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 < 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., PHPLC = 31.2% versus PSE-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.