Adsorption isotherm linear type

The major surfactant in the foam may usually be considered to be present at the bubble surfaces in the form of an adsorbed monolayer with a substantially constant F, often of the order of 3 X 10" (g mol)/ cm", for a molecular weight of several hundred. On the other hand, trace materials follow the linear-adsorption isotherm Tj = KiCj if their concentration is low enough. For a wider range of concentration a Langmuir or other type of isotherm may be applicable (Davies and Rideal, loc. cit.). 

A plot of v versus PA is of the same form as the Type I adsorption isotherm. At low values of PA the term KPA is small compared to unity, and the amount adsorbed will be linear in pressure. At high pressures the term KPA is large compared to unity, and the surface coverage is nearly complete. In this case v will approach vm. 

Instead of ion-exclusion, size exclusion has been used in the separation of NH4S04 from a protein [41]. In that case, the adsorption isotherms were found to be simply linear. A hydrophobic interaction separation has been used for desalting in the case of phenylalanine and NaCl [41]. NaCl shows almost no interaction with the packing and consequently has a linear adsorption isotherm. The phenylalanine, on the other hand, showed a classical Langmuir-type adsorption isotherm. 

The shape of the adsorption front, the width of the MTZ, and the profile of the effluent concentration depend on the nature of the adsorption isotherm and the rate of mass transfer. Practical bed depths may be expressed as multiples of MTZ, values of 5-10 multiples being economically feasible. Systems that have linear adsorption isotherms develop constant MTZs whereas MTZs of convex ones (such as Type I of Figure 15.1) become narrower, and those of concave systems become wider as they progress through... 

The most simple type, A, is that of a linear increase. It is described by the Henry adsorption isotherm equation ... 

Figure 34 shows the results for alcohol (methanol, ethanol, 1-propanol and 1-butanol), ketone (acetone and diacetyl), terpene (pinene and linalool), aldehyde (n-nonyl aldehyde) and ester (acetic acid n-amyl ester and n-butyric acid ethyl ester) of various concentrations. Because of the linear characteristics of the CTL-based sensor, the plots are located in a similar region for a certain type of gas of various concentrations where the Henry-type adsorption isotherm holds. Thus, we can identify these gases with various concentrations by simple data-processing. 

Equation (4.11) is reduced to the Langmuir equation [Equation (4.6)] if [A] is much smaller than [A]s and b is much greater than unity. A linear plot for each of three types of adsorption isotherms is illustrated in Figure 4.4. Furthermore, a generalized isotherm equation can be written as ... 

The important advances in adsorption technology made possible by the BET theory (S, 4) clearly justify Model 1 in many applications. But one of the Models 2, 3, or 4 is apparently required for first-layer adsorption in a Type II isotherm. That an important condensation potential at the solid-gas interface is the Lennard-Jones 3-9 potential now seems well established (3, 7, 9, 10, 15). Equally clear is the fact that this potential is not solely responsible for physical adsorption the type of surface polarization predicted by the theory of structural adsorption (10) has been demonstrated by observed changes due to adsorption in linear... 

Even if it can sometimes be linear in a wide concentration range, the relation C vs C is usually not linear. Moreover, in the case of a multicomponent mixture, there is usually a competition between the various compounds to access to the adsorption sites. Consequently, C, depends not only on C, but on all liquid phase concentrations. Each component adsorption isotherm is a relation of the following type ... 

Other modeling efforts include soil acidification models of the macroscopic type that account for the process of S04 sorption in different ways. These approaches, which assume equilibrium conditions to prevail, include the adsorption isotherm, solubility product, and anion exchange. Prenzel (1994) discussed the various limitations of the above approaches in their capability to account for changes in pH. Recently, Fumoto and Sverdrup (2000) used a constant capacitance approach to describe the pH dependency of S04 sorption isotherms in an andisol. Other modeling efforts of S04 isotherms were reported by Gustafsson (1995) in a spodosol. Such isotherm models are of the equilibrium type and include linear and Temkin types of models. 

At room temperature only a small amount of hydrogen is stored in porous materials and the adsorption isotherm typically does not show any saturation described by a plateau. Instead a linear increase in the hydrogen uptake is observed up to relatively high pressure. Therefore, at room temperature the adsorption is better described by a linear Henry type isotherm [Ij. 

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