Ideal adsorbed multilayer thin films: some thermodynamic implications

With a proper choice of coordinates and for certain substances over a limited temperature range, the information contained in a whole family of adsorption isotherms coalesces into a single universal curve. Such behaviour can be related to a particularly simple thermodynamic model. This model and some of its implications are explored in detail. In particular, thermodynamic internal self-consistency demands that there be a unique (generally non-linear) relationship between the mass adsorbed and the film thickness which is completely deducible from measured adsorption isotherms plus bulk thermodynamic data. It is independent of assumptions regarding the form of the van der Waals attraction binding the adsorbate to the adsorbent substrate. The integral equation embodying this relationship is derived and exhibited. As an example of its use the equation is applied to the case of thin films of helium II.