Lateral interactions analyte molecules

The extension of the potential theory was studied by Bering et al (1963), Doong and Yang (1988) and Mehta and Dannes (1985) to multicomponent systems. We shall present below a brief account of a potential theory put forward by Doong and Yang (1988). The approach is simple in concept, and it results in analytical solution for the multicomponent adsorption isotherm. The basic assumption of their model is that there is no lateral interaction between molecules of different types and pure component isotherm data are described by the DA equation. With this assumption, the parameters of the DA equation (Wq, Eq, n) of each species are not affected by the presence of the other species, but the volume available for each species is reduced. This means that the volume available for the species i is ... 

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). 

When the amount of the sample is comparable to the adsorption capacity of the zone of the column the migrating molecules occupy, the analyte molecules compete for adsorption on the surface of the stationary phase. The molecules disturb the adsorption of other molecules, and that phenomenon is normally taken into account by nonlinear adsorption isotherms. The nonlinear adsorption isotherm arises from the fact that the equilibrium concentrations of the solute molecules in the stationary and the mobile phases are not directly proportional. The stationary phase has a finite adsorption capacity lateral interactions may arise between molecules in the adsorbed layer, and those lead to nonlinear isotherms. If we work in the concentration range where the isotherms are nonlinear, we arrive to the field of nonlinear chromatography where thermodynamics controls the peak shapes. The retention time, selectivity, plate number, peak width, and peak shape are no longer constant but depend on the sample size and several other factors. 

Satisfactory qualitative agreement between experimental and theoretical concentration profiles for polar analytes suggests their retention is substantially affected by lateral interactions, which are probably even more complex than is assumed in this isotherm model. Overlapping of the adsorption fronts can be explained solely on the basis of the lateral interactions among the adsorbed molecules. 

Thus, including the lateral interactions between adsorbed molecules does not change the analytical form of the Elovich equation but does change the parameters of the equation. Deviations from the Elovich equation at higher surface coverages cannot, therefore, be attributed to lateral interactions between adsorbed molecules. Apart from peculiarities of some adsorption systems, the most probable source of these deviations may therefore be the neglect of the simultaneous desorption rate, i.e., the term Rj in Eq. (4). 

The site energy distribution function f Q) can be calculated by using the experimentally observed overall isotherm (p,T) and a theoretical local isotherm function d(p,T,Q). Here a Langmuir type model equation 9(p,T,Q) with corrections for multilayer adsorption and lateral interactions between the adsorbed molecules is chosen [54—56]. Then the integral equation can be solved by an analytical iterative method based on numerical integration [57]. More details about this procedure are found in [22,53]. 

Indeed, some of the eluted molecules that are not ionized can be adsorbed on the metallic surfaces of electrodes within the ion trap. During the desorption that occurs a few moments later (interactions with the surface are more or less strong), these molecules are ionized. These are the ions formed after the elution of the analyte in the source that are responsible for the tailing of the chromatographic peak. 

---