Extended Langmuir isotherm

Markham andBenton. This model (34) is known as the extended Langmuir isotherm equation for two components, i and j. 

Adsorption equilibrium was represented by extended Langmuir isotherm with the same saturation capacity (qs) for both adsorbates and constants (bj) following Arrhenius temperature dependence ... 

For multicomponent adsorption the most commonly used isotherm is the extended Langmuir isotherm (Eq. 18). Another, frequently used approach is the Ideal Adsorption Solution theory (IAS theory), which was developed by Prausnitz [53] and applied to mixtures of gases by, for example, Kaul [54] and Rees [52,55]. 

The last three chapters deal with the fundamental and empirical approaches of adsorption isotherm for pure components. They provide the foundation for the investigation of adsorption systems. Most, if not all, adsorption systems usually involve more than one component, and therefore adsorption equilibria involving competition between molecules of different type is needed for the understanding of the system as well as for the design purposes. In this chapter, we will discuss adsorption equilibria for multicomponent system, and we start with the simplest theory for describing multicomponent equilibria, the extended Langmuir isotherm equation. This is then followed by a very popularly used IAS theory. Since this theory is based on the solution thermodynamics, it is independent of the actual model of adsorption. Various versions of the IAS theory are presented, starting with the Myers and Prausnitz theory, followed by the LeVan and Vermeulen approach for binary systems, and then other versions, such as the Fast IAS theory which is developed to speed up the computation. Other multicomponent equilibria theories, such as the Real Adsorption Solution Theory (RAST), the Nitta et al. s theory, the potential theory, etc. are also discussed in this chapter. 

The treatment of the extended Langmuir isotherm of a binary system is due to Markham and Benton (1931). Here, we present the general treatment for a multicomponent gaseous system containing N species. The assumptions made by... 

This equation is known in the literature as the extended Langmuir isotherm equation, which gives the adsorbed concentration of the species i in the multicomponent system. For a binary system. Figure 5.2-1 shows plots of the fractional coverage of the component 1 versus biPj with the parameter b2P2 as the varying parameter. We see that the presence of the additional component 2 causes a decrease in the surface concentration of the component 1 and vice versa due to the competition of the two species. The reduction in the adsorbed concentration of the species 1 is... 

It is reminded that the extended Langmuir isotherm is derived assuming the surface is ideal and the adsorption is localised, and one molecule can adsorb onto one adsorption site. 

In the case of extended Langmuir isotherm, which is the simplest case of dealing with multicomponent mixtures, the isotherm expression of the component i... 

We shall illustrate the utility of the theory by applying to a multicomponent system in which the adsorption isotherm is described by the following extended Langmuir isotherm equation ... 

The diffusivity matrix is a function of the concentrations of all species. Eq. (10.5-9) is the constitutive flux equation. The explicit functional form of the diffusivity matrix in terms of concentration depends on the choice of the adsorption isotherm. What we shall do in the next section is to show this form for the case of the extended Langmuir isotherm. 

The computation of the non-dimensional governing equations is carried out after we specify the functional form for the multicomponent isotherm. We shall do it here with the extended Langmuir isotherm (eq. 10.5-10). 

For the case where the extended Langmuir isotherm can describe the multicomponent equilibria, the non-dimensional diffusivity matrix is given by ... 

Extended Langmuir isotherm is assumed to be valid at the patch level... 

Using the local extended Langmuir isotherm (eq. 11.6-1), we obtain the following equation for the local flux written in terms of only the adsorbed concentrations ... 

AffyILM Relies on inputs from hybridization thermodynamics and uses an extended Langmuir isotherm model to compute transcript concentrations Berger and Carlon (2011)... 

The Langmuir isotherm for pure-component adsorption can readily be extended to an n-component mixture, known as the extended Langmuir isotherm (Yang, 1987) ... 

When two or more adsorbable components exist with the possibility of occupying the same adsorption sites, isotherm relationships become more complex. The simplest is extension of the Langmuir type isotherm by assuming no interaction between adsorbing molecules. In the case two components, the extended Langmuir isotherm (Markham and Benton, 1931) is given as... 

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