COMSOL 6.4 - Lithium-Ion Battery with Multiple Intercalating Electrode Materials

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Lithium-Ion Battery with Multiple Intercalating Electrode Materials

Lithium-ion batteries can have multiple intercalating materials in both the positive and negative electrodes. For example, the negative electrode can have a mix of different forms of carbon. Similarly, the positive electrode can have a mix of active materials such as transition metal oxides, layered metal oxides, olivines, and so forth. These materials can have different design properties (such as volume fractions, particle sizes), thermodynamic properties (such as equilibrium potentials, maximum lithium concentrations), transport properties (such as solid diffusivities) and kinetic properties (such as intercalation reaction rate constants).

This model example demonstrates the Additional Porous Electrode Material feature in the Lithium-Ion Battery interface. The model describes a lithium-ion battery with two different intercalating materials in the positive electrode, whereas the negative electrode consists of one intercalating material only. The battery performance during discharge for different mixing fractions of the two intercalating materials in the positive electrode is studied. The geometry is in one dimension and the model is isothermal.

Model Definition

This example models the battery cross section in 1D, which implies that edge effects in the length and height of the battery are neglected. The example uses the following three domains:

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Negative graphite porous electrode (50 μm thick)

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Separator (50 μm thick)

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Positive blended NCA/LMO porous electrode (thickness depending on NCA:LMO ratio; see below)

Two active intercalating materials are considered in the positive electrode and the negative electrode consists of a single intercalating material. The model includes the following processes (Ref. 1).

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Electronic current conduction in the electrodes

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Ionic charge transport in the pores of the electrodes and separator

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Material transport in the electrolyte, allowing for the introduction of the effects of concentration on ionic conductivity and concentration overpotential, which in this case are obtained from experimental data

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Material transport within the spherical intercalating particles that form the electrodes

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Butler–Volmer electrode kinetics using experimentally measured discharge curves for the equilibrium potential of the intercalating materials in the electrodes.

For the porous electrodes, the effective electrolyte properties are calculated using the Bruggeman relation. Transport in the spherical particles is described using the Baker-Verbrugge diffusion model. This diffusion model considers the gradient of the chemical potential of the intercalating lithium as the driving force for diffusion, as opposed to considering the gradient of lithium concentration for dilute solution treatment (Fick’s Law) of lithium transport in the active material particles. The diffusion equation is expressed in spherical coordinates for the material balance of lithium in the particles. Butler–Volmer electrode kinetics describes the local charge transfer current density in the electrodes. The Butler–Volmer expressions are introduced as source or sink terms in the charge balances and material balances.

Material Properties

The electrolyte consists of 1 M LiPF6 salt in 1:1 EC:DEC (by weight) solvent. The two active materials in the positive electrode are NCA (LiyNi0.80Co0.15Al0.15O2) and LMO (LiyMn2O4 spinel). For the negative electrode, MCMB graphite (LixC6) is used in the model. The material properties of the electrolyte and active materials are taken from the Battery material library.

The equilibrium potentials of the positive electrode materials are shown in Figure 1

Figure 1: The equilibrium potentials of NCA (top) and LMO (bottom).

The x-axis data in Figure 1 depicts the lithiation level of the active material, which is calculated by dividing the concentration of lithium with the maximum concentration of lithium in the material (the host capacity).

Electrode Balancing

The thickness of the negative electrode is set to 50 μm, whereas the positive electrode thickness is set to vary with the relative volume fractions of LMO and NMC. The electrode balancing is based on the following criteria:

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In order to avoid lithium plating during fast charging, the host capacity of the negative graphite electrode should be in excess so that an approximate lithiation level of 80% is reached at 100% cell state-of-charge (SOC).

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In order to avoid gassing and other harmful side reactions, the positive electrode potential is limited to about 4.1 V at 100% SOC, corresponding to lithiation levels of 30% and 19% for NCA and LMO, respectively (Figure 1).

Based on the host capacities (cs,max) and volume fractions (εs) of the electrode materials, the thickness of the positive electrode may now be computed as

Results and Discussion

Figure 2 shows the voltage profile for a 1:2 volume ratio of the two positive electrode materials at a constant current discharge of 1C.

Figure 2: Discharge voltage profile at 1C.

Figure 3 shows the lithium concentration at the surface of the active material particles in the positive electrode (at the positive electrode current collector end) during 1C discharge. The variation of the surface concentration with time is different in the two active materials. This is because of the different electrochemical properties of the two active materials.

Figure 3: Surface concentration in the active material particles in the positive electrode during 1C discharge.

Figure 4 shows the lithium concentration inside a particle at a particular position in the negative graphite electrode (at the center of the negative electrode) during 1C discharge. The concentration profiles show characteristic ridges, thereby capturing the staging phenomenon seen in multiphase electrodes like graphite. The Baker–Verbrugge diffusion model accounts for the interactions of the lithium-ions within the solid phase through an activity correction term, and hence provides a realistic representation of the intercalation process.

