Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

Molecular modeling of interfacial properties of the hydrogen + water + decane mixture in three-phase equilibrium

The understanding of interfacial phenomena between H2 and geofluids is of great importance for underground H2 storage, but requires further study. We report the first investigation on the three-phase fluid mixture containing H2, H2O, and n-C10H22. Molecular dynamics simulation and PC-SAFT density gradient theory are employed to estimate the interfacial properties under various conditions (temperature ranges from 298 to 373 K and pressure is up to around 100 MPa). Our results demonstrate that interfacial tensions (IFTs) of the H2-H2O interface in the H2 + H2O + C10H22 three-phase mixture are smaller than IFTs in the H2 + H2O two-phase mixture. This decrement of IFT can be attributed to C10H22 adsorption in the interface. Importantly, H2 accumulates in the H2O-C10H22 interface in the three-phase systems, which leads to weaker increments of IFT with increasing pressure compared to IFTs in the water + C10H22 two-phase mixture. In addition, the IFTs of the H2-C10H22 interface are hardly influenced by H2O due to the limited amount of H2O dissolved in nonaqueous phases. Nevertheless, positive surface excesses of H2O are seen in the H2-C10H22 interfacial region. Furthermore, the values of the spreading coefficient are mostly negative revealing the presence of the three-phase contact for the H2 + H2O + C10H22 mixture under studied conditions.

Molecular dynamics simulation study on the mass transfer across vapor-liquid interfaces in azeotropic mixtures

Mass transfer through fluid interfaces is an important phenomenon in industrial applications as well as in naturally occurring processes. In this work, we investigate the mass transfer across vapor-liquid interfaces in binary mixtures using molecular dynamics simulations. We investigate the influence of interfacial properties on mass transfer by studying three binary azeotropic mixtures known to have different interfacial behaviors. Emphasis is placed on the effect of the intermolecular interactions by choosing mixtures with the same pure components but different cross-interactions such that different azeotropic behaviors are obtained. The molar flux is created by utilizing a non-stationary molecular dynamics simulation approach, where particles of one component are inserted into the vapor phase over a short period of time before the system's response to this insertion is monitored. From a direct comparison of the density profiles and the flux profiles in close proximity to the interface, we analyze the particles' tendency to accumulate in the interfacial region throughout the different stages of the simulation. We find that for mixtures with strong attractive cross-interactions, the inserted particles are efficiently transported into the liquid phase. For systems with weak attractive cross-interactions, the inserted particles show a tendency to accumulate in the interfacial region, and the flux through the system is lower. The results from this work indicate that the accumulation of particles at the interface can act as a hindrance to mass transfer, which has practical relevance in technical processes.

Mass Transfer through Vapor-Liquid Interfaces Studied by Non-Stationary Molecular Dynamics Simulations

Molecular dynamics (MD) simulations are highly attractive for studying the influence of interfacial effects, such as the enrichment of components, on the mass transfer through the interface. In a recent work, we have presented a steady-state MD simulation method for investigating this phenomenon and tested it using model mixtures with and without interfacial enrichment. The present study extends this work by introducing a non-stationary MD simulation method. A rectangular simulation box that contains a mixture of two components 1 + 2 with a vapor phase in the middle and two liquid phases on both sides is used. Starting from a vapor-liquid equilibrium state, a non-stationary molar flux of component 2 is induced by inserting particles of component 2 into the center of the vapor phase in a pulse-like manner. During the isothermal relaxation process, particles of component 2 pass through the vapor phase, cross the vapor-liquid interface, and enter the liquid phase. The system thereby relaxes into a new vapor-liquid equilibrium state. During the relaxation process, spatially resolved responses for the component densities, fluxes, and pressure are sampled. To reduce the noise and provide measures for the uncertainty of the observables, a set of replicas of simulations is carried out. The new simulation method was applied to study mass transfer in two binary Lennard-Jones mixtures: one that exhibits a strong enrichment of the low-boiling component 2 at the vapor-liquid interface and one that shows no enrichment. Even though both mixtures have similar transport coefficients in the bulk phases, the results for mass transfer differ significantly, indicating that the interfacial enrichment influences the mass transfer.

Free energy of critical droplets-from the binodal to the spinodal

Arguably, the main challenge of nucleation theory is to accurately evaluate the work of formation of a critical embryo in the new phase, which governs the nucleation rate. In Classical Nucleation Theory (CNT), this work of formation is estimated using the capillarity approximation, which relies on the value of the planar surface tension. This approximation has been blamed for the large discrepancies between predictions from CNT and experiments. In this work, we present a study of the free energy of formation of critical clusters of the Lennard-Jones fluid truncated and shifted at 2.5σ using Monte Carlo simulations, density gradient theory, and density functional theory. We find that density gradient theory and density functional theory accurately reproduce molecular simulation results for critical droplet sizes and their free energies. The capillarity approximation grossly overestimates the free energy of small droplets. The incorporation of curvature corrections up to the second order with the Helfrich expansion greatly remedies this and performs very well for most of the experimentally accessible regions. However, it is imprecise for the smallest droplets and largest metastabilities since it does not account for a vanishing nucleation barrier at the spinodal. To remedy this, we propose a scaling function that uses all relevant ingredients without adding fitting parameters. The scaling function reproduces accurately the free energy of the formation of critical droplets for the entire metastability range and all temperatures examined and deviates from density gradient theory by less than one k_BT.

