Isotherm generalized

Adsorption isotherm, general form, 60 Langmuir, 60 Anisotropic media, flux relations, 73... 

If the membrane and its immediate surroundings are isothermal (generally except for pervaporation) and if S is a function only of temperature, then ... 

The assumptions mentioned above for the Langmuir isotherm generally do not hold true in a complex heterogeneous medium such as soil. The deep-well environment is similarly complex and... 

Effect of Temperatures. The isothermsof electrolytes at any temperature between 25°C and 120°C all fall into the curve family of Figure 1, and so conform to equation 4. However, an electo-lyte s isotherm generally shifts somewhat in position as temperature changes, due to a change in q°. Knowing q° at 25°C, its... 

Steroid hormones form a group of pollutants that includes natural hormones such as estradiol, testosterone, and their metabolites as well as several synthetic analogues. Steroid hormones used as growth promoters have already been found in water and sediments (Lai et al. 2000 Thorpe et al. 2003), and their adsorption properties on earth materials have been considered. Lee et al. (2003) report batch experiments where simultaneous sorption of three hormones (17- 3-estradiol, 17-a-ethyl estradiol, and testosterone) on four midwestem U.S. soils and a freshwater sediment were performed. Apparent sorption equilibria were reached within a few hours. Sorption isotherms generally were linear for the chemicals studied on one of these soils (Drummer soil), ranged from 23.4 to 83.2 L kg and log ranged... 

The measurements of n versus A isotherms generally exhibit, when compressed, a sharp break in the isotherms that has been connected to the collapse of the mono-layer under given experimental conditions. The monolayer of some lipids, such as cholesterol, is found to exhibit an unusual isotherm (Figure 4.7). The magnitude of FI increases very little as compression takes place. In fact, the collapse state or point is the most useful molecular information from such studies. It has been found that this is the only method that can provide information about the structure and orientation of amphiphile molecules at the surface of water (Birdi, 1989). 

Unfortunately, experimental adsorption isotherms generally can be fitted by a number of semiempirical equations, and agreement with some particular one provides no assurance that its basic assumptions are correct. 

The ability of palladium to adsorb or absorb large amounts of hydrogen was known before the end of the last century. Much more precise work has been reported in recent years (I, 2, 3, 18). Such studies accurately showed the dependence of the sorption process on pressure and temperature. The isotherms generally indicated a sudden increase in the sorption of hydrogen at a certain pressure, which was very temperature-dependent. This sudden rise in the amounts sorbed at definite pressures suggested a phase shift in the crystalline structure of the palladium from a hydrogen-poor cr-phase to a hydrogen-rich / -phase. Such... 

Chemisorption isotherms generally exhibit a plateau at lower pressures than the micropore filling plateau. This limiting adsorption is due to the completion of a chemically bound monolayer. In our view, these isotherms may be referred to as Langmuir isotherms, even if the mechanism involved may not be strictly in... 

The relationship between equilibrium moisture content and water activity, known as the sorption isotherm, is an important characteristic that influences many aspects of dehydration and storage. It can be constructed graphically or derived mathematically. The shape of the isotherm generally determines the storage stability of the dehydrated product. This concept is used to establish product specifications for the effective drying, packaging, and storage of foods. 

The results are commonly expressed in the form of a sorption isotherm or a plot of the concentration of chemical sorbed (jj,g/g) versus the concentration remaining in solution (jj,g/L). Sorption isotherms generally exhibit one of three characteristic shapes depending on the sorption mechanism. These isotherms are referred to as the Langmuir isotherm, the Freundlich isotherm, and the linear isotherm (a special case of the Freundlich isotherm). The reader is referred to ref 1 for more details on sorption isotherms. 

For non-isothermal generalized Newtonian flows, the conversation of energy equation is DT... 

Behaviors of the 17 vs. log i relation expected under various experimental conditions are reproduced in Figure 9 for the case of the positive Temkin isotherm. The shape is naturally dependent upon the adsorption isotherm, but several conclusions below can be drawn without having precise information concerning the isotherm. Generally speaking, the use of the Temkin isotherm yields smoother curves, and possibly better fit with experiment, than the use of the Langmuir isotherm. ... 

Corrosion and inhibition phenomena often involve the adsorption of reaction intermediates or dissolved species. The Langmuir isotherm generally serves as a starting point in the modeling of these phenomena as will be discussed in later chapters of this book. 

It is important to realize that from the adsorption equilibrium data (i.e., the experimental isotherm), generally it cannot be distinguished between the effects of surface heterogeneity and lateral interactions. Consider the adsorption equilibrium constant K it can be related to the Gibbs standard free energy of adsorption ... 

Figure 8.8. The sorbent was prepared by thermal dispersion of 0.554 g/g on NaY. Monolayer spreading of CuCl was confirmed by X-ray diffraction. Interactions between CuCl and the other gas molecules are weak due to the close proximity between Cu+ and Cl, while each Cu+ can bond one CO molecule. The steepness of the isotherm generally decreases at higher temperatures, at the expense of lower capacity. Hence a maximum working capacity (between two fixed working pressures) is achieved at an optimum temperature. Two strategies then become clear for the PSA operation vacuum desorption and an increase in temperature. Indeed, 70 °C was the temperature of the PSA operation using the CuCl/NaY sorbent (Xie et al., 1996).

Adsorption of gases on non-porous surfaces and in porous solids has been increasingly studied by Monte Carlo, Molecular Dynamics and Density Functional Theory methods [1-5]. Equilibria of simple gases is now routinely studied with these methods, and the predicted adsorption isotherms generally agree well with experimental data of well-defined surfaces, such as graphitized thermal carbon black (GTCB) [6-8]. However, the success of the predictions depends on the choice of the potential equations and the correct selection of the... 

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