Properties of argon liquid-vapor interface

The short-wave cutoff boundary of the capillary wave spectrum is established. Effective thickness L _b of the “bare” density profile in the interfacial layer is calculated according to experimental data on the ellipticity ratio of reflected light. The free parameters of the extended van der Waals theory of capillarity are determined. The positions of the equimolecular dividing surface and tension surface are calculated, as well as the temperature dependence of the Tolman parameter.     

A revisit to the Gibbs dividing surfaces and helium adsorption

This paper addresses the long-standing problem of the so-called Gibbs dividing surface and the use of helium as a “non-adsorbing” gas for the determination of the “helium”-void volume and thence the Gibbs excess. Using helium is subject to some uncertainty because helium does adsorb (to call it a non-adsorbing gas is misleading) and it is able to access pore spaces that other larger adsorbates cannot. On the other hand, even helium atoms can not physically probe all the space described by the helium-void volume. To avoid these difficulties, we suggest an alternative to the formulation of the Gibbs dividing surface and the definition of the excess amount. We illustrate this with the two common tools to study adsorption—the volumetric and gravimetric techniques, and justify our new analysis with a computer simulation of a number of model adsorption systems. Furthermore, we also show that by using the correct accessible volume and inaccessible volume the excess amount obtained from a volumetric experiment is exactly the same as that obtained from a gravimetric experiment.     

THE MECHANICAL VIEW OF THE SURFACE TENSION IS FALSE

The concept of surface tension is usually introduced as a force per unit length originated from the “stress tensor” at the liquid surface (and vaguely extended to solids). This mechanical model of the surface tension, a paradigm for many workers in the field, is wrong. The inferences from the model, however, are correct in the more common uses. Some contradictions may appear but not sufficient to abandon such a simple and intuitive concept. The origin of the surface tension, of a liquid or solid surface, is in the molecular interactions, when some other phase is put in contact with such a surface. Recent developments using the surface tension components allow to predict interfacial surface tensions and to measure surface tension of solids. Although the power of this approach is evident, its use is only incipient because some results, particularly the presence of negative interfacial tensions, are difficult to interpret using the erroneous vision of surface tension as a consequence of a “stress tensor” at the liquid (or solid) surface. We present here some properties of liquids useful to fundament the concept of surface tension and briefly refer to Laplace's equation, Young's equation and capillarity, attempting to correct some misinterpretations.     

Surface tension of equilibrium spherical drops in the vapor phase

The properties of metastable and equilibrium drops that occur in the vapor phase and differ in the size and position of the dividing surface are compared. Using an equimolecular dividing surface, it was found that the total free energy and the total mass of the substance in drops of the same size over a broad temperature range differ by not more than 0.3%. A similar comparison for a dividing surface chosen from the equality condition of the moments of forces gives rather similar results. Using the surface where the maximum surface tension is attained as the dividing surface is impossible at low temperatures, because under these conditions, the notion of surface tension has no physical meaning. At high temperatures, the difference between the total mass of the substance for metastable and equilibrium drops does not exceed 0.6%. The calculations were carried out over a broad temperature range on the basis of the lattice-gas model in the quasichemical approximation.     

Three-Dimensional Aspect of the Surface Tension: An Approach Based on the Total Pressure Tensor

The conditions of mechanical equilibrium were considered, and the generalized notion of the surface tension at an arbitrarily curved surface layer was analyzed on the basis of the total nondiagonal pressure tensor including the external fields and anisotropic even in the bulk phases. It was shown that the transverse surface tension can be eliminated using the selection of a dividing surface; however, in the general case, this surface does not exhibit the properties of the tension surface. On the whole, three-dimensional and nondiagonal character of the tensors of excess surface stresses determined by the integration over the volume and the cross section of the surface layer is retained at any selection of the dividing surface.     

