Edge Effects in a Spirally Wound Lithium-Ion Battery

Due to the large differences in length scales in a lithium-ion battery, with the thickness of the different layers typically being several orders of magnitude smaller than the extension in the sheet direction, a lithium-ion battery is often well represented by a one-dimensional model. However, the packing and stacking of the battery may cause edge effects which motivate modeling in higher dimensions.

This example investigates the geometrical effects that occur when a constructing a lithium-ion battery by spirally winding the active battery components to construct a cylindrical “jelly-roll” battery.

Model Definition

The battery is constructed by winding a laminated bi-battery sheet into a spiral, which is placed in a cylinder and filled with liquid electrolyte. The battery model consists of the following parts (See Figure 1):

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Two negative porous electrodes (60 μm thick)

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Two positive porous electrodes (60 μm thick)

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One negative current collector (14 μm thick)

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One positive current collector (20 μm thick)

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Two separator regions (30 μm thick)

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One inner and one outer liquid electrolyte region, filling up the hollow space between the active components and the circular battery casing

The spiral revolves three full laps.

Figure 1: Modeled geometry. Spirally wound bi-battery in circular casing filled with liquid electrolyte.

The Lithium-Ion Battery interface is used to model the battery. For a detailed model description, see the accompanying example 1D Isothermal Lithium-Ion Battery found in the Battery Design Module Application Libraries.

The negative current collector at the outer end of the spiral is grounded, and a current density condition is applied to the end of the positive current collector at the inner end of the spiral.

The load cycle investigated is a constant discharge of the battery to approximately 50% state-of-charge. Two different constant discharge rates are compared, 1C and 10C, where 1C corresponds to the discharge current needed for a 100% discharges in one hour, and 10C a ten times higher discharge current. A 10,000 second relaxation simulation after the 1C discharge is also performed.

Results and Discussion

Figure 2 shows the cell potential versus time during the 1C discharge.

Figure 2: Cell potential versus time during the 1C discharge.

Figure 3 and Figure 4 show the relative lithium concentration at the surface of the electrode particles for the negative and positive porous electrode regions at the end of the 1C discharge (t = 1800 s). Due to the resulting large electrolyte resistivity for lithium transport from and to the innermost and outermost parts of the spiral, these areas of the porous electrodes are hardly discharged at all.

The discharge rate is higher for the negative electrode at the inner end of the spiral and at the outer end for the positive electrodes. This is an effect of the outermost or innermost porous electrode regions contributing to the electrochemical current close to the spiral ends.

These locally higher discharge rates at the ends typically results in a shorter lifetime for these regions than for the inner parts of the spiral, which are discharged more uniformly. However, for a battery with more windings, the relative area of these end regions is small compared to the inner part of the spiral.

Figure 3: Relative lithium concentration at the surface of the negative electrode particles during at t = 1800 s for the 1C discharge.

For this system, there is an excess of negative porous electrode material, and therefore the negative electrode does not get fully depleted in areas where the positive electrode reaches lithium saturation (a relative lithium concentration close to unity in relation to the maximum possible concentration).

Figure 4: Relative lithium concentration at the surface of the positive electrode particles during at t = 1800 s for the 1C discharge.

Figure 5 shows the electrolyte potential at the end of the 1C discharge cycle (t = 1800 s). There is a significant drop in potential from the outer liquid electrolyte region through the spiral into the inner electrolyte region. This is an effect of the outermost and innermost porous electrode regions being discharged at a much lower rate than the rest of the system due to large ohmic drops in the electrolyte, and thereby in effect having almost constant equilibrium potentials throughout the discharge. The potential gradients indicate that there is a current flowing also in the spiral direction close to the spiral ends.

Figure 5: Electrolyte potential at t = 1800 s for the 1C discharge.

Figure 6 shows the electrolyte salt concentration at the end of the 1C discharge (t = 1800 s). The concentration gradients close to the spiral ends are due to the current flowing in the spiral direction.

Figure 6: Electrolyte salt concentration at t = 1800 s for the 1C discharge.

The plots for the 10C discharge of cell voltage versus time, lithium concentrations, the electrolyte potential, and electrolyte salt concentration and lithium concentrations are shown in Figure 7 to Figure 11.

Figure 7: Cell potential versus time during the 10C discharge.

Figure 8: Relative lithium concentration at the surface of the negative electrode particles during at t = 180 s for the 10C discharge.

Figure 9: Relative lithium concentration at the surface of the positive electrode particles during at t = 180 s for the 10C discharge.

The higher discharge rates result in higher gradients in the battery direction compared to the spiral direction, giving less pronounced edge effects and a more uniform discharge.

Figure 10: Electrolyte potential at t = 180 s for the 10C discharge.

Figure 11: Electrolyte salt concentration at t = 180 s for the 10C discharge.

Figure 12 to Figure 16 depict the cell potential, lithium concentrations, electrolyte potential, and electrolyte salt concentration at the end of a 10,000 s relaxation simulation after the 50% discharge at 1C. After approx 3 h of relaxation the battery has not yet reached complete equilibrium.

The first steep rise in cell voltage (Figure 12) is closely related to the same relaxation phenomenon seen in the 1D Isothermal Lithium-Ion Battery model, whereas the slower rise after the first minutes is attributed to moving lithium to and from the outermost and innermost part of the spiral, a process that is very slow due to the long traveling distance in the spiral direction.