The capacity of a lithium-ion battery decreases during cycling. This capacity loss or fade occurs due to several different mechanisms which are due to or are associated with unwanted side reactions that occur in these batteries. These reactions occur during overcharge or overdischarge and cause electrolyte decomposition, passive film formation, active material dissolution, and other phenomena. These capacity loss mechanisms are not included in the present lithium-ion battery mathematical models available in the open literature. Consequently, these models cannot be used to predict cell performance during cycling and under abuse conditions. This article presents a review of the current literature on capacity fade mechanisms and attempts to describe the information needed and the directions that may be taken to include these mechanisms in advanced lithium-ion battery models. lnfroduction The typical lithium-ion cell'-3 (Fig. 1) is made up of a coke or graphite negative electrode, an electrolyte which serves as an ionic path between electrodes and separates the two materials, and a metal oxide (such as LiCoO2,

Proper water and heat management are essential for obtaining high-power-density performance at high energy efficiency for proton-exchange-membrane fuel cells. A water and heat management model was developed and used to investigate the effectiveness of various humidification designs. The model accounts for water transport across the membrane by electro-osmosis and diffusion, heat transfer from the solid phase to the gas phase and latent heat associated with water evaporation and condensation in the flow channels. Results from the model showed that at high current densities (> 1 A/ cm~) ohmic loss in the membrane accounts for a large fraction of the voltage loss in the cell and back diffusion of water from the cathode side of the membrane is insufficient to keep the membrane hydrated (i.e., conductive). Consequently, to minimize this ohmic loss the anode stream must be humidified, and when air is used instead of pure oxygen the cathode stream must also be humidified.

A first principles-based model has been developed to simulate the capacity fade of Li-ion batteries. Incorporation of a continuous occurrence of the solvent reduction reaction during constant current and constant voltage ͑CC-CV͒ charging explains the capacity fade of the battery. The effect of parameters such as end of charge voltage and depth of discharge, the film resistance, the exchange current density, and the over voltage of the parasitic reaction on the capacity fade and battery performance were studied qualitatively. The parameters that were updated for every cycle as a result of the side reaction were state-of-charge of the electrode materials and the film resistance, both estimated at the end of CC-CV charging. The effect of rate of solvent reduction reaction and the conductivity of the film formed were also studied.

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A mathematical model is presented for a complete lithium-sulfur cell. The model includes various electrochemical and chemical ͑precipitation͒ reactions, multicomponent transport phenomena in the electrolyte, and the charge transfer within and between solid and liquid phases. A change in the porosity of the porous cathode and separator due to precipitation reactions is also included in the model. The model is used to explain the physical reasons for the two-stage discharge profiles that are typically obtained for lithium-sulfur cells.

The processes that lead to capacity fading affect severely the cycle life and rate behavior of lithium-ion cells. One such process is the overcharge of the negative electrode causing lithium deposition, which can lead to capacity losses including a loss of active lithium and electrolyte and represents a potential safety hazard. A mathematical model is presented to predict lithium deposition on the negative electrode under a variety of operating conditions. The Li x C 6 |1 M LiPF 6 , 2:1 ethylene carbonate/dimethyl carbonate, poly(vinylidene fluoride-hexalfuoropropylene)|LiMn 2 O 4 cell is simulated to investigate the influence of lithium deposition on the charging behavior of intercalation electrodes. The model is used to study the effect of key design parameters (particle size, electrode thickness, and mass ratio) on the lithium deposition overcharge reaction. The model predictions are compared for coke and graphite-based negative electrodes. The cycling behavior of these cells is simulated before and after overcharge to understand the effect of overcharge on extended cycling. These results can be used to establish operational and design limits within which safety hazards and capacity fade problems, inherent in these cells, can be minimized.

This work presents a rigorous continuum mechanics model of solvent diffusion describing the growth of solid-electrolyte interfaces ͑SEIs͒ in Li-ion cells incorporating carbon anodes. The model assumes that a reactive solvent component diffuses through the SEI and undergoes two-electron reduction at the carbon-SEI interface. Solvent reduction produces an insoluble product, resulting in increasing SEI thickness. The model predicts that the SEI thickness increases linearly with the square root of time. Experimental data from the literature for capacity loss in two types of prototype Li-ion cells validates the solvent diffusion model. We use the model to estimate SEI thickness and extract solvent diffusivity values from the capacity loss data. Solvent diffusivity values have an Arrhenius temperature dependence consistent with solvent diffusion through a solid SEI. The magnitudes of the diffusivities and activation energies are comparable to literature values for hydrocarbon diffusion in carbon molecular sieves and zeolites. These findings, viewed in the context of recent SEI morphology studies, suggest that the SEI may be viewed as a single layer with both micro-and macroporosity that controls the ingress of electrolyte, anode passivation by the SEI, and cell performance during initial cycling as well as long-term operation.

The single-particle model presented by Santhanagopalan et al. ͓J. Power Sources, 156, 620 ͑2006͔͒ is extended to include an energy balance. The temperature dependence of the solid phase diffusion coefficient of the lithium in the intercalation particles, the electrochemical reaction rate constants, and the open circuit potentials ͑OCPs͒ of the positive and negative electrodes are included in the model. The solution phase polarization is approximated using a nonlinear resistance, which is a function of current and temperature. The model is used to predict the temperature and voltage profiles in a lithium-ion cell during galvanostatic operations. The single-particle thermal model is validated by comparing the simulated voltage and temperature profiles to the results obtained using a distributed porous electrode model. The simulation results from the single-particle thermal model also show good agreement with experimental voltage data obtained from lithium-ion pouch cells under different discharge rates ͑C/33, C/2 and C͒ at different temperatures ͑15, 25, 35, and 45°C͒.