1. A virtual Li/S battery: Modeling, simulation and computer-aided development David N. Fronczek 1,2,3 and Wolfgang G. Bessler 1,2,4 1 German Aerospace Center (DLR) 2 Helmholtz Institute Ulm (HIU) 3 Lawrence Berkeley National Laboratory (LBNL) 4 From 09/2012: Offenburg University of Applied Sciences

2. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 A virtual Li/S battery: Modeling, simulation and computer-aided development Introduction Fundamentals of Li/S batteries Modeling approach Simulation results Outlook & Summary www.DLR.de Chart 2

3. DLR – The German Aerospace Center Locations and employees -~8000 employees across 33 institutes and facilities at 13 sites. -Offices in Brussels, Paris and Washington. -DLR Institute of Technical Thermodynamics: R&D activity of Electrochemical Energy Technology since 1986 Cologne Oberpfaffenhofen Braunschweig Göttingen Berlin Bonn Neustrelitz Weilheim Bremen Trauen Dortmund Lampoldshausen Hamburg Stuttgart > 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/

4. Electrochemical Energy Technology Head: Prof. K. Andreas Friedrich Personnel About 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 > 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 4

5. Modeling and simulation of lithium batteries LiFePO 4 batteries: Electrochemistry and impedance -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 properties and chemical reversibility Lithium-air cells: Multi-phase chemistry and reversibility -Improvement of porous air electrode Lithium-ion technologyPost lithium-ion cells > 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 5

6. Helmholtz Institute Ulm for Electrochemical Energy Storage Center of Excellence for research in electrochemical energy storage Started in Jan. 2011 New building on University Ulm campus for 80 scientists (2013) DLR battery modeling activities are integrated into HIU > 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 6 http://www.hiu.kit.edu/

7. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 A virtual Li/S battery: Modeling, simulation and computer-aided development Introduction Fundamentals of Li/S batteries Modeling approach Simulation results Outlook & Summary www.DLR.de Chart 7

8. 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-Ion high E PbLi-Ion high P Li/SLi-air gasoline (50 % of theoretical max.) 101001 00010 000 Specific Energy / Wh/kg Y. Mikhaylik et al., Sion Power Corp., ECS presentation, 2009. USABC targets Li/S (2009) Rate Cap. Lower T Power Density Specific Power Recharge Time Specific Energy Energy density Upper T Cycle life

9. 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: S 8 + 16 Li ⇄ 8 Li 2 S + 3400 kJ/mol Complex chemistry, complex multi-phase behavior! Positive Electrode Negative Electrode Separator Lithium (metal) Sulfur / Carbon matrix Organic Electrolyte Li + Li 0 Discharge Charge S8S8 Li 2 S 8 Li 2 S 4 Li 2 S 2 Li 2 S S 8 2− S 6 2− S 4 2− S 2 2− S 2− Li 2 S 6 Current collector

10. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 A virtual Li/S battery: Modeling, simulation and computer-aided development Introduction Fundamentals of Li/S batteries Modeling approach Simulation results Outlook & Summary www.DLR.de Chart 10

11. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 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 Positive Electrode Separator Negative Electrode www.DLR.de Chart 11 * 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.

12. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 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 www.DLR.de Chart 12

13. 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)

14. Electrochemical model Chemical reactions considered on the positive electrode side: sulfur reductionprecipitation S 8(s) ⇌ S 8(l) S 8(l) + 2 e − ⇌ S 8 2− 2 Li + + S 8 2− ⇌ Li 2 S 8(s) S 8 2− + 2 ⁄ 3 e − ⇌ 4 ⁄ 3 S 6 2− 2 Li + + S 6 2− ⇌ Li 2 S 6(s) S 6 2− + e − ⇌ 3 ⁄ 2 S 4 2− 2 Li + + S 4 2− ⇌ Li 2 S 4(s) S 4 2− + 2 e − ⇌ 2 S 2 2− 2 Li + + S 2 2− ⇌ Li 2 S 2(s) S 2 2− + 2 e − ⇌ 2 S 2− 2 Li + + S 2− ⇌ Li 2 S (s) Lithium plating/stripping on the negative electrode side: Li (s) ⇌ Li + + e − Global reaction: 16 Li + S 8 ⇌ 8 Li 2 S + 3400 kJ/mol, EMF = ~2.2 V > 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 14 * K. Kumaresan, Y. Mikhaylik and R. E. White, J. Electrochem. Soc. 155, A576 (2008)

