Classical density functional theory of orientational order at interfaces: application to water

A classical density functional formalism has been developed to predict the position-orientation number density of structured fluids. It is applied to the liquid-vapor interface of pure water, where it consists of a classical term, a gradient correction, and an anisotropic term that yields order through density gradients. The model is calibrated to predict that water molecules have their dipole moments almost parallel to a planar interface, while the molecular plane is parallel to it on the liquid side and perpendicular to it on the vapor side. For a planar interface, the surface tension obtained is twice its experimental value, while the surface potential is in qualitative agreement with that calculated by others. The model is also used to predict the orientation of water molecules near the surface of droplets, as well as the dependence of equilibrium vapor pressure around them on their size.     

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.     

On the applicability of Young–Laplace equation for nanoscale liquid drops

Debates continue on the applicability of the Young–Laplace equation for droplets, vapor bubbles and gas bubbles in nanoscale. It is more meaningful to find the error range of the Young–Laplace equation in nanoscale instead of making the judgement of its applicability. To do this, for seven liquid argon drops (containing 800, 1000, 1200, 1400, 1600, 1800, or 2000 particles, respectively) at T = 78 K we determined the radius of surface of tension R_s and the corresponding surface tension γ_s by molecular dynamics simulation based on the expressions of R_s and γ_s in terms of the pressure distribution for droplets. Compared with the two-phase pressure difference directly obtained by MD simulation, the results show that the absolute values of relative error of two-phase pressure difference given by the Young–Laplace equation are between 0.0008 and 0.027, and the surface tension of the argon droplet increases with increasing radius of surface of tension, which supports that the Tolman length of Lennard-Jones droplets is positive and that Lennard-Jones vapor bubbles is negative. Besides, the logic error in the deduction of the expressions of the radius and the surface tension of surface of tension, and in terms of the pressure distribution for liquid drops in a certain literature is corrected.     

Analysis of the linear tension of two-dimensional droplets on heterogeneous adsorbents

A procedure for analyzing the formation processes of two-dimensional droplets of an adsorbate on a rigid adsorbent support is considered. The molecular theory is based on data on the potential functions between adsorbent atoms and adsorbate molecules. Interactions between nearest neighbors are considered in the quasi-chemical approximation. The internal motions of adsorbent atoms and adsorbate molecules are ignored. Problems of describing the formation of droplets on heterogeneous adsorbents are associated with calculations for binodals (illustrated with the simplest example of two different homogeneous crystal faces) due to the choice of methods for calculating linear tension and the structural model of the region of the liquid–vapor transition. The dependence of the characteristics of droplets in the layered structural model on the method for determining the reference lines of the tension is shown for their metastable and equilibrium states. It is found that for a number of structural parameters, the thermodynamic determination of the line of tensions of metastable droplets can result in nonmonotonic dependences of the linear tension on their radii. The characteristics of two-dimensional liquid–vapor interfaces are compared for two structural models: coordination sphere and layered. It is found that the coordination sphere model allows the exclusion of the structural parameter of the layered model, but both models need refinement at small radii.     

Nucleation from supersaturated water vapors onn-dodecane substrate: A reverse Wilson chamber (RWC) method study

The reverse Wilson chamber method (RWC), developed for heterogencous nucleation investigation is applied to critical supersaturation measurements and determination of the surface concentration of nuclei (droplets) vs. supersaturation dependence in the case of nucleation from supersaturated water vapors onn-dodecane substrate. The experimental results obtained are interpreted in terms of the classical (Volmer) theory of heterogeneous nucleation as well as in the framework of the theory of barrierless nucleation. The several times lower critical supersaturations measured at four different temperatures, covering the range between 20° and 35° C, are explained by taking into account the effect of the negative line tension of three-phase contact. The temperature dependence of line tension for the three-phase systemn-dodecane/water/water vapor is extracted from the data to fir the theory. The results obtained are in complete disagreement with those ones obtained by Wu and Maa for the same system using jet-tensimeter technique, however, in another temperature interval. This discrepancy is discussed in detail in the text.     

