Surface tension of associating fluids by Monte Carlo simulations

Canonical Monte Carlo (NVT-MC) simulations were performed to obtain surface tension and coexistence densities at the liquid-vapor interface of one-site associating Lennard-Jones and hard-core Yukawa fluids, as functions of association strength and temperature. The method to obtain the components of the pressure tensor from NVT-MC simulations was validated by comparing the equation of state of the associative hard sphere system with that coming from isothermal-isobaric Monte Carlo simulations. Surface tension of the associative Lennard-Jones fluid determined from NVT-MC is compared with previously reported results obtained by molecular dynamics simulations of a pseudomixture model of monomers and dimers. A good agreement was found between both methods. Values of surface tension of associative hard-core Yukawa fluids are presented here for the first time.     

Surface tension and scaling of critical nuclei in diatomic and triatomic fluids

Density functional theory has been used to investigate surface tension and scaling of critical clusters in fluids consisting of diatomic and rigid triatomic molecules. The atomic sites are hard spheres with attractive interactions obtained from the tail part of the Lennard-Jones potential. Asymmetry in attractive interactions between the atomic sites has been introduced to cause molecular orientation and oscillatory density profiles at liquid-vapor interfaces. The radial dependence of cluster surface tension in fluids showing modest orientation in unimolecular layer at the interface or no orientation at all resembles the surface tension behavior of clusters in simple monoatomic fluids, although the surface tension maximum becomes more pronounced with increasing chain length of the molecule. Surface tension of clusters having multiple oscillatory layers at the interface shows a prominent maximum at small cluster sizes; however, the surface tension of large clusters is lower than the planar value. The scaling relation for the number of molecules in the critical cluster and the nucleation barrier height developed by McGraw and Laaksonen [Phys. Rev. Lett. 76, 2754 (1996)] are well obeyed for fluids with little structure at liquid-vapor interface. However, fluids having enhanced interfacial structure show some deviation from the particle number scaling, and the barrier height scaling breaks up seriously.     

Determination of surface tension in binary mixtures using transition-matrix Monte Carlo

We present a methodology based on grand-canonical transition-matrix Monte Carlo and finite-size scaling analysis to calculate surface tensions in binary mixtures. In particular, mixture transition-matrix Monte Carlo is first used to calculate apparent, system-size-dependent free-energy barriers separating coexisting fluid phases. Finite-size scaling is then used to extrapolate these values to the infinitely large system limit to determine the true thermodynamic surface tension. A key distinction of the methodology is that it yields the entire isothermal surface-tension curve for a binary mixture in a relatively small number of simulations. We demonstrate the utility of the method by calculating surface-tension curves for three binary Lennard-Jones mixtures. While we have only examined the surface tension of simple fluids in this work, the method is general and can be extended to molecular fluids as well as to determine interfacial tensions of liquid-liquid interfaces.     

Anomalous corresponding-states surface tension of hydrogen fluoride and of the Onsager model

In a corresponding-states analysis of the liquid-vapor surface tension originally suggested by Guggenheim, we study the behavior of different simple (i.e., nonpolar), polar and ionic fluids. The results are compared to the corresponding ones for model fluids of each of the three types. For simple and weakly polar fluids (both real and model), the data map onto a master curve, as demonstrated by Guggenheim. For strongly dipolar, associating fluids, which also exhibit hydrogen bonding, one finds deviations from the master curve at low temperatures and, thus, observes the characteristic sigmoid behavior of the reduced surface tension as a function of temperature. The same is obtained for the model ionic fluid, the restricted primitive model. Truly exceptionally low values of the reduced surface tension are found for hydrogen fluoride and for the Onsager model of dipolar fluids, the surface tension of which we evaluate using an approximate hypernetted chain relation to obtain the square-gradient term in a modified van der Waals theory. Remarkably, in the corresponding-states plot, the surface tensions of HF and of the Onsager model agree very closely, while being well separated from the values for the other fluids. We also study the gradual transition of a model fluid from a simple fluid to a strongly dipolar one by varying the relative strength of dipolar and dispersion forces.     

