Some estimates of the surface tension of curved surfaces using density functional theory

Density functional theory is used to calculate the surface tension of planar and slightly curved surfaces, which can be written as gamma(R)=gamma(infinity)(1-2delta(infinity)R), where R is the radius of curvature of the surface. Calculations are performed for a Lennard-Jones fluid, split into a hard-sphere repulsive potential and an attractive part. The repulsive part is treated using the local density approximation. The attractive part is treated using a high temperature approximation (HTA) in which the pair correlation function is approximated by the Percus-Yevick pair correlation function of a uniform hard-sphere fluid evaluated at a position-dependent average density. An expression relating the Tolman length delta(infinity) to the density profile of the planar surface is derived. Numerical results are presented for the planar surface tension gamma(infinity) and for delta(infinity) and are compared with those using mean field theory (MFT) and with those using the square-gradient approximation. Values for gamma(infinity) using the HTA are 30%-40% higher than those using MFT. Values for delta(infinity) using the HTA are around -0.1 (in units of the Lennard-Jones parameter sigma) and only weakly dependent on temperature. These values are less negative than the values from MFT. The square-gradient approximation gives reasonable estimates of the more accurate nonlocal results for both the MFT and the HTA.     

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.     

Surface tension and tolman length of spherical particulate in contact with fluid

The structure, surface tension and Tolman length of particulate-fluid interfaces were studied theoretically. Within the framework of density functional theory, the nonlocal, modified fundamental measure theory and direct correlation function from the first-order mean spherical approximation were incorporated. The theory accurately predicted the structure of fluid and the particulate-vapor surface tensions. The predictions of surface tensions for particulate-liquid interface and particulate in supercritical fluid are also reasonable. Especially, Tolman lengths for particulate-fluid interfaces were investigated systematically. The correct prediction of surface tension from Tolman length indicates that our analysis is reliable. Furthermore, Tolman length as a function of spherical particulate diameter, particulate-fluid interaction energy, and the properties of the fluid is fully discussed.     

Surface properties and wetting characteristics of liquid Ag–Bi–Sn alloys

Abstract  

Surface tension and density measurements of liquid Ag–Bi–Sn alloys were carried out over a wide temperature range using the sessile drop method. The experimental data of surface tension were analyzed by the Butler thermodynamic model in the regular solution approximation. The Sn-rich Ag–Bi–Sn liquid alloys show better wetting behavior on the Cu substrates as compared to the Ni substrates.     

Scaled equations for the coexistence curve,the capillary constant and the surface tension of n-alkanes

A review of experimental data of several fluids shows that their coexistence curve follows a power law in reduced temperature at the approach of the critical point, with an universal exponent equal to 0.325, their capillary constant a power law with an universal exponent equal to 0.925 and their surface tension a power law with an universal exponent equal to 1.26. In the critical region, the concept of two-scale-factor universality was used to predict the density difference amplitude, the capillary constant amplitude, and the surface tension amplitude between near critical vapor and liquid phases. A comparison with amplitudes determined from experimental data is given. In order to extend this universality all along the liquid–gas coexistence curve from the triple point to the critical point for n-alkanes, a mean field approximation was used far away from T_C. We show that the density difference, the capillary constant and the surface tension can be calculated with a reasonable accuracy by generalized scaled equations adding only two empirical constants. A comparison between calculated and experimental data is presented.     

Yukawa流体的相平衡和界面张力研究

应用二阶微扰理论, Duh-Mier-Y-Teran状态方程和在平均球近似(mean spherical approximation, MSA)的基础上获得的直接相关函数, 建立了适用于均匀流体和非均匀流体的状态方程. 结合此状态方程, 重整化群理论(renormalization group theory, RG)和密度泛函理论(density functional theory, DFT), 分别研究了Yukawa流体的相平衡和界面张力. 结果与分子模拟数据吻合良好.     

