Capillary waves at the liquid-vapor interface and the surface tension of water

Capillary waves occurring at the liquid-vapor interface of water are studied using molecular dynamics simulations. In addition, the surface tension, determined thermodynamically from the difference in the normal and tangential pressure at the liquid-vapor interface, is compared for a number of standard three- and four-point water models. We study four three-point models (SPC/E, TIP3P, TIP3P-CHARMM, and TIP3P-Ew) and two four-point models (TIP4P and TIP4P-Ew). All of the models examined underestimate the surface tension; the TIP4P-Ew model comes closest to reproducing the experimental data. The surface tension can also be determined from the amplitude of capillary waves at the liquid-vapor interface by varying the surface area of the interface. The surface tensions determined from the amplitude of the logarithmic divergence of the capillary interfacial width and from the traditional thermodynamic method agree only if the density profile is fitted to an error function instead of a hyperbolic tangent function.     

Oscillatory surface tension due to finite-size effects

The simulation results of surface tension at the liquid-vapor interface are presented for fluids interacting with Lennard Jones and square-well potentials. From the simulation of liquids we have reported [M. González-Melchor et al., J. Chem. Phys. 122, 4503 (2005)] that the components of pressure tensor in parallelepiped boxes are not the same when periodic boundary conditions and small transversal areas are used. This fact creates an artificial oscillatory stress anisotropy in the system with even negative values. By doing direct simulations of interfaces we show in this work that surface tension has also an oscillatory decay at small surface areas; this behavior is opposite to the monotonic decay reported previously for the Lennard Jones fluid. It is shown that for small surface areas, the surface tension of the square-well potential artificially takes negative values and even increases with temperature. The calculated surface tension using a direct simulation of interfaces might have two contributions: one from finite-size effects of interfacial areas due to box geometry and another from the interface. Thus, it is difficult to evaluate the true surface tension of an interface when small surface areas are used. Care has to be taken to use the direct simulation method of interfaces to evaluate the predicted surface tension as a function of interfacial area from capillary-wave theory. The oscillations of surface tension decay faster at temperatures close to the critical point. It is also discussed that a surface area does not show any important effect on coexisting densities, making this method reliable to calculate bulk coexisting properties using small systems.     

Effect of flexibility on surface tension and coexisting densities of water

Molecular dynamics simulations of pure water at the liquid-vapor interface are performed using direct simulation of interfaces in a liquid slab geometry. The effect of intramolecular flexibility on coexisting densities and surface tension is analyzed. The dipole moment profile across the liquid-vapor interface shows different values for the liquid and vapor phases. The flexible model is a polarizable model. This effect is minor for liquid densities and is large for surface tension. The liquid densities increase from 2% at 300 K to 9% at 550 K when the force field is changed from a fully rigid simple point charge extended (SPCE) model to that of a fully flexible model with the same intermolecular interaction parameters. The increases in surface tension at both temperatures are around 11% and 36%, respectively. The calculated properties of the flexible models are closer to the experimental data than those of the rigid SPCE. The effect of the maximum number of reciprocal vectors (h(z) (max)) and the surface area on the calculated properties at 300 K is also analyzed. The coexiting densities are not sensitive to those variables. The surface tension fluctuates with h(z) (max) with an amplitude larger than 10 mN m(-1). The effect of using small interfacial areas is slightly larger than the error in the simulations.     

Criticality of a liquid-vapor interface from an inhomogeneous integral equation theory

A microscopic theory is developed to study the liquid-vapor interfacial properties of simple fluids with ab initio treatment of the inhomogeneous two-body correlation functions, without any interpolation. It consists of the inhomogeneous Ornstein-Zernike equation coupled with the Duh-Henderson-Verlet closure and the Lovett-Mou-Buff-Wertheim equation. For the liquid-vapor interface of the Lennard-Jones fluid, we obtained the density profile and the surface tension, as well as their critical behaviour. In particular, we identified non-classical critical exponents. The theory accurately predicts the phase diagram and the interfacial properties in a very good agreement with simulations. We also showed that the method leads to true capillary-wave asymptotics in the macroscopic limit.     

Thermodynamic study of interfacial tension between oil and aqueous phases composed of ionic liquids and brine

The first fundamental step in determining the physicochemical properties of an equilibrium system is to determine the activity coefficient of electrolyte and non-electrolyte ions. Based on understanding the importance of activity coefficient in thermodynamic systems in this study, in order to predict interfacial tension between oil and aqueous phases composed of ionic liquids and brine, a modified thermodynamic equation based on concentration and coefficient of activity of ionic liquids is defined. For this study, the Extended UNIQUAC model is desired and its adjustable parameters are optimized with Genetic + PSO algorithm. The modified model has practical features such as investigating the effect of concentrations of salts in the water of oil fields formation on the interfacial tension of the system, investigating the effect of concentrations of various organic compounds such as ionic liquids on the interfacial tension of the system and investigating the interaction energy between organic and inorganic ions. In this study, the optimization of the modified thermodynamic equation to predict the interfacial tension of solutions containing [C₈Py][Cl], [C₁₈Py][Cl], [C₁₂mim][Cl] and [C₁₈mim][Cl] with the presence of brine and distilled water is investigated. Also, the effect of ionic strength of the solution in 32 equilibrium systems on interfacial tension is investigated. According to the optimization results of this study, the design of a computer program can be considered to predict the interfacial tension with the presence of ionic liquids and salts.     

