Stochastic Phase Transformation in LiFePO 4 Porous Electrodes

1. Stochastic Phase Transformation in LiFePO4 Porous Electrodes Peng Bai,1,3 Martin Bazant1,2 and Guangyu Tian3 1Chemical Engineering and 2Mathematics, MIT, USA 3Automotive Engineering, Tsinghua University, P. R. China

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

3. Background • LiFePO4 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)

4. Lithium Intercalation in Single Particle

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

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

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

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

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

10. Another Example Sato et al. ECS Meeting Abstract (2012) LiNi0.5Mn1.5O4 Nr Na Nt

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

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

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

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

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

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)

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

18. Fitting Examples Bai and Bazant, under review

19. Charge/Discharge Asymmetry

20. Qualitative Explanations