Prediction of the surface tension of cesium in the whole liquid range

Surface tension is an important quantity, both as physical and technological features. We applied the general form of Lennard-Jones potential model, LJ (m-n), and some thermodynamic arguments in the Kirkwood and Buff equation to calculate the surface tension of liquid cesium. To find out the surface tension in a wide temperature range, only pVT data are required. By this method, we investigated the influence of the potential model on the surface tension. For two selected potential models [LJ (6–3) and LJ (8.5–4)], the values of the calculated surface tension and the predicted surface energy agree with the experimental values.     

Monte Carlo simulations of Lennard-Jones nonionic surfactant adsorption at the liquid/vapor interface

We present Monte Carlo simulations of nonionic surfactant adsorption at the liquid/vapor interface of a monatomic solvent. All molecules in the system, solvent and surfactant, are characterized by the Lennard-Jones (LJ) potential using differing interaction parameters. Surfactant molecules consist of an amphiphilic chain with a solvophilic head and a solvophobic tail. Adjacent atoms along the surfactant chain are connected by finitely extensible harmonic springs. Solvent molecules move via the Metropolis random-walk algorithm, whereas surfactant molecules move according to the continuum configurational bias Monte Carlo (CBMC) method. We generate quantitative thermodynamic adsorption and surface tension isotherms in addition to surfactant radius of gyration, tilt angles, and potentials of mean force. Surface tension simulations compared to those calculated from the simulated adsorbed amounts and the Gibbs adsorption isotherm agree confirming equilibrium in our simulations. We find that the classical Langmuir isotherm is obeyed for our LJ surfactants over the range of head and tail lengths studied. Although simulated surfactant chains in the bulk solution exhibit random orientations, surfactant chains at the interface orient roughly perpendicular and the tails elongate compared to bulk chains even in the submonolayer adsorption regime. At a critical surfactant concentration, designated as the critical aggregation concentration (CAC), we find aggregates in the solution away from the interface. At higher concentrations, simulated surface tensions remain practically constant. Using the simulated potential of mean force in the submonolayer regime and an estimate of the surfactant footprint at the CAC, we predict a priori the Langmuir adsorption constant, KL, and the maximum monolayer adsorption, Gammam. Adsorption is driven not by proclivity of the surfactant for the interface, but by the dislike of the surfactant tails for the solvent, that is by a "solvophobic" effect. Accordingly, we establish that a coarse-grained LJ surfactant system mimics well the expected equilibrium behavior of aqueous nonionic surfactants adsorbing at the air/water interface.     

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.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

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.     

Quantum computation of the properties of helium using two-body and three-body intermolecular potentials: a molecular dynamics study

We have performed the molecular dynamics simulation to obtain energy, pressure, and self-diffusion coefficient of helium at different temperatures and densities using Lennard–Jones (LJ), Hartree–Fock dispersion-Individual damping (HFD-ID) potential, and the HFD-like potential which has been obtained with an inversion of viscosity data at zero pressure supplemented by quantum corrections following the Feynman–Hibbs approach. The contribution of three-body interactions using an accurate simple relationship reported by Wang and Sadus between two-body and three-body interactions has been also involved for non-effective potentials (HFD-ID and HFD-like) in simulation. Our results show a good agreement with corresponding experimental data. A comparison of our simulated results with other molecular simulations using different potentials is also included.     

Molecular dynamics simulation of potassium along the liquid-vapor coexistence curve

