Enrichment at vapour–liquid interfaces of mixtures: establishing a link between nanoscopic and macroscopic properties

Component density profiles at vapour–liquid interfaces of mixtures can exhibit a non-monotonic behaviour with a maximum that can be many times larger than the densities in the bulk phases. This is called enrichment and is usually only observed for low-boiling components. The enrichment is a nanoscopic property which can presently not be measured experimentally – in contrast to the classical Gibbs adsorption. The available information on the enrichment stems from molecular simulations, density gradient theory, or density functional theory. The enrichment is highly interesting as it is suspected to influence the mass transfer across interfaces. In the present work, we review the literature data and the existing knowledge on this phenomenon and propose an empirical model to establish a link between the nanoscopic enrichment and macroscopic properties – namely vapour–liquid equilibrium data. The model parameters were determined from a fit to a dataset on the enrichment in about 100 binary Lennard-Jones model mixtures that exhibit different types of phase behaviour, which has recently become available. The model is then tested on the entire set of enrichment data that is available in the literature, which includes also mixtures containing non-spherical, polar, and H-bonding components. The model predicts the enrichment data from the literature (2,000 data points) with an AAD of about 16%, which is below the uncertainty of the enrichment data. This establishes a direct link between measurable macroscopic properties and the nanoscopic enrichment and enables predictions of the enrichment at vapour–liquid interfaces from macroscopic data alone.