离子液体表/界面性质与结构

离子液体与气体、溶剂等物质组成的多相体系为吸收、萃取、两相催化等技术的发展提供了新的平台。离子液体的表/界面性质与结构是含离子液体多相体系的重要科学问题,可在介观尺度下显著影响多相体系反应和分离过程的效率。近年来,离子液体表/界面性质和结构的研究得到了广泛的关注。本文综述了离子液体及其与水、有机溶剂组成的混合物的表/界面张力及结构研究进展,介绍了现有的研究方法、研究对象与研究成果,归纳了离子液体及其混合物表/界面张力及结构的变化规律,分析了表/界面结构与表/界面张力之间的关系,探讨了离子液体表/界面研究存在的问题和未来的发展方向。     

Stress anisotropy induced by periodic boundary conditions

Finite size effects due to periodic boundary conditions are investigated using computer simulations in the canonical ensemble. We study liquids with densities corresponding to typical liquid coexistence densities, and temperatures between the triple and critical points. The components of the pressure tensor are computed in order to analyze the finite size effects arising from the size and geometry of the simulation box. Two different box geometries are considered: cubic and parallelepiped. As expected the pressure tensor is isotropic in cubic boxes, but it becomes anisotropic for small noncubic boxes. We argue this is the origin of the anomalous behavior observed recently in the computation of the surface tension of liquid-vapor interfaces. Otherwise, we find that the bulk pressure is sensitive to the box geometry when small simulation boxes are considered. These observations are general and independent of the model liquid considered. We report results for liquids interacting through short range forces, square well and Lennard-Jones, and also long range Coulombic interactions. The effect that small surface areas have on the surface tension is discussed, and some preliminary results at the liquid vapor-interface for the square well potential are given.     

Influence of the anion on the surface tension of 1-ethyl-3-methylimidazolium-based ionic liquids

The air–liquid interfacial tensions of eight ionic liquids, from (298 to 343) K, are presented in this work. The studied ionic liquids are formed by the fixed 1-ethyl-3-methylimidazolium cation combined with the anions acetate, dicyanamide, dimethylphosphate, methylphosphonate, methanesulfonate, thiocyanate, tosylate, and trifluoromethanesulfonate. The selected ionic liquids allowed a comprehensive study through the influence of the anion nature on the surface tension and on their surface ordering. A slight dependence of the surface tension with the ionic liquid molar volume was identified. The surface thermodynamic functions are mainly controlled by the anion which constitutes a given ionic liquid. The hypothetical critical temperatures of all ionic liquids were estimated by means of the Eötvos and Guggenheim correlations and are presented.     

Surface tension of 1-alkyl-3-methylimidazolium based ionic liquids with trifluoromethanesulfonate and tetrafluoroborate anion

The amount of available accurate experimental data on the surface tension of ionic liquids is still limited; in many cases the data are rare or even absent. In the present study, air-liquid interfacial tension data were determined experimentally for five 1-C_n-3-methylimidazolium based ionic liquids (n = 2, 4, and 6), three with trifluoromethanesulfonate and two with tetrafluoroborate anion, at atmospheric pressure in the temperature range from 268 to 356 K. The resultant surface tension data are average values of the measurements repeated many times at each set point temperature. The accuracy of the results, was confirmed by employing the Wilhelmy plate and the du Noüy ring methods in parallel, using the Krüss K100MK2 tensiometer. For the Wilhelmy plate data the combined standard uncertainty is estimated to be about 0.05 mN m⁻¹. The data obtained by du Noüy method show about up to seven times greater scatter than those obtained by the Wilhelmy plate method. To the 50 up to now published surface tension values for the five studied ionic liquids the present study adds further 175 data points. In contrast to that of n-alkanes, the surface tension of 1-alkyl-3-methylimidazolium based ionic liquids decreases and their surface entropy increases with the cation alkyl chain length.     

