2D Lithium-Ion Battery

This tutorial is a two-dimensional model of a lithium-ion battery. The cell geometry could be a small part of an experimental cell, but here it is only meant to demonstrate a 2D model setup. The battery contains a positive porous electrode, electrolyte, a negative lithium metal electrode, and a current collector. This cell configuration is sometimes called a “half-cell”, since the lithium metal electrode has negligible impact on cell voltage and polarization. A more realistic 2D geometry is exemplified in the model Edge Effects in a Spirally Wound Lithium-Ion Battery available in the Battery Design Module Application Library.

For a detailed description of this model, in particular step-by-step instructions with several screen shots showing how to build it, see the book Introduction to the Battery Design Module.

Model Definition

The 3D cell geometry is shown in Figure 1. Due to symmetry along the height of the battery, the 3D geometry can be modeled using a 2D cross section. Figure 1 shows the positioning of the positive and negative electrodes, and the current collector attached to the positive electrode. The positive electrode is porous and the negative electrode consists of lithium metal. The modeled 2D cross section is highlighted in the light blue section in the rightmost figure of Figure 1.

Since the electrochemical reaction only takes place at the surface of the lithium metal, and the electronic conductivity is very high, the thickness of the metal is neglected in the model geometry. The modeled 2D cell geometry is shown in Figure 2. During discharge, the positive electrode acts as the cathode and the contact of the metallic tab acts as a current collector. The negative lithium metal electrode acts as the anode and current feeder.

The model defines and solves the current and material balances in the lithium-ion battery. The intercalation of lithium inside the particles in the positive electrode is solved using a fourth independent variable for the particle radius (x, y, and t are the other three). The reaction kinetics and the intercalation are coupled to the material and current balances at the surface of the particles. The model equations are found in the Battery Design Module User’s Guide. The model equations were originally formulated for 1D simulations by John Newman and his coworkers at the University of California at Berkeley.

Figure 1: 3D model geometry of Lithium-ion model.

Figure 2: A 2D cross-sectional model geometry with the thickness of the negative lithium metal electrode neglected.

The purpose of the 2D simulation is to reveal the distribution of the depth of discharge in the positive electrode, as a function of discharge time. This distribution depends on the positioning of the current collector and the thickness of the positive electrode and electrolyte, in combination with the electrode kinetics and transport properties.

Results and Discussion

Figure 3 shows the lithium concentration distribution at the surface of the positive electrode particles at time equal to 2700 s during the simulation. The initial concentration of lithium in the positive electrode is 10,000 mol/m3. During the discharge, as lithium is dissolved on the negative lithium metal electrode, the concentration in the positive electrode increases.

Figure 3: Lithium concentration at the surface of the electrode particles at 2700 s.

The concentration in the positive electrode particles at two selected locations within the positive porous electrode is displayed in Figure 4. Both selections are positioned at the same distance from the electrolyte domain but at different distances from the current collector. The blue line displays the concentration at the location furthest away from the current collector and shows that less discharge has taken place there (concentration lower). This is consistent with Figure 3.The difference in concentration between the particle center and surface indicate limitations in the lithium transport within the particles.

Figure 4: Lithium concentration in the positive electrode particles at two selected positions, (x=0.5 mm, y=0.1 mm) and (x=0.5 mm, y=0.55 mm), within the model geometry.

The time-dependent cell voltage predicted by the model during the discharge simulation is shown in Figure 5.

Figure 5: Cell voltage variation during discharge.

Battery_Design_Module/Batteries,_Lithium-Ion/li_battery_tutorial_2d

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

(The will perform a time-dependent simulation, using a initialization study step to calculate the initial potentials in the cell.)

Click

Geometry 1

Insert a prepared geometry sequence from a file. After insertion you can study each geometry step in the sequence Appendix — Geometry Modeling Instructions.

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file li_battery_tutorial_2d_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

Materials

Use the Battery Material Library to set up the material properties for the electrolyte and electrode materials. By adding the electrolyte material to the model first, this material becomes the default material for all domains. (In the Materials node, cEeqref denotes the maximum lithium concentration in the active material.)