Chemistry of Interfaces,M. J. Jaycock and G. D. Parfitt. Halstead Press,John Wiley and Sons,New York, 1981. 279 pp. $90. Paul Becher,Wilmington

A unique physical model is proposed for relating the dimensions and properties of droplets in aqueous diesel fuel invert mlcroemulsions to the measured water vapor pressures over such systems. The model assumes discrete droplets containing surfactant-sheathed liquid cores. A dynamic equilibrium condition is visualized wherein a closed mass transfer cycle e3tists, involving the movement of water molecules from the droplet interior, through the surfactant sheath into the continuous medium and vapor space above the pool. The flat-surface fugacity of the liquid water in the aqueous core would be reduced relative to that of normal water because of Increased intermolecular association stemming from high pressure in the aqueous core caused by surface tension forces. The possible presence of dissolved surfactant constituents would reduce this fugacity even further. The mass transfer cycle is assumed to be completed by the absorption of water vapor into transitory, flat surfaces of reduced fugacity, droplet core water exposed by collapsing droplets at the pool surface. These are assumed to be continually reforming into submerged microemulsion droplets as additional droplets collapse at the pool surface.

Analytical relationships based upon the described model allowed calculation of droplet core and sheath dimensions and droplet external interfacial tension. The efficacy of the proposed model is supported by the congruity of the thus derived values.     

Molecular dynamics simulation of the density and surface tension of water by particle-particle particle-mesh method

In this work, molecular dynamics simulation is performed to study the density and surface tension of water for a range of temperatures from 300 to 600 K. The extended simple point charge interaction potential for water is used. The particle-particle particle-mesh method, which automatically includes untruncated long-range terms, is used for the Lennard-Jones and the Coulombic terms. The results show that the long-range correction for the Lennard-Jones term is very important for the calculation of surface tension. It is found that the calculated density and surface tension of water fit well with experimental data for temperatures less than 500 K. Near the critical temperature, the simulation results are off from the experimental data.     

Microstructuring of Polystyrene Surfaces with Nonsolvent Sessile Droplets

Herein, we study the microstructuring of toluene‐vapor‐softened polystyrene surfaces with nonsolvent sessile droplets. Arrays of microvessels are obtained by depositing non‐evaporating droplets of ethylene glycol/water on the original polystyrene surfaces and subsequently exposing them to saturated toluene vapor. The droplets act as a mask on the polymer, thereby impeding the toluene vapor to diffuse and soften the polystyrene surface below them. Alternatively, the formation of microcraters at random positions—with an average depth‐to‐width aspect ratio of 0.5 and a diameter as small as 1.5 μm—is achieved by condensing water droplets on a softened polystyrene surface. The cross‐sections of the microvessels and the contact angle of the sessile water droplets suggest that the structures are formed by the combined action of the Laplace pressure at the bottom of the droplet and the surface tension acting at the three‐phase contact line of the droplets. As a support, the rim height and the depth of the microvessels are fitted with an elastic theory to provide Young’s modulus of the softened polystyrene surface.     

Numerical simulation of water droplet evaporation into vapor–gas medium

Numerical simulation has been employed to consider water droplet evaporation into a vapor–gas medium. An approximate approach has been proposed that makes it possible to take into account the effect of a noncondensable component on the character of variations in the droplet temperature during evaporation. The results of the calculations have been compared with the published experimental data.     

Some consequences of high temperature water vapor spectroscopy: water dimer at equilibrium

It is shown that the evolution of water vapor spectra in the 2500-5000 cm(-1) range recorded at 650 K and pressures up to 130 atms after subtraction of monomer contribution may be interpreted qualitatively well on the basis of experimental data on water dimer and trimer obtained from cold molecular beams and in He droplets. The proposed spectroscopic model considers water vapor as a mixture of nonideal monomers, dimers, and trimers at chemical equilibrium. The effect of line mixing is taken into account in the monomer spectrum modeling. Decomposition of the high temperature spectra allowed determining a dimer equilibrium constant that was compared with the previously known values. The contribution of water trimer is assessed. The performed analysis indicates that the number of bound dimers in water vapor is quite large, even at such a high temperature.     

