Calculation of the surface tension from Monte Carlo simulations: Does the model impact on the finite-size effects?

Intrinsic Stress Field for Liquid Surfaces

The microscopic stress field inhomogeneity in the interfacial region adjacent to the liquid surface is the fundamental origin of the liquid surface tension, but because of broadening due to capillary fluctuations, a detailed molecular level understanding of the stress field remains elusive. In this work, we deconvolute the capillary fluctuations to reveal the intrinsic stress field and show that the atomic-level contributions to the surface tension are similar in functional form across a variety of monatomic systems. These contributions are confined to an interfacial region approximately 1.5±0.1 times the particle diameter for all systems studied. In addition, the intrinsic density and stress profiles show a strong spatial correlation that should be useful in the development of a statistical mechanical theory for the prediction of surface stress and surface tension.

100 Years of the Lennard-Jones Potential

It is now 100 years since Lennard-Jones published his first paper introducing the now famous potential that bears his name. It is therefore timely to reflect on the many achievements, as well as the limitations, of this potential in the theory of atomic and molecular interactions, where applications range from descriptions of intermolecular forces to molecules, clusters, and condensed matter.

Impact of the Force Field on the Calculation of Density and Surface Tension of Epoxy-Resins

The molecular simulation of interfacial systems is a matter of debate because of the choice of many input parameters that can affect significantly the performance of the force field of reproducing the surface tension and the coexisting densities. After developing a robust methodology for the calculation of the surface tension on a Lennard-Jones fluid, we apply it with different force fields to calculate the density and surface tension of pure constituents of epoxy resins. By using the model that best reproduces the experimental density and surface tension, we investigate the impact of composition in mass fraction on uncured epoxy resins and the effects of degree of cross-linking on cured resins.

Quantitative Predictions and Experimental Validation of Liquid-Vapor Interfacial Tension in Binary and Ternary Mixtures of Alkanes Using Molecular Dynamics Simulations

Liquid-vapor interfacial properties of alkane mixtures present a challenge for experimental determination, especially under conditions relevant to the energy industry processes. Molecular dynamics (MD) simulations can accurately predict interfacial tensions (IFTs) for complex alkane mixtures under virtually any conditions, thereby alleviating the need for difficult and costly experiments. MD simulations with the CHARMM force field and empirical corrections for the IFT and pressure were used to obtain the IFT for three binary mixtures of ethane (with n-pentane, n-hexane, and n-nonane) and a ternary system (ethane/n-butane/n-decane) under a variety of conditions. The results were thoroughly validated against experimental data from the literature, and new original IFT data were collected using the pendant drop method. The simulations are able to reproduce the experimental IFT to better than 0.5 mN/m or 5% on average and within 1 mN/m or 10% in the worst case. IFTs for the studied three binary and ternary alkane mixtures were predicted for wide ranges of conditions with no known experimental data. Finally, using the MD simulation data, the reliability of the widely used empirical parachor model for predicting IFT was reaffirmed, and the significance of the empirical parameters examined to establish an optimal balance between the accuracy and broad applicability of the model.

Ideal Conductor Model: An Analytical Finite-Size Correction for Nonequilibrium Molecular Dynamics Simulations of Ion Transport through Nanoporous Membranes

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional molecular dynamics (MD). Recently, path sampling techniques, such as forward-flux sampling (FFS), have emerged as attractive alternatives for efficiently and accurately estimating arbitrarily long ionic passage times. Here, we use non-equilibrium MD and FFS to explore how the kinetics and mechanisms of pressure-driven chloride transport through a nanoporous graphitic membrane are affected by its lateral dimensions. We not only find ionic passage times and free energy barriers to decrease dramatically upon increasing the membrane surface area but also observe an abrupt and discontinuous change in the locus of the transition state. These strong finite size effects arise due to the cumulative effect of the periodic images of the leading ion entering the pore on the distribution of the induced excess charge at the membrane surface in the feed. By assuming that the feed is an ideal conductor, we analytically derive a finite size correction term that can be computed from the information obtained from a single simulation and successfully use it to obtain corrected free energy profiles with no dependence on the system size. We then estimate ionic passage times in the thermodynamic limit by assuming an Eyring-type dependence of rates on barriers with a size-independent prefactor. This approach constitutes a universal framework for removing finite size artifacts in molecular simulations of ion transport through nanoporous membranes and biological channel proteins.

Molecular interactions at the metal-liquid interfaces

We reported molecular simulations of the interactions among water, an epoxy prepolymer diglycidic ether of bisphenol A (DGEBA), and a hardener isophorone diamine (IPDA) on an aluminum surface. This work proposes a comprehensive thermodynamic characterization of the adhesion process from the calculation of different interfacial tensions. The cross-interactions between the atoms of the metal surface and different molecules are adjusted so as to reproduce the experimental work of adhesion. Water nanodroplets on the metal surface are then simulated to predict their contact angle. Liquid-vapor surface tensions of the epoxy prepolymer (DGEBA) and hardener (IPDA) and the solid-vapor surface tension of the aluminum surface are also calculated to provide the solid-liquid interfacial tension that remains very difficult to obtain from the mechanical definition.