Probing the neutral graphene-ionic liquid interface: insights from molecular dynamics simulations

We study basic mechanisms of the interfacial layer formation at the neutral graphite monolayer (graphene)-ionic liquid (1,3-dimethylimidazolium chloride, [dmim][Cl]) interface by fully atomistic molecular dynamics simulations. We probe the interface area by a spherical probe varying the charge (-1e, 0, +1e) as well as the size of the probe (diameter 0.50 nm and 0.38 nm). The molecular modelling results suggest that: there is a significant enrichment of ionic liquid cations at the surface. This cationic layer attracts Cl(-) anions that leads to the formation of several distinct ionic liquid layers at the surface. There is strong asymmetry in cationic/anionic probe interactions with the graphene wall due to the preferential adsorption of the ionic liquid cations at the graphene surface. The high density of ionic liquid cations at the interface adds an additional high energy barrier for the cationic probe to come to the wall compared to the anionic probe. Qualitatively the results from probes with diameter 0.50 nm and 0.38 nm are similar although the smaller probe can approach closer to the wall. We discuss the simulation results in light of available experimental data on the interfacial structure in ionic liquids.     

Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Liquid-liquid interfacial tension of equilibrated mixtures of ionic liquids and hydrocarbons

Ionic liquids are possible alternative solvents for the separation of aromatic and aliphatic hydrocarbons by liquid-liquid extrac- tion. Interfacial tension is an important property to consider in the design of liquid-liquid extraction processes. In this work, the liquid-liquid interfacial tension and the mutual solubility at 25 °C have been measured for a series of biphasic, equilibrated mixtures of an ionic liquid and a hydrocarbon. In particular, the ionic liquids 1-alkyl-3-methylimidazolium bis(trifluorome- thanesulfonyl)imide (with the alkyl substituent being ethyl, hexyl or decyl), 1-ethyl-3-methylimidazolium ethylsulfate, and 1-ethyl-3-methylimidazolium methanesulfonate have been selected, as well as the hydrocarbons benzene, hexane, ethylben- zene, and octane. The selected sets of ionic liquids and hydrocarbons allow the analysis of the influence of a series of effects on the interfacial tension. For example, the interfacial tension decreases with an increase in the length of the alkyl substituent chain of the cation or with an increase of the degree of charge delocalisation in the anion of the ionic liquid. Also, the interfa- cial tension with the aromatic hydrocarbons is markedly lower than that with the aliphatic hydrocarbons. A smaller effect is caused by variation of the size of the hydrocarbon. Some of the observed trends can be explained from the mutual solubility of the hydrocarbon and the ionic liquid.     

Finite-size effects in dissipative particle dynamics simulations

We have performed dissipative particle dynamics (DPD) simulations to evaluate the effect that finite size of transversal area has on stress anisotropy and interfacial tension. The simulations were carried out in one phase and two phases in parallelepiped cells. In one-phase simulations there is no finite-size effect on stress anisotropy when the simulation is performed using repulsive forces. However, an oscillatory function of stress anisotropy is found for attractive-repulsive interactions. In the case of liquid-liquid interfaces with repulsive interaction between molecules, there is only a small effect of surface area on interfacial tension when the simulations are performed using the Monte Carlo method at constant temperature and normal pressure. An important but artificial finite-size effect of interfacial area on surface tension is found in simulations in the canonical ensemble. Reliable results of interfacial tension from DPD simulations can be obtained using small systems, less than 2000 particles, when they interact exclusively with repulsive forces.     

The surface tension of polymer liquids

A brief review of the surface tension of polymer liquids is presented. A strong emphasis is placed on recent measurements of surface tensions of homologous liquid series up to high-molecular-weight polymers, and the thermodynamic liquid properties of these same homologous series obtained from sources such as pressure-volume-temperature (PVT) data. The accuracy and limitations of the thermodynamic information which are used as input to many of the theories applied to the surface properties of polymer molecules are discussed. By scaling the surface tension data using a true measure of the cohesive energy density of the liquid state, we can clearly observe the entropic contribution to the surface tension caused by the conformational restriction of a large molecule at the liquid-vapor interface. The scaling implies the existence of a corresponding states principle for both polymer liquids and for low-molecular-weight liquids. The ramifications of the existence of a corresponding states principle for the surface tension of polymer melts are discussed. One consequence of the corresponding states principle is that it allows us to use surface tension measurements to compute the cohesive energy density of polymer melts using PVT data.     

