A dividing-plane interpretation of thermodynamic void volume in reversed-phase liquid chromatography from PS-DVB and...

Accurate adsorption isotherms in liquid chromatography require an operational definition of the mobile-stationary phase boundary, which is commonly embedded in the hold-up (void) volume. In the minor-disturbance method (MDM), the corresponding thermodynamic void volume V_th​ is often interpreted as a substitute for the true liquid volume; however, in reversed-phase systems V_th​ can depend on the probe adsorbate, implying an underlying reference-state ambiguity. Here we investigate the physical meaning of V_th​ in reversed-phase liquid chromatography by applying MDM to methanol (MeOH), acetonitrile (MeCN), and acetone (ACE) on a highly cross-linked polymeric poly(styrene-divinylbenzene) (PS-DVB) phase and a hybrid-silica C18 phase, and by comparing these results with previously reported data on a silica-based C8 phase. MDM migration data were reconstructed using shape-preserving PCHIP interpolation and integrated to obtain V_th​ and surface-excess isotherms. The hybrid C18 phase yielded an essentially adsorbate-independent V_th (1.088-1.094 mL), whereas PS-DVB exhibited a modest but systematic increase in the order MeOH < MeCN < ACE (1.231-1.247 mL); the silica C8 phase showed larger adsorbate-to-adsorbate variation even after length normalization. Neither PS-DVB nor hybrid C18 exhibited an apparent negative surface-excess region over the explored concentration range, consistent with an interfacial concentration profile that places the effective liquid-solid boundary close to the solid surface under neat-adsorbate conditions. To parameterize thermodynamic descriptors, we further fitted the raw MDM migration data using a self-consistent total-uptake convention by treating the reference hold-up volume V_L^' as an adjustable parameter and adopting a finite-layer BET model. MeOH and MeCN were described up to 70 vol.% for all phases, whereas ACE could be represented only at low concentration. The first-layer affinity parameter K_M​ provided the most robust cross-column metric, yielding similar values for silica C8 and hybrid C18 but substantially larger values for PS-DVB. The corresponding apparent first-layer adsorption free energy showed a steeper dependence on the equivalent molecular diameter for PS-DVB than for C8/C18, consistent with the stronger enhancement of neat-water retention on PS-DVB. Overall, the results demonstrate that V_th​ in reversed-phase systems is a dividing-plane-dependent thermodynamic reference that reflects stationary-phase microstructure and neat-adsorbate accessibility rather than a universal measure of the true void volume, and provide a practical basis for consistent excess-to-total isotherm interpretation across materially distinct reversed-phase stationary phases.