Adsorption isotherms and thermal fluctuations

The influence of thermal fluctuations on adsorption isotherms is calculated within the context of a self consistent mean-held theory, and it is found that such fluctuations cannot be neglected in the analysis of adsorption data. This result arises from our observation that substrate-induced hindrance of thermal fluctuations can significantly alter the form of an adsorption isotherm, particularly in the thin-film regime (approximate to 0-5 nm) which is most commonly probed by adsorption experiments. Previous experiments involving room-temperature adsorption on flat surfaces have been reanalyzed, and the reported discrepancies with the Lifshitz theory of van der Waals forces are found to be much reduced when thermal fluctuations of the thickness of the adsorbed layer are taken into account. Recently published data for nitrogen adsorption on rough substrates have also been reanalyzed, and the thermal fluctuations are found to be more important for thin adsorbed layers than undulations of the film induced by the roughness of the substrate. The analysis reveals that, as long suspected, the scaling regime of asymptotic divergence has not yet been reached for film thicknesses remaining below 5 nm.