The applicability of pair potential functions to liquid alkali metals is questionable. On the one hand, some recent reports in the literature suggest the validity of two-parameter pair-wise additive Lennard-Jones (LJ) potentials for liquid alkali metals. On the other hand, there are some reports suggesting the inaccuracy of pair potential functions for liquid metals. In this work, we have performed extensive molecular dynamics simulations of vapor-liquid phase equilibria in potassium to check the validity of the proposed LJ potentials and to improve their accuracy by changing the LJ exponents and taking into account the temperaturedependencies of the potential parameters. We have calculated the orthobaric liquid and vapor densities of potassium using LJ (12–6), LJ (8.5–4) and LJ (5–4), effective pair potential energy functions. The results show that using an LJ (8.5–4) potential energy function with temperature-independent parameters, ε and σ, is inadequate to account for the vapor-liquid coexistence properties of potassium. Taking into account the temperature-dependencies of the LJ parameters, ε(T) and σ(T), we obtained the densities of coexisting liquid and vapor potassium in a much better agreement with experimental data. Changing the magnitude of repulsive and attractive contributions to the potential energy function shows that a two-parameter LJ (5–4) potential can well reproduce the densities of liquid and vapor potassium. The results show that LJ (5–4) potential with temperature-dependent parameters produces the densities of liquid and vapor potassium more accurately, compared to the results obtained using LJ (12–6) and LJ (8.5–4) potential energy functions.     

Long-range Lennard-Jones and electrostatic interactions in interfaces: application of the isotropic periodic sum method

Molecular dynamics (MD) simulations of heptane/vapor, hexadecane/vapor, water/vapor, hexadecane/water, and dipalmitoylphosphatidylcholine (DPPC) bilayers and monolayers are analyzed to determine the accuracy of treating long-range interactions in interfaces with the isotropic periodic sum (IPS) method. The method and cutoff (rc) dependences of surface tensions, density profiles, water dipole orientation, and electrostatic potential profiles are used as metrics. The water/vapor, heptane/vapor, and hexadecane/vapor interfaces are accurately and efficiently calculated with 2D IPS (rc=10 A). It is demonstrated that 3D IPS is not practical for any of the interfacial systems studied. However, the hybrid method PME/IPS [Particle Mesh Ewald for electrostatics and 3D IPS for Lennard-Jones (LJ) interactions] provides an efficient way to include both types of long-range forces in simulations of large liquid/vacuum and all liquid/liquid interfaces, including lipid monolayers and bilayers. A previously published pressure-based long-range LJ correction yields results similar to those of PME/IPS for liquid/liquid interfaces. The contributions to surface tension of LJ terms arising from interactions beyond 10 A range from 13 dyn/cm for the hexadecane/vapor interface to approximately 3 dyn/cm for hexadecane/water and DPPC bilayers and monolayers. Surface tensions of alkane/vapor, hexadecane/water, and DPPC monolayers based on the CHARMM lipid force fields agree very well with experiment, whereas surface tensions of the TIP3P and TIP4P-Ew water models underestimate experiment by 16 and 11 dyn/cm, respectively. Dipole potential drops (DeltaPsi) are less sensitive to long-range LJ interactions than surface tensions. However, DeltaPsi for the DPPC bilayer (845+/-3 mV proceeding from water to lipid) and water (547+/-2 mV for TIP4P-Ew and 521+/-3 mV for TIP3P) overestimate experiment by factors of 3 and 5, respectively, and represent expected deficiencies in nonpolarizable force fields.     

Ordering layers of [bmim][PF6] ionic liquid on graphite surfaces: molecular dynamics simulation

Microscopic structures of room temperature ionic liquid (IL) [bmim][PF6] on hydrophobic graphite surfaces have been studied in detail by molecular dynamics simulation. It is clearly shown that both the mass and electron densities of the surface adsorbed ionic liquid are oscillatory, and the first peak adjacent to the graphite surface is considerably higher than others, corresponding to a solidlike IL bottom layer of 6 angstroms thick. Three IL layers are indicated between the graphite surface and the inner bulk IL liquid. The individually simulated properties of single-, double-, and triple-IL layers on the graphite surface are very similar to those of the layers between the graphite surface and the bulk liquid, indicating an insignificant effect of vapor-IL interface on the ordered IL layers. The simulation also indicates that the imidazolium ring and butyl tail of the cation (bmim+) of the IL bottom layer lie flat on the graphite surface.     

