<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>
On the Mechanisms of Alumina Cluster Formation in Molten Iron