Determining Brown's Characteristic Curves Using Molecular Simulation

Brown's characteristic curves define lines on the thermodynamic surface where special thermodynamic conditions hold. These curves are an important tool for the development of thermodynamic models of fluids. Yet, practically no experimental data for Brown's characteristic curves is available. In this work, a rigorous and generalized method for determining Brown's characteristic curves based on molecular simulation was developed. As multiple thermodynamic equivalent definitions apply for the characteristic curves, different simulation routes were compared. Based on this systematic approach, the most favorable route for determining each characteristic curve was identified. The computational procedure developed in this work combines molecular simulation, molecular-based equation of state, and the evaluation of the second virial coefficient. The new method was tested on a simple model system (the classical Lennard-Jones fluid) and different types of real substances (toluene, methane, ethane, propane, and ethanol). It is thereby shown that the method is robust and yields accurate results. Moreover, a computer code implementation of the method is presented.

Interfacial properties of binary azeotropic mixtures of simple fluids: Molecular dynamics simulation and density gradient theory

Interfacial properties of binary azeotropic mixtures of Lennard-Jones truncated and shifted fluids were studied by molecular dynamics (MD) simulation and density gradient theory (DGT) in combination with an equation of state. Three binary mixtures were investigated, which differ in the energetic cross interaction parameter that yields different types of azeotropic behavior. This study covers a wide temperature and composition range. Mixture A exhibits a heteroazeotrope at low temperatures, which changes to a low-boiling azeotrope at high temperatures, mixture B exhibits a low-boiling azeotrope, and mixture C exhibits a high-boiling azeotrope. The phase behavior and fluid interfacial properties as well as their relation were studied. Vapor-liquid, liquid-liquid, and vapor-liquid-liquid equilibria and interfaces were considered. Density profiles, the surface tension, the interfacial thickness, as well as the relative adsorption and enrichment of the components at the interface were studied. The results obtained from the two independent methods (MD and DGT) are overall in good agreement. The results provide insights into the relation of the phase behavior, particularly the azeotropic behavior, of simple fluid mixtures and the corresponding interfacial properties. Strong enrichment was found for the mixture with a heteroazeotrope in the vicinity of the three-phase equilibrium, which is related to a wetting transition.

Perturbation theories for fluids with short-ranged attractive forces: A case study of the Lennard-Jones spline fluid

It is generally not straightforward to apply molecular-thermodynamic theories to fluids with short-ranged attractive forces between their constituent molecules (or particles). This especially applies to perturbation theories, which, for short-ranged attractive fluids, typically must be extended to high order or may not converge at all. Here, we show that a recent first-order perturbation theory, the uv-theory, holds promise for describing such fluids. As a case study, we apply the uv-theory to a fluid with pair interactions defined by the Lennard-Jones spline potential, which is a short-ranged version of the LJ potential that is known to provide a challenge for equation-of-state development. The results of the uv-theory are compared to those of third-order Barker–Henderson and fourth-order Weeks–Chandler–Andersen perturbation theories, which are implemented using Monte Carlo simulation results for the respective perturbation terms. Theoretical predictions are compared to an extensive dataset of molecular simulation results from this (and previous) work, including vapor–liquid equilibria, first- and second-order derivative properties, the critical region, and metastable states. The uv-theory proves superior for all properties examined. An especially accurate description of metastable vapor and liquid states is obtained, which might prove valuable for future applications of the equation-of-state model to inhomogeneous phases or nucleation processes. Although the uv-theory is analytic, it accurately describes molecular simulation results for both the critical point and the binodal up to at least 99% of the critical temperature. This suggests that the difficulties typically encountered in describing the vapor–liquid critical region are only to a small extent caused by non-analyticity.

Molecular Dynamics Study of Wetting and Adsorption of Binary Mixtures of the Lennard-Jones Truncated and Shifted Fluid on a Planar Wall

The wetting of surfaces is strongly influenced by adsorbate layers. Therefore, in this work, sessile drops and their interaction with adsorbate layers on surfaces were investigated by molecular dynamics simulations. Binary fluid model mixtures were considered. The two components of the fluid mixture have the same pure component parameters, but one component has a stronger and the other a weaker affinity to the surface. Furthermore, the unlike interactions between both components were varied. All interactions were described by the Lennard-Jones truncated and shifted potential with a cutoff radius of 2.5σ. The simulations were carried out at constant temperature for mixtures of different compositions. The parameters were varied systematically and chosen such that cases with partial wetting as well as cases with total wetting were obtained and the relation between the varied molecular parameters and the phenomenological behavior was elucidated. Data on the contact angle as well as on the mole fraction and thickness of the adsorbate layer were obtained, accompanied by information on liquid and gaseous bulk phases and the corresponding phase equilibrium. Also, the influence of the adsorbate layer on the wetting was studied: for a sufficiently thick adsorbate layer, the wall's influence on the wetting vanishes, which is then only determined by the adsorbate layer.

