We present a mathematical model of the solid-polymer-electrolyte fuel cell and apply it to (i) investigate factors that limit cell performance and (it) elucidate the mechanism of species transport in the complex network of gas, liquid, and solid phases of the

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A mathematical model for an ion-exchange membrane attached to a gas-fedporous

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Current lithium‐ion battery technology is gearing towards meeting the robust demand of power and energy requirements for all‐electric transportation without compromising on the safety, performance, and cycle life. The state‐of‐charge (SOC) of a Li‐ion cell can be a macroscopic indicator of the state‐of‐health of the battery. The microscopic origin of the SOC relates to the local lithium content in individual electrode particles and the effective ability of Li‐ions to transport or shuttle between the redox couples through the cell geometric boundaries. Herein, micrometer‐resolved Raman mapping of a transition‐metal‐based oxide positive electrode, Li1‐x(NiyCozAl1‐y‐z)O2, maintained at different SOCs, is shown. An attempt has been made to link the underlying changes to the composition and structural integrity at the individual particle level. Furthermore, an SOC distribution at macroscopic length scale of the electrodes is presented.

The proper balance between water production and removal is particularly important for successfully operating solid‐polymer‐electrolyte fuel cells. Imbalance between production and evaporation rates can result in either flooding of the electrodes or membrane dehydration, both of which severely limit performance. We present a mathematical model of the solid‐polymer‐electrolyte fuel cell that identifies operating conditions that result in a water balance. The model is one‐dimensional and is derived from basic principles of gas‐phase transport. The mechanisms of membrane water transport are not included explicitly in the model, and the membrane is taken as uniformly wetted, which renders the model most applicable to thin membranes. We suggest how humidification of reactant gases can be adjusted as current density is varied during an experiment (at constant temperature, pressure, and reactant feed rates) in order to accommodate the fuel cell's changing demands for water. Humidification requirements of inlet reactant gases for a wide range of practical operating temperatures, pressures, and gas feed rates have been identified. The analysis also identifies conditions in which reactant transport limitations govern the behavior of the fuel cell.

In lithium ion batteries, intercalation and deintercalation of lithium may result in volume changes that induce stresses in the lithiumhost electrode-material particles. At relatively high rates of charging or discharging, the host electrode particles may see large lithium concentration gradients which may result in fracture and pulverization due to large diffusion-induced stresses. Conversely, during low-rate charge/discharge operations, the lithium concentration gradients in the particle are minimal; in turn, the internal stresses to which the electrode particles are subjected are low. The electrode particle-cracking models fail to explain why cells exhibit higher coulombic capacity loss during low-rate cycling than during storage. The primary reason being that most of these models focus on understanding the host particle pulverization but fall short of recognizing the importance of possible mechanical degradation of the solid electrolyte interphase (SEI) layer. In this article, we develop a mathematical model to study stresses experienced by the SEI and demonstrate that stresses of large magnitude are exerted on the SEI layer during the expansion/contraction of an electrode particle which may fracture the SEI layer. With these stress calculations we also show that the larger the state-of-lithiation (SOL) change (or 'swing') during a lithiation event, the larger the possibility of SEI fracture. We propose that at lower discharge/charge rates of battery operation the SEI cracking and reforming, rather than the host particle fatigue, is a dominant mechanism of cell capacity loss. The capacity loss due to SEI cracking is shown to be proportional to the square of the SOL swing of the electrode particle during lithiation. An equation is derived to estimate battery capacity fade with SEI fracture and reformation as the main capacity-loss mechanism. The equation is used to estimate capacity fade during actual cell cycling experiments with satisfactory agreement between estimated and observed capacity fade with only one adjustable parameter. Chemical and mechanical degradation of component materials are major reasons for coulombic capacity fade in lithium ion batteries (LIBs).1 Chemical degradation occurs due to the instability of commonly used solvent electrolytes at the operating potentials, resulting in parasitic reactions.2,3 The parasitic electrochemical reactions that form the Solid Electrolyte Interphase (SEI) are generally solvent decomposition reactions that cause an irreversible capacity loss of a cell. In spite of this, SEI formation is important for the durability of LIBs since a stable, a coherent SEI passivates further decomposition of the electrolyte solvent and thus preserves battery life. 4 Intense efforts to understand the composition, mechanical and transport properties as well as the formation mechanism of the SEI are underway in the research community. 5,6 Electrolyte additives such as vinylene carbonate are being explored to improve the stability of the SEI.7 There are also attempts to make a mor...