Equilibrium dynamics of an associating polymer melt in narrow slits by computer simulation

Molecular dynamics simulations have been used to study the dynamics of a coarse-grained model of a melt of polymer chains with associating terminal groups, confined in a narrow slit by two layers of Lennard-Jones sites. Simulations were carried out as a function of wall separation and attracting strength. We found that confinement has an important effect on the overall dynamics of the system. Strongly attracting walls can significantly modify the dynamics of the melt, giving an aggregation structure with extremely long relaxation times. A noticeable degree of anisotropy was found for the dynamics of both the individual chains and the aggregates formed by the associating terminal groups.     

Computation of surface tensions using expanded ensemble simulations

A method for the direct simulation of the surface tension is examined. The technique is based on the thermodynamic route to the interfacial tension and makes use of the expanded ensemble simulation method for the calculation of the free energy difference between two inhomogeneous systems with the same number of particles, temperature, and volume, but different interfacial area. The method is completely general and suitable for systems with either continuous or discontinuous interactions. The adequacy of the expanded ensemble method is assessed by computing the interfacial tension of the planar vapor-liquid interface of Lennard-Jones, Lennard-Jones dimers, Gay-Berne, and square-well model fluids; in the latter, the interactions are discontinuous and the present method does not exhibit the asymmetry of other related methods, such as the test area. The expanded ensemble simulation results are compared with simulation data obtained from other techniques (mechanical and test area) with overall good agreement.     

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.     

First-order mean-spherical approximation for interfacial phenomena: a unified method from bulk-phase equilibria study

The recently proposed first-order mean-spherical approximation (FMSA) [Y. Tang, J. Chem. Phys. 121, 10605 (2004)] for inhomogeneous fluids is extended to the study of interfacial phenomena. Computation is performed for the Lennard-Jones fluid, in which all phase equilibria properties and direct correlation function for density-functional theory are developed consistently and systematically from FMSA. Three functional methods, including fundamental measure theory for the repulsive force, local-density approximation, and square-gradient approximation, are applied in this interfacial investigation. Comparisons with the latest computer simulation data indicate that FMSA is satisfactory in predicting surface tension, density profile, as well as relevant phase equilibria. Furthermore, this work strongly suggests that FMSA is very capable of unifying homogeneous and inhomogeneous fluids, as well as those behaviors outside and inside the critical region within one framework.     

Effective potential approach to bulk thermodynamic properties and surface tension of molecular fluids I. Single component n-alkane systems

The aim of this work is to develop spherically symmetric effective potentials allowing bulk thermodynamic properties and surface tension of molecular fluids to be predicted semiempirically by the use of statistical mechanical methods. Application is made to the straight chain alkane fluids from methane to decane. An effective Lennard-Jones potential is generated with temperature-dependent parameters fitted to the critical temperature and pressure and to Pitzer's acentric factor. Insertion of this potential into the generalised van der Waals (GvdW) density functional theory yields bulk properties in good agreement with experiments. The surface tension is overestimated for the longer alkane chains. In order to account for the surface tension, an independently adjustable attractive range of interaction is required and obtained through the use of square-well potentials chosen so as to leave the bulk thermodynamics unaltered while the attractive range is fitted to the surface tension at a single temperature. The GvdW theory, which includes binding energy, entropic and profile shape contributions, then generates surface tension estimates that are of good accuracy over the full range of available experimental data. It appears that, given a sufficiently flexible form, effective potentials combined with simple statistical mechanical theory can reproduce both bulk and non-uniform fluid data of great variety in an insighful and practically useful way.     

