Diffusion Batteries Performance

The perfoimance of fifinaon batteries can be diaracteiized in terms of the dimensionless concentration, 

Duhamel s Theorem can be used in conjunction with experimental (1 - S) versus 0 condations for single fixed beds to develop (1 - S ) versus 0 equations which (uedict die replicating nature of 1 and ym for the fixed beds in diffusion batteries. These equations may possibly alro accoum for the average effects produced by unstable displacement. If Dohamel s Theorem can be validly applied when such displacement occurs, the equations may also wovide an adequate basis for accurately pir icting difftision battery yields. 

The perfomiance of diffusion batteries can be characterized in terms of the dimensionless concentration, Sb = (Tout - MXo)l(Yb,.b - MX ), where Ki is most spent cell in the battery. (1 - 5 ) versus 

0 curves for cells in diiliision batteries somewhat resemble the (1 — S) versus 0 curve shown in Fig. 10.10-1. In (1 - S), Fin is constent, whereas in diffijsion batteries, F, varies with t and Fi .i, is usually zero. Ideally, (1 - Sb) versus 0 for each cell of the batteiy should exactly duplicate (1 — for the next cell, when 0 is measured from the start of discharge from the cell in question. After product extract drawoff, the extract discharged from a cell provides the feed to the next cell in the batteiy. Therefore, after t = r Km, fbr any cell should ideally equal for the same cell earlier. In practice, the (1 - Sb) and Fj and Fog, curves exhibit considerable cycle to cycle variation. These variations are probably caus by unstable displacement. 

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The problems relating to mass transfer may be elucidated out by two clear-cut yet different methods one using the concept of equilibrium stages, and the other built on diffusional rate processes. The selection of a method depends on the type of device in which the operation is performed. Distillation (and sometimes also liquid extraction) are carried out in equipment such as mixer settler trains, diffusion batteries, or plate towers which contain a series of discrete processing units, and problems in these spheres are usually solved by equilibrium-stage calculation. Gas absorption and other operations which are performed in packed towers and similar devices are usually dealt with utilizing the concept of a diffusional process. All mass transfer calculations, however, involve a knowledge of the equilibrium relationships between phases. 

Estimates of the diffusion parameters R and capacitance Cd obtained from data fitting can be used to calculate the chemical diffusion coefficient D (cm sec ), if the particle radius is known, as D = t l(3CdRd)- The diffusion pseudocapacitance Cd is related to the Emf-relation of the material so dEldc (volt cmVmole) can be obtained from Cd as dEldc = AFzia SIOCd)- All these specific parameters can be used as sample-independent characteristics of a particular intercalation material and allow one to predict the change of impedance spectra (and battery performance) with changing active layer particle size or thickness (Barsoukov et al. [2000]). 

Because the specific conductivity k (S/m) of an electrolyte is determined readily and easy, this property is widely used for optimizing the battery performance. In contrast, other parameters which are more difficult to obtain, e.g., diffusion coefficients of ions near to or in the electrode materials or transference numbers of ions, are seldom studied and not yet included in optimization. We expect that automated measurement systems will be used in the future to optimize this and other critical parameters of solutions as long as no valid theoretical approach is available. These systems should be able to measure selected quantities automatically as a function of temperature and composition of solutions according to proposals made by optimization methods such as simplex. First steps on this way were undertaken by Schweiger et al., who presented an equipment that is able to measure K(T(t)) and T(t) automatically in up to 32 cells [34-38]. 

This expression is referred to as Pick s second law of diffusion. Solution of Eqs. (2.34) and (2.35) requires that boundary conditions be imposed. These are chosen according to the electrode s expected discharge regime dictated by battery performance or boundary conditions imposed by relevant electroanalytical technique. Several of the electroanalyticai techniques are discussed in Sec. 2.6. 

Diffusion processes are typically the mass-transfer processes operative in the majority of battery systems where the transport of species to and from reaction sites is required for maintenance of current flow. Enhancement and improvement of diffusion processes are an appropriate direction of research to follow to improve battery performance parameters. Equation (2.34) may be written in an approximate, yet more practical, form, remembering that i = nFq, where q is the flux through a plane of unit area. Thus,... 

Currently the most commonly employed anode material for lithium based batteries is graphite, due to its high Coulombic efficiency (the ratio of the extracted Li to the inserted Li) [54] where it can be reversibly charged and discharged under intercalation potentials with a reasonable specific capacity [93], However, researchers are looking for improvements in battery performance and wish to increase the relatively low theoretical capacity associated with graphite batteries (372 mA h g ) and the long diffusion distances of the Li-ions in such devices [51, 54],... 

In addition, several KMC simulation models have been developed to study in more detail the diffusion processes in Li-ion batteries, since the distribution and kinetics of the Li-ion motion have direct consequences in terms of the battery performance and stability. These models include work on Li-ion hopping in polymer electrolytes, parameterized by polarization energy calculations, and a KMC study " of ambipolar Li-ion and electron-polaron (e ) diffusion in nanostructured Ti02 (which investigated the simultaneous diffusion of both LC and e in the electrode). 

The poor efficiencies of coal-fired power plants in 1896 (2.6 percent on average compared with over forty percent one hundred years later) prompted W. W. Jacques to invent the high temperature (500°C to 600°C [900°F to 1100°F]) fuel cell, and then build a lOO-cell battery to produce electricity from coal combustion. The battery operated intermittently for six months, but with diminishing performance, the carbon dioxide generated and present in the air reacted with and consumed its molten potassium hydroxide electrolyte. In 1910, E. Bauer substituted molten salts (e.g., carbonates, silicates, and borates) and used molten silver as the oxygen electrode. Numerous molten salt batteiy systems have since evolved to handle peak loads in electric power plants, and for electric vehicle propulsion. Of particular note is the sodium and nickel chloride couple in a molten chloroalumi-nate salt electrolyte for electric vehicle propulsion. One special feature is the use of a semi-permeable aluminum oxide ceramic separator to prevent lithium ions from diffusing to the sodium electrode, but still allow the opposing flow of sodium ions. 

The thermodynamic properties of magnesium make it a natural choice for use as an anode material in rechargeable batteries, as it may provide a considerably higher energy density than the commonly used lead-acid and nickel-cadmium systems, while in contrast to Pb and Cd, magnesium is inexpensive, environmentally friendly, and safe to handle. However, the development of Mg-ion batteries has so far been limited by the kinetics of Mg " " diffusion and the lack of suitable electrolytes. Actually, in spite of an expected general similarity between the processes of Li and Mg ion insertion into inorganic host materials, most of the compounds that exhibit fast and reversible Li ion insertion perform very poorly in Mg " ions. Hence, there... 

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