Theoretical calculations are compared with well-controlled experiments conducted on a porous, graphite-based, lithiated-carbon electrode. The interpretation of the electrode behavior is facilitated by the use of a reference electrode in a cell that maintains a substantially uniform current distribution. A solvent-casting procedure for constructing graphite anodes, employing a hydrocarbon ͓poly(ethylene ϩ propylene ϩ norborene)͔ binder is implemented. Nonlinear diffusion of lithium intercalate within the host carbon particles is considered; previously published concentration-dependent diffusion-coefficient data are employed for the lithium intercalate species. Other important resistances result from ionic diffusion and migration within the solvent phase, interfacial reaction at the surface of the carbon particles, and electron transport within the solid phase. Calculations are used to assess the impact of particle shape and the nature of the carbon precursor. The overall analysis indicates that interfacial resistance plays a dominant role in limiting the available capacity at high rates of current passage.

To clarify the electrochemical processes governing the performance of lithiated carbon electrodes and obtain appropriate physicochemical properties, experiments conducted with a single-fiber carbon microelectrode (3.5 p.m radius, 1 cm length) are mathematically simulated. Equilibrium-potential data are used to determine the activity coefficient of the lithium intercalate and associated host sites. Transport within the carbon fiber is influenced significantly by activitycoefficient variations; the use of the guest chemical-potential gradient as the driving force for transport phenomena is shown to yield constant physicochemical properties that are independent of the degree of intercalation. The theoretical calculations display good agreement with several different experimental data sets. The diffusion coefficient of lithium in partially graphitic carbon is obtained along with rate constants (i.e., the exchange current density) associated with the electrochemical reaction that takes place on the fiber surface. InfroduclionThe ease with which lithium can be intercalated and deintercalated from carbon cokes and graphites has led to recent studies of lithiated-carbon anodes and cells formed with dual insertion electrode systems.15 A brief discussion of the literature associated with this topic can be found in Ref. 16, wherein an experimental technique was described to investigate single-fiber carbon electrodes.The distinguishing feature of this approach is that it allows one to isolate the properties intrinsic to the lithiated-carbon fiber, and the results are not complicated by the influence of binders, electronically conductive additives, current collectors, or other components necessary for the fabrication of porous carbon electrodes. In addition, the electrochemically active surface area is known for the single-fiber electrode, in contrast to that of the active carbon in porous electrodes, and the lithiation process can be analyzed quantitatively. This work provides the theoretical complement to Ref. 16.The energy density of the carbon anode is related to the amount of lithium within the carbon fiber, and the power performance is related to the rate at which lithium can be removed from the fiber. Both energy and power density depend on the electrode potential. The overall rate of charge and discharge, lithium intercalation and de-intercalation, respectively, is governed by both lithium diff usion within the carbon host and electrochemical reaction at the carbon surfaces. The underlying chemical processes that determine these characteristics of technological importance can be quantified for the partially graphitic material of the single-fiber electrodes.A schematic illustration of the fiber geometry is shown in Fig. 1. The fiber radius a is indicated along with the cylindrical coordinates r and z. Since the fiber length to radius ratio is about 3000 (1 cm length, 3.5 p.m radius), and

We derive and implement a method to describe the thermodynamics of electrode materials based on a substitutional lattice model. To assess the utility and generality of the method, we compare model results with experimental data for a variety of electrode materials: lithiated graphite and layered nickel-manganese-cobalt oxide (Chevrolet Bolt Electric Vehicle negative and positive electrode materials, respectively), manganese oxide (in the positive electrodes of the Gen 1 and Gen 2 Chevrolet Volt Extended Range Electric Vehicle and the positive electrode of many high-power-density batteries), and iron phosphate (Gen 1 Chevrolet Spark Electric Vehicle positive electrode material and of immediate interest for 12 and 48 V applications). An early version of the model has been applied to lithiated silicon (Li-Si). As was found in the Li-Si study, the model enables one to quantitatively represent experimental data from these different electrode materials with a small number of parameters, and, in this sense, the approach is both general and efficient. An open question is the utility of controlled-potential vs. controlled-current experiments for the elucidation of the system thermodynamics. We provide commentary on this question, and we highlight other open questions throughout this work. Central to the modeling of electrochemical systems, particularly batteries relying on solid-state diffusion within the active materials, is an accurate description of the system thermodynamics.1-4 We describe and implement a thermodynamic model for substitutional electrode materials. At the heart of the model is a simple expression for the open-circuit potential U in terms of the fraction of filled sites x within a host material. To assess the value of the model, we apply it to four electrode materials of commercial interest today: lithiated graphite, spinel manganese oxide, iron phosphate, and nickel-manganese-cobalt oxide. The model is an expanded version of that described in Ref. 12. A slight alteration is needed to describe the nickel-manganese-cobalt oxide so that inaccessible lithium can be considered (giving rise to x 0 in Table I), and we also describe how reactions between sites within the electrode material can be addressed.This document is organized as follows. First, we provide an overview of the materials and instrumentation for the experimental characterization of the electrode materials. An introduction of the thermodynamic model is then presented, followed by a detailed description of the model. A discussion of results is then presented, followed by a brief Appendix devoted to the convergence properties of the series summation employed in the U(x) model. • C under about 0.01 Torr vacuum. Other materials were dried at 100 Experimental• C under vacuum of about 0.01 Torr. Cell assembly and cycling were performed under an inert argon atmosphere with O 2 and H 2 O concentrations < 1 ppm. Cycling was performed with a Princeton Applied Research PMC 2000 potentiostat/galvanostat. For the voltammetry work on the Ni 0.6 Mn 0.2 Co ...

For the research, development, and eventual manufacture of lithium‐ion batteries, it is necessary to understand the phenomena limting cell performance and incorporate this knowledge into battery design. While methods exist for the determination of electrolyte‐phase properties, procedures for the assessment of analogous solid‐state properties in battery electrode materials are more difficult to implement. The perturbation solution derived in this work is implemented to determine the intercalate diffusion coefficient in a solvent‐cast porous electrode containing carbonized poly(acrylonitrile) fibers suitable for a lithium‐ion battery. It is shown that both intercalate and vacant site contributions to the excess free energy of the solid phase influence significantly the nonequilibrium behavior of the electrode. In addition, the analysis is shown to provide insight into the processes that govern the pulse‐power performance of batteries based on insertion electrodes (e.g., lithium‐ion and metal‐hydride batteries). © 1999 The Electrochemical Society. All rights reserved.

We derive and implement an algorithm that can accommodate an arbitrary number of model parameters, thereby allowing for more complicated battery models to be employed in formulating model reference adaptive systems as part of an energy management scheme for systems employing batteries. We employ the (controls) methodology of weighted recursive least squares with exponential forgetting. The output from the adaptive algorithm is the battery state of charge (remaining energy), state of health (relative to the battery’s nominal rating), and power capability. The adaptive characterization of lead acid, nickel metal hydride, and lithium-ion batteries is investigated with the algorithm. The algorithm works well for lithium-ion and lead-acid batteries; more work is needed on nickel metal hydride batteries.