Electrochemical Modeling of a Lithium-Metal Anode

The use of a lithium-metal anode in both current and future battery technologies, including lithium-sulfur and lithium-air batteries, is of great interest due to its high energy density and specific energy. Significant effort has been devoted to understanding the cathode in these technologies and toward mitigating dendrite formation, the largest failure mechanism for lithium-metal batteries. This research addresses the problems that could occur even if dendrite propagation is controlled, namely large-scale movement of the lithium at the lithium-metal anode, resulting in a shape change of the lithium/separator interface./nIn the first part of Chapter 1, a two-dimensional electrochemical model is created which forms the basis for the latter half of Chapter 1, Chapter 2, and Chapter 3. In Chapter 1, modeling was done using COMSOL Multiphysics, which uses a finite-element approach. This model incorporates electrode tabbing where, during discharge, the current is drawn from the top of the positive tab and inserted into the bottom of the negative tab. Also modeled is a moving boundary at the negative electrode, a CoO2 intercalation electrode as the cathode, and a lithium-metal negative electrode. The positive electrode is modeled using porous electrode theory, the separator as a liquid electrolyte with a binary salt, and the total volume changes are assumed to be zero. Finally, the negative electrode in this model is stoichiometrically twice the thickness required, to avoid the need for a separate negative current collector./nIn the second part of Chapter 1, the model was cycled at various rates, and shows that, even without dendrites, there is significant large-scale movement of lithium both during each half cycle and after a full cycle of a discharge followed by a charge. Specifically, more lithium is depleted near the negative tab while discharging the cell, yet after a full cycle of a discharge followed by a charge, there is a net migration of lithium towards the negative tab. The model shows that this migration is caused by three separate phenomena. First, the geometry strongly affects the current density distribution, which directly correlates to the asymmetric depletion of lithium during the discharge phase. The second driving force is the open-circuit-potential function, the slope of which not only affects the magnitude of the movement, but also is the largest nonlinearity that contributes to the movement of lithium after a full cycle. The third, and smallest, contributor to the movement of lithium is the concentration gradient in the liquid electrolyte. When the OCP is flat and the concentration gradients are reduced by increasing the diffusivity, the lithium will return to its starting position after a full cycle./nChapter 2 builds on the work developed in Chapter 1 through modeling the movement over extended cycling. The model was cycled at various rates, depths of discharge, and lengths of the rest over multiple cycles. From this, we saw that, with a large excess of lithium at the negative electrode, the movement of the lithium reaches a quasi-steady state where the movement during each subsequent cycle remains at the same magnitude. The rate at which the movement of the lithium reaches that steady state depends on the slope of the open-circuit-potential function, the rate of discharge and charge, the depth of discharge, and the length of time that the cell is allowed to rest both after the discharge and charge phase./nFirst, the slope of the open-circuit-potential function strongly affects both the magnitude of the movement of lithium seen during cycling and the rate at which a steady state is reached. A more steeply sloped open-circuit-potential function causes less movement of lithium during cycling, and a steady state is reached more quickly than with a flatter open-circuit-potential function./nNext, the assumption that there is a large excess of lithium in the negative electrode is relaxed, and the utilization of the negative electrode is increased to 80 percent. This is achieved by reducing the thickness of the negative electrode from 50 to 15 μm with the result that pinching of the negative electrode is seen and is another nonlinearity that leads to a progression of the movement of lithium over multiple cycles./nWith a 50 μm thick negative electrode, the effect of the discharge and charge rate is discussed. Here we see that increasing the C-rate both increases the magnitude of the movement of lithium during cycling and delays the quasi-steady state seen previously. We then explore the effect that the depth of discharge has on the movement of lithium during cycling, and the effects of the rest periods. Finally, we compare the magnitude of the effect of the C-rate with that of the rest periods and find that the lithium is more uniform if the cell was charged quickly and allowed to rest for longer and is less uniform if the cell is charged slowly with a limited rest period following charging./nChapter 3 builds on the model developed in Chapter 1 by relaxing the assumption that the separator, while inhibiting dendrites, also allowed the lithium to move unhindered. Therefore, in this chapter, a dendrite-inhibiting polymer separator which has a shear modulus twice that of lithium is included in the model. Such a separator resists the movement of lithium seen in Chapters 1 and 2 though the generation of stresses in the cell. As can be imagined, as the lithium moves, the separator is either compressed or stretched. This translates into stresses in the separator and lithium that affect the negative electrode through two mechanisms: altering the thermodynamics of the negative electrode and deforming the negative electrode mechanically. Both of these mechanisms are treated in this chapter./nFirst, the effect of the stress on the thermodynamics is developed. From this, we see that it takes very high pressures to modify the kinetics enough to have an appreciable effect on the movement of lithium. Under these pressures, the assumption that the lithium is rigid is invalid, thus the elastic deformation of lithium is included. This relaxes the stresses in the negative electrode through the elastic compression of the lithium; however, the stresses in the negative electrode are still significantly larger than the yield strength of lithium, meaning that plastic deformation of the negative electrode must be included./nWith the inclusion of elastic and plastic deformation of the negative electrode the model shows that a dendrite-inhibiting polymer separator significantly resists the lithium movement seen in Chapters 1 and 2. In addition, we find that the plastic deformation plays a much larger role in the flattening of the lithium than either the pressure-modified reaction kinetics or elastic deformation. Furthermore, the flattening of the negative electrode causes only very slight differences in the local state of charge in the positive electrode. Thus, we can safely say that including a dendrite-inhibiting separator benefits a lithium-metal battery through forcing the negative electrode to be more uniform without causing negative effects in the positive electrode such as larger swings in the local state of charge./nIn Chapter 4, a second method to inhibit dendrite growth is explored through the use of a ceramic that is conductive to lithium ions. While ceramics tend to be very stiff, they are also very brittle and exhibit little or no plastic deformation and fail catastrophically when their yield point is reached. This lack of plastic deformation combined with their high elastic moduli, means that ceramics can operate safely in a very narrow window of strains making them especially susceptible to fracture due to small deformations. Therefore, the stress profile due to bending of a ceramic layer is calculated for two different bending programs and two different geometries./nFirst, as a base case, the stress profile for a block ceramic is calculated for constant radius bending. This stress profile is then compared to a constant radius bending of a laminated polymer-ceramic layer. It is found that the stress reduction due to the addition of a polymer layer only reduces the maximum stress in the ceramic layer by 9 percent. Because of this, a second, periodic geometry, with a polymer section followed by a ceramic section, is introduced. Due to the unique nature of constant radius bending, the stress profile in this periodic geometry is the same as if it were a solid ceramic. Therefore, a new bending program of a cantilevered beam with a point force at the end is used to compare the periodic geometry to a block ceramic. The resulting reduction in stress due to the addition of the polymer section is found to be significant, between about 50 and 99 percent depending on the ratio of Young's moduli.

Advisor: Newman, John