Optimal Porosity Distribution for Minimized Ohmic Drop across a Porous Electrode

This paper considers the design of spatially varying porosity profiles in next-generation electrodes based on simultaneous optimization of a porous-electrode model. Model-based optimal design not including the solid-phase intercalation mechanism is applied to a porous positive electrode made of lithium cobalt oxide, which is commonly used in lithium-ion batteries for various applications. For a fixed amount of active material, optimal grading of the porosity across the electrode was found to decrease the ohmic resistance by 15%‐33%, which in turn increases the electrode capacity to hold and deliver energy. The optimal porosity grading was predicted to have 40% lower variation in the ohmic resistance to variations in model parameters due to manufacturing imprecision or capacity fade. The results suggest that the potential for the simultaneous model-based design of electrode material properties that employ more detailed physics-based first-principles electrochemical engineering models to determine optimal design values for manufacture and experimental evaluation. © 2010 The Electrochemical Society. DOI: 10.1149/1.3495992 All rights reserved. Electrochemical power sources have had significant improvements in design and operating range and are expected to play a vital role in the future in automobiles, power storage, military, and space applications. Lithium-ion chemistry has been identified as a preferred candidate for high-power/high-energy secondary batteries. Applications for batteries range from implantable cardiovascular defibrillators operating at 10 A current to hybrid vehicles requiring pulses of up to 100 A. Today, the design of these systems have been primarily based on i matching the capacity of anode and cathode materials; ii trial-and-error investigation of thickness, porosity, active material, and additive loading; iii manufacturing convenience and cost; iv ideal expected thermal behavior at the system level to handle high currents; and v detailed microscopic models to understand, optimize, and design these systems by changing one or few parameters at a time. Traditionally, macroscopic models have been used to optimize the electrode thickness or spatially uniform porosity in lithium-ion battery design. Many applications of mathematical modeling to design Li-ion batteries are available in the literature. 1-10 An approach to identify the optimal values of system parameters such as electrode thickness has been reported by Newman and co-workers. 2,5-10 Simplified models based on porous-electrode theory can provide analytical expressions to describe the discharge of rechargeable lithium-ion batteries in terms of the relevant system parameters. Newman and co-workers 2,5-8 have utilized continuum electrochemical engineering models for design and optimization as a tool for the identification of system limitations from the experimental data. Equations were developed that describe the time dependence of potential as a function of electrode porosity and thickness, the electrolyte and solid-phase conductivities, specific ampere-hour capacity, separator conductivity and thickness, and current density. Analysis of these equations yields the values of electrode porosity and electrode thickness so as to maximize the capacity for discharge to a given cutoff potential. 2 Simplified models based on porous-electrode theory were used to describe the discharge of rechargeable lithium batteries and derive analytical expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions were used for design and optimization purposes and for the identification of system limitations from experimental data. 5 Studies were performed by comparing the Ragone plots for a range of design parameters. A single curve in a Ragone plot involves hundreds of simulations wherein the applied current is varied over a wide range of magnitude. Ragone plots for different configurations are obtained by changing the design parameters e.g., thickness one at a time and by keeping the other parameters at constant values. This process of generating a Ragone plot is quite tedious, and typically Ragone curves reported in the literature are not smooth due to computational constraints. Batteries are typically designed only to optimize the performance at the very first cycle of operation of the battery, whereas in practice most of the battery’s operation occurs under significantly degraded conditions. Further, multivariable optimization is not computationally efficient using most first-principles models described in the literature. A reformulated model 11,12 is sufficiently computationally efficient to enable the simultaneous optimal design of multiple parameters over any number of cycles by including the mechanisms for capacity fade. Further, this model can be used to quantify the effects of model uncertainties and variations in the design parameters on the battery performance. Recently, such an application was reported in which the utilization averaged over 1000 cycles was maximized for a battery design obtained by simultaneous optimization of the applied current density I and thickness of the separator and the two electrodes ls,ln,lp for cycle 1, and the effects of variations in these four design parameters due to imprecise manufacturing were investigated. 13 The battery design optimized for cycle 1 did not maximize the cycle-averaged utilization. This paper designs spatially varying porosity profiles in porous electrodes based on simultaneous optimization applied to a porouselectrode model. The next section describes the simple electrochemical porous-electrode model used in this study. Then different methods for the simultaneous optimization of model parameters are discussed. The optimization procedure used in this study is then described, followed by the results and discussion and conclusions.