Lithium Ion Battery Research
Overview
There is a continual need to improve the performance of lithium ion batteries. Ionix Power Systems is developing advanced technologies to improve the performance and safety of these devices. Ionix was recently awarded an contract with the navy to develop advanced models of lithium ion battery performance.
Modeling of a Lithium Ion Cell
The discharge characteristics of an insertion battery are
complex.
Many different processes and design
parameters can limit performance of the battery.
In addition many other factors can limit rate capability of the system.
These include electrode thickness, electrode porosity, electrode
conductivity, availability of reactants in the electrolytic solution, separator
resistance, SEI resistance, etc. A detailed mathematical model of a lithium ion cell can be a
useful development tool. Recently, a mathematical model of a lithium ion battery was
published by Fuller, Doyle, and Newman that allows consideration and
optimization of these complex characteristics (1). The model describes the galvanostatic charge and discharge of
a dual insertion lithium ion battery.
The
model considers one-dimensional transport of lithium from the negative electrode
through the separator and into the positive electrode.
Figure 1 diagrams the modeled cell.
The model allows many design parameters to be optimized and the
complicated interactions of these design features to be understood.
The model is derived from porous electrode theory developed by Newman (2). Table 1 contains a basic description of the variables, parameters, and conditions of the model. Transport phenomena are described using concentrated solution theory. The model considers six variables: electrolyte concentration in the liquid phase (c), electric potential in the solution phase (F2), the concentration in the insertion phase (cs), the current in the solution phase (i2), the pore wall flux on at the surface in the insertion particle in the electrode (jn), and the solid phase electrical potential (F2). Table 1 also lists the parameters and boundary conditions used in the model. The listed equations are a set of coupled non-linear differential equations that can be solved for simultaneously at each time step of a battery charge or discharge process. A method described by Newman was used to solve the equations (2). More detailed information can be found in the listed references.
Figure 1.
Schematic
of modeled lithium ion cell.
In order to evaluate the effect of increasing electrolyte conductivity the model will be applied to a known battery design using a standard electrolytic solution. The modeled performance of this battery will then be compared to the predicted performance using the same design parameters except substitution of a high conductivity electrolytic solution.
The baseline design selected was the same battery data that was used by Fuller et. al. to verify the published model. The experimental parameters used were taken from data presented by Guyomard and Tarascon. This battery system uses a spinel manganese oxide cathode in conjunction with a petroleum coke anode. The electrolytic solution was 1 M LiClO4 in propylene carbonate (3). More details about the input parameters are listed in Fuller’s paper (1). Figure 2 shows the modeled voltage and utilization curves under four different conditions. The first three are the predicted performance of the baseline cell at three different current levels. These plot show excellent agreement with the results presented by Fuller (compare with Figure 2 of ref 4). The forth plot show the predicted performance of the battery with the substitution of an electrolytic solution with a conductivity of 0.050 S/cm. The performance of the system with the higher conductivity solution is increased markedly. The ultilization of the electrode material at the relatively high current rate of 5 mA/cm² is increased from 74% to over 98%. The higher utilization rate translates to a higher delivered energy density. Figure 3 show a Ragonne plot for the baseline cell and the high conductivity cell with a relatively thin electrode design of 100 mm and 123 mm for the cathode and anode respectively. At high power levels the improved performance of the higher conductivity solution is seen. The modeled battery is able to discharge at roughly three times the rate of the baseline cell. At 1700 W/kg the battery is still able to deliver 75 Wh/kg. At a rate of 4900 W/kg the cell delivered 8.1 Wh/kg. The weights in these calculations represent the electrolyte, electrode, separator,
Figure 2. Modeled
comparison of cathode utilization for low and high conductivity solutions.
Curves a, b, c are with low conductivity 1 M LiClO4 in PC (5.8
mS/cm).
Curve d is with high
conductivity solution.
Note higher cathode utilization, y, for high conductivity case.
Figure 3. Modeled energy and power performance of the baseline cell with low (PC) and high conductivity solutions (HCS). The same parameters are used as in Figure 2 except electrode thickness has been increased to 100 and 123 mm for the cathode and anode respectively.
and current collector. Packing weight is not considered in the calculation. Fuller, et. al , pointed out that at high discharge rates the utilization of the positive electrode is limited by the availability of lithium ions in the electrolytic solution. Initially the concentration of electrolyte is uniform. As the battery is discharge a concentration gradient develops. This change in concentration balances migration of anions in solution and is also caused by consumption of Li+ at the positive electrode. At high current densities the concentration of the electrolyte is driven to zero at the back face of the positive electrode. Insertion in this region can not occur without lithium so the cathode material is under utilized. This limitation causes the rapid drop in energy density of the system at high discharge rates. The same limitations are seen with the higher conductivity systems except at a much higher current density. Optimizations beyond what is described in Figure 3 will be possible if the issues of electrolytic availability are addressed. The performance can be improved by decreasing electrode thickness, increasing electrode porosity, or increasing electrolyte concentration. Many other improvements in the design of the baseline cell with higher conductivity solutions can be made. The results of this analysis show the dramatic effect ionic conductivity can have on the rate capability of a lithium ion battery.
References
1. Fuller, T. F. and M. Doyle, and J. Newman, Journal of the Electrochemical Society, Vol 141, no 1, p. 1 (1994)
2. Newman, J., “Electrochemical Systems,” Prentice Hall, Englewood Cliffs NJ, (1991).
3. Guyomard D, and J. M. Tarascon, Journal of the Electrochemical Society, vol139, No. 4, p. 937 April (1992).