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

LMO, LiMn2O4 Spinel (Positive, Li-ion Battery) (mat2)

The first material you added was assigned by default to all domains. Override this default selection by assigning the electrode material to domain 1.

Select Domain 1 only.

The LMO material node will now be marked with a small red cross in the model tree, indicating missing material properties. This is expected at this point and will be resolved when setting up the physics for the porous electrode node.

Lithium-Ion Battery (liion)

An node has already been added to the model by default. Now set up the physics in the positive porous electrode.

Porous Electrode 1

In the window, under right-click and choose .

Select Domain 1 only.

The porous electrode contains both an electrode and an electrolyte phase. You therefore need to assign different materials to the different phases. By default, the material properties for each phase will be taken from the material assigned to the domain under , which in this case is LMO electrode material. You hence need to set the electrolyte phase material selection manually.

In the window for , locate the section.

From the list, choose .

In this model we will assume that the porous electrode consists of a mix of 40% electrode and 15% inert binder material. The remaining volume is filled up with electrolyte.

Locate the section. In the εl text field, type 1-0.4-0.15.

Materials

LMO, LiMn2O4 Spinel (Positive, Li-ion Battery) (mat2)

The small red cross on the LMO material node should now have disappeared in the model tree.

Lithium-Ion Battery (liion)

Particle Intercalation 1

The has two child nodes added by default. The node adds an extra dimension to the selected domain, and solves for the diffusion of solid lithium in this extra dimension, assuming spherical particles. Keep the default settings for this node.

Porous Electrode Reaction 1

The node sets up the equilibrium potential, kinetics and stoichiometry of the lithium insertion reaction occurring at the interface between the electrolyte and electrode phases within the porous matrix. Keep the default settings also for this node.

Electrode Current 1

Finish the model by setting up the boundary conditions. At the positive electrode, set an average current density.

In the toolbar, click

and choose .

Select Boundary 10 only.

In the window for , locate the section.

From the list, choose .

In the is,average text field, type -50[A/m^2].

Electrode Surface 1

The negative electrode is a lithium metal foil. This is modeled as a planar electrode using the node.

In the toolbar, click

and choose .

Select Boundaries 5, 7, and 12 only.

Electrode Reaction 1

For this reaction, set the equilibrium potential to 0[V].

In the window, click .

In the window for , locate the section.

From the Eeq list, choose . Click to expand the section. From the dEeq/dT list, choose .

Mesh 1

Use the default physics-controlled mesh for this model.

In the window, under right-click and choose .

The generated mesh should look as follows:

Study 1

Step 2: Time Dependent

Set up a 2700 s time-dependent solver to store the solution at 10 s intervals during the first 100 s, and 100 s intervals during the last 2600 s.

In the window, under click .

In the window for , locate the section.

Click

(the small icon to the right of the text field).

In the dialog box, type 10 in the text field.

In the text field, type 100.

Click .

In the window for , locate the section.

Click

again.

In the dialog box, type 200 in the text field.

In the text field, type 100.

In the text field, type 2700.

Click .

(Alternatively, you may also type in the expression range(0,10,100) range(200,100,2700) directly in the text field.)

In the toolbar, click

Results

Battery Voltage

A plot of the electrode voltage where you set the electrode current condition is created by default. Since you grounded the other electrode this equals the battery voltage during the simulation(Figure 5):

In the window for , type Battery Voltage in the text field.

In the toolbar, click

Lithium Concentration on Particle Surface

The following steps create a plot of the lithium concentration at the surface of the electrode particles at 2700 s (Figure 3):

In the toolbar, click

and choose .

In the window for , type Lithium Concentration on Particle Surface in the text field.

Surface 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

In the toolbar, click

Study 1/Solution 1 (3) (sol1)

As mentioned before, the node adds an extra dimension to the porous electrode domain, and solves for the concentration of solid lithium in this extra dimension. Proceed as follows to create a plot of the lithium concentration in the particles in the positive electrode (Figure 4). In order to do this you need to first create a dataset that refers to the extra dimension.

In the toolbar, click