Figure 4: Concentration profiles inside a particle at a particular position in the negative electrode, at various times during 1C discharge.

The voltage profiles during 1C discharge for different volume mix fractions of the active materials in the positive electrode are shown in Figure 5. The shape of the discharge profile has a pronounced dependence on the mix fraction of the active materials in the electrode.

Figure 5: Voltage profiles during 1C discharge for different volume mix fractions of the active materials in the positive electrode.

1. P. Albertus, J. Christensen, and J. Newman, “Experiments on and Modeling of Multiple Active Materials in Positive Electrodes for Lithium-Ion Batteries,” J. Electrochem. Soc., vol. 156, no. 7, pp. A606–A618, 2009.

Battery_Design_Module/Lithium-Ion_Batteries,_Performance/li_battery_multiple_materials_1d

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > > .

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In the tree, select > .

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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Browse to the model’s Application Libraries folder and double-click the file li_battery_multiple_materials_parameters.txt.

The geometry contains three domains. Create the geometry by specifying the coordinates of the boundaries.

Interval 1 (i1)

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In the window, under right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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In the table, enter the following settings:


Lengths (m)
L_neg
L_sep
L_pos

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All materials are available in the Material Library. Note: In the Materials node, cEeqref denotes the maximum lithium concentration in the active material.

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

NCA, LiNi0.8Co0.15Al0.05O2 (Positive, Li-ion Battery) (mat3)

In the window, expand the node.

Interpolation 1 (Eeq, Eeq_inv)

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In the window, expand the > > > node, then click .

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In the window for , click to expand the section.

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Clear the checkbox.

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LMO, LiMn2O4 Spinel (Positive, Li-ion Battery) (mat4)

In the window, expand the node.

Interpolation 1 (Eeq, Eeq_inv)

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In the window, expand the > > > node, then click .

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In the window for , click to expand the section.

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Clear the checkbox.

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Lithium-Ion Battery (liion)

Set up the physics in the insertion electrodes. In this model, the Baker-Verbrugge diffusion model is used in the Particle Intercalation nodes. Note that the Baker-Verbrugge diffusivities are typically different from the Fickian diffusivity values. In this model, the intercalation diffusivities are simply set to the values available in the Material Library.

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In the window, under > click .

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In the window for , locate the section.

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In the εl text field, type epsl_sep.

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Locate the section. From the list, choose . In the fl text field, type epsl_sep^brugl_sep.

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From the list, choose . In the fDl text field, type epsl_sep^brugl_sep.

Porous Electrode 1

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In the toolbar, click

and choose .

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Select Domain 1 only.

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In the window for , locate the section.

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In the σs text field, type sigmas_neg.

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Locate the section. In the εs text field, type epss_neg.

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In the εl text field, type epsl_neg.

Particle Intercalation 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

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In the rp text field, type rp_neg.

The concentration profiles inside a graphite electrode particle will be analyzed during postprocessing. Hence, it is useful to have a finer resolution along the particle dimension, by setting a linear distribution with 20 elements.

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Click to expand the section. From the list, choose .

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In the Nel text field, type 20.

Porous Electrode Reaction 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the i0,ref(T) text field, type i0ref_neg.

Porous Electrode 2

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In the toolbar, click

and choose .

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Select Domain 3 only.

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In the window for , locate the section.

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In the σs text field, type sigmas_pos.

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Locate the section. In the εs text field, type epss_pos_NCA.

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In the εl text field, type epsl_pos.

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Locate the section. From the list, choose . In the fl text field, type epsl_pos^brugl_pos.

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From the list, choose . In the fDl text field, type epsl_pos^brugl_pos.

Particle Intercalation 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

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In the rp text field, type rp_pos_NCA.

Porous Electrode Reaction 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the i0,ref(T) text field, type i0ref_pos_NCA.

Additional Porous Electrode Material 1

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In the toolbar, click

and choose .

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Select Domain 3 only.

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In the window for , locate the section.

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In the εs text field, type epss_pos_LMO.

Particle Intercalation 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

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In the rp text field, type rp_pos_LMO.

Porous Electrode Reaction 1

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. In the i0,ref(T) text field, type i0ref_pos_LMO.

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In the window, click .

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In the window for , locate the section.

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Select the checkbox.

SOC and Initial Charge Distribution 1

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose . In the Ecell0%SOC text field, type E_0_SOC.

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In the Ecell100%SOC text field, type E_100_SOC.

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Locate the section. In the SOC0 text field, type SOC_cell0.

Negative Electrode Domain Selection 1

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In the window, click .

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Select Domain 1 only.

Positive Electrode Domain Selection 1

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In the window, click .

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Select Domain 3 only.

Electric Ground 1

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In the toolbar, click

and choose .

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Select Boundary 1 only.

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In the toolbar, click

and choose .

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Select Boundary 4 only.

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In the window for , locate the section.

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From the list, choose .

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Locate the section. From the list, choose .

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In the Emin text field, type 3[V].

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the Cset text field, type -1.

