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 softness of the potential on the stress anisotropy in liquids

We have performed molecular dynamics simulations of dense liquids using nonconformal and Gaussian potential models. We investigate the effect of the softness of the potential on the pressure tensor of liquids and dense fluids when the simulations are carried out using parallelepiped cells. The combination of periodic boundary conditions and small cross sectional areas induces an anisotropy in the diagonal components of the pressure tensor. This anisotropy results in an artificial stress in the system that has to be taken into account in simulations of explicit interfaces, where the artificial stress introduces errors in the computation of the surface tension. At high liquid densities the stress anisotropy exhibits an oscillatory dependence with the cross sectional area of the simulation box. We find that the softness of the potential has a dramatic effect on the amplitude of the oscillations, which can be significantly reduced in soft potentials, such as those used in the modeling of hydrocarbon liquids or polymers.     

纳米尺度氩液体线物性的分子动力学模拟

运用分子动力学模拟方法,对纳米尺度氩液体线的物理性质进行了研究。文中模拟计算了纳米线的熔点温度以及气液平衡状态下液态区密度、气态区密度和液体线的半径,并分析了模拟盒子尺寸和模拟温度对液体线物性的影响。结果表明,由于在初始结构中增加了气体分子,当模拟温度不变时,随模拟盒子尺寸的增加,液态区密度增大,气态区密度减小。但模拟盒子尺寸较小时,液体线半径不随模拟盒子尺寸发生变化。模拟计算所得的液态区密度十分接近宏观尺度氩液体密度时,模拟盒子的尺寸较合适。当模拟盒子尺寸固定不变时,液态区密度和气态区密度随温度的变化趋势与文献中宏观尺度氩液体和气体密度的变化趋势相同。结论可以为进一步系统地分析纳米尺度液体线的稳定性提供一定的依据。     

An absolute droplet pressure interfacial tensiometer and its application to bituminous systems of vanishing density contrast

Experimental problems preclude or limit measurements of interfacial tension in bitumen or extra-heavy crude oil-containing systems when there exists a vanishing density difference between the phases. We describe a novel droplet pressure method that allows such measurements to be made. This method is based on a liquid/liquid adaptation of the capillary displacement differential maximum bubble pressure surface tension method of Schramm and Green [29]. In this method, interfacial tension is calculated from the difference between maximum droplet pressures reached at capillaries of differing internal radii, immersed to slightly different depths. The elimination of the influence of liquid densities allows the measurement of interfacial tensions without independently determining the liquid densities, and in particular, permits measurements in systems for which the density difference is vanishingly small. The absolute measuring technique is illustrated for several systems of pure and practical liquids. Received: 8 March 2000/Accepted: 30 May 2000     

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.     

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.     

Comparison of the capillary wave method and pressure tensor route for calculation of interfacial tension in molecular dynamics simulations

We have studied the calculation of surface and interfacial tension for a variety of liquid–vapor and liquid–liquid interfaces using molecular dynamics (MD) simulations. Because of the inherently small scale of MD systems, large pressure fluctuations can cause imprecise calculations of surface tension using the pressure tensor route. The capillary wave method exhibited improved precision and stability throughout all of the simulated systems in this study. In order to implement this method, the interface was defined by fitting an error function to the density profile. However, full mapping of the interface from coordinate files produced enhanced accuracy. Upon increasing the system size, both methods exhibited higher precision, although the capillary wave method was still more reliable. © 2013 Wiley Periodicals, Inc.     

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.     

Monte Carlo simulation study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Calculating the surface tension between a flat solid and a liquid: a theoretical and computer simulation study of three topologically different methods

We discuss three topologically different methods for calculating the surface tension between a flat solid and a liquid from theoretical and computer simulation viewpoints. The first method, commonly used in experiments, measures the contact angle at which a static droplet of liquid rests on a solid surface. We present a new analysis algorithm for this method and explore the effects of line tension on the contact angle. The second method, commonly used computer simulations, uses the pressure tensor through the virial in a system where a thick, infinitely extended slab of liquid rests on a solid surface. The third method, which is original to this paper and is closest to the thermodynamic definition of surface tension, applies to a spherical solid in contact with liquid in which the flat solid is recovered by extrapolating the sphere radius to infinity. We find that the second and third methods agree with each other, while the first method systematically underestimates surface tension values.     

