COMSOL 6.4 - Lithium Plating and Stripping

Lithium plating on the negative electrode in preference to lithium intercalation is known to reduce capacity and to be a safety concern for lithium-ion batteries. Harsh charge conditions such as high currents (fast charging) and/or low temperatures can lead to lithium plating. The plated lithium is partially reversible in a process called stripping during battery discharge.

This example shows how to model the lithium plating/stripping reaction in the negative graphite electrode in a lithium-ion battery. The resulting capacity loss is predicted for different C-rates and temperatures. The example demonstrates how the Porous Electrode node can incorporate the electrochemical plating/stripping reaction.

Model Definition

general

The model is set up in 1D for a graphite/NMC battery cell using a 1.0 M LiPF6 in EC:EMC (3:7 by weight) electrolyte. Properties for these materials are taken from the Battery material library.

The model consists of the following three domains:

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Negative porous electrode: Graphite (MCMB LixC6) active material (~112 μm).

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Separator (30 μm).

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Positive porous electrode: NMC 811 active material (70 μm).

The Arrhenius equation is used to model the temperature variation of the intercalation exchange current densities. In addition, temperature-dependent electrolyte properties are defined automatically by adding the electrolyte from the material library.

The Lithium-Ion Battery interface is used, accounting for:

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Electronic conduction in the electrodes

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Ionic charge transport in the electrodes and electrolyte/separator

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Material transport in the electrolyte, allowing for including the effects of concentration on ionic conductivity and concentration overpotentials

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Material transport within the solid spherical particles in the electrodes

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Butler–Volmer electrode intercalation kinetics using experimentally measured equilibrium potentials

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An additional electrochemical reaction, in this case lithium plating/stripping (detailed description below).

More information on the general description can be found in the 1D Isothermal Lithium-Ion Battery example. The lithium plating/stripping formulations are based on the investigations in Ref. 1–Ref. 3 and the details are presented below.

Lithium plating/stripping Reaction

The lithium plating/stripping is defined as an additional reaction to the main graphite-lithium intercalation reaction on the negative electrode. This is done using an additional in the node for the negative electrode.

The plating is considered to be a pure electrochemical reaction:

The reverse reaction, stripping, is considered to only partially dissolve the plated lithium electrochemically. The remaining plated lithium is regarded to be irreversibly lost (a loss in lithium inventory) and is often referred to as “dead lithium” (Ref. 1). The stoichiometric coefficient of the dead lithium fraction, YLi, dead, is set to 0.1 in this example, can be incorporated into the stripping reaction expression in the following way:

The electrochemical reaction current, iLi, is defined by concentration-dependent Butler–Volmer kinetics:

(1)

where the pre-exponential factor for the anodic term Fa is defined as:

(2)

In the expressions above

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i0,ref is the reference exchange current density defined at 1 M lithium ion concentration.

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cl is the lithium ion concentration in the electrolyte.

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cl,ref is the reference lithium ion concentration, equal to 1 M.

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cLi(s),cov is the concentration of a monolayer fully covered with plated lithium on the negative active material. The monolayer thickness is set to 0.1 nm.

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cLi(s) is the plated lithium concentration.

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ηLi is the lithium plating/stripping overpotential in which the equilibrium potential, Eeq,Li, is 0 V versus lithium:

(3)

The plated and dead lithium concentrations, cLi(s) and cLi, Dead, are computed using the in-built feature in the main Porous Electrode node. The dissolving–deposited concentrations are computed by integrating the reaction source/sink terms using the following two equations:

(4)

(5)

where av is the specific surface area (m2/m3) of the active material particles.

The stoichiometric coefficients, νLi(s) and νLi, Dead, follow the reaction expression above and are set as follows:

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For plating, iplate < 0:

(6)

(7)

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For stripping, iplate > 0:

(8)

(9)

Charge–Discharge cycle

To evaluate the plating/stripping reaction, a full charge-discharge cycle is simulated. The upper and lower cutoff voltages are set to 4.2 V and 2.7 V, respectively. The cycle consists of a constant current charge period up to the upper cutoff voltage followed by a constant voltage charge period at the upper cutoff voltage and a constant current discharge period to the lower cutoff voltage. The battery is set to be completely discharged initially.

Results and Discussion

To investigate the impact of current, the charge-discharge cycle is simulated for three different constant current rates (C-rates) at 298 K. The influence of temperature is studied by simulating the cycle for 1C current at three different temperatures.

The cell voltages as functions of SOC are displayed in Figure 1 and Figure 2 for the C-rate and temperature studies, respectively. Large variations with cycling conditions are shown.

Figure 1: Cell voltage versus SOC for 1C, 3C, and 5C charge-discharge cycles at 298 K.

Figure 2: Cell voltage versus SOC at 298 K, 283 K, and 268 K for 1C charge-discharge cycle.

The susceptibility to plating can be seen in the electrode potential at the negative electrode. A potential equal to or lower than 0 V is indicative of lithium plating. In Figure 3 and Figure 4, the electrode potential at the electrode-separator and current collector-electrode boundaries are shown during charge. The former boundary is most susceptible to lithium plating in all results. The lowest cell temperature case has a potential below 0 V for a long period during charge.

Figure 3: Negative electrode potential at the electrode–separator and current collector–electrode boundaries for 1C, 3C, and 5C charge-discharge cycles at 298 K.

Figure 4: Negative electrode potential at the electrode–separator and current collector–electrode boundaries at 298 K, 283 K, and 268 K for 1C charge-discharge cycle.

The total lithium film thickness, that is, plated and dead lithium, at the electrode–separator interface is displayed in Figure 5 and Figure 6 over the cycle. Increased C-rate increases the plating to some extent. Lowered temperature increases the plating to the greatest extent. Most of the plating is reversible during the cycle. The irreversible part is due to the formation of dead lithium and reduces the lithium inventory.

Figure 5: Total lithium film thickness variation at the electrode-separator boundary for 1C, 3C, and 5C at 298 K.

Figure 6: Total lithium film thickness variation at the electrode–separator boundary for 298 K, 283 K, and 268 K at 1C constant current rate.

In the two last figures (Figure 7 and Figure 8), the amount of dead lithium in terms of lithium inventory loss in the cell during cycling is shown. The loss is substantial at the lowest temperature, in all other cases most of the lithium is reversible.