Capillary Imbibition of Binary Fluid Mixtures in Nanochannels

Many-body Dissipative Particle Dynamics (MDPD) simulations of binary fluid mixtures imbibing cylindrical nanochannels reveal a strong segregation of fluids differing in their affinities to the pore walls. Surprisingly, the imbibition front furthest into the channel is highly enriched in the fluid with the lower affinity for the walls, i.e., the fluid less prone to enter the pore. This effect is caused by the more-wetting fluid forming a monolayer covering the walls of the pore, while the lesser-wetting fluid is expelled from the walls to the interior of the pore where the higher axial flow velocity carries it to the front. The fluids remix after cessation of the flow. Nonwetting fluids can be made to enter a pore by mixing with a small amount of wetting fluid. The imbibition depth of the mixtures scales with the square root of time, in agreement with Bell-Cameron-Lucas-Washburn theory for pure fluids.

Learning Coarse-Grained Potentials for Binary Fluids

For a multiple-fluid system, CG models capable of accurately predicting the interfacial properties as a function of curvature are still lacking. In this work, we propose a new probabilistic machine learning (ML) model for learning CG potentials for binary fluids. The water-hexane mixture is selected as a typical immiscible binary liquid-liquid system. We develop a new CG force field (FF) using the Shinoda-DeVane-Klein (SDK) FF framework and compute parameters in this CG FF using the proposed probabilistic ML method. It is shown that a standard response-surface approach does not provide a unique set of parameters, as it results in a loss function with multiple shallow minima. To address this challenge, we develop a probabilistic ML approach where we compute the probability density function (PDF) of parameters that minimize the loss function. The PDF has a well-defined peak corresponding to a unique set of parameters in the CG FF that reproduces the desired properties of a liquid-liquid interface. We compare the performance of the new CG FF with several existing FFs for the water-hexane mixture, including two atomistic and three CG FFs with respect to modeling the interface structure and thermodynamic properties. It is demonstrated that the new FF significantly improves the CG model prediction of both the interfacial tension and structure for the water-hexane mixture.

The pair distribution function in the planar gas-liquid interface: Application to the calculation of the surface tension

A Monte Carlo simulation is used to calculate the pair distribution function g⁽²⁾r₁,r₂ for a planar gas-liquid interface. Due to the cylindrical symmetry of the system, g⁽²⁾ can be stored as a three-dimensional array that can be readily manipulated and used to calculate the surface tension and the single atom density profile directly. The consistency and accuracy of our calculation of g⁽²⁾(r₁, r₂) is demonstrated by a calculation of the single atom density through the first Born-Green-Yvon equation. We show that the surface tension calculated directly from the pair distribution function and from other well-established routes is completely consistent. In the case of the gas-liquid interface for argon modeled with an explicit inclusion of the three-body forces, an accurate pair distribution can be used to estimate the long-range contribution to the three-body part of the surface tension. A detailed analysis of this correction, its dependence on the three-body cutoff, and its overall contribution to the surface tension are presented.

Calculation of the interfacial tension of the graphene-water interaction by molecular simulations

We report the calculation of the solid-liquid interface tension of the graphene-water interaction by using molecular simulations. Local profiles of the interfacial tension are given through the mechanical and thermodynamic definitions. The dependence of the interfacial tension on the graphene area is investigated by applying both reaction field and Ewald summation techniques. The structure of the interfacial region close to the graphene sheet is analyzed through the profiles of the density and hydrogen bond number and the orientation of the water molecules. We complete this study by plotting the profiles of the components of the pressure tensor calculated by the Ewald summation and reaction field methods. We also investigate the case of a reaction field version consisting in applying a damped shifted force in the case of the calculation of the pressure components.

Importance of the tail corrections on surface tension of curved liquid-vapor interfaces

We report molecular simulations of the liquid-vapor cylindrical interface of methane. We apply the truncated Lennard-Jones potential and specific long-range corrections for the surface tension developed especially for cylindrical interfaces. We investigate the impact of the cutoff on the radial density profile, the intrinsic and long-range correction parts to the surface tension, and Tolman length. We also study the curvature dependence of the surface tension as a function of the cutoff used. In this work we shed light that both density and Tolman length are cutoff-dependent whereas the total surface tension is slightly curvature and cutoff dependent.

Unexpected finite size effects in interfacial systems: Why bigger is not always better-Increase in uncertainty of surface tension with bulk phase width

We present an unexpected finite size effect affecting interfacial molecular simulations that is proportional to the width-to-surface-area ratio of the bulk phase L_l/A. This finite size effect has a significant impact on the variance of surface tension values calculated using the virial summation method. A theoretical derivation of the origin of the effect is proposed, giving a new insight into the importance of optimising system dimensions in interfacial simulations. We demonstrate the consequences of this finite size effect via a new way to estimate the surface energetic and entropic properties of simulated air-liquid interfaces. Our method is based on macroscopic thermodynamic theory and involves comparing the internal energies of systems with varying dimensions. We present the testing of these methods using simulations of the TIP4P/2005 water forcefield and a Lennard-Jones fluid model of argon. Finally, we provide suggestions of additional situations, in which this finite size effect is expected to be significant, as well as possible ways to avoid its impact.