Monte Carlo study of interfacial properties of associating fluids

Canonical Monte Carlo Simulations have been performed to calculate liquid-vapor properties of the associating square well and Lennard-Jones fluids with one and two sites. Simulations were carried out by using several values of reduced temperatures and association energies. The orthobaric densities, as well as the surface tension of associating square well fluids, were calculated and compared with those reported previously in literature; a good agreement was found among them. Results of surface tension of two-sites associating Lennard-Jones fluids are presented here for the first time.     

Liquid-liquid phase separation of binary Lennard-Jones fluid in slit nanopores

The capillary phase separation of a binary mixture of two truncated and shifted Lennard-Jones (LJ) Ar liquids in slit-shaped oxygen nanopores is examined. The LJ parameters—ε(Ar(A)–Ar(A))=ε(Ar(B)–Ar(B))=0.8ε(Ar(A)–Ar(B)) and 0.5ε(Ar(A)–O)?=?ε(Ar(B)–O)—were used to distinguish the two Ar liquids. The cut off distance for Ar was 3.5σ. We employed a molecular dynamics (MD) technique in which a pore space was connected with a bulk solution to easily determine the equilibrium bulk concentration. Liquid phase isotherms were obtained for pores with widths ranging from 5.5σ to 9.5σ, and the relation between the pore width and the phase separation concentration was determined. Each simulation was run until the bulk concentration attained equilibrium (1–2 μs). The MD results show that the Patrick model overestimates the bulk concentration for a given pore size. We proposed a modified Patrick model in which the pore wall potential is considered. In our model, the Gibbs-Tolman-Koenig-Buff effect is not considered for the interfacial tension since two surfaces of tension exist on both sides of the equimolar dividing surface of the two-Ar liquid phase. The two surfaces of tension neutralized Gibbs-Tolman-Koenig-Buff effect each other. The present simple model successfully describes the relation to prove its reliability.     

Beyond the Lennard-Jones model: a simple and accurate potential function probed by high resolution scattering data useful for molecular dynamics simulations

Scattering data, measured for rare gas-rare gas systems under high angular and energy resolution conditions, have been used to probe the reliability of a recently proposed interaction potential function, which involves only one additional parameter with respect to the venerable Lennard-Jones (LJ) model and is hence called Improved Lennard-Jones (ILJ). The ILJ potential eliminates most of the inadequacies at short- and long-range of the LJ model. Further reliability tests have been performed by comparing calculated vibrational spacings with experimental values and calculated interaction energies at short-range with those obtained from the inversion of gaseous transport properties. The analysis, extended also to systems involving ions, suggests that the ILJ potential model can be used to estimate the behavior of unknown systems and can help to assess the different role of the leading interaction components. Moreover, due to its simple formulation, the physically reliable ILJ model appears to be particularly useful for molecular dynamics simulations of both neutral and ionic systems.     

Evaluation of high-frequency elastic moduli and shear relaxation time of the Lennard-Jones fluid using three known analytical expressions for radial distribution function

High-frequency elastic moduli (G_∞ and K_∞) for a Lennard-Jones (LJ) fluid have been calculated using three known analytical expressions for radial distribution function (RDF) at different temperatures and densities and compared with the corresponding values of these properties obtained from molecular dynamics (MD).     

Solvation force for long-ranged wall--fluid potentials

The solvation force of a simple fluid confined between identical planar walls is studied in two model systems with short ranged fluid-fluid interactions and long-ranged wall-fluid potentials decaying as -Az(-p),z--> infinity, for various values of p. Results for the Ising spins system are obtained in two dimensions at vanishing bulk magnetic field h=0 by means of the density-matrix renormalization-group method; results for the truncated Lennard-Jones (LJ) fluid are obtained within the nonlocal density functional theory. At low temperatures the solvation force f(solv) for the Ising film is repulsive and decays for large wall separations L in the same fashion as the boundary field f(solv) approximately L(-p), whereas for temperatures larger than the bulk critical temperature f(solv) is attractive and the asymptotic decay is f(solv) approximately L(-(p+1)). For the LJ fluid system f(solv) is always repulsive away from the critical region and decays for large L with the the same power law as the wall-fluid potential. We discuss the influence of the critical Casimir effect and of capillary condensation on the behavior of the solvation force.     

