Hybrid Micellar Systems

The addition of an organic modifier to a micellar solution can modify the characteristics of the micellar system (c.m.c. and the aggregation number). This can cause a variation of the solute-micelle interactions that, in turn, can change the chromatographic retention. On the one hand, a high concentration of alcohol can destroy the micellar structure, but on the other hand, the alcohol modifies the structure and composition of the stationary phase because it sol-vates the bonded hydrocarbon chain. Logically, the separation mechanism with the so-called hybrid mobile phases (micellar phases modified by alcohols) should be more similar to that for conventional aqueous-organic mobile phases than for purely aqueous micellar phases. However, if the integrity of the micelles remains, the addition of an alcohol to micel-lar mobile phases will not create an aqueous-organic system.

Both physicochemical and empirical models have been developed to describe the retention of solutes with hybrid mobile phases.

Physicochemical models Equation [5] (Table 1), which relates a solute retention factor with the micel-lized surfactant and alcohol concentrations, can be considered an extension of eqn [2]. This model considers the modification of stationary phase sites and micelle concentration due to the presence of an alcohol, that is, the alcohol can compete with the solute for interaction with the stationary phase and micelles. [AM] is the alcohol concentration in the mobile phase, and K3 and K4 are the association constants of the alcohol with the modified stationary phase and the micellar mobile phase, respectively. Based on the value of these constants and alcohol concentration, some simplified equations can be obtained. This model can predict a nonlinear, linear or quadratic variation of the retention factor with the alcohol concentration in the mobile phase (when micellized surfactant concentration is constant) and a linear variation of the inverse of retention factor with the micellized surfactant concentration (when alcohol concentration remains constant).

Empirical equations These models have no chemical background but are very valuable tools for predicting solute retention as a function of different variables. Among the different empirical equations reported in literature, models can be found relating solute retention to: (1) the organic modifier concentration, and (2) organic modifier and surfactant concentrations.

Empirical equations relating solute retention in MLC to organic modifier concentration Equation [6] (Table 1) is the simplest model relating the retention factor to the organic modifier concentration when surfactant concentration is constant. p is the volume fraction of the organic modifier, S the eluent-strength parameter, and k0 the retention factor in the absence of the organic modifier. Although this model can explain the decrease in solute retention observed in the presence of organic modifiers, deviations from linearity can be seen and some significant differences are obtained between the intercept and the experimental retention factor in the absence of an organic modifier. From an experimental viewpoint, its applicability is limited because the variation of the surfactant concentration is not considered.

Empirical equations relating solute retention in MLC to organic modifier and surfactant concentrations Equations have been obtained relating the logarithm of the retention factor to the volume fraction of the organic modifier (p) and to the total surfactant concentration in the mobile phase (u), but their applicability is limited. Other models have been proposed relating the inverse of the retention factor with these two variables and these, from which eqns [7] and [8] (Table 1) are examples, have shown a more general application range.

An extension of the iterative regression optimization strategy to multiparameter optimizations for the separation of ionic compounds in MLC has also been reported. The parameters examined are surfactant concentration, alcohol concentration and pH. Fairly regular (linear, weakly curved) retention behaviour of compounds as a function of the parameters results in an efficient optimization using a relatively small number of initial experiments.

All the models presented above require a mathematical equation, derived from chemical considerations, or are empirical in nature, but there are other methods that, although also empirical, do not have such requirements; these are artificial neural networks (ANNs). Although ANNs have been known for years, they have been applied only recently to model retention in MLC with hybrid eluents. ANNs are a very promising alternative to classical statistical methods for retention modelling studies in MLC.

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