A study of sulfur homogeneous nucleation from supersaturated vapor. Determination of surface tension of sulfur nanoparticles

Homogeneous nucleation in sulfur vapor is studied in a laminar-flow chamber. Concentration and size distribution of resulting aerosol particles are measured with a diffusion spectrometer of aerosols and a PK.GTA-0,3-002 photoelectric particle counter. The crystal structure of the formed particles is studied by X-ray diffraction analysis. The rate of sulfur evaporation from a boat and the profile of a deposit on the chamber wall along the axial coordinate are determined by gravimetry. Axial and radial temperature profiles are measured using a chromel-alumel thermocouple. The vapor concentration distribution in the chamber is found and the supersaturation is calculated from the solution of the mass-transfer problem. An experimental low-laborious method is developed for the supersaturation cutoff. This method enables one to rapidly deter-mine the position of the zone in which the nucleation proceeds at the highest rate. The position of the zone of nucleation found by this method is in good agreement with the results of calculations based on experimental data and theoretical calculation of the rate of nucleation by an exact formula that has been recently derived based on the works by Kusaka and Reiss, as well as the Frenkel liquid kinetics theory. The surface tension of critical sulfur nuclei resulting from the nucleation is calculated based on this formula and experimental data on the nucleation. It is established that, in a temperature range of 312–319 K, the critical nuclei have tension surface radius R _s ～ 10.6 Å and surface tension σ = 72.5 ± 1.1 dyn/cm. The surface tension of critical sulfur nuclei in this temperature range is constant and approximately 5% higher than that of a planar surface.     

Water vapor nucleation on ion pairs under the conditions of a planar nanopore

Computer simulation has been employed to study the effect of a confined space of a planar model pore with structureless hydrophobic walls on the hydration of Na⁺Cl^– ion pairs in water vapor at room temperature. A detailed many-body model of intermolecular interactions has been used. The model has been calibrated relative to experimental data on the free energy and enthalpy of the initial reactions of water molecule attachment to ions and the results of quantum-chemical calculations of the geometry and energy of Na⁺Cl^– (H₂O)_N clusters in stable configurations, as well as spectroscopic data on Na⁺Cl^– dimer vibration frequencies. The free energy and work of hydration, as well as the adsorption curve, have been calculated from the first principles by the bicanonical statistical ensemble method. The dependence of hydration shell size on interionic distance has been calculated by the method of compensation potential. The transition between the states of a contact (CIP) and a solvent-separated ion pair (SSIP) has been reproduced under the conditions of a nanopore. The influence of the pore increases with the hydration shell size and leads to the stabilization of the SSIP states, which are only conditionally stable in bulk water vapor.     

Effects of thermodynamic ensembles and mineral surfaces on interfacial water structure

While performing molecular dynamics simulations of water or aqueous solutions in a slab geometry, such as at mineral surfaces, it is important to match bulk water density in the diffuse region of the model system with that expected for the appropriate experimental conditions. Typically, a slab geometry represents parallel surfaces with a variable region of confined water (this region can range in size from a few ?ngstroms to many tens of ?ngstroms). While constant-pressure simulations usually result in appropriate density values in the bulk diffuse region removed from either surface, constant-volume simulations have also been widely used, sometimes without careful consideration of the method for determining water content. Simulations using two thermodynamic ensembles as well as two methods for calculating the water-accessible volume have been investigated for two distinct silicate surfaces-hydrophilic cristobalite (111) and hydrophobic pyrophyllite (001). In cases where NPT simulations are not feasible, a simple geometry-based treatment of the accessible volume can be sufficient to replicate bulk water density far from the surface. However, the use of the Connolly method can be more appropriate in cases where a surface is less well-defined. Specific water-surface interactions (e.g., hydrophobic repulsion) also play a role in determining water content in a confined water simulation. While reported here for planar surfaces, these results can be extended to an interface with any solvent, or to other types of surfaces and geometries.     

