Twenty years of development of dual and multi‐selector models in capillary electrophoresis: A review

Abstract

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.

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

“…Since the individual mobilities of the free analyte forms, i0 , as well as that of the analyte-selector complexes, ij , depend on the viscosity to the same extend, Eqs. (24) and (25) guarantee that the same correction applies to the M A M Soverall effective mobilities. pH is kept constant using BGEs with defined pH and a sufficient buffer capacity.…”

“…(21) reveals that the previously published models of electromigration in the presence of selector(s) [25] are naturally included in the M A M S -overall model. Eq.…”

“…Following the approach described by the group of Rawjee, Williams and Vigh [8], the same formula results for the effective charge of the analyte, z eff , as for the effective mobility, Eqs. (22)- (25), if every mobility is replaced by the respective charge.…”

“…(4) in 1994. This equation has then become a basis for further method optimization in the dual-selector systems, predominantly in enantioseparations [25]. Similarly to the pH-overall model, Kranack et al [26] and later us [27] have shown that, effective mobility of an analyte (present in a single free form) interacting with a mixture of selectors can be expressed in a form of the S A S S Eq.…”

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

“…Along with their increasing applications in analytical chemistry, theoretical models have been developed describing the electromigration of fully dissociated, neutral, or partly dissociated analytes interacting with one selector [10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Several models dealing with dual-and multi-selector systems have also been published [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] (we recently summarized them in a review [41]). However none of these models takes into account the possible protonation equilibria of the analyte along with its simultaneous interaction with multiple selectors.…”