Adsorption isotherm anti-Langmuir

FIGURE 2.3 The anti-Langmuir isotherm of adsorption and the corresponding nonsymmetrical distribution of the analyte s concentration in the chromatographic band. 

Also, in this case, with the adsorbate concentration low enongh, the anti-Langmuir isotherm transforms into the linear equation and becomes the simplest isotherm of adsorption, as described by Henry s law. 

There are several isotherm models for which the isotherm shapes and peak prohles are very similar to that for the anti-Langmuir case. One of these models was devised by Fowler and Guggenheim [2], and it assumes ideal adsorption on a set of localized active sites with weak interactions among the molecules adsorbed on the neighboring active sites. It also assumes that the energy of interactions between the two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the adsorbent surface is not significandy affected. For the liquid-solid equilibria, the Fowler-Guggenheim isotherm has been empirically extended, and it is written as ... 

Also, the mititilayer isotherms have the anti-Langmuir shape. The mititilayer isotherm models can easily be derived, assuming an infinitely fast adsorption of the adsorbate on the adsorbent active sites, followed by a subsequent adsorption of the molecules on the first, the second, and consecutive adsorbed layers [7,8]. 

From the asymmetrical concentration profile with front tailing (see Figure 2.4b), it can correctly be deduced that (1) the adsorbent layer is already overloaded by the analyte (i.e., the analysis is being run in the nonlinear range of the adsorption isotherm) and (2) the lateral interactions (i.e., those of the self-associative type) among the analyte molecules take place. The easiest way to approximate this type of concentration profile is by using the anti-Langmuir isotherm (which has no physicochemical explanation yet models the cases with lateral interactions in a fairly accurate manner). 

The exemplary peak profiles, simulated with use of Equation 2.20 for the linear, Langmuir, and the anti-Langmuir isotherms of adsorption are presented in Figure 2.21. 

The tendency of carboxylic acid analytes to form associative multimers can also be viewed as multilayer adsorption. Analysis of the concentration profiles presented in Fig. 2 reveals that for low concentrations of the analyte, peaks a and b are similar to the band profiles simulated by use of the Langmuir isotherm, whereas peaks c-f resemble profiles obtained by use of the anti-Langmuir isotherm (tailing toward the front of the chromatogram is more pronounced than tailing toward the start of the chromatogram.). 

Anti-Langmuir isotherm An isotherm which is convex downward or, by extension, an adsorption behavior which is opposite to the one observed with a Langmuir isotherm. With the Langmuir isotherm (see Chapter 3), the solute concentration at equilibrium in the adsorbent, q, increases less rapidly than the solution concentration, C. With an anti-Langmuir isotherm, q increases more rapidly... 

Besides the heterogeneity of the adsorbent surface, the second major reason for the adsorption of a compound to deviate from Langmuir isotherm behavior is that the adsorbed molecules interact. In this category, we find the Fowler isotherm, the anti-Langmuirian isotherm, and several S-shaped isotherm models, including the quadratic isotherm, the extended BET isotherm models, and the Moreau model. 

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