# (200c) Modeling Capacity Fade of Lithium-Ion Batteries – Challenges in Identifying and Quantifying Possible Mechanisms

- Conference: AIChE Annual Meeting
- Year: 2009
- Proceeding: 2009 AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Session:
- Time:
Tuesday, November 10, 2009 - 9:10am-9:30am

Literature is abundant with various possible mechanisms for understanding capacity fade.^{1} However, mathematical models that include these phenomena are very few^{2} and don't include all postulated mechanisms. Adding a possible mechanism to an existing model may not be fruitful because of (1) lack of fade parameters, (2) cumulative non-separable effects of individual mechanisms occurring simultaneously, (3) Numerical inability and lack of efficient solver schemes. Often times in the quest for adding detailed mechanisms, unfortunately researchers have neglected important electrochemical/transport phenomenon typically included in physics/porous electrode based battery models.

Different mechanisms causing capacity fade include (1) capacity fade during formation cycles, (2) overcharging which results in decrease in capacity in both positive and negative electrodes and the electrolyte, (3) decomposition of the electrolyte during the reduction process, (4) self-discharge depending on the purity of materials used in manufacturing, (5) formation of a passive film on the electrode that grows in thickness as the cycle number increases.

This talk will consist of a brief review of electrochemical engineering models and describe step by step what a possible mechanism means in terms of model formulation and numerical simulation. Because of the combination of multiple mechanisms possible for capacity fade (Figure 1), the data available (discharge curves at different cycles) may not be sufficiently sensitive to all possible scenarios and mechanism.

To address this, model discrimination and Bayesian estimation for uncertainty analysis will be used to quantify the mechanisms for capacity fade. The use of reformulated models^{3-4} for discharge curves facilitates the application of latest system theory to quantify and discriminate models and mechanisms using MCMC and Polynomial Chaos theory^{5-6}.

To begin with, our approach looks at changes in transport and kinetic parameters with increasing cycle number. This work concludes that for the Quallion^{®} cells and chemistry^{7}, D_{sn}, and k_{n} (effective) change with cycle. Figure 2 shows the variation of diffusion coefficient with cycles. A power law fit was made for variations in each parameter as a function of cycle number. The inset plot in Figure 2 shows a comparison between extrapolated model prediction and experimental data at cycle 600 using the power law fit or capacity fade expressions.

As a next step, mechanisms are added to the existing battery model and predictions and confidence intervals are compared.

In addition, progress made towards multiscale (detailed KMC coupled with continuum models from electrochemical engineering) will also be presented. The numerical difficulty, computational cost, etc., will be compared for the inclusion of each mechanism.

**Acknowledgements**

The authors are thankful for the partial financial support of this work by the National Science Foundation (CBET ? 0828002), U.S. Army Communications-Electronics Research, Development and Engineering Center (CERDEC) under contract number W909MY-06-C-0040, Oronzio de Nora Industrial Electrochemistry Postdoctoral Fellowship of The Electrochemical Society and the United States government.

Figure 1: A schematic representing a few capacity fade mechanisms postulated in a Li-ion Battery.

Figure 2: Solid-phase diffusion coefficient variation at the negative electrode.

**References**

1. P. Arora, R.E. White and M. Doyle, *J. Electrochem. Soc*., 145, 3647 (1998). *[and references therein]*

2. P. Ramadass, P. M. Gomadam, R.E. White and B. N. Popov, *J. Electrochemical Society*, 151, A196 (2004).

3. V. R. Subramanian, V. Boovaragavan, V. Ramadesigan, and M. Arabandi, *J. Electrochem. Soc*., 156, A260 (2009).

4. V.R. Subramanian, V. Boovaragavan, V. Ramadesigan, K. Chen and R. Braatz. ?Model Reformulation and Design of Lithium Ion Batteries,? in *Design for Energy and the Environment* *? Proceedings of the 7th International Conference on Foundations of Computer-Aided Process Design (FOCAPD)*, edited by A.A. Linninger and M.M. El-Halwagi, CRC Press, Taylor and Francis - London, Chapter 94, 987-1005, 2009.

5. R. Gunawan, M. Y. L. Jung, E. G. Seebauer, and R. D. Braatz, *AIChE J*., 49, 2114 (2003).

6. J. V. Beck and K. J. Arnold. ?*Parameter Estimation in Engineering and Science*,? Wiley,

New York, 1977.

7. http://www.quallion.com as on 04/24/2009.