Models of Multicomponent Competitive Adsorption Isotherms

As in the previous chapter, we simplify the problem by considering the adsorption isotherm of the solute-adsorbate separately from the solvent, adopting a convention that the solvent is not adsorbed [2]. We do not consider the Gibbs excess isotherms. Admittedly, this would be more rigorous, but it would lead to a complicated presentation, and this complexity does not seem warranted in the present state of development of competitive excess isotherms and because the concentration of the solutions considered in HPLC rarely exceeds 10% (v/v). 

Strong solvents can act and modify the retention of solutes in two different ways. In some cases, they compete with the feed components for adsorption. This is the mechanism through which they reduce the adsorption of the feed components and accelerate their elution. This is what occurs in normal phase chromatography when polar solvents are used as components of the mobile phase e.g., propanol added to dichloromethane). Usually, the concentration at which these additives are used is low, often of the order of a few percent. However, not all additives act by competition for retention. 

In the case in which the additive or strong solvent is strongly adsorbed by the stationary phase, it competes with the feed components. As a result, the individual band profiles can exhibit unique shapes and be considerably different compared to the band profiles obtained for the same compmmds in a pme mobile phase with which the components have the same apparent isotherms (see Chapter 13). 

The Langmuir equilibrium isotherm model can be extended to multicomponent systems [7,8]. However, when several components are simultaneously present in the solution, these compounds interfere. The amount of each of them that is adsorbed at equilibrium is smaller than if this compoimd were alone. Although 

At equilibrium, in the presence of a binary solution of components A and B, a part of the surface is free, that is, it is covered only by the solvent, part is covered by molecules of the first component, and the rest by molecules of the second component. Let the fractions of the surface covered by the molecules of solvent and components A and B be Sq, S,.i, and Sg, respectively. Then we have 

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The multicomponent Langmuir adsorption isotherm given in Eq. (7) is the simplest model for the description of non-linear, multicomponent, adsorption equilibrium. At high concentration, the model predicts saturation of the stationary phase and overload of the chromatographic column. At low concentration (high dilution) the behavior can be correctly described by the non-competitive linear adsorption isotherm ... 

Multicomponent pollutants in an aqueous environment and/or leachate of SWMs, which are COMs, usually consist of more than one pollutant in the exposed environment [1, 66-70]. Multicomponent adsorption involves competition among pollutants to occupy the limited adsorbent surface available and the interactions between different adsorbates. A number of models have been developed to predict multicomponent adsorption equilibria using data from SCS adsorption isotherms. For simple systems considerable success has been achieved but there is still no established method with universal proven applicability, and this problem remains as one of the more challenging obstacles to the development of improved methods of process design [34,71 - 76]. 

All cases of practical importance in liquid chromatography deal with the separation of multicomponent feed mixtures. As shown in Chapter 2, the combination of the mass balance equations for the components of the feed, their isotherm equations, and a chromatography model that accounts for the kinetics of mass transfer between the two phases of the system permits the calculation of the individual band profiles of these compounds. To address this problem, we need first to understand, measure, and model the equilibrium isotherms of multicomponent mixtures. These equilibria are more complex than single-component ones, due to the competition between the different components for interaction with the stationary phase, a phenomenon that is imderstood but not yet predictable. We observe that the adsorption isotherms of the different compounds that are simultaneously present in a solution are almost always neither linear nor independent. In a finite-concentration solution, the amount of a component adsorbed at equilib-... 

The prediction of multicomponent equilibria based on the information derived from the analysis of single component adsorption data is an important issue particularly in the domain of liquid chromatography. To solve the general adsorption isotherm, Equation (27.2), Quinones et al. [156] have proposed an extension of the Jovanovic-Freundlich isotherm for each component of the mixture as local adsorption isotherms. They tested the model with experimental data on the system 2-phenylethanol and 3-phenylpropanol mixtures adsorbed on silica. The experimental data was published elsewhere [157]. The local isotherm employed to solve Equation (27.2) includes lateral interactions, which means a step forward with respect to, that is, Langmuir equation. The results obtained account better for competitive data. One drawback of the model concerns the computational time needed to invert Equation (27.2) nevertheless the authors proposed a method to minimize it. The success of this model compared to other resides in that it takes into account the two main sources of nonideal behavior surface heterogeneity and adsorbate-adsorbate interactions. The authors pointed out that there is some degree of thermodynamic inconsistency in this and other models based on similar -assumptions. These inconsistencies could arise from the simplihcations included in their derivation and the main one is related to the monolayer capacity of each component [156]. 

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. 

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