The Effect of Volume Change on the Accessible Capacities of Porous Silicon-Graphite Composite Anodes
Authors: Pereira Drew Joseph , Garrick Taylor R , Weidner John W. 
Published: February 2020

Lithium-silicon chemistries show promise to increase battery capacity; however, silicon expands significantly during lithium intercalation, leading to inaccessible capacities caused by cell and pack failure. Silicon-graphite (Si/C) composite anodes are used to increase the anode capacity while maintaining a tolerable degree of active material volume expansion. Recently, Dash and Pannala [1] modeled anodes with increasing Si/C ratios and explored the tradeoff between increasing gravimetric capacity and the increasing volume expansion upon Li intercalation. Their conclusion highlights that while the gravimetric capacity increases, there is ultimately a “threshold value” where the volumetric capacity will begin to decrease to account for the significant silicon volume expansion.
Here, we built upon this concept to account for electrochemical and mechanical design limitations applicable to pack design for electric vehicles (EVs). We propose that increasing the Si/C ratio does not directly lead to an increase in the accessible capacity, because excessive volume expansion can lead to unacceptable cell pressure or electrode porosity. In order predict the accessible capacity as a function of Si/C ratio, we integrated mechanical behavior for each individual cell component (e.g., composite anode, cathode, and packing) into our previous battery model. [2-4] Our previously developed model predicted the split between changes in electrode porosity and dimensions by coupling mechanical and electrochemical phenomena.
We employed our model to simulate a full charge of a battery within a rigid cell casing as well as a flexible packing, similar to those seen in current automotive battery packs. The simulations were used to determine the accessible capacity as a function of Si/C ratios, using mechanical design limitations relevant to EV batteries, pressure and porosity. Pressure limitations represent the pressures that may cause capacity loss, the strain of a frame element containing of the cells, or the cracking of a cooling component. Minimum porosity limitations represent the porosity requirements of different cell types (e.g., a power cell must have a high porosity while an energy cell can tolerate lower porosities). Figure 1 shows the pressure generation as a function of state of charge for anodes with increasing Si/C ratios. The significant difference in the pressure generation shows the importance of properly representing mechanical behavior and selecting proper Si/C ratios for safe and effective pack design. This data was then used to illustrate the tradeoff between the capacity gained by increasing the Si/C ratio and the accessible capacity lost based on the pressure design limitations. These types of simulations can help battery designers identify the ideal Si/C ratio for a given set of components and design requirements in order to maximize capacity in an operating cell, or even be used to drive cell and pack design for future applications.
References
[1] R. Dash, and S. Pannala, Theoretical Limits of Energy Density in Silicon-Carbon Composite Anode Based Lithium Ion Batteries. Sci. Rep. 6, 27449; doi: 10.1038/srep27449 (2016).
[2] T. R. Garrick, K. Kanneganti, X. Huang, and J. W. Weidner, “ Modeling Volume Change due to Intercalation into Porous Electrodes”, Electrochem. Soc. 2014 volume 161, issue 8, E3297-E3301 (2014).
[3] T. R. Garrick, X. Huang, V. Srinivasan, and J. W. Weidner,”Modeling Volume Change in Dual Insertion Electrodes”, J. Electrochem. Soc. 2017 volume 164, issue 11, E3552-E3558 (2017).
[4] T. R. Garrick, K. Higa, S. Wu, Y. Dai, X. Huang, V. Srinivasan, and J. W. Weidner, “Modeling Battery Performance Due to Intercalation Driven Volume Change in Porous Electrodes”, J. Electrochem. Soc. 2017 volume 164, issue 11, E3592-E3597 (2017).

Figure 1