Electro-Chemo-Mechanics of Si-C Composite Anode Particles Using Cyclic Voltammetry Simulations
Authors: Mohanty Shaswat , Kumbhar Pramod Yallappa , Annabattula Ratna Kumar , Swaminathan Narasimhan 
Published: February 2020

Lithium-ion batteries are being used extensively due to various beneficial characteristics such as the absence of memory effect, wider range of operating temperatures and superior operating voltages. However, they still suffer from drawbacks such as low power density and capacity fade due to the failure of electrode particles during cyclic charging and discharging. Recently, high energy density anode particles such as silicon are being considered due to their potential for enhancing battery performance. However, these materials are associated with large volumetric changes on lithiation and de-lithiation. Furthermore, the stresses associated with these deformations can interfere with the electrode’s electrochemical performance. Composite anode particles made of graphite and Si can be alternatives to enhance performance, while at the same time retain the structural integrity of the anodes.

In this work, a core-shell configuration of the anode particle is modeled with a silicon core and graphite shell. A two-way coupling between mechanics and diffusion is taken into account. Since silicon undergoes a large volumetric expansion on lithiation, a finite strain framework is employed for mechanics. The influence of hydrostatic stresses and higher order stress terms on the chemical potential arising from the changing material properties is also incorporated to fully couple the deformation with the electrochemical response. The interactions between mechanics and diffusion are switched on and off through a parameter. Cyclic voltammetry simulations are then carried out to study the effect of stresses on the electrochemical response of the composite particle.

Specifically, two experiments have been simulated. In the first, the composite particle was first charged and then discharged, while in the second, the opposite was done. It was found that when the stress effects were included, the response of the bulk of the particle to the influx and efflux of the particles at the surface was delayed, leading to a lower observed current density. This delayed response of the bulk is due to the accumulated charge within the silicon core, arising from its relatively lower diffusivity as compared to graphite. A sharp stress gradient occurs at the material interface, and this affects the nature of the concentration profile at it. When the stresses were considered a sharp decrease was observed at the interface, whereas the concentration profile was smooth when the effect of the stresses was neglected. These experiments were also conducted for various core radius to shell thickness ratios. It was found that for larger particles, the effect of the stresses on the current density was negligible, since the volume fraction of the silicon core, responsible for the delayed bulk response, was lesser. However, the current density in smaller particles varies significantly with and without the consideration of the stresses. These observations were the same for the 42 particle sizes that were studied for the charge-discharge and discharge-charge voltammetry simulation. Smaller charge particles allow for a greater available surface, resulting in higher current density. Therefore, it can be concluded that is essential that we consider the effect of the stress on the electrochemistry while modeling anode particles for lithium-ion batteries.

Figure 1