Surface tension and refractive index of pure and water-saturated tetradecyltrihexylphosphonium-based ionic liquids

Experimental data on the surface tension and refractive index of tetradecyltrihexylphosphonium-based ionic liquids with bromide, chloride, decanoate, methanesulfonate, dicyanimide, bis(2,4,4-trimethylpentyl)phosphinate and bis(trifluoromethylsulfonyl)imide anions are reported. The data were obtained for pure and water saturated samples at temperatures from 283 K to 353 K and at atmospheric pressure. The refractive index of the investigated ionic liquids decreases with increasing the water content in the sample. On the other hand, no clearly dependence of the surface tension with the water content up to a weight fraction of 16% was found. The prediction of the refractive index for the studied ionic liquids was also accomplished by a group contribution method and new values for the cation and diverse anions were estimated and proposed. The studied ionic liquids show lower surface tension in comparison with imidazolium-, pyridinium- or pyrrolidinium-based ionic liquids with a similar anion; also they show higher surface entropy than cyclic nitrogen-based fluids which indicates a lower surface organization. The anion dependence of the surface tension and surface entropy for the investigated ionic liquids is weaker than that for short-chain imidazolium-based ionic liquids. Their critical temperatures evaluated from Eötvos and Guggenheim equations are also lower than those of N-heterocyclic ionic fluids.     

Finite system size effects in the interfacial dynamics of binary liquid films

We study the relaxation dynamics of capillary waves in the interface between two confined liquid layers by means of molecular dynamics simulations. We measure the autocorrelations of the interfacial Fourier modes and find that the finite thickness of the liquid layers leads to a marked increase of the relaxation times as compared to the case of fluid layers of infinite depth. The simulation results are in good agreement with a theoretical first-order perturbation derivation, which starts from the overdamped Stokes' equation. The theory also takes into account an interfacial friction, but the difference with no-slip interfacial conditions is small. When the walls are sheared, it is found that the relaxation times of modes perpendicular to the flow are unaffected. Modes along the flow direction are relatively unaffected as long as the equilibrium relaxation time is sufficiently short compared to the rate of deformation. We discuss the consequences for experiments on thin layers and on ultralow surface tension fluids, as well as computer simulations.     

Fluctuating hydrodynamics for multiscale simulation of inhomogeneous fluids: mapping all-atom molecular dynamics to capillary waves

We introduce a multiscale framework to simulate inhomogeneous fluids by coarse-graining an all-atom molecular dynamics (MD) trajectory onto sequential snapshots of hydrodynamic fields. We show that the field representation of an atomistic trajectory is quantitatively described by a dynamic field-theoretic model that couples hydrodynamic fluctuations with a Ginzburg-Landau free energy. For liquid-vapor interfaces of argon and water, the parameters of the field model can be adjusted to reproduce the bulk compressibility and surface tension calculated from the positions and forces of atoms in an MD simulation. These optimized parameters also enable the field model to reproduce the static and dynamic capillary wave spectra calculated from atomistic coordinates at the liquid-vapor interface. In addition, we show that a density-dependent gradient coefficient in the Ginzburg-Landau free energy enables bulk and interfacial fluctuations to be controlled separately. For water, this additional degree of freedom is necessary to capture both the bulk compressibility and surface tension emergent from the atomistic trajectory. The proposed multiscale framework illustrates that bottom-up coarse-graining and top-down phenomenology can be integrated with quantitative consistency to simulate the interfacial fluctuations in nanoscale transport processes.     

Temperature dependence of viscosity and relation with the surface tension of ionic liquids

Viscosities of ionic liquids were correlated with two linear relations. The first one presents the temperature dependence of imidazolium-, pyridinium-, pyrrolidinium-, quaternary ammonium-, and nicotinium-based ionic liquids with high accuracy. The second one is a linear relation between logarithm of surface tension and fluidity involving the characteristic exponent ?, and fits the ionic liquids uniquely with ? = 0.30. Our previously measured surface tension data of ionic liquids and literature's were used in this study. The dependence of surface tension–fluidity relation of the imidazolium-based ionic liquids on the anion type is likely disappeared as alkyl chain length increases.     

On the validity of the Cassie equation via a mean-field free-energy lattice Boltzmann approach

We studied wetting phenomena on heterogeneous surfaces by a mean-field free-energy lattice Boltzmann method recently proposed [Phys. Rev. E 69 (2004) 32,602]. Our results suggest that the Cassie equation in macroscopic contact angle measurements is in general not valid. It was found that the Cassie equation is valid only when the patch size is on the same order of the liquid-vapor interfacial thickness. We also demonstrated that contact angle manifests itself from local surface properties near the contact point and does not result from the specific solid-liquid interactions across the contact area.     

Multiple histogram reweighting method for the surface tension calculation

The multiple histogram reweighting method takes advantage of calculating ensemble averages over a range of thermodynamic conditions without performing a molecular simulation at each thermodynamic point. We show that this method can easily be extended to the calculation of the surface tension. We develop a new methodology called multiple histogram reweighting with slab decomposition based on the decomposition of the system into slabs along the direction normal to the interface. The surface tension is then calculated from local values of the chemical potential and of the configurational energy using Monte Carlo (MC) simulations. We show that this methodology gives surface tension values in excellent agreement with experiments and with standard NVT MC simulations in the case of the liquid-vapor interface of carbon dioxide.