Lithium-ion batteries (LIBs) are considered as the most widely used energy storage systems for electronic devices and electric vehicles (EVs). It has been suggested that, the energy density of the LIBs can be increased significantly if the graphite in anode can be replaced with silicon (Si) because the Si’s energy density, 3,579 mAh/g, is much higher than conventional graphite’s energy density, 372 mAh/g. However, during the lithiation-delithiation cycle, curves of electrode voltage *vs*. capacity differs and forms a hysteresis loop. However, this voltage hysteresis decreases power density of Si-based batteries. Therefore, several research groups have tried to implement a physics-based model that can investigate the reasons behind this hysteresis in Si anode. In addition, a number of researchers have studied on Si nanowire and amorphous Si anode experimentally and analytically. However, this work focuses on analysis on microparticle silicon (SiMP) using physics-based mathematical model. In 2013, Wang *et al*. reported that they made SiMP lithium half cells and ran lithiation-delithiation cycling experiments with different C-rates. Using the data, they successfully demonstrated a self-healing chemistry of Si in battery applications was developed and it was effective. Their experiment also showed a large voltage hysteresis during the cycling experiment of SiMP half cells. In addition, similar to traditional LIBs, it was observed that the cell capacity decreases as the C-rate increases. In this work, a physics-based electrochemical model of the SiMP half cell was developed to explain the causes of voltage gap in lithiation and delithiation cycles, and the capacity differences at different C-rates. To develop the model, at first, particular physics such as lithium diffusion, reaction kinetics, thermodynamics, and mechanical stress and strain was selected, and the relevant equations were included in the model. To investigate the influence of hydrostatic stresses on electrochemical reactions in battery electrodes, a modified version of the Butler-Volmer (BV) kinetics equation associated with hydrostatic stress was implemented in the model. In addition, Verburgge & Cheng's analytical approach was applied to identify the importance of mechanical stress in the voltage hysteresis of Si-anode batteries in lithiation-delithiation cycles. Then, literature surveys were conducted to get the physical properties required to make the model a physics-based one. The parameters such as radius of spherical particles, solid diffusivity, exchange current density, Young’s modulus, Poisson’s ratio, and partial molar volume were identified and previously reported values were found.  Finally, the electrochemical model investigated the impact of hydrostatic stress on the output voltage of the SiMP half cells. In addition, the model was used to identify performance limitations. By checking the impact of the key parameters on the voltage gap during battery cycling, the model provided the possible reasons of capacity differences with different C-rates.


Development of a Physics-Based Mathematical Model to Analyze the Limitations of Micro-Particle Silicon Based Lithium Half Cells

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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