Model of electromigration
Dotaz
Zobrazit nápovědu
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.
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 β-cyclodextrin and monovalent positively charged 6-monodeoxy-6-monoamino-β-cyclodextrin) serve as a model system.
The continuity equations that describe the movement of ions in liquid solutions under the influence of an external stationary electric field, as it is utilized in electrophoresis, were introduced a long time ago starting with Kohlrausch in 1897. From that time on, there have been many attempts to solve the equations and to discuss the results. In electrophoresis, special attention has always been devoted to the peak shapes obtained by the detector since the shapes have a tight connection with the phenomena taking place during electromigration and influence the efficiency and selectivity of the separation. Among these phenomena, the most important is electromigration dispersion. In this commented review paper, we compare various models of electromigration, try to find points that connect them, and discuss the range of their validity in light of the linear and nonlinear theory of electromigration.
The linear theory of electromigration, including the first-order nonlinear approximation, is generalized to systems with any equilibria fast enough to be considered instantaneous in comparison with the timescale of peak movement. For example, this theory is practically applied in the electrokinetic chromatography (EKC) mode of the CZE. The model enables the calculation of positions and shapes of analyte and system peaks without restricting the number of selectors, the complexation stoichiometry, or simultaneous acid-base equilibria. The latest version of our PeakMaster software, PeakMaster 6-Next Generation, implements the theory in a user-friendly way. It is a free and open-source software that performs all calculations and shows the properties of the background electrolyte and the expected electropherogram within a few seconds. In this paper, we mathematically derive the model, discuss its applicability to EKC systems, and introduce the PeakMaster 6 software.
We discuss several possible phenomena in electrophoretic systems with complexing agents present in the background electrolyte. In our previous work, we extended the linear theory of electromigration with the first-order nonlinear term, which originally applied to acid-base equilibria only, by generalizing it to any fast chemical equilibria. This extension provides us with a fresh insight into the well-established technique of elecktrokinetic chromatography (EKC). We combine mathematical analysis of the generalized model with its solution by means of the new version of our software PeakMaster 6, and experimental data. We re-examine the fundamental equations by Wren and Rowe and Tiselius in the frame of the generalized linear theory of electromigration. Besides, we show that selector concentration can increase inside the interacting-analyte zone due to its complexation with the analyte, which contradicts the generally accepted idea of a consumption of a portion of the selector inside the zone. Next, we focus our discussion on interacting buffers (i.e., buffer constituents that form a complex with the selector). We demonstrate how such side-interaction of the selector with another buffer constituent can influence measuring analyte-selector interactions. Finally, we describe occurrence and mobilities of system peaks in these EKC systems. We investigate systems with fully charged analytes and neutral cyclodextrins as selectors. Although the theory is not limited in terms of the charge and/or the degree of (de)protonation of any constituent, this setup allows us to find analytical solutions to generalized model under approximate, yet realistic, conditions and to demonstrate all important phenomena that may occur in EKC systems. An occurrence of system peaks in a system with fully charged selector is also investigated.
This contribution introduces a new separation principle in CE which offers focusing of weak nonamphoteric ionogenic species and their inherent transport to the detector. The prerequisite condition for application of this principle is the existence of an inverse electromigration dispersion profile, i.e. a profile where pH is decreasing toward the anode or cathode for focusing of anionic or cationic weak analytes, respectively. The theory presented defines the principal conditions under which an analyte is focused on a profile of this type. Since electromigration dispersion profiles are migrating ones, the new principle offers inherent transport of focused analytes into the detection cell. The focusing principle described utilizes a mechanism different from both CZE (where separation is based on the difference in mobilities) and IEF (where separation is based on difference in pI), and hence, offers another separation dimension in CE. The new principle and its theory presented here are supplemented by convincing experiments as their proof.
This paper deals with unwanted effects of carbonate in capillary zone electrophoretic analyses of anions in alkaline BGEs with indirect UV absorption and conductivity detection. Computer simulations and experimental study of selected model systems have shown that carbon dioxide absorbed from air into BGEs and samples induce important electrophoretic effects like formation of new additional zones and/or boundaries that may further induce strong and pronounced temporary changes in the migration of analytes. Examples are reduction of the pH of alkaline BGEs around pH 11 by up to 1 unit or formation of a pronounced detectable carbon dioxide peak comparable with peaks of analytes at 1 mM level. The higher the pH of the BGE, the stronger these effects and the broader their spectrum, involving (i) changes of effective mobilities and selectivity due to changes in pH of the BGE, (ii) occurrence of additional system zones appearing in form of peaks, dips or more complex disturbances in the detection signal, (iii) temporary interactions with the sample components and subsequent modification of the separation process and of its result. This paper reveals all these effects and brings the knowledge necessary to prevent problems with qualitative and quantitative evaluation of the analysis results.
Electrophoretic focusing on inverse electromigration dispersion (EMD) gradient is a new analytical technique based on a unique separation principle where weak non-amphoteric ionogenic species are focused, separated and transported to the detector by an EMD profile of suitable properties. The present work extends the theoretical description of this method by introducing the concept of resolution and deriving the fundamental equation expressing resolution as function of basic system parameters. The results indicate that at constant current operation, resolution is proportional to the square root of time. For variable current regimes (e.g. constant voltage), the time variable is replaced by the product of electric current and passed electric charge. Computer simulations for a model pair of substances support the validity of the presented theory and confirm the theoretical conclusion that resolution can be increased by allowing longer electromigration of the gradient in terms of time or passed charge. The experimental example shown comprises an anionic electrolyte system based on maleic acid and 2,6-lutidine, combined with ESI-MS detection and operated in the reverse mode due to strong electroosmotic flow and ESI suction. The practical implementation of the proposed methodology is done by application of negative pressure at the inlet vial, resulting in very substantial resolution enhancement and baseline separation of otherwise unresolved substances. The performance and high sensitivity of the developed technique is demonstrated on the example of simultaneous analysis of four sulfonamides and three dichlorophenols in waters with limits of detection on the 1 nM level.
- MeSH
- chlorfenoly analýza MeSH
- elektroforéza kapilární MeSH
- elektrolyty chemie MeSH
- hmotnostní spektrometrie s elektrosprejovou ionizací * MeSH
- limita detekce MeSH
- maleáty chemie MeSH
- pitná voda analýza MeSH
- pyridiny chemie MeSH
- sulfonamidy analýza MeSH
- tlak MeSH
- Publikační typ
- časopisecké články MeSH
The complete mathematical model of electromigration dispersion in systems that contain a neutral complex forming agent and a fully charged analyte was introduced in the previous part of this series of papers (Part III - Theory). The model was implemented in the newest version of our simulation program PeakMaster 5.3 that calculates the effective mobility of the analyte and its nonlinear electromigration mobility slope, S(EMD), in the presence of a complex forming agent in the background electrolyte. The mathematical model was verified by both experiments and simulations, which were performed by our dynamic simulator Simul 5 Complex. Three separation systems differing in the chiral selector used (having different values for the complexation constant and the mobility of the complex) were chosen for the verification. The nonlinear electromigration mobility slope values were calculated from the simulations and the experiments that were performed at different complex forming agent concentrations. These data agree very well with those predicted by the mathematical model and provided the foundation for the discussion and explanation of the electromigration dispersion process that occurs in systems which contain a complex forming agent. The new version of PeakMaster 5.3 was shown to be a powerful tool for optimization of the separation conditions by minimizing electromigration dispersion which improves the symmetry of the analyte peaks and their resolution.
