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.

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.

Activity coefficients from molecular simulations using the OPAS method.

A method for determining activity coefficients by molecular dynamics simulations is presented. It is an extension of the OPAS (osmotic pressure for the activity of the solvent) method in previous work for studying the solvent activity in electrolyte solutions. That method is extended here to study activities of all components in mixtures of molecular species. As an example, activity coefficients in liquid mixtures of water and methanol are calculated for 298.15 K and 323.15 K at 1 bar using molecular models from the literature. These dense and strongly interacting mixtures pose a significant challenge to existing methods for determining activity coefficients by molecular simulation. It is shown that the new method yields accurate results for the activity coefficients which are in agreement with results obtained with a thermodynamic integration technique. As the partial molar volumes are needed in the proposed method, the molar excess volume of the system water + methanol is also investigated.

Influence of bidisperse self-assembled monolayer structure on the slip boundary condition of thin polymer films.

Alkylsilane self-assembled monolayers (SAMs) are often used as model substrates for their ease of preparation and hydrophobic properties. We have observed that these atomically smooth monolayers also provide a slip boundary condition for dewetting films composed of unentangled polymers. This slip length, an indirect measure of the friction between a given liquid and different solids, is switchable and can be increased [R. Fetzer et al., Phys. Rev. Lett. 95, 127801 (2005); O. Bäumchen et al., J. Phys.: Condens. Matter 24, 325102 (2012)] if the alkyl chain length is changed from 18 to 12 backbone carbons, for example. Typically, this change in boundary condition is affected in a quantized way, using one or the other alkyl chain length, thus obtaining one or the other slip length. Here, we present results in which this SAM structure is changed in a continuous way. We prepare bidisperse mixed SAMs of alkyl silanes, with the composition as a control parameter. We find that all the mixed SAMs investigated show an enhanced slip boundary condition as compared to the single-component SAMs. The slip boundary condition is accessed using optical and atomic force microscopy, and we describe these observations in the context of X-ray reflectivity measurements. The slip length, varying over nearly two orders of magnitude, of identical polymer melts on chemically similar SAMs is found to correlate with the density of exposed alkyl chains. Our results demonstrate the importance of a well characterized solid/liquid pair, down to the angstrom level, when discussing the friction between a liquid and a solid.

Solvent activity in electrolyte solutions from molecular simulation of the osmotic pressure.

A method for determining the activity of the solvent in electrolyte solutions by molecular dynamics simulations is presented. The electrolyte solution is simulated in contact with the pure solvent. Between the two phases, there is a virtual membrane, which is permeable only for the solvent. In the simulation, this is realized by an external field which acts only on the solutes and confines them to a part of the simulation volume. The osmotic pressure, i.e., the pressure difference between both phases, is obtained with high accuracy from the force on the membrane, so that reliable data on the solvent activity can be determined. The acronym of the new method is therefore OPAS (osmotic pressure for activity of solvents). The OPAS method is verified using tests of varying complexity. This includes a comparison of results from the OPAS method for aqueous NaCl solutions to results from the literature which were obtained with other molecular simulation methods. Favorable agreement is observed not only for the solvent activity but also for the activity coefficient of NaCl, which is obtained by application of the Gibbs-Duhem equation.

Surface tension of the two center Lennard-Jones plus point dipole fluid.

Molecular dynamics simulations are used for systematically studying the surface tension of the two center Lennard-Jones plus point dipole (2CLJD) model fluid. In a dimensionless representation, this model fluid has two parameters describing the elongation and the dipole moment. These parameters were varied in the entire range relevant for describing real fluids resulting in a grid of 38 individual models. For each model, the surface tension was determined at temperatures between 60% and 90% of the critical temperature. For completeness, the vapor pressure and the saturated densities were also determined. The latter results agree well with the literature data, whereas for the surface tension, only few data were previously available. From the present results, an empirical correlation for the surface tension of the 2CLJD model as a function of the model parameters is developed. The correlation is used to predict the surface tension of 46 2CLJD molecular models from the literature, which were adjusted to bulk properties, but not to interfacial properties. The results are compared to the experimental data. The molecular models overestimate the surface tension, and deviations between the predictions and experimental data are below 12% on average.

Characterization of alkylsilane self-assembled monolayers by molecular simulation.

Self-assembled monolayers (SAM) of dodecyltrichlorosilane (DTS) and octadecyltrichlorosilane (OTS) on silica are studied by molecular dynamics simulations at 298 K and 1 bar. The coverage (number of alkylsilane molecules per surface area) is systematically varied. The results yield insight into the properties of the alkylsilane SAMs, which complement experimental studies from the literature. Relationships are reported between thickness, tilt angle, and coverage of alkylsilane SAMs, which also hold for alkylsilanes other than DTS and OTS. They are interpreted based on the information on molecular ordering in the SAMs taken form the simulation data. System size and simulation time are much larger than in most former simulation works on the topic. This reduces the influence of the initial configuration as well as the periodic boundary conditions and hence minimizes the risk of artificial ordering. At the same time, more reliable statistics for the calculated properties can be provided. The evaluation of experimental data in the field is often based on strongly simplified models. The present simulation results suggest that some of these lead to errors, concerning the interpretation of experimental results, which could be avoided by introducing more realistic models.

Contact angle of sessile drops in Lennard-Jones systems.

