Gibbs Excess and the Calculation of the Absolute Surface Composition of Liquid Binary Mixtures

Abstract

Adsorption at the liquid-vapor interphase of a liquid binary mixture is traditionally quantified by means of the Gibbs solute excess. Despite several theoretical reviews on the meaning of Gibbs excess defined by the Gibbs dividing surface, it is still misinterpreted as the excess concentration under Guggenheim's finite-depth surface layer approach. In this work, both concepts are clarified in a practical way, aided by a graphical representation without loss of generality. The understanding of both quantities led to the development of a thermodynamic procedure for the calculation of the actual number of solute and solvent molecules at a finite-depth surface layer (not a monolayer), what is called the absolute surface composition. From surface tension and density data, the absolute surface composition of the binary aqueous mixtures of methanol, ethanol, 1-propanol, and 1-butanol was calculated. Results show thermodynamic consistency and agree with experimental reports and with an empirical mixing rule. The increasing alcohol surface concentration throughout the entire concentration range casts doubt on the formation of an alcohol monolayer, as was suggested by other authors. Furthermore, the use of Guggenheim's monolayer model does not reproduce the experimental data, nor does it show thermodynamic consistency.

A Monolayer Partitioning Scheme for Droplets of Surfactant Solutions

“…Comparison of predicted surface thickness and n ‐butanol surface mole fraction for water‐ n ‐butanol mixtures from the monolayer model, to experimental values from neutron reflection (circles), and Gibbs' adsorption equation based analysis of experimental surface tension data (diamonds; Li et al, ) as recalculated by Bermúdez‐Salguero and Gracia‐Fadrique () assuming δ = 0.7 nm, and from mass spectrometry (squares; Raina et al, ).…”

“…Considering the neutron reflection data, Bermúdez‐Salguero and Gracia‐Fadrique () have noted a thermodynamic inconsistency in the values calculated by Raina et al (; corrected values are given in Figure ), which highlights a yet another potential source of uncertainty.…”

Surface properties of the ethanol/water mixture: Thickness and composition

“…The partial molar volumes were calculated as described by [16] from published data [17]. The molar fractions of ethanol in the bulk and interfacial zones can be defined as follows: We define BE e N ("bulk equivalent") as the concentration of solute that would be expected if the molar fractions in the bulk and interfacial layers were equivalent.…”

STAND: Surface Tension for Aggregation Number Determination

“…Several attempts to obtain more information from surface tension measurements have been proposed, including the determination of equilibrium constants for supramolecular complex formation, 5 the surface excess 6,7 and activity coefficients. 8,9 Surface tension measurements are typically employed to characterize surfactant molecules.…”