Silicon Anodes in Lithium-Ion Batteries

Background

Lithium-ion batteries (LIBs) are currently the largest component of the energy storage industry, due to lithium ions being able to store a huge amount of charge given their small size and mass, giving them high power and capacity for low size and weight. The performance of an LIB depends heavily on the materials used for the anode and the cathode. Graphite has been used as the main anode material for a long time, however, the maximum theoretical capacity for LIBs with graphite anodes is believed to have been reached. Therefore, to produce LIBs with higher capacity, new anode materials are being investigated.

The most promising of these new anode materials is silicon as it has the highest theoretical capacity of any material currently being developed. However, when the silicon anode is charged and lithium ions move into it, the silicon expands to around 3 times its original size. This causes high stresses in the anode, causing cracks which in turn cause loss of connectivity inside the battery, damaging it and worsening the performance.

The aim of this project is to understand how the insertion of lithium ions into the anode upon charging causes the observed expansion and stresses and how to mitigate them without sacrificing the high capacity of silicon.

Progress

Homogenisation

Many different techniques have been used in an attempt to constrain the expansion of the silicon. Two types we have modelled are an agglomeration of micro-scale anode particles and a graphite shell around silicon particles to constrain their expansion. To model the former, we use a technique called homogenisation to find the effective expansion of the whole anode if a certain design of micro-scale particle is used. The micro-scale particle design we are mainly looking at is a spherical silicon core with a graphite shell (see Figure 1). We have investigated how changes in this design (for example, the size of the silicon core) change the expansion and the capacity of the whole macro-scale anode.

We have found that an anode made up of entirely silicon without any graphite produces the highest capacity-to-expansion ratio and so using this measure, a fully silicon anode is the ideal design.

Figure 1: Example of micro-scale particles inside a macro-scale anode.

Porosity

As well as varying the size of the silicon core, we can also change the micro-scale design by incorporating porosity into the micro-scale particles and between them. Through our homogenisation process, we have found that the best micro-particle designs do not have any porosity in them. This is because, although the expansion is decreased when porosity is included, the lower fraction of anode material means there is less material to absorb the lithium ions and so the capacity is lower when porosity is used.

Future Work

The model that we use for the homogenisation process described above is very simple with unphysical assumptions made. However, including more processes to make the model more accurate while using this homogenisation process is very complicated. Therefore, we are shifting our attention away from the homogenised whole anode made up of micro-scale particles and instead concentrating on a single radially-symmetric spherical particle. This simplifies the equations in our model and thus allows us to include more complicated phenomena in our model, some of which are described below.

Electrochemistry

The materials will have the same chemical potential at equilibrium, which is determined by the concentration of lithium ions in each material. The lithium ions move between the materials to ensure they have the same chemical potential. In future work, we will find the distribution of lithium ions within the particle using experimental results for the chemical potential of graphite and silicon at different lithium ion concentrations. We will also be able to include a phenomenon called stress-assisted diffusion in which the concentration of lithium ions is influenced by the stresses in each material and in turn the concentration causes the stresses (a two-way coupling). Our preliminary results have shown that stress-assisted diffusion changes the lithium ion distribution substantially compared to when it is not included, showing that this effect is important to include in the model.

Nonlinear Elasticity

The large expansion of the silicon in the anode means that the strains are large when the anode has absorbed the lithium ions. In our work so far, linear elasticity has been used which assumes small strains, which is obviously not the case for silicon. Therefore, we are now looking to include nonlinear elasticity into our model, which is made much simpler by the radial symmetry of the spherical particle.

Nonlinear Homogenisation

Once the simple spherical case has been understood better, we can use the intuition gained from this to find a homogenisation technique for the nonlinear elasticity model. We will then apply this to an agglomeration of micro-scale particles. The homogenisation technique we use currently relies on the elasticity equations being linear and so a different homogenisation process will need to be developed to incorporate the nonlinearity. Using this more physically accurate mechanical model will hopefully shed light onto what the optimal design for a particle-based anode is.