Self-consistent determination of hold-up volume in normal-phase liquid chromatography: A dividing-plane framework for adsorption isotherm interpretation.

The determination of total adsorption isotherms in liquid chromatography is fundamentally sensitive to the definition of the hold-up volume (VL'), which implicitly fixes the Gibbs-like dividing plane between the mobile and stationary phases. Conventional approaches often rely on arbitrary dead-time markers, leading to inconsistencies between excess and total adsorption quantities and potentially inducing artificial saturation artifacts in model fitting. To resolve this ambiguity, this study establishes a self-consistent dividing-plane framework coupled with affinity energy distribution analysis. Using minor disturbance method data for homologous alcohols (ethanol to butanol) on a cyano-silica column, we propose an iterative approach that adjusts the dividing plane until the model-derived isotherm slope reconciles with experimental perturbation times. This approach robustly deconvolutes the adsorption landscape into two distinct contributions: a high-affinity family (sites B) governing specific hydrogen-bonding interactions at the ligand surface, and a low-affinity family (sites A) representing non-specific solute accumulation within the diffuse interfacial region. Thermodynamic analysis further validates this mechanism, revealing that sites B exhibit a strongly exothermic enthalpy of adsorption (ΔH0≈-35 kJ/mol for 2-propanol), whereas sites A are energetically weaker and geometrically sensitive to the choice of the dividing plane. By strictly defining the reference state, this framework offers a rigorous route to separate specific binding from interfacial accumulation, yielding adsorption parameters that are physically interpretable and thermodynamically consistent.