Development of non‐bonded interaction parameters between graphene and water using particle swarm optimization

New Lennard‐Jones parameters have been developed to describe the interactions between atomistic model of graphene, represented by REBO potential, and five commonly used all‐atom water models, namely SPC, SPC/E, SPC/Fw, SPC/Fd, and TIP3P/Fs by employing particle swarm optimization (PSO) method. These new parameters were optimized to reproduce the macroscopic contact angle of water on a graphene sheet. The calculated line tension was in the order of 10⁻¹¹ J/m for the droplets of all water models. Our molecular dynamics simulations indicate the preferential orientation of water molecules near graphene–water interface with one O H bond pointing toward the graphene surface. Detailed analysis of simulation trajectories reveals the presence of water molecules with ≤∼1, ∼2, and ∼4 hydrogen bonds at the surface of air–water interface, graphene–water interface, and bulk region of the water droplet, respectively. Presence of water molecules with ≤∼1 and ∼2 hydrogen bonds suggest the existence of water clusters of different sizes at these interfaces. The trends observed in the libration, bending, and stretching bands of the vibrational spectra are closely associated with these structural features of water. The inhomogeneity in hydrogen bond network of water at the air–water and graphene–water interface is manifested by broadening of the peaks in the libration band for water present at these interfaces. The stretching band for the molecules in water droplet shows a blue shift as compared to the pure bulk water, which conjecture the presence of weaker hydrogen bond network in a droplet. © 2017 Wiley Periodicals, Inc.     

Protein charge-state distributions in electrospray-ionization mass spectrometry do not appear to be limited by the surface tension of the solvent

According to a current model for protein electrospray, the charge-state distributions (CSDs) observed by electrospray-ionization mass spectrometry (ESI-MS) are controlled by the Rayleigh-limit charge of the droplets that generate the gas-phase protein ions. A testable prediction of this model is that the maximum charge state displayed by proteins in ESI-MS should respond to changes in the surface tension of the ESI droplets according to the Rayleigh equation. In this work, we subject this specific hypothesis to direct experimental testing. We show data obtained by time-of-flight (TOF) nano-ESI-MS with several different proteins in aqueous solutions containing 20-50% 1-propanol or 40% 1,2-propylene glycol. Both of these compounds have lower vapor pressure and lower surface tension than water. Propylene glycol also has a lower evaporation rate than water, providing an even more stringent test for surface tension effects in late ESI droplets. None of these cosolvents affects the CSDs of either folded or unfolded proteins as predicted by the Rayleigh-charge model. The only changes induced by 1-propanol can be ascribed to protein unfolding triggered above critical concentrations of the alcohol. Below such a threshold, no shift of the CSDs toward lower charge states is observed. The presence of 40% propylene glycol in the original protein solutions gives rise to CSDs that either are the same as those in the control samples or present much smaller changes than those calculated by the Rayleigh equation. Thus, the charge states of gas-phase protein ions produced by electrospray do not seem to be limited by the surface tension of the solvent. They rather appear to be quite protein-specific.     

The Effect of Temperature on Nucleation of Condensed Water Phase on the Surface of a β-AgI Crystal. 2. Formation Work

