We propose a method for determining the specific surface area, A s , of a nanopowder from its measured (mass-specific) N2 vapor adsorption isotherm. The reported cross-sectional area of an adsorbed N2 molecule and the (mass-specific) zeta adsorption isotherm are used to calculate A s . The (area-specific) zeta adsorption isotherm is then determined using the calculated A s . The method is demonstrated by applying it to three nanopowders of each of three materials (α-alumina, carbon, and silica). The values of A s and mass-specific adsorption isotherms vary widely. However, when A s is used to convert the reported adsorption measurements from mass-specific to area-specific, it is found that they very nearly coincide with the calculated (area-specific) zeta adsorption isotherm. The zeta adsorption isotherm is then used to determine the entropy of the adsorbate. It indicates the wetting phase transition when the substrate is cooled sufficiently. We assume that the surface tension of the solid–vapor interface is transformed to that of the liquid–vapor at wetting. We then combine the zeta adsorption isotherm with the Gibbs adsorption equation. After integrating the result and applying the wetting condition to evaluate the integration constant, we obtain expressions for the surface tension of the three solids in the absence of adsorption.

For N2 vapor adsorbing on a nanopowder at 77 K, we use a multicomponent canonical ensemble to determine the conditions for equilibrium between a contacting vapor phase and the adsorbed molecular clusters. Provided the substrate variations (heterogeneities) do not cause a phase transition, such as wetting or capillary condensation, we show that the equilibrium conditions allow an expression for an adsorption isotherm to be formed. The isotherm expression contains four constants that are to be obtained empirically from mass-specific adsorption measurements. The specific surface area of a substrate is expressed in terms of the specific number of adsorption sites and the cross-sectional area of an adsorbed N2 molecule on materials. This procedure is investigated by using the respective specific surface areas of different samples of a given material to transform the data into an area-specific basis. We pooled data sets from multiple samples with possibly different specific surface areas to form a single data set. The thermodynamic (zeta adsorption) isotherm is formulated after a regression analysis is performed on the pooled data set. This isotherm is used with the Gibbs adsorption equation to obtain the solid surface energy of a material as a function of the amount adsorbed. Five materials are examined: silica, α-alumina, γ-alumina, carbon black, and graphitized carbon. Their respective solid surface energies are each shown to be a material property.

The zeta adsorption isotherm, ZAI, is used with heterogeneity-free adsorption measurements, reported by Baker and Sing, to determine the area of a water molecule adsorbed on TK 800 silica at 298 K. We examine this value by using measured water vapor adsorption isotherms of three non-TK 800 silicas, convert them to thermodynamic adsorption isotherms, and show that they coincide. Then, all four water adsorption measurements are pooled to form a single data set and used to formulate a thermodynamic isotherm for water vapor on silica. We then examine the stability of the adsorbate as a function of the vapor-phase pressure, P V. This analysis indicates that a phase change occurs for silica when P V reaches the value of a ZAI constant and this is interpreted as the wetting transition, which is assumed to transform the solid–vapor surface energy to that of the liquid–vapor interface. These assumptions are examined using the ZAI thermodynamic isotherm and the Gibbs adsorption equation to predict the surface energy of any fully hydroxylated silica in the absence of adsorption. Further examination showed that the number of adsorption sites determined by the ZAI corresponds to the surface concentration of silanol groups, which act as centers of water vapor adsorption.

The surface characterization of nanopowders is widely attempted by both N2 and Ar vapor adsorption methods. They are used as complementary probe molecules because of their similarities and certain differences. However, the respective reported analyses, using the Brunauer–Emmett–Teller method, suffer from inconsistencies between the determined values of the specific surface areas, A s. We examine this issue by using the zeta adsorption isotherm approach on the reported data for both vapors on two different samples from the same batch of a nanopowder material. By assuming the equivalence of the A s determined by both of the vapors, we obtain the average occupied area of an adsorbed argon atom, σA(Ar), on silica and carbon black at the solid- and liquid-state temperatures of 77 and 87 K, respectively. We then examine the determined value of σA(Ar) by obtaining A s for other samples of the same material with varying specific areas. By transforming the adsorption data from mass-specific to area-specific, the respective thermodynamic isotherms, n SV, of Ar vapor adsorbing on silica and carbon black are obtained. The determined n SV are then used with the Gibbs adsorption equation to determine the solid surface energy, γS0, and solid–vapor interface energy, γSV, for both substrates. The obtained γSV(x V) on both substrates is used to interpret the phase transition state of the Ar adsorbate at 77 K. The determined thermodynamic isotherms for Ar and N2 vapors are further used in a comparative study to show that the Ar vapor adsorption is negligibly affected by the change in silanol concentration on the silica surface in contrast with N2 vapor adsorption.

The objective of this study was to investigate the prediction of the wetting characteristics obtained from the equilibrium adsorption analysis using the Zeta adsorption isotherm approach with an experimental study. Water vapor’s adsorption and wetting characteristics on a hydroxylated and nano-polished silica substrate were studied in near-equilibrium conditions at temperatures near 298 K. Using a UV–visible interferometer, water vapor adsorbate film thicknesses were measured and converted into amount adsorbed per unit area. The current results show that the wetting transition occurred at an average subcooling value of 0.39 K, less than the predicted value of 0.49 K. All the different experimental observations showed growth of film thickness as a function of subcooling value with a maximum film thickness of 12.6 nm. The analysis of the results further showed that the maximum stable film was in a metastable state that then condensed in a dropwise manner, if perturbed by increasing the subcooling. The study further revealed that the adsorbate is unstable after transitioning. The solid surface energy calculated by including the near-equilibrium observations was comparable and close to that of the equilibrium studies, thus supporting solid surface energy as a material property.