Effect of Adsorption on the Surface Tensions of Solid−Fluid Interfaces

Abstract

A method is proposed for determining the surface tensions of a solid in contact with either a liquid or a vapor. Only an equilibrium adsorption isotherm at the solid-vapor interface needs to be added to Gibbsian thermodynamics to obtain the expressions for the solid-vapor and the solid-liquid surface tensions, gamma[1](SV) and gamma[1](SL), respectively. An equilibrium adsorption isotherm relation is formulated that has the essential property of not predicting an infinite amount adsorbed when the pressure is equal to the saturation-vapor pressure. Five different solid-vapor systems from the literature are examined, and found to be well described by the new isotherm relation. The surface-tension expressions obtained from the isotherm relation are examined by determining the surface tension of the solid in the absence of adsorption, gamma[1](S0), a material property of a solid surface. The value of gamma[1](S0) can be determined by adsorbing different vapors on the same solid, determining the isotherm parameters in each case, and then from the expression for gamma[1](SV) taking the limit of the pressure vanishing to determine gamma[1](S0). From previously reported measurements of benzene and of n-hexane adsorbing on graphitized carbon, the same value of gamma[1](S0) is obtained.

Adsorption at the solid–liquid interface as the source of contact angle dependence on the curvature of the three-phase line

“…This provides a method by which the theory may be tested: if two vapours are used to determine the value of γ S0 , and the theory is correct, the same value of γ S0 must be obtained from the isotherm parameters for the two vapours. This condition was found to be satisfied for the adsorption of benzene and for n-hexane adsorbing on the basal plane of graphite [31] and for Ar and N 2 adsorbing at 77 K on alpha-alumina, titania, magnesia and borosilicate glass [12].…”

“…Both positive and negative values have been reported, and the reported values differ in magnitude by several orders [5,11,14,18]. Finally, the authors investigating line tension as an explanation for the dependence of the contact angle on droplet size neglected adsorption, particularly that at the solid-liquid interface [31].…”

“…For smooth homogeneous surfaces, a new method was recently proposed for determining these surface tensions that avoids the earlier pitfalls [31]. Only a suitable adsorption isotherm for the solid-vapour interface is added to the necessary conditions for equilibrium in order to express γ SV and γ SL in terms of the isotherm parameters.…”

“…These isotherms were not intended for application for pressures near P s (T), but only for pressures corresponding to approximately monolayer coverage [4,10,15,16]. The ζ isotherm is intended for the full pressure range and when applied to benzene and n-hexane adsorbing on basal plane of graphite, and water vapour adsorbing on silica and alumina, it indicates the amount adsorbed remains finite in the limit of P V approaching P s (T) [31]. Importantly, the theoretical isotherm to be included in the procedure for determining γ SV , and γ SL can be experimentally examined before it is used in the procedure to determine γ SV and γ SL .…”

“…Although the effect of n SL on the contact angle has been neglected, with few exceptions [20,22,29,31,35], a recent study found that n SL is negative [33]. Although a negative value of n SL is consistent with the Gibbs method of defining the position of the interface [8,21,25], the prediction that follows is that, independently of any line tension, for a given curvature of the three-phase line, the contact angle increases as the pressure in the liquid at the three-phase line, P 3 L , is increased [35], but that, for a given value of P 3 L , the contact angle decreases as C cl increases [32].…”