Test-area surface tension calculation of the graphene-methane interface: Fluctuations and commensurability

The surface tension (γ) of methane on a graphene monolayer is calculated by using the test-area approach. By using a united atom model to describe methane molecules, strong fluctuations of surface tension as a function of the surface area of the graphene are evidenced. In contrast with the liquid-vapor interfaces, the use of a larger cutoff does not fully erase the fluctuations in the surface tension. Counterintuitively, the description of methane and graphene from the Optimized Potentials for Liquid Simulations all-atom model and a flexible model, respectively, led to a lessening in the surface tension fluctuations. This result suggests that the origin of fluctuations in γ is due to a model-effect rather than size-effects. We show that the molecular origin of these fluctuations is the result of a commensurable organization between both graphene and methane. This commensurable structure can be avoided by describing methane and graphene from a flexible force field. Although differences in γ with respect to the model have been often reported, it is the first time that the model drastically affects the physics of a system.

The line tension of two-dimensional ionic fluids

Pressure tensor components are very useful in the calculation of the tension associated with a liquid-vapor interface. In this work, we present expressions for the pressure tensor components of two-dimensional ionic fluids, modeled at the level of the primitive model. As an application, we carried out molecular dynamics simulations of liquid-vapor interfaces to calculate the line tension of the 1:1 two-dimensional ionic fluid, whose liquid-vapor coexistence curve had already been obtained in a previous work. The pressure tensor components were validated by simulating states of one phase and reproducing the scalar pressure, previously obtained from bulk simulations and reported in the literature. The effects on the line tension and the coexisting densities, originated by the choice of the Ewald parameters, the cutoff radius, and the interfacial length were also evaluated.

Computer modelling of the surface tension of the gas–liquid and liquid–liquid interface

This review presents the state of the art in molecular simulations of interfacial systems and of the calculation of the surface tension from the underlying intermolecular potential.

Quantitative Predictions of the Interfacial Tensions of Liquid-Liquid Interfaces through Atomistic and Coarse Grained Models

We report molecular simulations of oil-water liquid-liquid interfaces by using atomistic and coarse grained (CG) MARTINI force fields. We also apply the electronic continuum (EC) model to the MARTINI force field for the calculation of the interfacial tension of oil/water-salt systems. In a first step, we propose to calculate the interfacial tensions using thermodynamic and mechanical definitions of hydrocarbon-water interfacial systems modified by the addition of salts and alcohol. We also establish here the order of magnitude of the long-range corrections to the interfacial tension in fluid-fluid interfaces. Whereas the atomistic models are able to reproduce quantitatively the interfacial tension and the coexisting densities of oil-water systems, the coarse-description shows some deviations in the prediction of the interfacial tensions. Nevertheless, the physical features of these liquid-liquid interfaces are well-captured by this CG description. The CG force field offers then a very challenging alternative that will require however a more developed calibration of the parameters on the basis of liquid-liquid properties.

Constant-force approach to discontinuous potentials

Aiming to approach the thermodynamical properties of hard-core systems by standard molecular dynamics simulation, we propose setting a repulsive constant-force for overlapping particles. That is, the discontinuity of the pair potential is replaced by a linear function with a large negative slope. Hence, the core-core repulsion, usually modeled with a power function of distance, yields a large force as soon as the cores slightly overlap. This leads to a quasi-hardcore behavior. The idea is tested for a triangle potential of short range. The results obtained by replica exchange molecular dynamics for several repulsive forces are contrasted with the ones obtained for the discontinuous potential and by means of replica exchange Monte Carlo. We found remarkable agreements for the vapor-liquid coexistence densities as well as for the surface tension.

Recent advances in Many Body Dissipative Particles Dynamics simulations of liquid-vapor interfaces

Many Body Dissipative Particles Dynamics (MDPD) simulation is a novel promising mesoscopic method to model the liquid-vapor interfaces. Based upon works of Paganobarraga and Frenkel (J. Chem. Phys. 15, 5015 (2001)) and Trofimov (J. Chem. Phys. 117, 9383 (2002)) and of Warren (Phys. Rev. E 68, 066702 (2003)) this method has been critically reviewed during this last decade. We propose here to give an overview of the Many Body Dissipative Particles Dynamic simulation within the framework of the liquid-vapor interfaces. We recall the theoretical background of MDPD and we present some recent results of systems of interest such as water liquid-vapor interfaces and salt effect on water surface tension. Additionally we discuss the ability of MDPD to capture the mechanisms at the mesoscopic scale through the formation of micelles and the coalescence of a nanodroplet water on water surface.