Determination of relative enantiomer migration order using a racemic sample.

We developed a method that enables us to distinguish between the same or the opposite enantiomer migration order (EMO) of two enantiomers of a chiral compound with two different selectors. The method is applicable to racemic samples and thus a standard of the pure enantiomeric form(s) is not required. First, complexation constants and mobilities of complexes of the two enantiomers with the first and second selector are determined. However, for a racemic sample it is not possible to deduce whether the first migrating enantiomer with one selector is the same one as the first migrating enantiomer with the second selector. A specific mixture of the two selectors is designed to resolve this. In case the two enantiomers exhibit the same, respectively the opposite EMO in the two selectors, the mixture does, respectively does not separate the racemic sample. Thus two peaks are detected in the first case, while a single coalescent peak is recorded in the opposite case. We demonstrate the method on a racemic sample of amphetamine. Its relative EMO is determined with three cyclodextrins, heptakis(2,3,6-tri-O-methyl)-ß-cyclodextrin, (2-hydroxypropyl)-ß-cyclodextrin and heptakis(2,3-di-O-acetyl-6-O-sulfo)-ß-cyclodextrin.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part II. Application to dual systems and experimental verification.

Interactions among analyte forms that undergo simultaneous dissociation/protonation and complexation with multiple selectors take the shape of a highly interconnected multi-equilibrium scheme. This makes it difficult to express the effective mobility of the analyte in these systems, which are often encountered in electrophoretical separations, unless a generalized model is introduced. In the first part of this series, we presented the theory of electromigration of a multivalent weakly acidic/basic/amphoteric analyte undergoing complexation with a mixture of an arbitrary number of selectors. In this work we demonstrate the validity of this concept experimentally. The theory leads to three useful perspectives, each of which is closely related to the one originally formulated for simpler systems. If pH, IS and the selector mixture composition are all kept constant, the system is treated as if only a single analyte form interacted with a single selector. If the pH changes at constant IS and mixture composition, the already well-established models of a weakly acidic/basic analyte interacting with a single selector can be employed. Varying the mixture composition at constant IS and pH leads to a situation where virtually a single analyte form interacts with a mixture of selectors. We show how to switch between the three perspectives in practice and confirm that they can be employed interchangeably according to the specific needs by measurements performed in single- and dual-selector systems at a pH where the analyte is fully dissociated, partly dissociated or fully protonated. Weak monoprotic analyte (R-flurbiprofen) and two selectors (native ß-cyclodextrin and monovalent positively charged 6-monodeoxy-6-monoamino-ß-cyclodextrin) serve as a model system.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part I. Theory.

The model of electromigration of a multivalent weak acidic/basic/amphoteric analyte that undergoes complexation with a mixture of selectors is introduced. The model provides an extension of the series of models starting with the single-selector model without dissociation by Wren and Rowe in 1992, continuing with the monovalent weak analyte/single-selector model by Rawjee, Williams and Vigh in 1993 and that by Lelièvre in 1994, and ending with the multi-selector overall model without dissociation developed by our group in 2008. The new multivalent analyte multi-selector model shows that the effective mobility of the analyte obeys the original Wren and Row's formula. The overall complexation constant, mobility of the free analyte and mobility of complex can be measured and used in a standard way. The mathematical expressions for the overall parameters are provided. We further demonstrate mathematically that the pH dependent parameters for weak analytes can be simply used as an input into the multi-selector overall model and, in reverse, the multi-selector overall parameters can serve as an input into the pH-dependent models for the weak analytes. These findings can greatly simplify the rationale method development in analytical electrophoresis, specifically enantioseparations.

Determination of the correct migration time and other parameters of the Haarhoff-van der Linde function from the peak geometry characteristics.

