General Cluster Sorption Isotherm

Abstract

<p>Adsorption isotherms are an essential tool in chemical physics of surfaces. However, several approaches based on a different theoretical basis exist and for isotherms including capillary condensation existing approaches can fail. Here, a general isotherm equation is derived and applied to literature data both concerning type IV isotherms of argon and nitrogen in ordered mesoporous silica, and type II isotherms of disordered macroporous silica. The new isotherm covers the full range of partial pressure (10<sup>-6</sup> - 0.7). It relies firstly on the classical thermodynamics of cluster formation, secondly on a relationship defining the free energy during the increase of the cluster size. That equation replaces the Lennard-Jones potentials used in the classical density functional theory. The determination of surface areas is not possible by this isotherm because the cross-sectional area of a cluster is unknown. Based on the full description of type IV isotherms, most known isotherms are accessible by respective simplifications. </p>

General cluster sorption isotherm: surface area determination

“…1 Since the clusters were thought to be flexible without a preferential orientation, this new isotherm was assumed to be unsuitable for getting an information on the surface area. 14 In contrast to that first interpretation, it will be shown in the following that surface areas can be calculated, indeed, when the GCSI equations, presented so far, are somewhat modified.…”

“…The general cluster sorption isotherm (GCSI) 14 is theoretically founded by a free energy relationship depending on the cluster size and on the existence of a thermodynamic multiple sorbate-surface and sorbate-sorbate equilibria. The latter has been formally derived and applied to the description of protein-ligand interactions by Klotz in 1946.…”

“…The GCSI claims to be universal, its validity for experimental type II and IV isotherms has been proven, type III, V, and VI are possible in principle. 14 A special case is obtained when the exponent of eqn (6) tends to go to infinite. For n = 1 we obtain…”

“…13 Recently, an alternative theoretical isotherm modeling approach has been presented where the intuitive imagination of a layer-by-layer adsorption is replaced by the formation of clusters which are isolated from each other at low but merge at higher degrees of coverage. 14 The model, called general cluster sorption isotherm (GCSI), has been successfully applied to experimental high resolution sorption isotherms of type II and IV. 13,14 Theoretically, it may be conceived as a general extension of the original BET approach.…”

“…14 The model, called general cluster sorption isotherm (GCSI), has been successfully applied to experimental high resolution sorption isotherms of type II and IV. 13,14 Theoretically, it may be conceived as a general extension of the original BET approach. 1 Since the clusters were thought to be flexible without a preferential orientation, this new isotherm was assumed to be unsuitable for getting an information on the surface area.…”