Molecular dynamics simulations of ionic liquid-vapour interfaces: effect of cation symmetry on structure at the interface

The influence of alkyl chain symmetry of the imidazolium cation on the structure and properties of the ionic liquid-vapour interface has been addressed through molecular dynamics simulations. The anion chosen is bis(trifluoromethylsulfonyl)imide (NTf(2)). Profiles of number densities, orientation of cations, charge density, electrostatic potential, and surface tension have been obtained. At the interface, both cations and anions were present, and the alkyl chains of the former preferred to orient out into the vapour phase. A large fraction of cations preferred to be oriented with their ring-normal parallel to the surface and alkyl chains perpendicular to it. These orientational preferences are reduced in ionic liquids with symmetric cations. Although the charge densities at the interface were largely negative, an additional small positive charge density has been observed for systems with longer alkyl chains. The electrostatic potential difference developed between the liquid and the vapour phases were positive and decreased with increasing length of the alkyl group. The calculated surface tension of the liquids also decreased with increasing alkyl chain length, in agreement with experiment. The surface tension of an ionic liquid with symmetric cation was marginally higher than that of one with an asymmetric, isomeric cation.     

Monte Carlo Simulation of Microemulsion Phase Transitions by Solvent Accessible Surface Area

Results of lattice Monte Carlo simulation are presented for the behavior of a mixture of oil‐water‐amphiphile in different conditions. For the first time, the phase transitions between different types of microemulsion are modeled, in a qualitative manner, using the concept of solvent accessible surface area. All of the simulations are run in canonical (N, V, T) ensemble. Simple cubic lattices with the dimension of 50 have been used to avoid any size or surface effects of the boxes. Periodic boundary conditions and excluded volumes are used to mimic the box of simulation as a bulk of solution. All of the results are in good qualitative agreement with previous theoretical and experimental results.     

Quantitative testing of robustness on superomniphobic surfaces by drop impact

The quality of a liquid-repellent surface is quantified by both the apparent contact angle θ(0) that a sessile drop adopts on it and the value of the liquid pressure threshold the surface can withstand without being impaled by the liquid, hence maintaining a low-friction condition. We designed surfaces covered with nanowires obtained by the vapor-liquid-solid (VLS) growth technique that are able to repel most of the existing nonpolar liquids including those with very low surface tension as well as many polar liquids with moderate to high surface tension. These superomniphobic surfaces exhibit apparent contact angles ranging from 125 to 160° depending on the liquid. We tested the robustness of the surfaces against impalement by carrying out drop impact experiments. Our results show how this robustness depends on Young's contact angle θ(0) related to the surface tension of the liquid and that the orientational growth of nanowires is a favorable factor for robustness.     

Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Isothermal Compressibility, Volumetric Expansion Coefficient, and Dielectric Constant

The chemical composition of small organic molecules is often very similar to amino acid side chains or the bases in nucleic acids, and hence there is no a priori reason why a molecular mechanics force field could not describe both organic liquids and biomolecules with a single parameter set. Here, we devise a benchmark for force fields in order to test the ability of existing force fields to reproduce some key properties of organic liquids, namely, the density, enthalpy of vaporization, the surface tension, the heat capacity at constant volume and pressure, the isothermal compressibility, the volumetric expansion coefficient, and the static dielectric constant. Well over 1200 experimental measurements were used for comparison to the simulations of 146 organic liquids. Novel polynomial interpolations of the dielectric constant (32 molecules), heat capacity at constant pressure (three molecules), and the isothermal compressibility (53 molecules) as a function of the temperature have been made, based on experimental data, in order to be able to compare simulation results to them. To compute the heat capacities, we applied the two phase thermodynamics method (Lin et al. J. Chem. Phys.2003, 119, 11792), which allows one to compute thermodynamic properties on the basis of the density of states as derived from the velocity autocorrelation function. The method is implemented in a new utility within the GROMACS molecular simulation package, named g_dos, and a detailed exposé of the underlying equations is presented. The purpose of this work is to establish the state of the art of two popular force fields, OPLS/AA (all-atom optimized potential for liquid simulation) and GAFF (generalized Amber force field), to find common bottlenecks, i.e., particularly difficult molecules, and to serve as a reference point for future force field development. To make for a fair playing field, all molecules were evaluated with the same parameter settings, such as thermostats and barostats, treatment of electrostatic interactions, and system size (1000 molecules). The densities and enthalpy of vaporization from an independent data set based on simulations using the CHARMM General Force Field (CGenFF) presented by Vanommeslaeghe et al. (J. Comput. Chem.2010, 31, 671) are included for comparison. We find that, overall, the OPLS/AA force field performs somewhat better than GAFF, but there are significant issues with reproduction of the surface tension and dielectric constants for both force fields.     

How surface tension of surfactant solutions influences the characteristics of sprays produced by hydraulic nozzles used for pesticide application

The sprays produced by hydraulic agricultural nozzles are influenced by the surface tension of the spray liquid, but models of spray formation relate only to pure liquids with constant surface tension. The way surfactant solutions affect spray formation is studied by investigating sprays of pure liquids compared with a range of surfactant solutions. Some surfactants caused changes in the appearance of the liquid sheet produced by the nozzles, which did not occur with pure liquids, and smaller spray drop sizes than pure liquids, suggesting that other surface properties may also be important.     