For Gaussian peaks, the migration time of the analyte results as the position of the top of the peak and the zone variance is proportional to the peak width. Similar relations have not yet been derived for the Haarhoff-van der Linde (HVL) function, which appears as a fundamental peak-shape function in electrophoresis. We derive the relations between the geometrical measures of the HVL-shaped peak, that is the position of its maximum, its width and a measure of its asymmetry, and the respective parameters a1, a2, and a3, of the corresponding HVL function. Under the condition of the HVL-shaped peak, the a1 parameter reflects the true migration time of the analyte, which may differ from the peak top position significantly. Our procedure allows us to express the parameters without the need of any external data processing (nonlinear regression). We demonstrate our approach on simulated peaks and on experimental data integrated by the ChemStation software (delivered with the CE instrumentation by Agilent Technologies). A significant improvement is achieved reading the migration time of the experimental and simulated peaks, which draws the error of the HVL-shaped peak migration time evaluation down to the resolution of the data sampling rate.

Twenty years of development of dual and multi-selector models in capillary electrophoresis: a review.

It has been 20 years since Lurie et al. first published their model of electromigration of an analyte under simultaneous interaction with two cyclodextrins as chiral selectors. Since then, the theory of (enantio)separation in dual and complex mixtures of (chiral) selectors is well understood. In spite of this, a trial-and-error approach still prevails in analytical practice. Such a situation is likely caused by the fact that the entire theory is spread over numerous papers and the relations between various models are not always clear. The present review condenses the theory for the first time. Available mathematical models and feasible practical approaches are summarized and their advantages and limitations discussed.

Separation efficiency of dual-selector systems in capillary electrophoresis.

We introduce an easy but highly descriptive model of separation efficiency of dual-selector systems in capillary electrophoresis. The model expresses effective mobilities of analytes in dual-selector mixtures as a function of mixture composition and total concentration. The effective mobility follows the pattern familiar from single-selector systems, while complexation constant and mobility of the complex are replaced by the same but "overall" parameters and a total concentration of the mixture takes the role of a selector concentration. The overall parameters can be either calculated from the individual ones (an arbitrary mixture) or measured directly (a particular mixture). We inspected two model dual-selector systems consisting of heptakis(2,6-di-O-methyl)-ß-CD and ß-CD and of heptakis(2,6-di-O-methyl)-ß-CD and 6-O-α-maltosyl-ß-CD, and ibuprofen and flurbiprofen as model analytes (pH 8.2, non-enantioselective separation). Adopting any optimization strategy typically used in single-selector systems and finding an optimal mixture composition and total concentration is perhaps the prime benefit of the model. We demonstrate this approach on the selectivity parameter and show that the model is precise enough to be used in analytical practice. It also results that an electromigration order (reversal) of analytes can exhibit a rather curious dependency on the mixture composition and concentration. Last, the model can be used for better understanding of separation principles in dual-selector systems in general.

Determination of effective mobilities of EOF markers in BGE containing sulfated ß-cyclodextrin by a two-detector method.

A neutral marker of the EOF can gain a nonzero effective mobility because of its possible interaction with a charged complexing agent, such as a chiral selector in CE. We determined effective mobilities of four compounds often used as EOF markers (dimethyl sulfoxide, mesityl oxide, nitromethane, and thiourea) in the BGE-containing sulfated ß-CD (60 g/L). All the compounds studied were measurably mobilized by their interaction with the selector. The highest effective mobility (-3.0·10(-9) m(2) s(-1) V(-1)) was observed for thiourea and the lowest (-1.5·10(-9) m(2) s(-1) V(-1)) for dimethyl sulfoxide and nitromethane. The mobilities were determined by a new two-detector pressure mobilization method (2d method), which we propose, and the results were confirmed by standard CE measurements. In the 2d method, one marker zone is situated in the BGE containing the charged selector, while the second marker zone is surrounded with a selector-free BGE, which prevents its complexation. The initial distance between the two marker zones equals the capillary length from the inlet to the first detector. After a brief voltage application, the final distance between the marker zones is determined based on known capillary length from the first to the second detector. The difference between these two distances determines the effective mobility.