Thermodynamic aspects of capillarity and electrocapillarity of solid interfaces

In the previous paper (Gutman, JOSSEC 18:3217–3237, 2014), we have shown that the main problem in capillarity and electrocapillarity of solid surfaces is the lack of clarity in determining the surface stress and basic equations. Now, we continue the survey of efforts to solve this problem and show origins of erroneous results, accenting some important items: comparative analysis of Gibbs and Guggenheim approaches in surface thermodynamics (a geometrical dividing surface and finite-thickness surface layer, respectively), transformation of fundamental equations on per-unit-area basis to obtain Gibbs adsorption equation for finite-thickness surface layer, different attempts to derive the thermodynamic definition of “surface stress” in frames of Gibbs’ theory (including Shuttleworth’s approach), atomistic calculations of surface stress, surface stress in rational continuum mechanics, “modifications” of Gibbs–Duhem relations made for solid interface, and Maxwell relations in capillarity and electrocapillarity of solid interface. It is shown that the erroneous Shuttleworth’s approach is present in an explicit or implicit form in all efforts to introduce the surface stress in frames of Gibbsian theory (although Gibbs did not introduce surface stress). Therefore, “modernizations” or “generalizations” of the Gibbs–Duhem relation, the Gibbs adsorption equation, and the Lippmann equation to adopt them for a solid surface are unnatural and not necessary. Therefore, we recommend withdrawing the Shuttleworth equation and its consequences from circulation, including the IUPAC Recommendations.     

A molecular dynamics simulation study of nanoscale liquid threads

The properties of liquid threads in angular direction are studied. On the basis of Gibbs theory, a thermodynamic model is constructed and a formula of surface of tension is derived. For the determination of surface tension, different methods are presented. We investigate seven different systems (the numbers of molecules N are 1600, 2240, 2880, 3360, 4000, 4800, and 5280) by molecular dynamics simulations. We analyze the surface tension obtained by various routes, then whether the classical Laplace equation is applicable in nanoscale can be determined. The results obtained by molecular dynamics simulations support that surface tension is dependent on the dividing surface curvature.     

On the closure conjectures for the Gibbsian approximation model of a binary droplet

Within the framework of Gibbsian thermodynamics, a binary droplet is regarded to consist of a uniform interior and dividing surface. The properties of the droplet interior are those of the bulk liquid solution, but the dividing surface is a fictitious phase whose chemical potentials cannot be rigorously determined. The state of the nucleus interior and free energy of nucleus formation can be found without knowing the surface chemical potentials, but the latter are still needed to determine the state of the whole nucleus (including the dividing surface) and develop the kinetics of nucleation. Thus it is necessary to recur to additional conjectures in order to build a complete, thermodynamic, and kinetic theory of nucleation within the framework of the Gibbsian approximation. Here we consider and analyze the problem of closing the Gibbsian approximation droplet model. We identify micro- and Gamma-closure conjectures concerning the surface chemical potentials and excess surface coverages, respectively, for the droplet surface of tension. With these two closure conjectures, the Gibbsian approximation model of a binary droplet becomes complete so that one can determine both the surface and internal characteristics of the whole nucleus and develop the kinetic theory, based on this model. Theoretical results are illustrated by numerical evaluations for binary nucleation in a water-methanol vapor mixture at T=298.15 K. Numerical results show a striking increase in the droplet surface tension with decreasing droplet size at constant overall droplet composition. A comparison of the Gibbsian approximation with density functional calculations for a model surfactant system indicate that the excess surface coverages from the Gibbsian approximation are accurate enough for large droplets and droplets that are not too concentrated with respect to the solute.     

A Conventional Surfactant Becomes CO2‐Responsive in the Presence of Switchable Water Additives

We have developed a new benign means of reversibly breaking emulsions and latexes by using “switchable water”, an aqueous solution of switchable ionic strength. The conventional surfactant sodium dodecyl sulfate (SDS) is not normally stimuli‐responsive when CO₂ is used as the stimulus but becomes CO₂‐responsive or “switchable” in the presence of a switchable water additive. In particular, changes in the air/water surface tension and oil/water interfacial tension can be triggered by addition and removal of CO₂. A switchable water additive, N,N‐dimethylethanolamine (DMEA), was found to be an effective and efficient additive for the reversible reduction of interfacial tension and can lower the tension of the dodecane/water interface in the presence of SDS surfactant to ultra‐low values at very low additive concentrations. Switchable water was successfully used to reversibly break an emulsion containing SDS as surfactant, and dodecane as organic liquid. Also, the addition of CO₂ and switchable water can result in aggregation of polystyrene (PS) latexes; the later removal of CO₂ neutralizes the DMEA and decreases the ionic strength allowing for the aggregated PS latex to be redispersed and recovered in its original state.     

