Unifying sorption isotherms in reversed-phase liquid chromatography

The use of adsorption isotherm models has contributed to understanding retention in chromatography. However, the common isotherm models (such as Langmuir, BET, and GAB) assume site-specific, layer-by-layer adsorption on a uniform surface, which is at odds with the reality of chromatographic interfaces (heterogeneous surfaces with sorbate mobility and adsorption-partitioning duality). Our goal is to clarify the interactions underlying chromatographic retention while overcoming the above contradiction caused by the overly idealized or unrealistic assumptions of the traditional isotherm models. This can be achieved by the statistical thermodynamic fluctuation theory and the ABC isotherm derived from it, which is capable not only of capturing the mono-, di-, and tri-sorbate interactions as its parameters but also of encompassing the Langmuir, BET, GAB, and even anti-Langmuir isotherm models as its special cases. We demonstrate how the parameters from the traditional models can be reinterpreted via sorbate interactions. The sorbate-sorbate interaction plays a key role in elucidating the origin of different IUPAC isotherm types: Type I (convex upward) and Type III (convex downward) represent the opposite end of sorbate-sorbate repulsion and attraction that are independent of sorbate concentration, whereas Type II lies in-between, in which sorbate-sorbate interaction, which is repulsive at low concentration, turns attractive once sufficient quantity of sorbate is present at the interface (convex upward to convex downward).