What does lithium battery modeling mean? Lithium battery modeling tips?

In the field of lithium-ion battery modeling, Newman model and its derivative model occupy a dominant position. Since such models are based on the homogenization of porous structures, users no longer need to describe the three-dimensional geometry of porous electrodes in detail.

In the model, homogenization refers to the approximate representation of the porous structure by treating the real porous structure into a uniform mixed solution composed of solid particles(blue part in the upper left) and pore electrolytes(green part). A block thick plate. One of the results of using homogeneous characterization is that pore electrolytes(ion conductors) and conductive particles(electron conductors) in electrodes are defined in the same geometric domain. After that, we use such variables as porosity and tortuous degree to describe the effective charge and mass transfer properties, and then investigate the significant influence of pore structure and particles on geometric shape.

The homogeneous porous electrode model contains the charge transfer reaction between the electrode material and the pore electrolyte. This reaction, while realizing the current transmission, also acts as the source and sink of the current in the electrode and electrolyte region, and achieves the balance between the two. The reaction is similar to the reaction between the two chemicals in the solution. The charge transfer reaction of the cathode is the source of the equilibrium current of the conductor, and it is also the sink used to maintain the current balance of the pore electrolyte. Using the above source and sink, according to Faraday's law and the stoichiometric coefficient of the homogeneous charge transfer reaction, the material balance calculation in the model can be achieved.

These porous electrode models are helpful to the modeling and simulation of porous electrodes in various electrochemical cells. But are these models effective when describing the detailed design of the porous structure of a lithium-ion battery? Tommy Zavalis(battery expert, former employee of COMSOL, now a COMSOL client) and I discussed this issue during the tea break and concluded that the answer to this question can only be known if we compare the homogeneous model with the heterogeneous model. To this end, we created a heterogeneous model to verify the effectiveness of the Newman model for the ideal three-dimensional porous electrode simulation.

Create a heterogeneous model

In the heterogeneous model, we clearly describe conductive particles and pore electrolytes as three-dimensional structures, and treat them into two separate domains when modeling space.

The current conservation caused by ion migration is limited to the electrolyte domain in the pores, while the current conservation of conductive particles is limited to the solid electrode region. The mass transfer of ions is only defined in the pore electrolyte domain. At the same time, there is a boundary on the surface of the solid particle. At this boundary, other substances in the ion or solution can react through the phase electron transfer. The above model is in sharp contrast to the homogeneous model because in the homogeneous model, the material balance and reaction are defined in the calculation domain of the entire homogeneous electrode.

When simulating the metal lithium formed on the surface of a solid particle, it is assumed that it spreads only in the particle domain, where the particle surface acts as an external boundary.

Now, we can start comparing the Newman model and the heterogeneous model which can be used more effectively to describe the fine three-dimensional model. The modeling experiment is very simple: We constructed an ideal cell with an ideal three-dimensional porous structure. The left and right porous structures are equivalent to the negative and positive poles in lithium ion batteries. The final geometric model is shown in the figure below, where the streamline is used to illustrate the current flow in the free electrolyte and the pore electrolyte. Electrode particles consist of ellipsoids with different directions in the long axis, forming conductive arrays. Electrolytes are contained in the gaps between particles.

The charge transfer current density(A/m2) distribution in the positive and negative poles corresponds to the right and left geometric structures and color Legends, respectively.

The figure above shows the absolute value of the current density caused by the charge transfer on the surface of solid particles during discharge. In the figure, the use of positive and negative electrodes on the collector side is lower than on the free electrolyte(or separation membrane) side.

We can obtain two different porosity distributions along the direction of the electrode length by rotating the long axis direction of the particles, while keeping the void-to-solid ratio(porosity) generally unchanged. Because the Newman model uses only the overall average porosity as the input condition, the calculation results do not change when the electrode structure changes as described above.

If the electrode in Figure 3 is rotated 180 °, such as the positive electrode where the arrow is located in the following figure, the current density distribution will change, but this change will be very small(the contrast between the color diagrams of the two figures shows this). Even the use of electrochemical impedance spectroscopy makes it difficult to detect small differences in this current distribution, as discussed below.

When the positive and negative poles rotate horizontally 180 °, the current density distribution of the right positive and left negative poles. It is recommended to compare the observations with Figure 3(only the positive pole rotation is mentioned above).

When Tommy and I were drinking coffee and chatting, we speculated that we could separate the sub-processes of electrodes at different time scales using a method similar to electrochemical resistance spectroscopy(EIS). It may be able to capture differences in the current distribution caused by different geometric structures. For this reason, we use the heterogeneous geometry model and the homogeneous Newman model to simulate the EIS experiment.

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