• Appendix


Multi-scale modeling of electrochemical systems

- Knowledge-based advancement of fuel cells and batteries at DLR using multi-scale and multi-physics modeling and simulation methods

- Head: Wolfgang G. Bessler. Group: ~10 scientists and PhD students


Lis

t o

f eq

uat

ion

s


Results: Transport in the Li/S cell

• The sulfur content in the porous cathode changes significantly and non-uniformly

during discharge and charge

• Sulfur is redistributed in the cell


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