New thermodynamics for evaluating the surface-phase enrichment in the lower surface tension component

General Adsorption Model to Describe Sigmoidal Surface Tension Isotherms of Binary Liquid Mixtures

Surface tension (σ) isotherms of liquid mixtures can be divided into Langmuir-type (L-type, including L_I- and L_II-type) and sigmoid-type (S-type, including S_I- and S_II-type). Many models have been developed to describe the σ-isotherms. However, the existing models can well describe the L-type isotherms, but not the S-type ones. In the current work, a thermodynamic model, called the general adsorption model, was developed based on the assumption of surface aggregation occurring in the surface layers, to relate the surface composition with the bulk one. By coupling the general adsorption model with the modified Eberhart model, a two-parameter equation was developed to relate the σ with the bulk composition. Its rationality was examined using the σ data of 10 binary mixtures. The results indicate that the new model can accurately describe the S- and L-type isotherms of binary liquid mixtures, showing a good universality. One advantage of the model is that its two parameters, i.e., the adsorption equilibrium constant (K) and the average aggregation number (n), can be estimated by linear fitting experimental σ data, thereby obtaining unique values. This model suggests that the S- and L_II-type isotherms arise from the surface aggregation (n ≠ 1). In addition, the standard molar Gibbs free energy of surface adsorption (ΔG̃_ad⁰) and the apparent surface layer thickness (τ) were analyzed for 10 binary mixtures. The ΔG̃_ad⁰ data suggest that the order of adsorption tendency is L_I-type ≫ S_I-type ≈ S_II-type > L_II-type, and the strong adsorption usually corresponds to large τ. This work provides a feasible model for describing the S-type isotherms and a better understanding of the surface properties of liquid mixtures.

A simple theory for interfacial properties of dilute solutions

Recent studies suggest that cosolute mixtures may exert significant non-additive effects upon protein stability. The corresponding liquid–vapor interfaces may provide useful insight into these non-additive effects. Accordingly, in this work, we relate the interfacial properties of dilute multicomponent solutions to the interactions between solutes. We first derive a simple model for the surface excess of solutes in terms of thermodynamic observables. We then develop a lattice-based statistical mechanical perturbation theory to derive these observables from microscopic interactions. Rather than adopting a random mixing approximation, this dilute solution theory (DST) exactly treats solute–solute interactions to lowest order in perturbation theory. Although it cannot treat concentrated solutions, Monte Carlo (MC) simulations demonstrate that DST describes the interactions in dilute solutions with much greater accuracy than regular solution theory. Importantly, DST emphasizes a fundamental distinction between the “intrinsic” and “effective” preferences of solutes for interfaces. DST predicts that three classes of solutes can be distinguished by their intrinsic preference for interfaces. While the surface preference of strong depletants is relatively insensitive to interactions, the surface preference of strong surfactants can be modulated by interactions at the interface. Moreover, DST predicts that the surface preference of weak depletants and weak surfactants can be qualitatively inverted by interactions in the bulk. We also demonstrate that DST can be extended to treat surface polarization effects and to model experimental data. MC simulations validate the accuracy of DST predictions for lattice systems that correspond to molar concentrations.

Extension of the Gibbs-Duhem Equation to the Partial Molar Surface Thermodynamic Properties of Solutions