Molecular dynamics simulations are used for studying the contact angle of nanoscale sessile drops on a planar solid wall in a system interacting via the truncated and shifted Lennard-Jones potential. The entire range between total wetting and dewetting is investigated by varying the solid-fluid dispersive interaction energy. The temperature is varied between the triple point and the critical temperature. A correlation is obtained for the contact angle in dependence of the temperature and the dispersive interaction energy. Size effects are studied by varying the number of fluid particles at otherwise constant conditions, using up to 150,000 particles. For particle numbers below 10,000, a decrease of the contact angle is found. This is attributed to a dependence of the solid-liquid surface tension on the droplet size. A convergence to a constant contact angle is observed for larger system sizes. The influence of the wall model is studied by varying the density of the wall. The effective solid-fluid dispersive interaction energy at a contact angle of θ = 90° is found to be independent of temperature and to decrease linearly with the solid density. A correlation is developed that describes the contact angle as a function of the dispersive interaction, the temperature, and the solid density. The density profile of the sessile drop and the surrounding vapor phase is described by a correlation combining a sigmoidal function and an oscillation term.

ls1 mardyn: The Massively Parallel Molecular Dynamics Code for Large Systems.

The molecular dynamics simulation code ls1 mardyn is presented. It is a highly scalable code, optimized for massively parallel execution on supercomputing architectures and currently holds the world record for the largest molecular simulation with over four trillion particles. It enables the application of pair potentials to length and time scales that were previously out of scope for molecular dynamics simulation. With an efficient dynamic load balancing scheme, it delivers high scalability even for challenging heterogeneous configurations. Presently, multicenter rigid potential models based on Lennard-Jones sites, point charges, and higher-order polarities are supported. Due to its modular design, ls1 mardyn can be extended to new physical models, methods, and algorithms, allowing future users to tailor it to suit their respective needs. Possible applications include scenarios with complex geometries, such as fluids at interfaces, as well as nonequilibrium molecular dynamics simulation of heat and mass transfer.

Excess equimolar radius of liquid drops.

The curvature dependence of the surface tension is related to the excess equimolar radius of liquid drops, i.e., the deviation of the equimolar radius from the radius defined by the macroscopic capillarity approximation. Based on the Tolman [J. Chem. Phys. 17, 333 (1949)] approach and its interpretation by Nijmeijer et al. [J. Chem. Phys. 96, 565 (1991)], the surface tension of spherical interfaces is analyzed in terms of the pressure difference due to curvature. In the present study, the excess equimolar radius, which can be obtained directly from the density profile, is used instead of the Tolman length. Liquid drops of the truncated and shifted Lennard-Jones fluid are investigated by molecular dynamics simulation in the canonical ensemble, with equimolar radii ranging from 4 to 33 times the Lennard-Jones size parameter σ. In these simulations, the magnitude of the excess equimolar radius is shown to be smaller than σ/2. This suggests that the surface tension of liquid drops at the nanometer length scale is much closer to that of the planar vapor-liquid interface than reported in studies based on the mechanical route.

Contact angle dependence on the fluid-wall dispersive energy.

Menisci of the truncated and shifted Lennard-Jones fluid between parallel planar walls are investigated by molecular dynamics simulation. Thereby, the characteristic energy of the unlike dispersive interaction between fluid molecules and wall atoms is systematically varied to determine its influence on the contact angle. The temperature is varied as well, covering most of the range between the triple-point temperature and the critical temperature of the bulk fluid. The transition between obtuse and acute angles is found to occur at a temperature-independent magnitude of the fluid-wall dispersive interaction energy. On the basis of the present simulation results, fluid-wall interaction potentials can be adjusted to contact angle measurements.

Grand canonical steady-state simulation of nucleation.

Grand canonical molecular dynamics (GCMD) is applied to the nucleation process in a metastable phase near the spinodal, where nucleation occurs almost instantaneously and is limited to a very short time interval. With a variant of Maxwell's demon, proposed by McDonald [Am. J. Phys. 31, 31 (1963)], all nuclei exceeding a specified size are removed. In such a steady-state simulation, the nucleation process is sampled over an arbitrary time span and all properties of the metastable state, including the nucleation rate, can be obtained with an increased precision. As an example, a series of GCMD simulations with McDonald's demon is carried out for homogeneous vapor to liquid nucleation of the truncated-shifted Lennard-Jones (tsLJ) fluid, covering the entire relevant temperature range. The results are in agreement with direct nonequilibrium MD simulation in the canonical ensemble. It is confirmed for supersaturated vapors of the tsLJ fluid that the classical nucleation theory underpredicts the nucleation rate by two orders of magnitude.

Modification of the classical nucleation theory based on molecular simulation data for surface tension, critical nucleus size, and nucleation rate.

Nucleation in supersaturated vapor is investigated with two series of molecular-dynamics simulations in the canonical ensemble. The applied methods are (a) analysis of critical nuclei at moderate supersaturations by simulating equilibria of single droplets with surrounding vapors in small systems; (b) simulation of homogeneous nucleation during condensation with large systems containing 10(5)-10(6) particles for calculating the nucleation rate of vapors at high supersaturations. For the Lennard-Jones fluid, truncated and shifted at 2.5 times the size parameter, it is shown that the classical nucleation theory underestimates both the nucleation rate and the size of the critical nucleus. A surface property corrected modification of this theory is proposed to consistently cover data on the surface tension of the curved interface, the critical nucleus size, and the nucleation rate.

Homogeneous nucleation in supersaturated vapors of methane, ethane, and carbon dioxide predicted by brute force molecular dynamics.

Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a 10(6) particles were conducted with a massively parallel MD program. This leads to reliable statistics and makes nucleation rates down to the order of 10(30) m(-3) s(-1) accessible to the direct simulation approach. Simulation results are compared to the classical nucleation theory (CNT) as well as the modification of Laaksonen, Ford, and Kulmala (LFK) which introduces a size dependence of the specific surface energy. CNT describes the nucleation of ethane and carbon dioxide excellently over the entire studied temperature range, whereas LFK provides a better approach to methane at low temperatures.