Structure of Lennard-Jones fluids confined in square nanoscale channels from density functional theory

The density distribution of Lennard-Jones fluids confined in square nanoscale channels with Lennard-Jones walls has been studied using the nonlocal density functional theory (DFT) based on the Tarazona model. The effect of channel lengths on the density profiles with various chemical potentials was discussed. It was found that there is an apparent layering phenomenon for the confined fluids due to the combining influences of the enhancing solid-fluid interaction and the excluded volume effect. The pronounced density peaks were observed at the corners of square channels due to the strong fluid-solid interactions. The grand canonical ensemble Monte Carlo simulation (GCEMC) was applied to test the nonlocal DFT results. The DFT calculations are in relatively good agreement with the GCEMC simulations. The adsorption isotherms in a series of square channels were evaluated based on the obtained density distributions. The adsorption mechanism within the square pores was investigated. A comparison between the adsorptions of the square pores with those of the corresponding slit-size pores has been given.     

On the long-range corrections to computer simulation results for the Lennard-Jones vapor-liquid interface

The long-range corrections (LRCs) to the configurational energy have been taken into consideration in the Monte Carlo simulation of the vapor-liquid interface for a pure Lennard-Jones (LJ) fluid. The simulated bulk densities agree satisfactorily with those obtained from the Gibbs ensemble method, and the simulated surface tension values agree reasonably well with those reported in the literature for a larger number of molecules and a larger cut-off distance. To compare the influence of the potential forms on the simulation results, a truncated LJ potential, and a shifted and truncated LJ potential have been examined. Although the bulk densities and surface tensions calculated for different model fluids are strongly affected by the LRC, the different potentials essentially lead to similar density values and similar surface tension values when the respective calculated values are compared on the basis of a reduced temperature scale.     

Generalized van der Waals Theory of Interfaces in Simple Fluid Mixtures

An efficient implementation of the generalized van der Waals theory of fluids is presented for the calculation of surface tension in simple fluid mixtures. While detailed correlation analysis is avoided the dominant binding energy contribution and the negative contribution due to the nonlocal entropy are accounted for in the free energy density functional by simple physical approximations of the type originally introduced by van der Waals. Efficient computation is achieved by the use of a single-parameter optimization of a tanh-shaped profile representing the total density as well as the composition variation across the interface. This simple profile nevertheless incorporates the expected adsorption to the interface of the volatile component. Application is made to argon/krypton mixtures represented by Lennard-Jones potentials and Lorentz-Berthelot combining rules. Surface tension predictions compare well with both experimental observations and computer simulation results which also indicated close agreement in particle density profiles, especially if the Berthelot rule is amended with a binary interaction parameter slightly (3%) less than unity. Copyright 2001 Academic Press.     

Molecular simulation study of effect of molecular association on vapor-liquid interfacial properties

Vapor-liquid interfacial properties of square-well associating fluids are studied via transition-matrix Monte Carlo simulation. Results for one-site and two-site association models are presented. Coexistence properties, surface tension, cluster distribution, density profile, and orientation profile are presented. Molecular association affects the interfacial properties and cluster fractions more than it affects the bulk densities. We observe that the surface tension exhibits a maximum with respect to association strength. This behavior is in agreement with the recent study of Peery and Evans for one site system using a square-gradient approach.     

Effect of surface active sites on adsorption of associating chain molecules in pores: A Monte Carlo study

This work describes the adsorption behavior of associating and non-associating chains and their mixtures in pores with activated surfaces. The systems are studied using Gibbs ensemble Monte Carlo molecular simulations. Fluid molecules are modeled as freely jointed Lennard-Jones chains. Associating chains have, additionally, an associating square-well site placed in an end sphere. The pores are modeled as regular slit pores via an integrated Lennard-Jones potential (10-4-3); activation is achieved by placing specific association sites protruding from the surface. Two different solid-fluid interaction parameters are used, one of which corresponds roughly to alkanes on graphite, the other being a much weaker interaction. Adsorption isotherms are presented for several different cases: associating and non-associating chains confined within both neutral and activated walls. Mixtures of associating and non-associating chains are also considered. The effects of pore size, temperature and chain length are quantified. Selectivities obtained are in the range of those seen in adsorption experiments of alkane-alkanol mixtures.     