Molecular dynamics simulations of vapor/liquid coexistence using the nonpolarizable water models

The surface tension, vapor-liquid equilibrium densities, and equilibrium pressure for common water models were calculated using molecular dynamics simulations over temperatures ranging from the melting to the critical points. The TIP4P/2005 and TIP4P-i models produced better values for the surface tension than the other water models. We also examined the correlation of the data to scaling temperatures based on the critical and melting temperatures. The reduced temperature (T/T(c)) gives consistent equilibrium densities and pressure, and the shifted temperature T + (T(c, exp) - T(c, sim)) gives consistent surface tension among all models considered in this study. The modified fixed charge model which has the same Lennard-Jones parameters as the TIP4P-FQ model but uses an adjustable molecular dipole moment is also simulated to find the differences in the vapor-liquid coexistence properties between fixed and fluctuating charge models. The TIP4P-FQ model (2.72 Debye) gives the best estimate of the experimental surface tension. The equilibrium vapor density and pressure are unaffected by changes in the dipole moment as well as the surface tension and liquid density.     

Surface Tension of the Vapor–Liquid Interface with Finite Curvature

Based on the division of particles into internal and surface particles, the expression is derived closing the system of equations of classical thermodynamics for curvature-dependent surface tension, equimolar radius, and radius of tension surface. A solution to this system allows one to find the surface tension of new phase nucleus of any size (including minimal) and any sign of surface curvature. The obtained results indicate the weak size dependence of thermodynamic parameters that are the functions of surface tension; it is shown that Tolman's length cannot be determined using experimental determination of these parameters. It is shown that the work of nucleus formation strongly depends on its size and is the function of effective rather than true surface tension. Numerical simulation of clusters by the molecular dynamics method indicates that the pressure inside a fairly small cluster is described by Laplace's formula with the coefficient of surface tension for the plane surface of a liquid that agrees with the proposed theory.     

Determining the Surface Tension of Microliter Amounts of Liquid

We describe a method for determining the surface tension of liquids by measuring the pull-off force between curved surfaces with a bridging droplet. The technique is useful for cases when only very small amounts of liquid are available, as in medical and biological applications. Data on the surface tension of saliva samples are in agreement with literature values. Copyright 2000 Academic Press.     

Capillary rise of liquids over a microstructured solid surface

The location of the triple line as a function of time has been recorded for a series of organic liquids, with various surface tension to viscosity ratios, wicking upward a rough Cu(6)Sn(5)/Cu intermetallic (IMC) substrate. The complex topographical features of such an IMC rough surface are characterized by surface porosity and surface roughness. A theoretical model for wicking upward a rough surface has been established by treating the rough IMC surface as a two-dimensional porous medium featuring a network of open microtriangular grooves. The model is verified against experimental data. The study confirms that the kinetics of capillary rise of organic liquids in a nonreactive flow regime over a porous surface having arbitrary but uniformly distributed topographical features involves (i) surface topography metrics (i.e., permeability, tortuosity/porosity, and geometry of the microchannel cross section); (ii) wicking features (i.e., contact angle and filling factor); and (iii) physical properties of liquids (i.e., surface tension and viscosity). An excellent agreement between theoretical predictions and experimentally obtained data proves, for a selected filling factor η, validity of the analytically established model. Scaled data sets show that, for a given rough surface topography, (i) wicking kinetics of considered liquids depend on properties of liquids, that is, surface tension to viscosity ratios and contact angles; (ii) the filling factor for all tested liquids is an invariant, offering good prediction within the range of ~0.9-1.0. The distance of the wicking front versus square root of time relationship was well established throughout the whole considered wicking evolution time.     

Electron mobility in liquid and supercritical helium measured using corona discharges: a new semi-empirical model for cavity formation

Electron mobilities in supercritical and liquid helium were investigated as a function of the density. The mobilities were derived from I(V) curves measured in a high-pressure cryogenic cell using a corona discharge in point-plane electrode geometry for charge generation. The presented data spans a wide pressure and temperature range due to the versatility of our experimental set-up. Where data from previous investigations is available for comparison, very good agreement is found. We present a semi-empirical model to calculate electron mobilities both in the liquid and supercritical phase. This model requires the electron-helium scattering length and thermodynamic state equations as the only input and circumvents any need to consider surface tension. Our semi-empirical model reproduces experimental data very well, in particular towards lower densities where transitions from localised to delocalised electron states were observed.