New Thermodynamics for Evaluating the Surface‐phase Enrichment in the Lower Surface Tension Component

Abstract

Regarding the surface phase of liquid mixtures as a thermodynamic phase, ideal surface phases are designed so that at fixed bulk-phase composition, real and ideal surface phases have the same chemical composition and identical limiting slopes for the dependence of surface tension on mole fraction. Standard chemical potentials are introduced for surface phase components, and quasi-exact expressions are worked out to compute ideal surface tensions and surface-phase compositions of real liquid mixtures. Guidelines for choosing molecular models to estimate the molar surface area of pure constituents are given. Ideal and excess surface tensions are calculated by using literature data for aqueous ethanol solutions at 298 K. These results show treatment based on Butler's equations grossly overestimate predicted surface tensions, thus leading to lower ethanol content in the surface phase. These inaccuracies are ascribed to the use of molar surface areas in model equations that are too small.

Activity Coefficients in the Surface Phase of Liquid Mixtures

“…Moreover, the thermodynamic equilibrium between real surface and bulk phases is also observed between ideal surface and bulk phases, yielding Equations (3) and (4): [2] Our recent thermodynamic treatment of planar surface phases is also based on this feature.…”

“…Within this framework, assuming the thickness of pure-liquid surface phases is independent of the surface tension and molar surface area is simply related to some power of bulk molar volumes, we were able to express differences of standard chemical potentials in the form of Equations (5) and (6): [2] m à B À m 0;s B ðT; p; gÞ ¼…”

“…In addition, we obtained the workable Equations (7) and (8) for computing g id and x s B : [2] x A 1 þ In addition, we obtained the workable Equations (7) and (8) for computing g id and x s B : [2] x A 1 þ…”

“…In Figure 1 a, we observe that the activity coefficient of ethanol is larger Table 1. [5] Fitted Parameters : experimental data points from Koga and co-workers; [5] curves drawn by using parameters b k in Table 1 [a] Molar surface areas estimated by using the anisotropic surface (as) model for the surface molar volume and a cubic cell packing (cc): [2] A* i ðas; ccÞ ¼ L 1=3 ðV * c;i Þ 6=15 ðV * i Þ 4=15 in which L is the Avogadro constant and V* c;i is the critical volume. [5] Fitted Parameters : experimental data points from Koga and co-workers; [5] curves drawn by using parameters b k in Table 1 [a] Molar surface areas estimated by using the anisotropic surface (as) model for the surface molar volume and a cubic cell packing (cc): [2] A* i ðas; ccÞ ¼ L 1=3 ðV * c;i Þ 6=15 ðV * i Þ 4=15 in which L is the Avogadro constant and V* c;i is the critical volume.…”

“…Recently, we proposed [2] a new thermodynamic formalism to describe planar surface phases of liquid mixtures. Following the classic analyses by Butler [3] and Guggenheim, [4] we have treated the surface phase as a separate phase at equilibrium with the bulk homogeneous mixture.…”