Density functional theory of inhomogeneous liquids. I. The liquid-vapor interface in Lennard-Jones fluids

A simple model is proposed for the direct correlation function (DCF) for simple fluids consisting of a hard-core contribution, a simple parametrized core correction, and a mean-field tail. The model requires as input only the free energy of the homogeneous fluid, obtained, e.g., from thermodynamic perturbation theory. Comparison to the DCF obtained from simulation of a Lennard-Jones fluid shows this to be a surprisingly good approximation for a wide range of densities. The model is used to construct a density functional theory for inhomogeneous fluids which is applied to the problem of calculating the surface tension of the liquid-vapor interface. The numerical values found are in good agreement with simulation.     

Metastable extension of the liquid-vapor phase equilibrium curve and surface tension

The method of molecular dynamics has been used to calculate the parameters of liquid-vapor phase equilibrium and the surface tension in a two-phase system of 4096 Lennard-Jones particles. Calculations have been made in a range from the triple point to near-critical temperature and also at temperatures below the triple point corresponding to the metastable equilibrium of a supercooled liquid and supersaturated vapor. To determine the surface tension, along with a mechanical approach a thermodynamic one has been used as well. The latter was based on calculation of the excess internal energy of an interfacial layer. It has been shown that in accuracy the thermodynamic approach is as good as the more sophisticated mechanical one. Low-temperature asymptotics of the phase-equilibrium curve and also of liquid and vapor spinodals have been considered in the Lennard-Jones and the van der Waals models. The behavior of the surface tension and the excess internal energy of an interfacial layer at T-->0 is discussed.     

Calculation of surface tension via area sampling

We examine the performance of several molecular simulation techniques aimed at evaluation of the surface tension through its thermodynamic definition. For all methods explored, the surface tension is calculated by approximating the change in Helmholtz free energy associated with a change in interfacial area through simulation of a liquid slab at constant particle number, volume, and temperature. The methods explored fall within three general classes: free-energy perturbation, the Bennett acceptance-ratio scheme, and the expanded ensemble technique. Calculations are performed for both the truncated Lennard-Jones and square-well fluids at select temperatures spaced along their respective liquid-vapor saturation lines. Overall, we find that Bennett and expanded ensemble approaches provide the best combination of accuracy and precision. All of the methods, when applied using sufficiently small area perturbation, generate equivalent results for the Lennard-Jones fluid. However, single-stage free-energy-perturbation methods and the closely related test-area technique recently introduced by Gloor et al. [J. Chem. Phys. 123, 134703 (2005)] generate surface tension values for the square-well fluid that are not consistent with those obtained from the more robust expanded ensemble and Bennett approaches, regardless of the size of the area perturbation. Single-stage perturbation methods fail also for the Lennard-Jones system when applied using large area perturbations. Here an analysis of phase-space overlap produces a quantitative explanation of the observed inaccuracy and shows that the satisfactory results obtained in these cases from the test-area method arise from a cancellation of errors that cannot be expected in general. We also briefly analyze the variation in method performance with respect to the adjustable parameters inherent to the techniques.     

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.     

Wetting of Crystalline Solids by Associating Fluids

The wetting behavior of Lennard-Jones associating fluid on a crystalline surface is studied using Monte Carlo simulation in the isobaric-isothermal ensemble. We explore the structure of the adsorbed film, characterized by the distribution of all particles and the distributions of centers of mass of dimers, as well as by orientational distributions of the dimers. The simulations performed indicate the existence of a prewetting-like behavior of the adsorption isotherm. The results for a crystalline surface are compared with simular results obtained for a structureless surface. Finally, we present some density functional theory evaluations and compare them with the simulation results at a high temperature. Copyright 2000 Academic Press.     

Thermodynamic properties of short-range square well fluid

The interfacial properties of short-range square well fluid with lambda=1.15, 1.25, and 1.375 were determined by using single canonical Monte Carlo simulations. Simulations were carried out in the vapor-liquid region. The coexistence curves of these models were calculated and compared to those previously reported in the literature and good agreement was found among them. We found that the surface tension curves for any potential model of short range form a single master curve when we plot gamma* vs TT(c). It is demonstrated that the critical reduced second virial coefficient B(2)* as a function of interaction range or T(c)* is not constant.