New selection criterion for a base polar liquid in the Lifshitz-van der Waals/Lewis acid-base approach

To understand the adhesion of a colloid or a microbe to a solid surface in terms of thermodynamics, the interfacial energy should be calculated with the respective surface tensions. The Lifshitz-van der Waals/Lewis acid-base (LW-AB) approach is most widely used for the evaluation of these surface tension components and requires contact angles of the solid with an apolar liquid, water, and one base polar liquid. Holländer's criterion has been suggested for the selection of the base polar liquid regardless of the nature of the solid. However, large deviations in the AB surface tension components of the solid (γ_s⁺ and γ_s^-), especially γ_s⁺, and the positive AB component of the interfacial energy (ΔG_sl^AB) have often been found depending on the nature of the polar liquid. In this study, the following selection criterion for the base polar liquid has been derived from a mathematical analysis of the LW-AB approach: 0 > (γ_p ⁺)^1/2/(γ_w⁺) ^1/2ΔG_sw^AB > ΔG_sp ^AB > (γ_p⁺)^1/2/ (γ_w⁺)^1/2 ΔG_sw ^AB[(γ_p^-/γ_p ⁺)^1/2 - (γ_w ^-/γ_w⁺)^1/2 + 1] (s = solid; w = water; and p = the base polar liquid). Using four model solids, this criterion has been evaluated for the selection of the base polar liquid among glycerol, formamide, and ethylene glycol. Reliable surface tension components of the solid were obtained when the above criterion was satisfied. When γ _w⁺ and γ_w^- are set to be identical, the above criterion is then Q_γ > [(ΔG _sw^AB(γ_p^-)^1/2)/ (ΔG_sp^AB(γ_w^-) ^1/2)]² > 1, which is believed to be a detailed version of Holländer's criterion.