COMSOL 6.4 - 1D Isothermal Lithium

Metal-air batteries have an especially high specific energy density. Lithium–air batteries have a theoretical energy density value of about 11,400 Wh/kg, which is nearly 10 times greater than lithium-ion batteries. Such an increase in capacity versus conventional lithium-ion batteries would be useful in many applications. However, there are many challenges in realizing a practical lithium-air battery.

A unit cell of a lithium–air battery typically consists of a thin lithium sheet as the negative electrode, a porous carbon electrode filled with oxygen/air as the positive electrode, and a separator material between the electrodes. The organic electrolyte used consists of a dissolved lithium salt in an aprotic solvent. The oxidation of lithium at the anode and reduction of oxygen at the cathode induces a current flow.

In this model example, discharge of a lithium–air battery (Ref. 1) is simulated using the Lithium-Ion Battery interface. The transport of oxygen (from external air) in the porous carbon electrode is modeled using the Transport of Diluted Species in Porous Media interface. The electrochemical reaction of oxygen reduction in the carbon electrode leads to changes in concentration of the reaction product and electrode porosity. In this example a performance analysis is done for a range of discharge current densities. A comparison of the oxygen concentration, porosity, and film thickness in the positive electrode at low and high discharge current densities is done to understand their effect on the cell voltage profiles. This model can be used for studying the performance of lithium–air batteries and for providing insights with regards to the cell design.

Model Definition

A 1D isothermal cell model for lithium–air battery is presented. Figure 1 shows the 1D model geometry. It consists of two domains: the separator and the positive porous carbon electrode filled with oxygen. The lithium metal negative electrode is modeled as a boundary. The unit cell is filled with an organic electrolyte solution.

Figure 1: 1D model geometry of a lithium–air unit cell.

Electrochemical reactions

The porous carbon electrode provides a site for the electrochemical reduction of oxygen. During operation, oxygen from the external air dissolves in the electrolyte, moves through the pores of the positive electrode and reacts with lithium ions at the active site. The reaction considered at the positive electrode is

(1)

The reaction product (Li2O2) in the positive electrode is insoluble in the organic electrolyte (beyond its solubility limit in the electrolyte) and deposits as a film on the active surface area in the porous electrode. The kinetic expression for the electrode reaction above is

(2)

where iloc is the local current density, n is the number of electrons transferred, η is the overpotential, ka is the anodic transfer coefficient, kc is the cathodic transfer coefficient, and ci is the concentration of species i at the active site.

The overpotential η for the reaction is calculated from the electrode potential (ϕs), the electrolyte potential (ϕl), the potential drop due to the particle film resistance (Δϕfilm), and the equilibrium potential of the reaction (Eeq), as follows.

(3)

The potential drop due to the particle film resistance is given as

(4)

where Rfilm is the electric resistivity across the Li2O2 film and εLi2O2 is the volume fraction of solid Li2O2.

The reaction considered in the negative electrode is

(5)

Lithium metal kinetics is used for this reaction at the negative electrode.

Physics setup

The Lithium-Ion Battery interface describes the following processes:

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Electronic current conduction in the electrodes

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Ionic charge transport in the electrolyte present in the porous electrodes and separator

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Material transport in the electrolyte present in the porous electrodes and separator

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Electrochemical reaction kinetics in the porous electrodes

In the positive electrode, spherical nonintercalating particles with concentration dependent electrode kinetics are used in the Lithium-Ion Battery interface. The thin lithium sheet (negative electrode) is represented using the Electrode Surface node with lithium metal electrode kinetics. The Bruggeman correction is used for all the effective transport properties in the positive porous electrode and the separator.

The Transport of Diluted Species in Porous Media interface describes the mass transport of oxygen in the porous carbon positive electrode by diffusion, along with the consumption of oxygen due to the electrochemical reaction (Equation 1).

The change in the concentration of the reaction product (Li2O2) in the solution phase of the positive electrode is given as

(6)

where εl is the porosity and a is the active specific surface area, respectively, of the positive electrode, and cmax,Li2O2 is the solubility limit of Li2O2 dissolved in the electrolyte. Note that εl remains at the initial porosity value until the solubility limit of Li2O2 in the electrolyte is reached. The Domain ODEs and DAEs interface is used for modeling the changes in concentration of the reaction product in the solution phase of the positive electrode.

Beyond its solubility limit in the electrolyte, the reaction product (Li2O2) in the positive electrode deposits as a film on the active surface area. The change in the concentration of solid Li2O2, cs,Li2O2, in the positive electrode is given as

(7)

The porosity change due to solid Li2O2 deposition in the positive electrode is given as

(8)

where cs0,Li2O2, MWLi2O2, and ρLi2O2 are the initial concentration, molecular weight, and density of solid Li2O2 in the film, respectively. The Dissolving–Depositing Species section of the Porous Electrode node is used to solve for the changes in concentration of the solid reaction product and electrode porosity in the positive porous electrode.

The active specific surface area of the positive porous electrode is determined by the morphology and the dynamic change of porosity due to solid Li2O2 film formation. The effective local surface area per unit volume of the electrode is given by,

(9)

where εl,0 is the initial porosity and a0 is the initial active specific surface area, respectively, of the positive electrode. The value of 0.5 is related to the morphological shape of the solid Li2O2 reaction product.

Boundary conditions

The negative electrode (lithium metal) is set to a potential of 0 V (electric ground condition). At the positive electrode current collector boundary, a discharge current density is applied. A parametric study is performed for discharge current densities ranging from 0.05 mA/cm2 to 0.5 mA/cm2. The study includes a stop condition with a minimum voltage of 2.5 V.

Results and Discussion

Figure 2 shows the cell voltage profiles plotted as a function of capacity for different values of the discharge current density. At higher current densities, the discharge voltage and cell capacity are lower, as expected.

Figure 2: Cell voltage profiles as a function of specific capacity of the cell for different values of the applied discharge current density.

Figure 3 and Figure 4 show the oxygen concentration in the positive porous electrode at different times (discharge states of the battery), for a low and high value of the discharge current density, respectively. The decreased transport of oxygen in the positive electrode at high discharge currents, as seen in Figure 4, leads to the loss in capacity at high discharge rates. The electrochemical reaction of oxygen reduction is limited to regions close to the positive electrode/current collector edge, as the discharge rate increases.

Figure 3: Variation of oxygen concentration in the positive electrode at different times (discharge states of the battery), for a low value of the discharge current density.

Figure 4: Variation of oxygen concentration in the positive electrode at different times (discharge states of the battery), for a high value of the discharge current density.

Figure 5 and Figure 6 similarly show the variation of the volume fraction of Li2O2 in the positive electrode at different times, for a low and high value of the discharge current density, respectively. At high discharge rates, the Li2O2 deposition on the active surface area of the porous carbon electrode is predominantly limited to regions close to the positive electrode/current collector edge, as seen in Figure 6.

Figure 5: Variation of volume fraction of Li2O2 in the positive electrode at different times (discharge states of the battery), for a low value of the discharge current density.

Figure 6: Variation of volume fraction of Li2O2 in the positive electrode at different times (discharge states of the battery), for a high value of the discharge current density.

Figure 7 and Figure 8 similarly show the variation of porosity in the positive electrode at different times, for a low and high value of the discharge current density, respectively. The porosity of the porous carbon electrode decreases predominantly at regions close to the positive electrode/current collector edge at high discharge current densities, as seen in Figure 8. Incomplete utilization of the porous carbon electrode at high discharge rates leads to lower cell capacities at high rates as seen in Figure 2.