Global Definitions

Default Model Inputs

Set up the temperature value used in the entire model.

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In the window, under click .

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In the window for , locate the section.

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In the tree, select > .

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Find the subsection. In the text field, type T.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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Step 2: Time Dependent

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In the window, under click .

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In the window for , locate the section.

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In the text field, type 0 3600.

Store the actual steps taken by the solver to make sure to capture any sudden steep voltage changes.

Solution 1 (sol1)

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In the toolbar, click

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the window, click .

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In the window for , locate the section.

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Clear the checkbox.

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In the toolbar, click

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Reproduce the plots in the model documentation for 1C discharge, starting with the voltage profile (Figure 2).

Constant current 1C Discharge

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In the toolbar, click

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In the window for , type Constant current 1C Discharge in the text field.

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Right-click and choose .

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Select Boundary 4 only.

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

Constant current 1C Discharge

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In the window, click .

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In the window for , click to expand the section.

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From the list, choose .

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Locate the section.

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Select the checkbox. In the associated text field, type Voltage (V).

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Locate the section. Select the checkbox.

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In the text field, type 0.

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In the text field, type 3600.

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In the text field, type 3.0.

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In the text field, type 4.2.

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In the toolbar, click

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Surface concentration Positive

The following steps are for plotting the surface concentration in each active material in the positive electrode during 1C discharge (Figure 3).

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In the toolbar, click

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In the window for , type Surface concentration Positive in the text field.

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Right-click and choose .

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Select Boundary 4 only.

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

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Locate the section. From the list, choose .

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Click to expand the section. Select the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
NCA

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Right-click and choose .

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

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Locate the section. In the table, enter the following settings:


Legends
LMO

Surface concentration Positive

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section.

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Select the checkbox. In the associated text field, type Surface concentration (kmol/m<sup>3</sup>).

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Locate the section. Select the checkbox.

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In the text field, type 0.

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In the text field, type 3600.

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In the text field, type 4.

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In the toolbar, click

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Study 1/Solution 1 (sol1)

The following steps are for plotting the concentration profiles inside a particle at a particular position in the negative electrode, at various times during 1C discharge (Figure 4). To do this, create a solution dataset that refers to the extra dimension that is set up by the Porous Electrode node corresponding to the negative electrode.

Study 1/Solution 1: xdim Negative

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In the window, expand the > node.

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Right-click > > and choose .

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In the window for , type Study 1/Solution 1: xdim Negative in the text field.

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Locate the section. From the list, choose .

Time evolution of negative particle Concentration

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In the toolbar, click

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In the window for , type Time evolution of negative particle Concentration in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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In the text field, type range(0,100,3300).

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Right-click and choose .

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Select Domain 1 only.

The atxd1() operator evaluates the concentration at a specified position inside the negative electrode over the length of the particle dimension.

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In the window for , locate the section.

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In the text field, type atxd1(25e-6,liion.cs_pce1).

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From the list, choose .

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Click to expand the section. From the list, choose .

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From the list, choose .

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From the list, choose .

Time evolution of negative particle Concentration

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section.

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Select the checkbox. In the associated text field, type Normalized Particle Dimension.

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Select the checkbox. In the associated text field, type Particle concentration (kmol/m<sup>3</sup>).

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In the toolbar, click

.

Now set up a parametric study for different mix fractions of active materials in the positive electrode.

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In the toolbar, click

to open the window.

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Go to the window.

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Find the subsection. In the tree, select > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

Step 2: Time Dependent

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In the window, under click .

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In the window for , locate the section.

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In the text field, type 0 3600.

Parametric Sweep

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
fr_pos_NCA (Volume fraction of NCA in NCA/LMO mix)	0.05 0.25 0.55 0.75

Solution 3 (sol3)

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In the toolbar, click

.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

Store only every 3rd time step. This reduces the size of the stored solution and the size of model file.

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In the text field, type 3.

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In the window, click .

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In the window for , locate the section.

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Clear the checkbox.

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In the toolbar, click

.

You can plot the voltage profiles from the parametric study (Figure 5) by performing the following steps:

Voltage profiles for different mix fractions of NCA and LMO

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In the toolbar, click

.

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In the window for , type Voltage profiles for different mix fractions of NCA and LMO in the text field.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Select Boundary 4 only.

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Click in the upper-right corner of the section. From the menu, choose .

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Locate the section. Select the checkbox.

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From the list, choose .

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In the text field, type eval(fr_pos_NCA*100)/eval((1-fr_pos_NCA)*100) volume mix of NCA and LMO.

Voltage profiles for different mix fractions of NCA and LMO

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In the window, click .

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In the window for , locate the section.

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Select the checkbox. In the associated text field, type Voltage (V).

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Locate the section. From the list, choose .

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Locate the section. Select the checkbox.

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In the text field, type 0.

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In the text field, type 3600.

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In the text field, type 3.0.

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In the text field, type 4.2.

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Locate the section. From the list, choose .

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In the toolbar, click

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