15. -List of parameters www.DLR.de Chart 15> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012

16. A virtual Li/S battery: Modeling, simulation and computer-aided development Introduction Fundamentals of Li/S batteries Modeling approach Simulation results Outlook & Summary www.DLR.de Chart 16

17. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 Simulated experiment CC discharge, CCCV charge @ ~1/50 C www.DLR.de Chart 17

18. www.DLR.de Chart 18> Lithium/Sulfur Batteries: An Elementary Modeling Approach > D. N. Fronczek ModVal 9 > April 2, 2012 Results: Discharge / charge profile Two distinct stages during discharge can be reproduced Explanation: Presence of solid S 8 (Phase I) or Li 2 S (Phase II) CV charge phase necessary to re- cover full capacity Asymmetric phase behavior during charge/discharge

19. Results: Discharge / charge profile compared to experiment ExperimentSimulation www.DLR.de Chart 19> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 * N. Cañas, K. Hirose, N. Wagner, Ş. Sörgel and K. A. Friedrich, "In-situ XRD and electrochemical characterization of cathodes for Li-sulfur batteries“, 2 nd Ertl Symposium on Surface and Interface Chemistry, June 24–27 2012, Stuttgart, Germany, Poster.

20. 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 > 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 20 0.4 0.2 0.0 1.0 DischargeCC chargeCV charge 0.5

21. Results: Cathode composition compared to experiment www.DLR.de Chart 21> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 * N. Cañas, K. Hirose, N. Wagner, Ş. Sörgel and K. A. Friedrich, "In-situ XRD and electrochemical characterization of cathodes for Li-sulfur batteries“, 2 nd Ertl Symposium on Surface and Interface Chemistry, June 24–27 2012, Stuttgart, Germany, Poster. Li 2 S [2 2 2] S 8 [2 2 2] -*-*

22. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 Results: Concentrations Species concen- trations are highly time and SOC dependant S 8 and S 2− concen- trations buffered by presence of solid phases Current breaks down when electrolyte is depleted of (Poly-) sulfide ions Discharge ← → Charge www.DLR.de Chart 22

23. Results: Impedance EIS simulation based on physicochemical model (no equivalent circuit) * Non-ambivalent interpretation of results Cell performs best when discharged! > 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 23 * W. G. Bessler, "Rapid impedance modeling via potential step and current relaxation simulations," J. Electrochem. Soc. 154, B1186-B1191

24. Results: Impedance compared to experiment > 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 24 * W. G. Bessler, "Rapid impedance modeling via potential step and current relaxation simulations," J. Electrochem. Soc. 154, B1186-B1191 ExperimentSimulation

25. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 A virtual Li/S battery: Modeling, simulation and computer-aided development Introduction Fundamentals of Li/S batteries Modeling approach Simulation results Outlook & Summary www.DLR.de Chart 25

26. Outlook Li/S trends: Higher sulfur contents Engineered nanostructured materials Profound understanding is paramount to successful electrode/cell design www.DLR.de Chart 26> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 * E. J. Cairns, " Beyond Lithium Ion: The Lithium/Sulfur Cell “, Beyond Lithium Ion V Meeting, June 5–7, 2012, Berkeley, CA

27. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 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/kg Sulfur Cell voltage / V Volume fraction S8S8 Li 2 S 0.5 0.0 0.25 2.5 2.4 2.3 www.DLR.de Chart 27

28. > A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012 A virtual Li/S battery: Modeling, simulation and computer-aided development Appendix www.DLR.de Chart 28

29. 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 www.DLR.de Chart 29> Lithium/Sulfur Batteries: An Elementary Modeling Approach > D. N. Fronczek ModVal 9 > April 2, 2012

30. -List of equations www.DLR.de Chart 30> A virtual Li/S battery: Modeling, simulation and computer-aided development > D. N. Fronczek > Next Generation Batteries 2012 > July 19, 2012

31. 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 > 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 31