A Chemo-Mechanical Particle Model for the Fabrication and Cyclic Expansion of Silicon Composite Solid-State Batteries
Authors: So Magnus , Yano Takeru , Permatasari Agnesia , Nguyen Van Lap , Inoue Gen 
Published: December 2024

All-Solid-State Batteries (ASSBs) are increasingly perceived as a viable substitute to Li-ion batteries, primarily due to their enhanced safety and energy density. ASSBs utilize a non-flammable solid electrolyte, significantly reducing the risk of fire hazards. Furthermore, they can operate under a broader temperature and voltage spectrum. This research aims to optimize the composition of anode electrode materials, comprised of a particle mixture of Active Material (AM), Solid Electrolyte (SE), and conductive additive.
Graphite, a frequently used AM, is favored for its low voltage characteristics and its low volume expansion during charge cycling. Additionally, graphite's low Young Modulus is beneficial in preventing the build-up of substantial stresses within the battery cell. Silicon (Si) is another appealing material due to its high gravimetric capacity, which is up to ten times greater than that of graphite. However, during Li insertion, the crystalline structure transitions to an amorphous state, resulting in a substantial expansion of up to 300%, which triggers a significant accumulation of stress.
Numerous strategies have been explored to alleviate the stress build-up resulting from expansion by adding graphite or carbon nanotubes (CNTs). The latter provides void spaces which can accommodate the volumetric expansion. Furthermore, the CNTs possess the capacity to retain the electrode's structure during volume expansion, which is advantageous for maintaining structural integrity, preserving solid-solid contacts, and enhancing the electrical conduction network. Owing to these factors, ASSBs with the addition of CNTs have demonstrated improved cycling performance. 1

Simulating Si composite solid-state anodes presents a significant challenge due to the stress induced by localized Si particles. The substantial expansion of Si can lead to the formation of shell voids in minute localized regions surrounding the microscopic Si particles. This complexity makes it difficult to simulate the dynamics using traditional finite element (FE) based mechanical models. An alternative solution is to employ the Discrete Element Method (DEM) which is a type of particle-based models that solve for Newton's laws of motion for each particle. While continuum models are instrumental in deterministically calculating the properties of bulk materials, DEMs can be utilized to compute particle slippage and the evolution of void regions between individual particles, which influence the local contact area of solid-solid interactions.
In our previous research,2 we developed a multiscale chemo-mechanical DEM model for Si anode solid-state batteries. This model encompasses two stages: fabrication and cell operation. During the fabrication stage, particles were simulated within a high-pressure mold, for which we devised an elasto-plastic contact model. Throughout the cell operation stage, we simulated Li insertion and AM volume expansion. However, in current study it was observed that during charge cycling in confined cell volume, the pressure exceeded levels that are acceptable for practical applications. Furthermore, during discharge, the contact areas between particles declined and AM progressively lost its ability to form an electronic percolative chain, reducing the discharge capacity.
We successfully incorporated CNTs into the DEM model by linking particles into elongated fibers, each with robust adhesive fusion bonds. The electronic percolation network and interface contact areas saw significant improvement with the addition of CNTs. By further implementing this model, we can determine the optimal composition of Si, graphite and CNTs based on several performance indicators, including the electrode's power density and capacity fade. The study will be broadened to simulate various geometrical configurations, such as a particle mixture of Si and graphite, and coated Si and SE particles on CNT structures.

Acknowledgements

We gratefully acknowledge the support of the Japan Science and Technology Agency (JST) through the JST-Mirai Program, Grant number JPMJMI24G1.

References

L. Hu, X. Yan, Z. Fu, J. Zhang, Y. Xia, W. Zhang, Y. Gan, X. He, and H. Huang, ACS Appl. Energy Mater., 5, 14353–14360 (2022).

M. So, S. Yano, A. Permatasari, T. D. Pham, K. Park,. and G. Inoue, Journal of Power Sources, 546, 231956 (2022).