Localized adsorption with interactions

Contrary to the last two isotherms, which take into the account interactions between the neighboring molecities ortiy, the Kiselev model assumes the singlecomponent localized adsorption, with the specific lateral interactions among all the adsorbed molecules in the monolayer [4—6]. The equation of the Kiselev isotherm is given below ... 

In order to have localized adsorption with only physical interaction it is clear that either the interaction must be strong, or the kinetic energy of the adsorbed molecules must be small. As an example of the latter condition we have the work of Keesom and Schweers (24, 25) for low temperature adsorption of hydrogen and neon on glass. They assumed that the actual area of the glass was equal to the apparent area, and the results in Table IX were worked out for = 3 on that basis. The... 

The procedure is first illustrated in terms of its application to the analysis of an isotherm calculated from an arbitrary assumed site energy distribution, f(Q). For reasons discussed in more detail later, the Langmuir equation—i.e., localized adsorption with no lateral interaction—appears very satisfactory as the form to use for 0(P,T,Q) ... 

The first such solutions were carried out by Ross and Olivier [1, p. 129 6,7]. Using Gaussian distributions of adsorptive potential of varying width, they computed tables of model isotherms using kernel functions based on the Hill-de Boer equation for a mobile, nonideal two-dimensional gas and on the Fowler-Guggenheim equation [Eq. (14)] for localized adsorption with lateral interaction. The fact that these functions are implicit for quantity adsorbed was no longer a problem since they could be solved iteratively in the numerical integration. 

Before proceeding further a few words should be spent on the choice of the Langmuir isotherm. Obviously, the choice of this isotherm as local isotherm restricts the applications only to submonolayer localized adsorption with weak lateral interactions however, this seems the case where DR behaviour is observed. ... 

Adsorption occurs only on localized sites with no interactions among adjoining adsorbed molecules. 

If one develops this concept further it becomes evident that the general adsorption of the molecules at the surface proceeds continuously to a localized adsorption on distinct and specific surface sites. This appears entirely reasonable as an extreme case, i.e., for ion exchange interaction with basic or acidic surface sites. The consequence, of course, is that the effective area required by an adsorbed sample molecule increases. 

Other methods of surface area determination depend, in general, on adsorption under well defined conditions of various solute molecules of known dimensions (Sposito, 1984 Davis and Kent, 1990). Some of these are dipole molecules so that dipole interactions with the surface or H-bonding are involved. Water adsorbed at a fixed relative water vapour pressure (e. g. 0.2) to provide a monolayer is one example (Torrent et ah, 1990). An organic dipole frequently used for soils is ethylene glycol monoethylether (EGME) (Carter et al., 1965). The main problem with these dipole molecules lies in their mutual association which may lead to localized adsorption beyond a monolayer (capillary condensation), particularly on porous material. 

Strong interactions with the surface lead to localized adsorption which constrains the adsorbate to a specific site. The effective adsorbate cross-sectional area will then reflect the spacing between sites rather than the actual adsorbate dimensions. 

The Pt 6s and 6p orbitals are very diffuse, whereas the Pt 5d states are more localized orbitals with specific geometries. Due to their delocalized nature, the Pt 6s,p states will have more interaction with the support than the localized Pt 5d states. Consequently, the Pt 6s,p states are affected the most, even though the Pt 5d states are shifted to lower binding energies for basic supports. Since the Pt 6s and p states are more important for chemisorption of H than for CH3 adsorption, it can be concluded that the influence of the support is less important for the chemisorption of CH3. 

Instead of c, for adsorption from the gas phase, it is custom to use the partial pressure. For that isotherm it has to be assumed (a) that a localized adsorption (i.e., finite and defined number of adsorption sites) takes place at an isotropic surface, (b) that the adsorbed particles do not interact with each other, and (c) that the maximum coverage is a monolayer of the adsorbed particles [iii]. About the importance of the Langmuir isotherm in electrochemistry see - adsorption isotherm. 

As predicted, at low loadings, argon and nitrogen are adsorbed in a very similar manner on pure Silicalite. Thus, in each case the adsorption energy remains almost constant until TV" = 20 molec uc 1. This suggests that localized adsorption is taking place with very little adsorbate-adsorbate interaction. The adsorbed molecules are mainly located in the channels and at a lower concentration in the intersections. 

More complicated models take into account lateral interaction between the adsorbed molecules. One of these models was designed by Fowler and Guggenheim. It assumes ideal adsorption on a set of the localized sites, with weak interactions among molecules adsorbed on neighboring sites. It also assumes that the energy of interactions between two adsorbed molecules is so small that the principle of random distribution of the adsorbed molecules on the sorbent surface is not significantly affected. For liquid-solid equilibria, the Fowler and Guggenheim isotherm is empirically extended and written in the form ... 

The next model, which assumes single-component localized monolayer adsorption with specific lateral interactions among all the adsorbed molecules, is the Kiselev model. The final equation of this model is... 

Quinones, I. Guiochon, G. Isotherm models for localized monolayers with lateral interactions. Application to singlecomponent and competitive adsorption data obtained in RP-HPLC. Langmuir 1996, 12, 5433-5443. 

With such a surface, covered with two different kinds of sites that behave independently (and on each of which the two basic principles of the Langmuir model, local adsorption and lack of adsorbate-adsorbate interactions, apply), the equilibrium isotherm results from the addition of the two independent contributions of the two types of sites [35]. Since in most cases the Langmuir isotherm is appropriate to account for single-component adsorption on a homogeneous surface (in practice if not in principle, see earlier), we have the following isotherm (see example in Figure 3.12.)... 

The conditions of validity of this isotherm model are the same as those of the competitive Langmuir isotherm, ideal behavior of the mobile phase and the adsorbed layer, localized adsorption, and equal column saturation capacities of both t3q>es of sites for the two components. The excellent results obtained with a simple isotherm model in the case of enantiomers can be explained by the conjunction of several favorable circumstances [26]. The interaction energy between two enantiomeric molecules in solutions is probably very close to the interaction energy between two R or two S molecules and their interactions with achiral solvents are... 

Since different models can be used to represent local adsorption on sites of the same adsorption energy, i.e., energetically homogeneous sites, the current review starts with the very popular and simplistic model formulated by Langmuir in 1918 [96]. This model describes localized monolayer adsorption by neglecting lateral attractive interactions in the surface phase and leads to the following expression for 0 ... 

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