Peak capacity and peak capacity per unit time in capillary and microchip zone electrophoresis.

The origins of the peak capacity concept are described and the important contributions to the development of that concept in chromatography and electrophoresis are reviewed. Whereas numerous quantitative expressions have been reported for one- and two-dimensional separations, most are focused on chromatographic separations and few, if any, quantitative unbiased expressions have been developed for capillary or microchip zone electrophoresis. Making the common assumption that longitudinal diffusion is the predominant source of zone broadening in capillary electrophoresis, analytical expressions for the peak capacity are derived, first in terms of migration time, diffusion coefficient, migration distance, and desired resolution, and then in terms of the remaining underlying fundamental parameters (electric field, electroosmotic and electrophoretic mobilities) that determine the migration time. The latter expressions clearly illustrate the direct square root dependence of peak capacity on electric field and migration distance and the inverse square root dependence on solute diffusion coefficient. Conditions that result in a high peak capacity will result in a low peak capacity per unit time and vice-versa. For a given symmetrical range of relative electrophoretic mobilities for co- and counter-electroosmotic species (cations and anions), the peak capacity increases with the square root of the electric field even as the temporal window narrows considerably, resulting in a significant reduction in analysis time. Over a broad relative electrophoretic mobility interval [-0.9, 0.9], an approximately two-fold greater amount of peak capacity can be generated for counter-electroosmotic species although it takes about five-fold longer to do so, consistent with the well-known bias in migration time and resolving power for co- and counter-electroosmotic species. The optimum lower bound of the relative electrophoretic mobility interval [µr,Z, µr,A] that provides the maximum peak capacity per unit time is a simple function of the upper bound, but its direct application is limited to samples with analytes whose electrophoretic mobilities can be varied independently of electroosmotic flow. For samples containing both co- and counter-electroosmotic ions whose electrophoretic mobilities cannot be easily manipulated, comparable levels of peak capacity and peak capacity per unit time for all ions can be obtained by adjusting the EOF to devote the same amount of time to the separation of each class of ions; this corresponds to µr,Z=-0.5.

Stochastic approach for an unbiased estimation of the probability of a successful separation in conventional chromatography and sequential elution liquid chromatography.

A stochastic approach was utilized to estimate the probability of a successful isocratic or gradient separation in conventional chromatography for numbers of sample components, peak capacities, and saturation factors ranging from 2 to 30, 20-300, and 0.017-1, respectively. The stochastic probabilities were obtained under conditions of (i) constant peak width ("gradient" conditions) and (ii) peak width increasing linearly with time ("isocratic/constant N" conditions). The isocratic and gradient probabilities obtained stochastically were compared with the probabilities predicted by Martin et al. [Anal. Chem., 58 (1986) 2200-2207] and Davis and Stoll [J. Chromatogr. A, (2014) 128-142]; for a given number of components and peak capacity the same trend is always observed: probability obtained with the isocratic stochastic approach