Thermodynamic N2 Vapor Isotherms of Materials: Zeta Adsorption Isotherm Approach

Abstract

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.