Stochastic simulation of reactive separations in capillary electrophoresis

Abstract

A stochastic (Monte Carlo) simulation is used to investigate thermodynamic and kinetic contributions from the reversible A <--> B reaction in capillary electrophoresis (CE). The effects of equilibrium constant, rate constant, and electrophoretic mobility on the molecular zone profiles and the corresponding statistical moments are evaluated. As the reaction approaches steady state, the velocity of the zone is governed by the equilibrium constant and the electrophoretic mobilities of the reacting molecules. When the equilibrium constant is less than unity, the mean zone velocity is more similar to that of the reactant A. Conversely, when the equilibrium constant is greater than unity, the velocity is more similar to that of the product B. The extent of zone-broadening and asymmetry at steady state is dependent upon the equilibrium constant, the characteristic reaction lifetime, and the electrophoretic mobility difference between reacting molecules. If all other parameters are held constant, the plate height is greatest and skew is least when the equilibrium constant is unity. The plate height increases linearly with the characteristic reaction lifetime and electrophoretic mobility difference, whereas the skew is independent of these parameters. These conclusions have important implications for the elucidation of thermodynamic and kinetic information from experimental data.

Advances in CE for kinetic studies

“…The second of these time scales is that in which only a single, broad peak is observed. This regime is indicative of reactions that are sufficiently rapid relative to the experimental time scale that they are detected at or near steady state [19]. Figure 2 illustrates the experimental time scales employed to evaluate rate constants from first-order reactions and identifies, as well as summarizes, the experimental conditions for each of the methods discussed in this section.…”

Effects of nonequilibrium on velocity and plate height in reactive capillary electrophoresis

“…This means that the ability to experimentally access a broad range of rate constants is facilitated by increasing the applied voltage, by decreasing the column length, or by both. Figure 2B is a graph of plate height as a function of electroosmotic velocity for a range of mobility differences (2.00610 25 …”

“…The equations described in this manuscript are developed under the rubric of Giddings' generalized nonequilibrium theory for chromatography [30] and are validated with an independently developed stochastic (Monte Carlo) simulation [25,[31][32][33][34][35]. These equations show that velocity is directly dependent on the equilibrium constant, whereas plate height is inversely proportional to rate constant.…”

“…Consequently, the velocity of the reactive zone is dependent upon the extent of reaction (thermodynamic equilibrium constant), whereas zone-broadening is dependent upon both the extent and rates of reaction (kinetic rate constant) [25]. Some estimates of equilibrium constants and rate constants have been performed via computer modeling of electropherograms [8,20,23]; however, most have been calculated from peak parameters such as peak height, peak area, and migration time [6-9, 13-19, 22].…”

Dynamic computer simulations of electrophoresis: A versatile research and teaching tool

“…Other models with dynamic character can be found in the literature, including a 3-D stochastic simulation model for CE in the presence of electroosmosis [80], for reactive separations in CE [81,82] and for capillary electrochromatographic separations in the presence of electroosmosis and laminar flow [83]. In contrast to the dynamic models referred to above, this approach is based upon the modeling of the trajectories of each individual molecule, requires extremely powerful computers in order to compute the motion of a statistically significant number of molecules and is not further considered in this review.…”