In this paper, the Gibbs-Duhem equation is extended to the partial molar surface thermodynamic properties of solutions. According to the surface Gibbs-Duhem equations, the sum of the mole fractions of the components in the surface region of a bulk solution multiplied by different partial molar surface quantities should equal zero if summation is taken by all components of the solution. There are four different partial molar surface quantities identified in this paper for which the surface Gibbs-Duhem equation is proven to be valid: (i) the reduced surface chemical potential, (ii) the surface chemical potential, (iii) the partial molar surface area, and (iv) the partial molar excess surface Gibbs energy = the product of partial molar surface area and the partial surface tension. The first one is known since Guggenheim (1940), but the other three are presented here for the first time. It is also demonstrated here how to apply the surface Gibbs-Duhem equations: (i) it is proven that the model equation applied by us recently for the reduced chemical potential [Adv Coll Interf Sci 2020, 283, 102212] obeys one of the surface Gibbs-Duhem equations, (ii) in contrary, it is proven that the model equation suggested by us recently for the partial molar surface area contradicts one of the surface Gibbs-Duhem equations; therefore, a new (and simpler) model equation for the partial molar surface areas of the components is suggested here that obeys the surface Gibbs-Duhem equation. It is also shown that the Butler equation obeys one of the surface Gibbs-Duhem equations. It is also concluded that surface composition in equilibrium should be one that ensures minimum surface tension.

Foaming of Binary Mixtures: Link with the Nonlinear Behavior of Surface Tension in Asymmetric Mixtures

The lifetimes of single bubbles or foams that are formed in mixtures of liquids can be several orders of magnitude larger than the ones formed in pure liquids. We recently demonstrated that this enhanced stability results from differences between bulk and interfacial concentrations in the mixture, which induce a thickness dependence of the surface tension in liquid films, and thus a stabilizing Marangoni effect. Concentration differences may be associated with nonlinear variations of surface tension with composition and we further investigate their link with foamability of binary mixtures. We show that, for asymmetric binary mixtures, that is, made of molecules of very different sizes, strong nonlinearities in surface tension can be measured, that are associated with large foam lifetimes. When the molecules that occupy the largest surface areas have the smallest surface tension, the surface tension of the mixture varies sublinearly with composition, reflecting an enrichment in this species at the interface with air, as classically reported in the literature. In contrast, when they exhibit the largest surface tension, superlinear variations of surface tension are observed, despite a similar enrichment. We discuss these variations in light of a simple thermodynamic model for ideal mixtures and we demonstrate why foam stability is enhanced for both sublinear and superlinear surface tension variations, thus, shedding new light on foamability without added surfactants.

Examination of the Butler Equation for the Surface Tension of Liquid Mixtures

The classical Butler equation used to describe surface tension and the surface composition of liquid mixtures is revisited. A straightforward derivation is presented, separating basic chemical thermodynamics and assumptions proper to Butler's model. This model is shown to conceal an approximation not recognized by other researchers. The shortcoming identified consists of not allowing surface standard values to vary with surface tension by virtue of the changing composition. A more rigorous equation is derived and shown to yield the Butler equation in case of incompressible surface phases. It is concluded that the Butler equation slightly overestimates ideal surface tensions. Butler's surface-phase concentrations of the surface-active component are also slightly overestimated in the surface-active component dilute range, being just underestimated at higher concentrations. Despite this, Butler's model stands as a very good standard due to its versatility.

Revealing microheterogeneities and second order phase transitions in aqueous mixtures of 1-propoxypropan-2-ol at 298 K

Second-order phase transitions, identified by Kirkwood–Buff integrals, assigned to solution microheterogeneities are corroborated by ESI-MS, surface tension and solvatochromic parameters.

Gibbs excess and the calculation of the absolute surface composition of liquid binary mixtures

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.

Activity coefficients in the surface phase of liquid mixtures

A novel equation for evaluating surface activity coefficients is obtained from a recent thermodynamic formalism describing the surface phase of liquid mixtures. The input quantities are the surface tension, bulk activity coefficients and pure constituent thermophysical properties. It is demonstrated thermodynamically that the order of magnitude of each component surface and bulk activity coefficients must be the same. This order is intrinsically associated with the sign of excess surface tension. Reliable activity coefficients of ethanol and water in the surface phase of their mixtures are computed and reported for the first time, by using literature data for the required input quantities. It is shown that the so-called transferring method for estimating surface activity coefficients is severely flawed, because it leads to contradictory values of predicted excess surface tensions depending on which component this prediction is based.