Prediction of Density,Surface Tension,and Viscosity of Quaternary Ammonium-Based Ionic Liquids ([N222(n)]Tf2N) by Means of Artificial Intelligence Techniques

In this work, thermophysical properties of quaternary ammonium-based ionic liquids (ILs) including density, surface tension, and viscosity are produced by two powerful artificial intelligence techniques: genetic function approximation (GFA) and artificial neural network (ANN). In proposed GFA and ANN models, the critical temperature and water content of studied ILs ([N_222(n)]Tf₂N with n = 5, 6, 8, 10, and 12) as well as operation temperature were given as the input parameters and the density, surface tension, and viscosity were predicted as the output results. The obtained results reveal that the selected input parameters are appropriate for prediction of thermophysical properties of quaternary ammonium-based ILs. In addition, the high statistical quality represented by various criteria and the low prediction errors of the presented models indicate that they can accurately predict the density, surface tension, and viscosity of new ILs without recourse to experimental data.     

Changes in density and surface tension of water in silica pores

 The density and surface tension of water in small pores of silicas have been investigated. These physical properties of water in the pores were calculated from a comparison of pore volumes and pore radii which were estimated from adsorption and desorption isotherms of nitrogen and water. Below a pore radius of about 5 nm both the density and the surface tension of water in the pores were smaller than those of the bulk liquid and decreased with a decrease in pore size. The density of water in the pores decreased with an increase in the concentration of surface hydroxyl groups. Similarly the surface tension of water in the pores is influenced by the surface hydroxyl groups. Anomalous changes in the density and surface tension of the water in the pores are attributed to the interaction of water molecules with surface hydroxyl groups and hydrogen-bond formation among water molecules. Received: 20 April 1999 Accepted in revised form: 17 November 1999     

Molecular analysis of small drops in a metastable vapor

The molecular theory of curved vapor-liquid interfaces within the lattice gas model is applied to analyze supersaturated vapor states in dependence on the new phase size and system temperature. The molecular interaction is considered in the quasi-chemical approximation which describes effects of direct correlations of the nearest molecules. Two methods for determining the surface tension are discussed: equimolecular and according to the surface tension minimum in the intermediate region, i.e., on the tension surface. It is shown that a tension surface exists for metastable drops in supersaturated vapor over the temperature range, but its use leads to multivaluedness of solutions for its position; the minimum range of the existence of metastable drops is close to the previously determined lower limit for equilibrium.     

Effect of temperature on the density and surface tension of aqueous solutions of HMT

In this study, a systematic study of the effect of the temperature on the density and surface tension of HMT (hexamethylentetramine) in water was developed. The density and surface tension were determined at temperatures of 288.15, 293.15, 298.15, 303.15, and 308.15 K. Precise data of surface tension have not been reported previously in literature. From the density measurements, the apparent molar and partial molar volumes were calculated. The apparent molar volume decreases with concentration, the molar partial volume increases with temperature. The surface tension of the aqueous solutions of HMT decreases with concentration. The excess surface concentration was calculated, the values increase with concentration, indicating that the amount of HMT that goes to the interface gas liquid increases at higher concentrations of HMT.     

Density, refractive index, interfacial tension, and viscosity of ionic liquids [EMIM][EtSO4], [EMIM][NTf2], [EMIM][N(CN)2], and [OMA][NTf2] in dependence on temperature at atmospheric pressure

The density, refractive index, interfacial tension, and viscosity of ionic liquids (ILs) [EMIM][EtSO 4] (1-ethyl-3-methylimidazolium ethylsulfate), [EMIM][NTf 2] (1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide), [EMIM][N(CN) 2] (1-ethyl-3-methylimidazolium dicyanimide), and [OMA][NTf 2] (trioctylmethylammonium bis(trifluoromethylsulfonyl)imide) were studied in dependence on temperature at atmospheric pressure both by conventional techniques and by surface light scattering (SLS). A vibrating tube densimeter was used for the measurement of density at temperatures from (273.15 to 363.15) K and the results have an expanded uncertainty ( k = 2) of +/-0.02%. Using an Abbe refractometer, the refractive index was measured for temperatures between (283.15 and 313.15) K with an expanded uncertainty ( k = 2) of about +/-0.0005. The interfacial tension was obtained from the pendant drop technique at a temperature of 293.15 K with an expanded uncertainty ( k = 2) of +/-1%. For higher and lower temperatures, the interfacial tension was estimated by an adequate prediction scheme based on the datum at 293.15 K and the temperature dependence of density. For the ILs studied within this work, at a first order approximation, the quantity directly accessible by the SLS technique was the ratio of surface tension to dynamic viscosity. By combining the experimental results of the SLS technique with density and interfacial tension from conventional techniques, the dynamic viscosity could be obtained for temperatures between (273.15 and 333.15) K with an estimated expanded uncertainty ( k = 2) of less than +/-3%. The measured density, refractive index, and viscosity are represented by interpolating expressions with differences between the experimental and calculated values that are comparable with but always smaller than the expanded uncertainties ( k = 2). Besides a comparison with the literature, the influence of structural variations on the thermophysical properties of the ILs is discussed in detail. The viscosities mostly agree with values reported in the literature within the combined estimated expanded uncertainties ( k = 2) of the measurements while our density and interfacial tension data differ by more than +/-1% and +/-5%.     

