Single-molecule observation and chromatography unified by Lévy process representation

A renewed stochastic model of chromatography is proposed able to establish a conceptual link between the single-molecule dynamics observations in a given chromatographic system and chromatographic experiment results in the same media. The chromatographic peak is expressed through its Fourier transform as a function of the experimental sorption time distribution. The pertinent numerical procedure necessary for obtaining the chromatographic peak is described, and the numerical programming code is given. Two types of cases were considered, the first one where the sole discrete sorption time distribution is available, and the second one where the adsorption mechanism is made of a mixture of continuous and discrete sorption time distributions. The method is applied to experimental data found in the literature by determining typical chromatographic peak shapes on the basis of the experimental interface adsorption data. This renewed stochastic approach is based on the so-called Levy canonical description of stochastic processes and appears to be the most general basis for handling separation processes from a stochastic point of view.