Physicochemical ion-exchange model

The physicochemical phenomena of RPIPC, the basis for the retention mechanism, are still not fully understood. This mechanistic uncertainty is reflected by the many terms proposed for this kind of separation method in the past Here, we discuss two hypotheses, although both of them lack an unequivocal experimental basis. Horvath et al. [6,7] take the view that solute ions form neutral ion pairs with the hpophilic ions in the aqueous mobile phase. These neutral ion pairs are retained at the nonpolar stationary phase. In contrast, Huber et al, Hoffmann and Liao, and Kissinger [8-10] support the ion-exchange model, where the hpophihc reagent first adsorbs at the surface of the stationary phase. 

Note that the physicochemical mechanisms that enables us to perform the chromatographic bioseparations are not always adsorption-like but can involve ion exchange, ion exclusion, or size exclusion. Even if it is generally possible to fit experimental data with a mathematical function derived from the adsorption theory, it is strongly advisable to refer to the proper physicochemical process before modeling the separation. For instance, ion exchange can be modeled with selectivity coefficients (derived from the mass action law) that can be constant or not,18,19 ion-exclusion can be modeled thanks to theories based on the Donnan exclusion, etc. 

Contrary to empirical approaches, a fundamental approach has value in that the results demonstrate the validity or otherwise of a particular mechanism or model chosen for the system. For example, the application of thermodynamics to an ion exchange system does not necessarily require the setting up of a physicochemical model, but eventually the results must still be interpreted in terms of the molecular forces acting within the system. Selected molecular models enable the mechanisms of ion exchange phenomena to be better interpreted, but their success must be measured in terms of predicted accuracy which in turn depends upon the validity of the model and the accessibility of the various molecular parameters. Ideally, the mathematical equations describing the perfect model would contain quantities which were derived from the known fundamental data for the components of the system. 

A review of some leading semiempirical models precedes examination of physicochemical modeling of ion exchange. Such models will likely be used for the foreseeable future to describe ion-exchange phenomena in complex svstems. Thus, they represent the reference point for development of improved models. Methods of incorporating the semiempirical ion-exchange equations in general chemical equilibrium models are also described. 

Substantial efforts have been made to develop physicochemical models for ion exchange based on the Gouy-Chapman diffuse-layer theory (e.g., 9, 10). This work not only has provided insight into the role of diffuse-layer sorption in the ion-exchange process but also has pointed to the need to consider other factors, especially specific sorption at the surface. Consideration of specific sorption enables description of the different tendencies of ions to... 

Several physicochemical models of ion exchange that link diffuse-layer theory and various models of surface adsorption exist (9, 10, 14, 15). The difficulty in calculating the diffuse-layer sorption in the presence of mixed electrolytes by using analytical methods, and the sometimes over simplified representation of surface sorption have hindered the development and application of these models. The advances in numerical solution techniques and representations of surface chemical reactions embodied in modem surface complexation mod-... 

To demonstrate the physicochemical modeling of ion exchange via an extended surface complexation model, we consider an aqueous system containing a mineral solid that bears fixed- and variable-charge sites. As seen in Figure 6, the mineral-water interface is represented by a simple two-layer... 

Physicochemical models of partitioning at the solid-water interface, such as that used here to model ion exchange, require detailed knowledge about the particles. The surface properties of the mineral phases present, as well as equilibrium constants for ion binding to both fixed and variable charge sites associated with each phase, are required. These data requirements and the uncertainty about modeling sorption in mixtures of minerals (e.g., 48-50) make such models difficult to apply to complex natural systems. This is especially the case for modeling solute transport in soil-water systems, which... 

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