Microscopic models of liquid chromatography: From ensemble-averaged information to resolution of fundamental viewpoint at single-molecule level

• The microscopic stochastic theory of chromatography is revisited.
• The capability of this theory to handle discrete adsorption frequency distributions is discussed.
• Discrete adsorption frequency distributions are gathered by single-molecule studies.
• Modeling of rare events at molecular viewpoint provides new fundamental information.
• Examples of new insights into solid–liquid interfacial processes are discussed.

In this study, a microscopic probabilistic model of chromatography that establishes a conceptual link between single-molecule dynamics observation at liquid–solid interfaces and chromatographic experiments is described. This model is based on the discrete Lévy representation of stochastic processes and has the great advantage that it can be directly applied to the raw data set of single-molecule observations. The information contained in the molecular measurements includes some erratic rare events that are potentially very informative. Because experimental data need not be processed by mathematical–statistical transformation, application of this model preserves all the information that could be lost in an ensemble-averaged representation. In this approach, single-molecule experiments and stochastic interpretation are combined. It is of great importance to investigate superficial and interfacial phenomena in different areas, such as adsorption mechanisms in chromatography and mechanisms of biological activity, and to track the behavior of individual molecules in living cells.