Generalized model of the linear theory of electromigration and its application to electrokinetic chromatography: Theory and software PeakMaster 6—Next Generation

Abstract

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.

Determination of thermodynamic acidity constants and limiting ionic mobilities of weak electrolytes by capillary electrophoresis using a new free software AnglerFish

“…Our group introduced two software tools for the simulation and prediction of electromigration behavior and for method development–PeakMaster and Simul . Both tools use as the input data the set of limiting ionic mobilities and thermodynamic pKa constants, which is known as the Hirokawa database .…”

The dynamics of band (peak) shape development in capillary zone electrophoresis in light of the linear theory of electromigration

“…We prefer the terminology of “constituents” and their “forms” as it can be dated back to a paper by Alberty in 1950 . We provide a detailed commentary on the perception of constituents and forms in a separate paper in this special issue , where we also examine general equilibria that exist in electrophoretic systems such as in electrokinetic chromatography (EKC) ones. We limit our discussion to simple acid–base equilibria in this paper.…”

“…Additionally, Svensson pointed out that acid–base equilibria can be viewed as complex formation equilibria between various forms of weak electrolyte constituents and water ions, similarly to other possible complex‐formation equilibria between a constituent and other constituent(s), including non‐electrolytes, provided all of the reactions involved are fast enough. Although we are not aware of an explicit proof of this statement in MBE, its validity has been proven very recently in our group in the context of the EKC systems .…”

“…Štědrý, Gaš et al extensively developed this idea into LTEM for strong and weak electrolytes later . We completed the theory very recently by extending it to CZE systems with fast equilibria in general, e.g., to EKC, and we are publishing the results in a separate paper in this special issue . Therefore, we refer the reader to that paper for detailed description of LTEM while we summarize a few points relevant for our present discussion below.…”

“…We refer to this theory as the first‐order nonlinear theory of electromigration (NLTEM). An interested reader can find a thorough analysis of NLTEM in the other paper published in this special issue . In Eq.…”