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.     

Freezing of Lennard-Jones fluid in cylindrical nanopores under tensile conditions

We have shown the Lennard-Jones (LJ) phase diagram for a slit-shaped nanopore by molecular simulations and thermodynamically predicted the results with no adjustable parameter. With this success, LJ phase diagrams are predictable. In this study, the freezing of an LJ CH₄ capillary condensate under a tensile condition in a nonstructural carbon nanopore with a cylindrical geometry was examined using molecular dynamics (MD) simulation. We employ a unit cell in contact with a bulk vapor phase, which is useful for the determination of the bulk vapor pressure in equilibrium with the molecules in a pore. The MD simulation results show liquid-solid (amorphous) phase transitions with a variation in the bulk vapor pressure. The frozen particles are arranged in concentric circular regions along the wall similar to those reported by Maddox and Gubbins. The freezing points are determined from the variations in density, enthalpy, arrangement, and structural functions. The obtained liquid-solid coexistence points are found to exhibit a significant dependence of the freezing point on the equilibrium bulk vapor pressure, forming an extraordinarily skewed curve on the p-T diagram, in contrast to the bulk phase coexistence that is represented by an almost vertical line. The origin of the significant dependence is considered to be the Laplace effect on the capillary condensate similar to the case with a slit-shaped pore. A simple model, which the authors earlier presented for slit-shaped nanopores, successfully predicted the p-T relation of the freezing point for cylindrical nanopores as well.     

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.     

Nonequilibrium surface tension for mixed adsorption kinetics

Experimental nonequilibrium surface tension measurements of 1–9 nonanediol solutions obtained by the oscillating-jet method have been interpreted in terms of our theoretical predictions derived for a mixed-controlled adsorption kinetics of the surfactant. The surface tension values have been calculated from the Szyszkowski equation using the Langmuir model of surfactant adsorption. Our theoretical results, obtained by a numerical solution of the adsorption equations, agree well with experimental data giving a value of the kinetics Szyszkowski constant very similar to the thermodynamic equilibrium value determined from experimental measurements of the static surface tension of 1–9 nonanediol solutions of various concentration. The approximate kinetic equation derived by P. Joos, G. Bleys, and G. Petre (J. Chim. Phys.79, 387 (1982)) for purely barrier-controlled adsorption proved to be less accurate.     

Comparative study of the effect of tail corrections on surface tension determined by molecular simulation

We report results from a comparative study of the influence of tail corrections on the surface tension of the Lennard-Jones fluid. We find that cutoff-independent surface tensions can be obtained by applying a set of tail corrections recently introduced by Janecek at each step of an interfacial Monte Carlo (MC) or molecular dynamics (MD) simulation. The effect of tail corrections on an alternative methodology for calculating surface tension, the combination of finite-size scaling and grand-canonical transition-matrix Monte Carlo (FSS/GC-TMMC), was also investigated. Using this indirect method, surface tensions were calculated with standard (bulk-fluid) tail corrections and lattice sums, the latter usually considered more accurate but computationally more intensive than the former. With standard tail corrections, we find that the surface tension decreases with increasing cutoff distance, reaching a limiting value corresponding to the maximum cutoff possible, namely half the simulation box length. In contrast, surface tension values obtained with the lattice summation were cutoff-independent. More importantly, these values were equivalent to those surface tension values obtained using standard tail corrections and a cutoff distance of half the box length. We also find that the surface tension values obtained here are in agreement with those found in the literature. Last, we find that surface tension values obtained by MD and FSS/GC-TMMC are in decent agreement so long as the appropriate tail correction schemes are used, and that the relative uncertainties in the surface tensions calculated by MD are generally an order of magnitude greater than those calculated by FSS/GC-TMMC. However, the time required by MD on a single central processing unit is less than that required by FSS/GC-TMMC.