Unmasking the Thermodynamic Void Volume in the Minor-Disturbance Method: Clarifying Its Physical Meaning and Relation...

The minor-disturbance method is a convenient route to adsorption isotherms, but the thermodynamic void volume extracted from its data is often taken-sometimes uncritically-to be the column's geometrical void. Here, we investigate the thermodynamic void volume using an adsorption-dividing-plane framework. This framework clarifies that the choice of any hold-up volume implicitly defines a Gibbs-like dividing surface, which in turn determines the thermodynamic meaning of the resulting isotherm. Experiments were performed on two contrasting media: a cyano-silica normal phase with C₂-C₄ alcohols and acetone, and an octyl-bonded reversed phase with acetonitrile, methanol, and acetone, each probed at 15 or more bulk concentrations. On the cyano column, all solutes yielded an identical thermodynamic void volume (≈2.98 mL), indicating the dividing plane aligns with the silica surface and the resulting isotherms represent true surface excess. In contrast, the thermodynamic void volume on the octyl-bonded column was solute-dependent (acetonitrile > acetone > methanol), reflecting probe-specific penetration into the bonded phase rather than the physical void volume. Negative branches observed in the high-concentration excess isotherms of acetonitrile and acetone are rationalized by a conceptual three-zone concentration profile in which brush-induced depletion exceeds interfacial adsorption. Reprocessing the reversed-phase data with a single, fixed void volume shifted the excess isotherms as predicted while leaving the total-uptake isotherms unchanged, demonstrating that total adsorption is independent of the definition of the excess dividing plane when the saturation point is used to define the dividing surface. The study clarifies the physical meaning of the thermodynamic void volume: it equals the geometrical void only for phases with negligible bonded layers, but becomes probe-specific on densely bonded reversed-phase materials, where it serves as a quantitative indicator of brush penetration. A fixed dividing plane is therefore essential for meaningful cross-solute comparison of excess isotherms and for reliable interpretation of minor-disturbance data.