COMSOL 6.4 - Lithium-Ion Battery with Single-Ion Conducting Solid Electrolyte

Lithium-Ion Battery with Single-Ion Conducting Solid Electrolyte

In solid-state lithium-ion batteries the electrolyte is a solid-state ionic conductor. The absence of a liquid electrolyte — and hence the lack of need for a liquid container and separator — implies a larger freedom of design. Additionally, solid electrolytes offer certain advantages such as no electrolyte leakage and improved thermal stability. The risk of the formation of lithium metal dendrites, which short-circuit the battery cell, is also reduced when using a solid electrolyte.

Single-ion conducting electrolytes are typically synthesized by the immobilization of the counter-ion within an inorganic particle or a polymer backbone. These single-ion conductors have a transport number close to 1 and negligible concentration gradients with regards to the charge-carrying ions.

This tutorial models a lithium-ion battery with a single-ion conducting solid electrolyte. The geometry is in one-dimension and the model is isothermal. The behavior at various discharge currents and solid electrolyte conductivities is analyzed. Additionally, a lithium-ion battery with a binary liquid electrolyte is simulated and its performance is compared to the solid state battery.

Model Definition

The model is set up for a graphite/LCO battery with a solid electrolyte. The electrode materials are available from the Battery material library and mainly default settings are selected. The conductivity of the solid electrolyte is set using a user-defined parameter.

The model is set up using the Lithium-Ion Battery, Single-Ion Conductor interface. This adds a Lithium-ion Battery interface with the charge balance model set to Single-Ion Conductor, that is typically applicable to solid electrolytes. In a single-ion conducting electrolyte it is assumed that only one ion is allowed to move, whereas the counter-ion is fixed. The assumption of electroneutrality and a constant concentration of the immobilized ions results in a constant concentration for the mobile lithium ions in the electrolyte. The Single-Ion Conductor charge balance model, thereby, solves for the electrolyte potential by assuming that all charge in the electrolyte phase is carried by the positive lithium ions only, so that the concentration of lithium ions in the electrolyte can be assumed to be constant. The electrolyte concentration is hence not solved for as a dependent variable.

The interface, with the single-ion conductor charge balance model, accounts for the following:

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charge transport in the electrode and electrolyte using Ohm’s Law,

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material transport within the spherical particles that form the electrodes using Fick’s Law, and

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Butler–Volmer electrode kinetics using experimentally measured discharge curves for the equilibrium potential.

This tutorial, as defined in the Modeling Instructions section below, consists of two parts. The first part simulates the discharge of a lithium-ion battery with a solid electrolyte, using the Single-Ion Conductor charge balance model, for a range of discharge currents and electrolyte conductivities. In the second part of the model, a lithium-ion battery with a binary liquid electrolyte is simulated and its performance is compared to that of the solid-state battery for different discharge currents. Note that the model file available in Application Libraries contains the first part only.

The second part of the tutorial includes a binary liquid electrolyte, 1M LiPF6 in 3:7 EC:EMC (available from the Battery material library). In this case, the Binary 1:1 Liquid Electrolyte charge balance model is used along with concentration dependent electrolyte conductivity. Note that the Binary 1:1 Liquid Electrolyte charge balance model additionally accounts for material transport in the electrolyte (that is, electrolyte concentration is solved for as a dependent variable), allowing for the introduction of the effects of concentration on ionic conductivity and concentration overpotential.

Study settings

The Time Dependent with Initialization study is used in this model. This study solves for a Current Distribution Initialization study step followed by a Time Dependent study step. A stop condition is used in the Time Dependent study step to stop the solver when the cell voltage reaches 2.7 V. The SOC and Initial Charge Distribution feature is used to define the initial charge inventory in the cell.

The study corresponding to the first part of the tutorial (solid electrolyte battery) sets up an Auxiliary sweep over-discharge C-rates (1C, 2C, and 4C) and solid electrolyte conductivities (0.02 S/m, 0.05 S/m, 0.5 S/m, and 1 S/m). The study corresponding to the second part of the tutorial (binary liquid electrolyte battery) sets up an Auxiliary sweep over-discharge C-rates only.

Results and Discussion

Figure 1 and Figure 2 show the cell voltage profiles at electrolyte conductivity of 0.02 S/m and 1 S/m, respectively. The battery performance is higher at higher values of electrolyte conductivity. This is as expected, since the internal losses in the battery increase as the conductivity of the solid electrolyte is decreased.

Figure 1: Cell voltage profiles at electrolyte conductivity of 0.02 S/m.

Figure 2: Cell voltage profiles at electrolyte conductivity of 1 S/m.

Figure 3 and Figure 4 show the 1C discharge voltage profiles for different values of electrolyte conductivity ranging from 0.02 S/m to 1 S/m. The 4C discharge profiles (Figure 4) clearly indicate decreased battery performance for lower values of electrolyte conductivity.

Figure 3: Cell voltage profiles at 1C for different values of electrolyte conductivity.

Figure 4: Cell voltage profiles at 4C for different values of electrolyte conductivity.

Figure 5 and Figure 6 show the electrolyte potential drop across the cell at discharge rate of 1C, for two different values of electrolyte conductivity. The voltage drop in the electrolyte is higher for lower values of electrolyte conductivity, as seen in Figure 5.

Figure 5: Electrolyte potential drop at 1C and an electrolyte conductivity of 0.02 S/m.

Figure 6: Electrolyte potential drop at 1C and an electrolyte conductivity of 1 S/m.

Figure 7 shows a comparison of the cell voltage profiles for a battery with a solid electrolyte to that containing a binary liquid electrolyte. The electrolyte conductivity in the case of the solid electrolyte battery (modeled using the Single-Ion Conductor charge balance model) is considered to be 1 S/m. On the other hand, concentration dependent electrolyte conductivity is considered for the liquid electrolyte (1M LiPF6 in 3:7 EC:EMC) used in the binary liquid electrolyte battery (modeled using the Binary 1:1 Liquid Electrolyte charge balance model). Since the conductivity of the binary liquid electrolyte at initial electrolyte concentration of 1M is nearly 1 S/m, the initial voltage at each discharge rate would be identical for both the solid and liquid electrolyte cases. The cell profiles would begin to differ at later discharge times, as the local conductivity for the binary liquid electrolyte battery begins to change due to concentration gradients. Additionally, the concentration gradients would be higher at higher discharge rates, indicating a greater difference at higher discharge rates, as seen in Figure 7.

The comparison plot also indicates that for a battery with a binary liquid electrolyte, one can use the Single-Ion Conductor charge balance model for simulating low discharge/charge scenarios where significant concentration gradients would not be expected. In such cases of low discharge/charge scenarios, the Single-Ion Conductor charge balance model would provide reduced computational loads, since the electrolyte concentration is not solved for as a degree of freedom, without significant loss in accuracy (particularly useful in the case of large models).