In the condensation mechanism of heterogeneous ice formation, water crystallization occurs after a necessary amount of the liquid phase has accumulated on a substrate surface. In this way, the ice-forming activity of the surface is governed by its adsorption ability with respect to water vapor. The Monte Carlo canonical statistical ensemble method has been used to calculate the free energy, entropy, and work of nucleation of a disordered condensed water phase on the surface of crystalline silver iodide and to determine the surface tension. Comparative calculations have been performed at 260 and 320 K for the defect-free surface of a basal face of a crystal. The surface of a β-AgI crystal is completely covered with a monomolecular film even in unsaturated water vapors. The surface tension at the growing nucleus–substrate interface substantially increases due to the formation of the underlying film, and the growth of the nucleus becomes possible only in a supersaturated vapor. As the vapor density increases, the thickness of the condensed water layer grows, and, at negative Celsius temperatures, conditions are created for its crystallization. The underlying film with pronounced hydrophobic properties hinders nucleation, thereby decreasing the ice-forming activity of the surface in the condensation process. Under these conditions, the observed abnormally high ice-forming activity of silver-iodide aerosol particles may be explained by the presence of numerous crystal defects on the particle surface, with these defects representing channels that provide overcoming the hindering action of the film.     

Surface tension of different sized single-component droplets,according to macroscopic data obtained using the lattice gas model and the critical droplet size during phase formation

Size dependences of the surface tension of spherical single-component droplets are calculated using equations of the lattice gas model for 19 compounds. Parameters of the model are found from experimental data on the surface tension of these compounds for a macroscopic planar surface. The chosen low-molecular compounds satisfy the law of corresponding states. To improve agreement with the experimental data, Lennard-Jones potential parameters are varied within 10% deviations. The surface tensions of different sized equilibrium droplets are calculated at elevated and lowered temperatures. It is found that the surface tension of droplets grows monotonically as the droplet size increases from zero to its bulk value. The droplet size R ₀ corresponding to zero surface tension corresponds to the critical size of the emergence of a new phase. The critical droplet sizes in the new phase of the considered compounds are estimated for the first time.     

Effect of volume concentration and temperature on viscosity and surface tension of graphene–water nanofluid for heat transfer applications

In the present study, the effect of volume concentration (0.05, 0.1 and 0.15 %) and temperature (10–90 °C) on viscosity and surface tension of graphene–water nanofluid has been experimentally measured. The sodium dodecyl benzene sulfonate is used as the surfactant for stable suspension of graphene. The results showed that the viscosity of graphene–water nanofluid increases with an increase in the volume concentration of nanoparticles and decreases with an increase in temperature. An average enhancement of 47.12 % in viscosity has been noted for 0.15 % volume concentration of graphene at 50 °C. The enhancement of the viscosity of the nanofluid at higher volume concentration is due to the higher shear rate. In contrast, the surface tension of the graphene–water nanofluid decreases with an increase in both volume concentration and temperature. A decrement of 18.7 % in surface tension has been noted for the same volume concentration and temperature. The surface tension reduction in nanofluid at higher volume concentrations is due to the adsorption of nanoparticles at the liquid–gas interface because of hydrophobic nature of graphene; and at higher temperatures, is due to the weakening of molecular attractions between fluid molecules and nanoparticles. The viscosity and surface tension showed stronger dependency on volume concentration than temperature. Based on the calculated effectiveness of graphene–water nanofluids, it is suggested that the graphene–water nanofluid is preferable as the better coolant for the real-time heat transfer applications.     

Peristome‐Mimetic Curved Surface for Spontaneous and Directional Separation of Micro Water‐in‐Oil Drops

Separation of micro‐scaled water‐in‐oil droplets is important in environmental protection, bioassays, and saving functional inks. So far, bulk oil–water separation has been achieved by membrane separation and sponge absorption, but micro‐drop separation still remains a challenge. Herein we report that instead of the “plug‐and‐go” separation model, tiny water‐in‐oil droplets can be separated into pure water and oil droplets through “go‐in‐opposite ways” on curved peristome‐mimetic surfaces, in milliseconds, without energy input. More importantly, this overflow controlled method can be applied to handle oil‐in‐oil droplets with surface tension differences as low as 14.7 mN m⁻¹ and viscous liquids with viscosities as high as hundreds centipoises, which markedly increases the range of applicable liquids for micro‐scaled separation. Furthermore, the curved peristome‐mimetic surface guides the separated drops in different directions with high efficiency.