Design of Graded Porous Electrodes Based on Inverse Optimization of Li-Ion Battery Models

Several problems limit the use of Li-ion batteries: underutilization (low energy density at very high power density) requiring large expensive batteries, capacity fade requiring initial over-sizing, and potential for thermal runaway caused by operation outside of the safe window. This study provides a systematic method for designing high-performance Li-ion batteries by optimizing the porous electrode architecture to improve energy density and efficiency, and to increase battery lifetime. The approach is sufficiently generic that it can be applied for any material/chemistry, and would provide improved performance (energy density, life, and abuse tolerance) for any new materials yet to be discovered.

                Many experimental results have supported the idea that by improving the design of Li-ion battery electrodes, the overall battery performance can be improved. The key design parameters include particle size and morphology of active material ^[1] and additives ^[2], electrode length and density^[3], solid loading^[4] etc.. Porosity is a result of the interactions of all the above design parameters, and can link them to the electrochemical performance of the cell. The concept of graded electrodes with layers of different porosities has been proposed^[5] and patented (US 20110168550 A1) along with various methods to fabricate porosity variations, including using different particle sizes, materials and substrates with different properties, roll-to-roll and discrete substrate systems, different compression process. Besides the macroscopic approach, studies have also been done from the microscopic perspective to synthesize the active materials with controlled phase, size, morphology and porosity ^[6]. 

               To the best of our knowledge, the past work done related to electrode design mainly focus on studying the effects or manufacturing methods to get various values of different design parameters, as opposed to finding the best design profile with spatially varying porosity or particle size/shape distribution for the electrodes. The application of the graded electrodes concept has not been fully explored computationally or experimentally in Li-ion battery systems to maximize their performance.        

                Several researchers have applied optimization to design more efficient electrochemical power sources. Newman and his coworkers have applied macroscopic models to optimize the electrode thickness or porosity ^[7]. These studies have been performed by changing one parameter (e.g., thickness) at a time. The literature does not report many applications of first-principles models to the optimization of multiple battery design parameters. One of the first such attempts is our previous paper on optimal design of porous electrodes; key results are summarized in Figure 1^[5].      

                One solution to finding the best design profile for better performance is to do the inverse optimization of battery models with design parameters. Performing inverse optimization is a challenging task. As a first step in addition to ohmic resistance work published earlier, in this work, we will present results based on inverse optimization of another important issue, mass transfer limitation in electrolyte. Building on this, we plan to pursue inverse optimization of reformulated P2D models.

Acknowledgements

The authors are thankful for the financial support of this work by the Clean Energy Institute (CEI) at the University of Washington .

References

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2. Liu, G., Zheng, H., Kim, S., Deng, Y., Minor, a. M., Song, X., & Battaglia, V. S. J. Electrochem. Soc., 155(12), A887.
3. Shim, J., & Striebel, K. a. Journal of Power Sources, 119-121, 934–937.
4. Chen, Y. H., Wang, C. W., Zhang, X., & Sastry, a. M. (2010). Journal of Power Sources, 195, 2851–2862.
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7. V. Srinivasan and J. Newman, J. Electrochem. Soc., 2004. 151:A1530–A1538.

Figure 1. Base case and optimal spatially varying porosity distribution showing that spatially varying porosity can reduce the ohmic resistance and hence increase the supported current density by 30%, which implies that the cell can deliver 30 % higher current/power at the same loading with optimized electrode porosity. The dashed lines show current density and potential and the solid lines show the porosity.