Lithium is the lightest metal (6.94 g/mole, specific gravity=0.53 g/cm3) and is highly electropositive (-3.05 V versus standard hydrogen electrode)I. Hence lithium-ion cells have higher specific energy (Wh/kg), higher volumetric energy density (Wh/l), higher specific power (W/kg) and higher volumetric power density (W/l) than other battery chemistries such as lead acid and Ni-MH as seen in Figure 1 and Figure 2II. Therefore lithium-ion cells are being used in advance electric vehicles (EV)III in recent years. Vehicles with different levels of electrification are in the portfolio of most major automobile manufacturers to reduce tail pipe emissions, deliver higher fuel economy, and increase energy security by reducing dependence on foreign oil while delivering vehicles with good performance, durability, safety, customer satisfaction and acceptable range and United States Advanced Battery Consortium (USABC)IV lists the goals for these advanced EV batteries. The schematic of a typical dual lithium ion insertion ‘unit’ cell is given in Figure 3V. Copper current collector, negative porous electrode, separator, positive porous electrode and aluminum current collector are seen along the cell sandwich direction. The porous composite insertion electrodes consist of active material particles (into which lithium ion intercalates), binder, conductive carbon (if needed) and the pores filled with liquid electrolyte (lithium salt in an organic solvent). Electrolyte fills in the porous separator, which is an electronically insulating material. When the cell discharges, lithium ions shuttle from the negative insertion electrode to the positive insertion electrode and in the opposite direction when the cell is charged and therefore, this device is colloquially called the ‘rocking-chair’ cell. Detailed physics will be discussed at the workshop. Lithium-ion cells are usually available in cylindrical, prismatic rigid can or pouch configurations. Individual cells are assembled into a module and several modules comprise a battery pack that is used in the electric vehicles. Battery management system and thermal management by either liquid or air cooling are other integral components of advance electric vehicles. Models varying in complexity, fidelity and computational time are pursued at various scales (with coupling between them as needed) as shown in Figure 4VI for designing advance electric vehicle lithium-ion batteries. In this project, students will set up and solve a mathematical model to simulate the responses of interest such as lithium concentration, voltage, salt concentration, etc. during different modes of operation and compare their results with available experimental data for both validation purposes as well as to gain understanding of the underlying phenomena in these electrochemical systems. The complete project will be compiled as a technical report and presented by the students at the workshop. Figure 1. Comparison of the different battery technologies in terms of volumetric and gravimetric energy densityI. Figure 2. Ragone plots of various electrochemical energy storage and energy conversion devices. Figure 3. Schematic of a dual lithium-ion insertion cell sandwich Figure 4. Phenomena in lithium-ion battery systems at different length scales References: J.M. Tarascon, M. Armand, Building Better Batteries, Nature, Vol. 414, November 2001. Venkat Srinivasan, Batteries for Vehicular Applications, http://bestar.lbl.gov/venkat/files/batteries-for-vehicles.pdf Ford's Electric Vehicle Technology, http://ford.com/technology/electric/ USCAR Energy Storage System Goals http://www.uscar.org/guest/article_view.php?articles_id=85 R. Chandrasekaran, Ford Technical Report, SRR 2012-0069, June 2012. A Pesaran et al, Computer-Aided Engineering of Batteries for Designing Better Li-Ion Batteries http://www.nrel.gov/docs/fy12osti/53777.pdf Prerequisites: Interests in modeling, background in ODE and PDE. Keywords: lithium-ion cell, electrochemical energy storage, batteries, electric vehicles.