The density and surface tension of In–Sn and Cu–In–Sn alloys

Abstract  

The density and surface tension of binary In–Sn and ternary Cu–In–Sn alloys have been measured by a sessile-drop method. Decrease of the density and of the surface tension was observed with rising temperature. With increased Sn content in the alloys, the density increased while the surface tension reduced slightly. Addition of Cu could significantly increase the density and surface tension in the Cu–In–Sn system. The surface tension of the Cu–In–Sn alloys was also calculated by means of Butler’s equation, and compared with experimental values, showing good agreement.     

Effect of interparticle interactions on the rate of injection of charge carriers into electroactive polymer films

A phenomenological approach is used for deriving a difference equation for the density of reduced sites in films of electroactive polymers with conspicuous interparticle interactions. The approach involves simultaneous application of the lattice methods and Broensted’s rule. This leads to generalization of equations for the surface layer that are known in theory of surface tension for nonelectrolytic solutions. Together with the Poisson equation for electric potential, the derived relationships make a complicated system of differential equations. Nevertheless, it can be solved by iterative methods. In the framework of this approach, expressions for the rates of injection of charge carriers into polymer films are obtained. Within a first approximation with regard to allowance for the forces of short-range interactions, their influence on the rates of injection of electrons and protons into a film is discussed.     

Further investigation about Lagrangian theorem-based density functional approximation: test by non-uniform polymer melt

A Lagrangian theorem-based density functional approximation [S. Zhou, New J. Phys. 4 (2002) 36] for hard sphere fluid is employed to describe non-uniform polymer melt in the framework of density functional theory. A required bulk second order direct correlation function (DCF) within the whole density range is obtained by solving the polymer-RISM integral equation, the associated adjustable parameter is specified by a hard wall sum rule, and is found to be a negative value when the bulk density is low and the number of chain segment is large. However, the mathematically meaningless value can be physically meaningful by the observation that the present recipe can produce out density profile in very good agreement with simulation data not only at the contact region, but also at the region far away from the surface, and that the predicted global quantities such as surface excess and surface tension are also in good agreement with the simulation data. It is considered that the LTDFA has a property of self correction, which enables the LTDFA-based DFA for non-uniform polymer melt performs quite well even with a not very accurate second order DCF as input. Potential applications of the self correction peculiarity are discussed.     

Thermal fluctuations of clusters with the long-range interaction

Analysis of surface fluctuation spectra is performed for a large cluster of particles interacting via a sum of the short-range Lennard-Jones potential and long-range ±1/r potential, where the positive sign corresponds to the gravity, and negative corresponds to the electrostatic interaction. The spectral amplitudes of thermally driven capillary modes in a self-consistent field induced by cluster particles including the modes with no axial symmetry are derived in the approximation of small amplitudes. It is demonstrated that within used approximation, the surface tension is independent of the field strength. The low wave vector amplitudes are damped by attracting field that compresses the cluster and magnified by repulsing field leading to cluster fission. The fission threshold is found to be different from that found by Bohr and Wheeler and Frenkel due to the replacement of the ordinary surface tension by the bare one. Molecular dynamics study of a cluster with the long-range interaction in the vapor environment is performed using a novel integrator for a multiscale system. Simulation scheme implies rotation of the long-range components of forces acting on cluster particles thus vanishing an artificial torque. Simulation results justify theoretical conclusion of modes damping and independence of the surface tension of the field strength. Fission threshold evaluated from simulation data is in a good agreement with theory.     

