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The size-exclusion separation of a water-soluble polyelectrolyte polymer, sodium polystyrene sulfonate (NaPSS), was demonstrated on common reversed-phase (C 18, C 4 , phenyl, and cyano) and hydrophilic interaction chromatography (HILIC) columns. The effect of common solvents – acetonitrile (ACN), tetrahydrofuran (THF), and methanol (MeOH), used as mobile phase modifiers – on the elution of NaPSS and the effect of column temperature (within a relatively narrow range corresponding to typical chromatographic conditions, i.e. , 10 °C–60 °C) on the partition coefficient, K S E C , were also investigated. Non-size-exclusion chromatography (non-SEC) effects can be minimized by the addition of an electrolyte and an organic modifier to the mobile phase, and by increasing the column temperature ( e.g., to 50 °C or 60 °C). Strong solvents such as THF and ACN are more successful in the reduction of such effects than is the weaker solvent MeOH. The best performance is seen on medium polarity and polar stationary phases, such as cyanopropyl- and diol-modified silica (HILIC), where the elution of the NaPSS polyelectrolyte is by a near-ideal SEC mechanism. Hydrophobic stationary phases, such as C 18 , C 4 , and phenyl, require a higher concentration of a strong solvent modifier (THF) in the mobile phase to reduce non-SEC interactions of the solute with the stationary phase. [ABSTRACT FROM AUTHOR]

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 [μ r,Z , μ r,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 μ r,Z = −0.5. [ABSTRACT FROM AUTHOR]

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 < probability obtained with the gradient stochastic approach ≤ probability predicted by Davis and Stoll << probability predicted by Martin et al. The differences are explained by the positive bias of the Martin equation and the lower average resolution observed for the isocratic simulations compared to the gradient simulations with the same peak capacity. When the stochastic results are applied to conventional HPLC and sequential elution liquid chromatography (SE-LC), the latter is shown to provide much greater probabilities of success for moderately complex samples (e.g., P HPLC = 31.2% versus P SE-LC = 69.1% for 12 components and the same analysis time). For a given number of components, the density of probability data provided over the range of peak capacities is sufficient to allow accurate interpolation of probabilities for peak capacities not reported, <1.5% error for saturation factors <0.20. Additional applications for the stochastic approach include isothermal and programmed-temperature gas chromatography. [ABSTRACT FROM AUTHOR]