Partial molar surface areas in liquid mixtures. Theory and evaluation in aqueous ethanol

Abstract

Abstract Different definitions for the partial molar surface area (PMSA) of a mixture component are found in the literature. The advanced definition states that it is the change of surface area resultant from the addition of 1\u202fmol of that component to the surface region at constant temperature, T, pressure, p, surface tension and surface amounts of the other components. Estimating this quantity has long been hampered by the fact that a change of composition while holding constant the mixture surface tension cannot be attained in the laboratory. Using formal thermodynamics, a rigorous procedure for the calculation of PMSAs is worked out. As input, it only requires experimentally measurable properties of liquid mixtures and their pure constituents. This PMSA is shown to be comparable to the PMSA defined in terms of Gibbs surface excesses of the components, though not equivalent to the PMSA for changes in composition at fixed T and p only. From their relationship it is argued that the advanced PMSA is made up of two contributions, namely the area alteration at constant T and p, which leads to a change in the mixture surface tension, and an additional area variation for restoring the initial surface tension value. In a binary liquid mixture, the restoring area is necessarily positive for the surface active component and negative for the solvent. A new, robust thermodynamic derivative is used for the calculation of relative adsorptions and molar surface areas. Expressions are obtained for the analytic calculation of different PMSAs in thermodynamically ideal liquid mixtures. Standard molar surface areas are defined, and expressions are given for their calculation from model or experimental quantities. Real and ideal PMSAs of water and ethanol are estimated in their mixtures at 298\u202fK, using literature data. Thermodynamic consistency tests were developed and used to reject some PMSA values in water-rich and ethanol-rich solutions. This unfortunate situation is ascribed to calculation procedures that impose much stress on the experimental data. It is concluded that Rusanov s interpretation of a PMSA as a restoring area only accounts for a small part of this quantity, at least in aqueous ethanol solutions. The surface structure of water\u202f+\u202fethanol mixtures is re-examined at the light of PMSA values.