Multicomponent nucleation: thermodynamically consistent description of the nucleation work

A thermodynamically consistent formula is derived for the nucleation work in multicomponent homogeneous nucleation. The derivation relies on the conservative dividing surface which defines the nucleus as having specific surface energy equal to the specific surface energy sigma0 of the interface between the macroscopically large new and old phases at coexistence. Expressions are given for the radius of the nucleus defined by the conservative dividing surface and by the surface of tension. As a side result, the curvature dependence of the surface tension sigmaT of the nucleus defined by the surface of tension is also determined. The analysis is valid for nuclei of any size, i.e., for nucleation in the whole range of conditions between the binodal and the spinodal of the metastable old phase provided the inequality sigmaT < or = sigma0 is satisfied. It is found that under the conditions of validity of the analysis the nucleation rate is higher than the nucleation rate given by the classical nucleation theory. The general results are applied to nucleation of unary liquids or solids in binary gaseous, liquid or solid mixtures.     

The liquid–gas interface of oxygen–nitrogen solutions 2: Description in the Framework of the van der Waals gradient theory

The van der Waals gradient theory (vdW GT) is used to calculate surface tension, density profiles, adsorption, the Tolman length and to determine the position of dividing surfaces in the liquid–gas interface of an oxygen–nitrogen solution. The Helmholtz energy density (HED) is determined via an equation of state (EOS), unified for a liquid and gas, which describes stable, metastable and two-phase states of solutions. The influence parameters are calculated from data on the surface tension of pure components with the use of the mixing rule. At temperatures T > 100 K the vdW GT describes experimental data on the surface tension of oxygen–nitrogen solutions [V.G. Baidakov, A.M. Kaverin, V.N. Andbaeva, The liquid–gas interface of oxygen–nitrogen solutions: 1. Surface tension, Fluid Phase Equilib. 270 (2008) 116–120] within the experimental error. It is shown that the Tolman length, which determines the dependence of surface tension on the curvature of the dividing surface, depends considerably on the solution concentration.     

Parachors of liquid/vapor systems: A set of critical amplitudes

In light of the available experimental data and of our current understanding of liquid–vapor critical phenomena, we examine the values of the parachors and of the parachor exponent, which are commonly used to estimate surface tension from the density difference between coexisting liquid and vapor phases. This is a controversial issue, as values for the parachor exponent ranging from 3.5 to 4 have been proposed in the literature. The parachor exponent and parachors can be viewed as a critical exponent and critical amplitudes, respectively. The Ising value, equal to 3.88, should be observed for the exponent “close enough” to the liquid/vapor critical point, i.e., for “low enough” tensions and densities. However, a review of experimental data for several fluids suggests an effective value in the range of 3.6, in line with the effective values observed for the exponents that describe the vanishing of the density difference and capillary length with the distance to the critical temperature. In fact, the asymptotic Ising regime is not reached experimentally, as confirmed by an estimation of the parachors very near the critical point. Those (Ising) parachors can be inferred from other critical amplitudes corresponding to bulk properties by using two-scale factor universality. Their values exceed those deduced from off-critical tension and density data by more than 10%, corresponding to surface tension differences larger than 50%. We argue that effective parachors (i.e., corresponding to an exponent in the range of 3.6) can be utilized in combination with two-scale-factor universality for determining the critical behavior of fluid systems in an extended range around their liquid/vapor critical point.     

Pancakes

The equilibrium state of a microdroplet spreading spontaneously on a solid surface is usually expected to be a compact monolayer if the liquid is nonvolatile, i.e., if the temperature is well below the 2-dimensional critical temperature T_2C. More recently, it has been shown by de Gennes that this picture does not hold any more close to the wetting transition, where the initial spreading tension S₀ tends to vanish. Thicker, stable layers are predicted, the famous “pancakes”, the thickness of which diverges at the wetting transition. There is another case where the monolayer picture fails: some liquids composed of amphiphilic molecules, although they do not wet the substrate, build an autophobic film on it. On hydrophobic surfaces, this film is a perfectly organized bilayer of molecules. We give examples of the three situations, with the following nicknames: “French pancake” for the compact monolayer, “Swedish pancake” for the bilayer, “American pancake” for the thick film.     