Surface energy and surface tension of condensed matter and the principle of minimum potential energy of systems (revised)

We consider the essence and relation of the surface energy and surface tension of condensed matter: which is which … and (most important question here)—when? For the first time, this consideration is based not on reversible thermodynamics but, as an approximation, on the Principle of Minimum Potential Energy, given two factors: (1) the time-dependent dynamic transformation of the potential energy of the system into the surface energy and into the surface tension (stress); (2) elasticity of structured surface layers of the liquids.     

Liquid-vapor and liquid-liquid interfaces in Ising fluids: an integral equation approach

The microscopic structure and thermodynamic properties of liquid-vapor and liquid-liquid interfaces in Ising fluids are studied using an integral equation approach. The calculations are performed in the absence and presence of an external magnetic field by solving the corresponding set of Lovett-Mou-Buff-Wertheim integrodifferential equations for the one-particle density distribution functions. The two-particle inhomogeneous direct correlation functions are consistently constructed by nonlinear interpolation between the bulk ones. The bulk correlation functions of the coexisting phases are obtained from the Ornstein-Zernike equations with a modified soft mean spherical approximation for the closure relation. As a result, the density and magnetization profiles at liquid-vapor and liquid-liquid interfaces as well as the surface tension and adsorption coefficients are evaluated in a wide temperature range including subcritical regions. The influence of an external magnetic field on the liquid-vapor interfaces is also considered.     

Molecular dynamics study of structural and thermodynamic characteristics of nanodroplets of simple fluid

Equilibrium configurations of Lennard-Jones nanodroplets composed of 10–15000 spherically symmetric molecules placed in the center of a spherical container are studied at constant temperature by the molecular dynamics method. The distribution of local density is found and size dependences of density in the center of droplet, first coordination number, and energy surface tension coinciding for equimolecular dividing surface with specific excess free energy of droplet are studied. Radial distribution function is also determined. It is established that the passage of structural characteristics to their macroscopic values is observed for droplets containing as little as about 300 molecules, while, for energy surface tension, analogous passage for energy surface tension occurs for droplets containing 700–6000 molecules.     

Interfacial tension and interfacial profiles: an equation-of-state approach

A quasi-thermodynamic approach of inhomogeneous systems is used for modeling the fluid-fluid interface. It is based on the recently introduced QCHB (quasi-chemical hydrogen bonding) equation-of-state model of fluids and their mixtures, which is used for the estimation of the Helmholtz free energy density difference, Deltapsi(0), between the system with interface and another system of the same constitution but without interface. Consistent expressions for the interfacial tension and interfacial profiles for various properties are presented. The interfacial tension is proportional to the integral of Deltapsi(0) along the full height of the system, the proportionality constant being equal to 1, when no density gradient contributions are taken into consideration, 2, when the Cahn-Hilliard approximation is adopted, and 4, when the full density gradient contributions are taken into consideration. A satisfactory agreement is obtained between experimental and calculated surface tensions. Extension of the approach to mixtures is examined along with the associated problems for the numerical calculations of the interfacial profiles. A new equation is derived for the chemical potentials in the interfacial region, which facilitates very much the calculation of the composition profiles across the interface.     

Validity of the "sharp-kink approximation" for water and other fluids

The contact angle of a liquid droplet on a solid surface is a direct measure of fundamental atomic-scale forces acting between liquid molecules and the solid surface. In this work, the validity is assessed of a simple equation, which approximately relates the contact angle of a liquid on a surface to its density, its surface tension, and the effective molecule-surface potential. This equation is derived in the sharp-kink approximation, where the density profile of the liquid is assumed to drop precipitously within one molecular diameter of the substrate. It is found that this equation satisfactorily reproduces the temperature-dependence of the contact angle for helium on alkali metal surfaces. The equation also seems be applicable to liquids such as water on solid surfaces such as gold and graphite, on the basis of a comparison of predicted and measured contact angles near room-temperature. Nevertheless, we conclude that, to fully test the equation's applicability to fluids such as water, it remains necessary to measure the contact angle's temperature-dependence. We hypothesize that the effects of electrostatic forces can increase with temperature, potentially driving the wetting temperature much higher and closer to the critical point, or lower, closer to room temperature, than predicted using current theories.