Theory and simulation of open systems out of equilibrium

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

Characteristic Curves of the Lennard-Jones Fluid

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

Interfacial properties of binary mixtures of simple fluids and their relation to the phase diagram

Enrichment at vapour–liquid interfaces can be interpreted as a wetting transition in the vicinity of a three phase equilibrium.

Molecular interactions at vapor-liquid interfaces: Binary mixtures of simple fluids

Properties of vapor-liquid equilibria and planar interfaces of binary Lennard-Jones truncated and shifted mixtures were investigated with molecular dynamics simulations, density gradient theory, and conformal solution theory at constant liquid phase composition and temperature. The results elucidate the influence of the liquid phase interactions on the interfacial properties (surface tension, surface excess, interfacial thickness, and enrichment). The studied mixtures differ in the ratios of the dispersion energies of the two components ɛ_{2}/ɛ_{1} and the binary interaction parameter ξ. By varying ξ and ɛ_{2}/ɛ_{1}, a variety of types of phase behavior is covered by this paper. The dependence of the interfacial properties on the variables ξ and ɛ_{2}/ɛ_{1} reveals regularities that can be explained by conformal solution theory of the liquid phase. It is thereby shown that the interfacial properties of the mixtures are dominated by the mean liquid phase interactions whereas the vapor phase has only a minor influence.

The Influence of Lubrication and the Solid-Fluid Interaction on Thermodynamic Properties in a Nanoscopic Scratching Process

Liquid lubricants play an important role in contact processes; for example, they reduce friction and cool the contact zone. To gain better understanding of the influence of lubrication on the nanoscale, both dry and lubricated scratching processes in a model system are compared in the present work using molecular dynamics simulations. The entire range between total dewetting and total wetting is investigated by tuning the solid-fluid interaction energy. The investigated scratching process consists of three sequential movements: A cylindrical indenter penetrates an initially flat substrate, then scratches in the lateral direction, and is finally retracted out of the contact with the substrate. The indenter is fully submersed in the fluid in the lubricated cases. The substrate, the indenter, and the fluid are described by suitably parametrized Lennard-Jones model potentials. The presence of the lubricant is found to have a significant influence on the friction and on the energy balance of the process. The thermodynamic properties of the lubricant are evaluated in detail. A correlation of the simulation results for the profiles of the temperature, density, and pressure of the fluid in the vicinity of the chip is developed. The work done by the indenter is found to mainly dissipate and thereby heat up the substrate and eventually the fluid. Only a minor part of the work causes plastic deformation of the substrate.

Competitive Sorption of CO2 with Gas Mixtures in Nanoporous Shale for Enhanced Gas Recovery from Density Functional Theory

CO₂ competitive sorption with shale gas under various conditions from simple to complex pore characteristics is studied using a molecular density functional theory (DFT) that reduces to perturbed chain-statistical associating fluid theory in the bulk fluid region. The DFT model is first verified by grand canonical Monte Carlo simulation in graphite slit pores for pure and binary component systems at different temperatures, pressures, pore sizes, and bulk gas compositions for methane/ethane with CO₂. Then, the model is utilized in multicomponent systems that include CH₄, C₂H₆, and C3+ components of different compositions. It is shown that the selectivity of CO₂ decreases with increases in temperature, pressure, nanopore size, and average molecular weight of shale gas. Extending the model to more realistic situations, we consider the impact of water present in the pore and consider the effect of permeation of fluid molecules into the kerogen that forms the pore walls. The water-graphite interaction is calibrated with contact angle from molecular simulation data from the literature. The kerogen pore model prediction of gas absolute sorption is compared with experimental and molecular simulation values in the literature. It is shown that the presence of water reduces the CO₂ adsorption but improves the CO₂ selectivity. The dissolution of gases into the kerogen matrix also leads to the increase in CO₂ selectivity. The effect of kerogen type and maturity on the gas sorption amount and CO₂ selectivity is also studied. The associated mechanisms are discussed to provide fundamental understanding for gas recovery by CO₂.

Three-dimensional phase field modeling of inhomogeneous gas-liquid systems using the PeTS equation of state

Recently, an equation of state (EoS) for the Lennard-Jones truncated and shifted (LJTS) fluid has become available. As it describes metastable and unstable states well, it is suited for predicting density profiles in vapor-liquid interfaces in combination with density gradient theory (DGT). DGT is usually applied to describe interfaces in Cartesian one-dimensional scenarios. In the present work, the perturbed LJ truncated and shifted (PeTS) EoS is implemented into a three-dimensional phase field (PF) model which can be used for studying inhomogeneous gas-liquid systems in a more general way. The results are compared with the results from molecular dynamics simulations for the LJTS fluid that are carried out in the present work and good agreement is observed. The PF model can therefore be used to overcome the scale limit of molecular simulations. A finite element approach is applied for the implementation of the PF model. This requires the first and second derivatives of the PeTS EoS which are calculated using hyper-dual numbers. Several tests and examples of applications of the new PeTS PF model are discussed.