Surface tension of random copolymer melts

A mean-field theory is presented to describe the surface tension and interfacial profile of random A-B multiblock copolymer melts in contact with air or a solid substrate. The copolymer model accounts for variations in average composition and block sequence distribution, and reduces to a model for statistical copolymers as the block size approaches that of a monomer. Ideal copolymers lacking chemical correlations between successive segments are predicted to have a larger surface tension than “blocky” copolymers with a tendency for repeated segments of A or B. © 1992 John Wiley & Sons, Inc.     

Skin Constituents as Cosmetic Ingredients. Part I: A Study of Bio‐mimetic Monoglycerides Behavior at the Squalene‐Water Interface by the “Pendant Drop” Method in a Static Mode

This work presents the behavior of bio‐mimetic monoglycerides at the squalene/water interface. The study was done in the so‐called “static” mode using the “pendant drop method”, enabling us to characterize these molecules according to the value of their critical efficiency concentration (CEC), their maximum surface excess concentration (Γ_∞), the efficiency of the surface tension reduction parameter (pC20), and the minimum value of their interfacial tension (γ_min). It also permitted the study of the influence of the structure of the carbon chain of those monoglycerides on their interfacial behavior.

The analysis of the different parameters shows that monoglycerides with small hydrocarbon chains, monoglycerides with one or more double bonds, and monoglycerides possessing a hydroxyl function grafted in the middle of the chain constitute excellent surfactants. Two different groups can be found: one group composed of short saturated hydrocarbon chain monoglycerides (C12∶0 to C16∶0) and long hydrocarbon chain monoglycerides (C18∶0 to C22∶0); the second group, composed of unsaturated hydrocarbon chain monoglycerides, also includes hydroxystearate and isostearate monoglycerides. The first group could be used for the formulation of “hydrating” cosmetic products having secondary droplets, the second group for W/O emulsions.     

“Electrocapillary” curve on solid metal obtained by holographic interferometry

A new very sensitive method was developed for obtaining the “electrocapillary” curve of a solid metal. The method is based on the measurement of small elastic deformations of a strip caused by the changes of the surface tension forces. For the precise measurement of the strip bending (the radius of curvature) holographic interferometry was applied. It is shown that a change of the surface tension ±0.1 mN m^?1 can be registered. The “electrocapillary” curve of platinum in 0.05 M H₂SO₄ solution was obtained. It was found that the zero charge potential is +0.25 V versus normal hydrogen electrode. The double layer capacity was evaluated. The method is not very sensitive to temperature changes and can be applied in any case when the working electrode (metal strip) is mounted in a transparent glass cell.     

New approach to defining thermodynamic surface tension of solids

Using either the chemical potential of the immobile component of a solid dissolved in a fluid phase or the corresponding component of the tensor of chemical potential in solid phase, a new concept of the grand thermodynamic potential of solid-fluid two-phase system is proposed. For a planar interfacial surface, this makes it possible to generalize the notion of thermodynamic surface tension σ introduced by Gibbs that has the meaning of the formation work of a unit surface. This tension is determined as the specific surface excess of the grand thermodynamic potential. This definition of the thermodynamic surface tension does not depend on the position of the dividing surface and is common for fluids and solids. It is shown that, at the arbitrary position of dividing surface, the difference between thermodynamic σ and mechanical @[gamma] surface tensions for solid surface is determined by the nonuniformity of the tensor of chemical potential in a solid, as well as by its anisotropy in the bulk of solid phase.     

Thermodynamic studies on thin liquid films. V. General formulation for spherical films

Thermodynamic equations were derived for adsorption at interfaces of spherical films and interaction between interfaces in a film. The dependence of film tension on capillary pressure between external and film-forming phases gave thermodynamic film thickness and the one on pressure difference across the film the distance between the surface of tension for the film and the innermost dividing surface. Curvature dependence of film tension was numerically evaluated by using one of the derived equations.