The Effect of Volume Change on the Accessible Capacities of Porous Silicon-Graphite Composite Anodes
Authors: Garrick Taylor R , Pereira Drew Joseph , 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 as well as cell or pack failure due to pressure generation. 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 modeled anodes with increasing Si/C ratios and explored the tradeoff between increasing gravimetric capacity and the increasing active material volume expansion upon Li intercalation [1]. 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 battery 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 foam packing) into our previous battery model [2-4]. This model can predict the split between changes in electrode porosity and dimensions by coupling component mechanical behavior to the volume change governed by electrochemical phenomena.
We employed our model to simulate a full charge of a pouch-style battery within 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 the cells, or the cracking of a cooling components. 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). We can then predict the ideal Si/C ratio to optimize capacity while meeting the associated design requirements. Figure 1 shows the accessible gravimetric and volumetric capacities based on pressure limitations for a cell within flexible packing. The solid and dotted lines represent the accessible capacities for 250 kPa and 500 kPa design limitations, respectively. In addition to determining accessible capacities, our model could be used to observe individual component mechanical behavior as a function of SOC. Figure 2 shows each individual cell component displacement as well as the overall cell displacement as a function of SOC. Predicting the overall cell swelling is helpful when trying to select internal cell materials as well as the foam packing material. This information can also be useful in aiding EV battery designers to appropriately design the overall battery pack while accounting for the cell’s displacement and pressure generation inside the pack.
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).
[5] D. J. Pereira, J. W. Weidner, and T. R. Garrick, "The Effect of Volume Change on the Accessible Capacities of Porous Silicon-Graphite Composite Anodes", J. Electrochem. Soc. 2019. Volume 166, issue 6, A1251-A1256

Figure 1