Statistical Mechanics of Multilayer Sorption: Surface Concentration Modeling and XPS Measurement.

The concentration of solute molecules at the surface of a liquid is a factor in heterogeneous reactions, surface tension, and Marangoni-effect-driven surface flows. Increasingly, X-ray photoelectron spectroscopy (XPS) has enabled surface concentrations to be measured. In prior work, we employed statistical mechanics to derive expressions for surface tension as a function of solute activity in a binary solution. Here we use a Gibbs relation to derive concomitant expressions for surface concentration. Surface tension data from the literature for five alcohols are used to identify parameters in the surface tension equation. These parameters are then used in the surface concentration equation to predict surface concentrations. Comparison of these predictions to those measured with XPS shows a factor of three difference between measured and predicted surface concentrations. Potential reasons for the discrepancy are discussed, including lack of surface-bulk equilibrium in the measurements.