1. Stochastic Phase Transformation in LiFePO 4 Porous Electrodes Peng Bai, 1,3 Martin Bazant 1,2 and Guangyu Tian 3 1 Chemical Engineering and 2 Mathematics, MIT, USA 3 Automotive Engineering, Tsinghua University, P. R. China

2. Outline Background Phase Transformation Dynamics – Single Particles – Porous Electrodes – Statistical model – KJMA theory Discussion Conclusion 2

3. Background LiFePO 4 batteries – Wide voltage plateau – Binary phase-separating (PS) system – Properties are well explored – Implications for other PS materials Phase transformation dynamics – Single particle scale Slow two-phase mechanism Ultrafast discharge Suppression of phase separation – Porous electrode scale Padhi et. al., J. ECS 1997 Bai, et al. Nano Letters (2011) 3

4. Lithium Intercalation in Single Particle 4

5. Suppression of Phase Separation Bai, et al. Nano Letters (2011) 5

6. Oyama et al, JPCC (2012) Validation by Voltage-Step Experiments Kolmogorov-Johnson-Mehl- Avrami (KJMA) Theory KJMA Mechanism Monotonic  homogeneous Non-monotonic  two-phase Bai and Tian, Electrochimica Acta (2013) Porous Electrode = Single Particle ? 6

7. Porous Electrode: A Many-Particle System Bai and Tian, Electrochimica Acta (2013) Chueh et al., Nano Lett. (2013) Brunetti et al., Chem. Mater. (2011) Delmas et al., Nat. Mater. (2008) State of charge = number fraction Fraction of half-filled particles < 2% KJMA Mechanism 7

8. Population Dynamics of Active Particles Population Dynamics Homogenization Phase-separating Materials Bai and Tian, Electrochimica Acta (2013) 8

9. Transient Currents Oyama et al, JPCC (2012) Bai and Tian, Electrochimica Acta (2013) 9

10. Another Example Sato et al. ECS Meeting Abstract (2012) LiNi 0.5 Mn 1.5 O 4 Nr Na Nt 10

11. Nucleation Rates and Reaction Rates Bai and Tian, Electrochimica Acta (2013) 11

12. Transient currents of a monolayer Chidsey, Science (1991) 12

13. Transient Currents of Porous Electrodes ~200mV KJMA fails Not homogeneous n is finite Generalized activation rate: n =k A Apparent reaction rate: m =k Bai and Bazant, under review 13

14. Validation of the Population Dynamics Levi et al. J. Phys. Chem. C (2013) 14

15. Conclusion Non-monotonic transient currents do not necessary indicate the nucleation-and-growth mechasnim; it could simply be a result of population dynamics Statistical effects (population dynamics) must be considered in interpreting experimental results of porous electrodes. Generalized activation rate captures the random activation process, and is a indicator for whether the reaction is homogenous Reaction rate must be decoupled from the activation rate, which is not possible for the KJMA equation This simple model could be improved with transport effects and particle size distributions 15

16. Acknowledgements Collaborators – Prof. Chunsheng Wang, University of Maryland – Prof. Xiangming He, Tsinghua University – Prof. Jianbo Zhang, Tsinghua University Funding Sources – Tsinghua University – State Key Lab of Automotive Safety and Energy – MIT Lincoln Lab (Postdoc) 16

17. Thank You! Peng Bai Postdoctoral Associate Department of Chemical Engineering MIT pengbai@mit.edu

18. Fitting Examples 18 Bai and Bazant, under review

19. Charge/Discharge Asymmetry 19

20. Qualitative Explanations 20