Effect of Carboxylic Acid on the Wetting Properties of a Model Water-Octane-Silica System.

Monte Carlo simulations are employed to determine the effects of acetic acid on the wetting properties of a model water-octane-silica system. We first compute the bulk liquid-vapor saturation properties of pure acetic acid and subsequently explore the bulk liquid-liquid saturation properties of the ternary water-octane-acid system. We introduce an expanded ensemble approach to compute the coexistence properties of the ternary system. An interface potential approach is then used to capture the evolution of the wetting properties of the water-octane-silica system upon the addition of acetic acid. We track the change in the octane-water interfacial tension and the contact angle of water droplet on a silica substrate in a mother octane fluid over a range of acetic acid activities. The structure of the fluid, including the partitioning of acetic acid within the interfacial system, is also considered at several state points. We observe that acetic acid has a strong tendency to adsorb at the octane-water interface, resulting in a reduction in the octane-water interfacial tension. The response of the contact angle is more sensitive to the temperature and the hydrophilicity of the silica substrate.

Application of the interface potential approach for studying wetting behavior within a molecular dynamics framework.

We introduce a means to implement the interface potential approach for computing wetting properties within a molecular dynamics framework. The general approach provides a means to determine the contact angle of a liquid droplet on a solid substrate in a mother vapor. We present a framework for implementing "spreading" and "drying" versions of the method within an isothermal-isobaric ensemble. Two free energy methods are considered: cumulative integration of average force profile and multistate Bennett acceptance ratio. An umbrella sampling strategy is used to restrain volume fluctuations and to ensure adequate sampling of a broad volume range. We explore implementation of the approach with the GROningen MAchine for Chemical Simulations and the Large-scale Atomic/Molecular Massively Parallel Simulator. We test the accuracy and efficiency of the method with models consisting of a monoatomic Lennard-Jones fluid in the vicinity of a structureless or atomistically detailed substrate. Our results show that one can successfully generate the drying potential within the framework pursued here. The efficiency of the method is strongly dependent upon how one handles the dynamics of the two confining walls. These decisions impact the rate of volume fluctuations, and therefore, the quality of the volume distributions collected. Our efforts to implement the spreading method with molecular dynamics alone proved unsuccessful. The rate at which the configuration space of the vapor phase evolves is insufficient. We show how one can overcome this challenge by implementing a coupled molecular dynamics/Monte Carlo approach. Finally, we show how one can determine the variation in interfacial properties with temperature and substrate strength.

Using isothermal-isobaric Monte Carlo simulation to study the wetting behavior of model systems.

We introduce a molecular simulation method to compute the interfacial properties of model systems within the isothermal-isobaric ensemble. We use a free-energy-based approach in which Monte Carlo simulations are employed to obtain an interface potential associated with the growth of a fluid film from a solid substrate. The general method is implemented within "spreading" and "drying" frameworks. The interface potentials that emerge from these calculations provide direct access to spreading and drying coefficients. These macroscopic properties are then used to compute the liquid-vapor surface tension and the contact angle of a liquid droplet in contact with the substrate. The isothermal-isobaric ensemble provides a means to change the thickness of the fluid film adjacent to the substrate by modifying the volume of the simulation box. Molecular insertions and removals are not necessary. We introduce a framework for performing local volume change moves wherein one attempts to modify the density of a narrow region of the simulation box. We show that such moves improve the sampling efficiency of inhomogeneous systems. The approach is applied to a model system consisting of a monatomic Lennard-Jones fluid in the vicinity of a structureless substrate. Results are provided for direct spreading and drying interface potential calculations at several temperatures and substrate strengths. Expanded ensemble techniques are used to evaluate interfacial properties over a wide range of temperatures and substrate strengths. The results obtained using the isothermal-isobaric approach are compared with those previously obtained via a grand canonical approach.

Construction of the interface potential from a series of canonical ensemble simulations.

We introduce a method to construct the interface potential from a series of molecular dynamics simulations conducted within the canonical ensemble. The interface potential provides the surface excess free energy associated with the growth of a fluid film from a surface. We collect the force that the fluid exerts on the surface (disjoining pressure) at a series of film thicknesses. These force data are then integrated to obtain the interface potential. "Spreading" and "drying" versions of the general approach are considered. The spreading approach focuses on the growth of a thin liquid film from a solid substrate in a mother vapor. The drying approach focuses on the growth of a thin vapor film on a solid substrate in a mother liquid. The methods provide a means to compute the contact angle of a fluid droplet in contact with the surface. The general method is applied to two model systems: (1) a monatomic Lennard-Jones fluid in contact with atomistically detailed face centered cubic (FCC) substrate and (2) TIP4P/2005 water in contact with a rigid silica surface. For the Lennard-Jones model system, we generate results with both the drying and spreading methods at various temperatures and substrate strengths. These results are compared to those from previous simulation studies. For the water system, the drying method is used to obtain wetting properties over a range of temperatures. The water system also highlights challenges associated with application of the spreading method within the framework pursued here.

Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles.

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.

Position-Dependent Dynamics Explain Pore-Averaged Diffusion in Strongly Attractive Adsorptive Systems.

Using molecular simulations, we investigate the relationship between the pore-averaged and position-dependent self-diffusivity of a fluid adsorbed in a strongly attractive pore as a function of loading. Previous work (Krekelberg, W. P.; Siderius, D. W.; Shen, V. K.; Truskett, T. M.; Errington, J. R. Connection between thermodynamics and dynamics of simple fluids in highly attractive pores. Langmuir 2013, 29, 14527-14535, doi: 10.1021/la4037327) established that pore-averaged self-diffusivity in the multilayer adsorption regime, where the fluid exhibits a dense film at the pore surface and a lower density interior pore region, is nearly constant as a function of loading. Here we show that this puzzling behavior can be understood in terms of how loading affects the fraction of particles that reside in the film and interior pore regions as well as their distinct dynamics. Specifically, the insensitivity of pore-averaged diffusivity to loading arises from the approximate cancellation of two factors: an increase in the fraction of particles in the higher diffusivity interior pore region with loading and a corresponding decrease in the particle diffusivity in that region. We also find that the position-dependent self-diffusivities scale with the position-dependent density. We present a model for predicting the pore-average self-diffusivity based on the position-dependent self-diffusivity, which captures the unusual characteristics of pore-averaged self-diffusivity in strongly attractive pores over several orders of magnitude.

Multivariable extrapolation of grand canonical free energy landscapes.

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.

Temperature extrapolation of multicomponent grand canonical free energy landscapes.

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

Predicting low-temperature free energy landscapes with flat-histogram Monte Carlo methods.

We present a method for predicting the free energy landscape of fluids at low temperatures from flat-histogram grand canonical Monte Carlo simulations performed at higher ones. We illustrate our approach for both pure and multicomponent systems using two different sampling methods as a demonstration. This allows us to predict the thermodynamic behavior of systems which undergo both first order and continuous phase transitions upon cooling using simulations performed only at higher temperatures. After surveying a variety of different systems, we identify a range of temperature differences over which the extrapolation of high temperature simulations tends to quantitatively predict the thermodynamic properties of fluids at lower ones. Beyond this range, extrapolation still provides a reasonably well-informed estimate of the free energy landscape; this prediction then requires less computational effort to refine with an additional simulation at the desired temperature than reconstruction of the surface without any initial estimate. In either case, this method significantly increases the computational efficiency of these flat-histogram methods when investigating thermodynamic properties of fluids over a wide range of temperatures. For example, we demonstrate how a binary fluid phase diagram may be quantitatively predicted for many temperatures using only information obtained from a single supercritical state.

Understanding the influence of Coulomb and dispersion interactions on the wetting behavior of ionic liquids.

We study the role of dispersion and electrostatic interactions in the wetting behavior of ionic liquids on non-ionic solid substrates. We consider a simple model of an ionic liquid consisting of spherical ions that interact via Lennard-Jones and Coulomb potentials. Bulk and interfacial properties are computed for five fluids distinguished by the strength of the electrostatic interaction relative to the dispersion interaction. We employ Monte Carlo simulations and an interface-potential-based approach to calculate the liquid-vapor and substrate-fluid interfacial properties. Surface tensions for each fluid are evaluated over a range of temperatures that spans from a reduced temperature of approximately 0.6 to the critical point. Contact angles are calculated at select temperatures over a range of substrate-fluid interaction strengths that spans from the near-drying regime to the wetting regime. We observe that an increase in the relative strength of Coulombic interactions between ions leads to increasing deviation from Guggenheim's corresponding states theory. We show how this deviation is related to lower values of liquid-vapor excess entropies observed for strongly ionic fluids. Our results show that the qualitative nature of wetting behavior is significantly influenced by the competition between dispersion and electrostatic interactions. We discuss the influence of electrostatic interactions on the nature of wetting and drying transitions and corresponding states like behavior observed for contact angles. For all of the fluids studied, we observe a relatively narrow range of substrate-fluid interaction strengths wherein the contact angle is nearly independent of temperature. The influence of the ionic nature of the fluid on the temperature dependence of contact angle is also discussed.

Predicting how nanoconfinement changes the relaxation time of a supercooled liquid.

The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing. We find that the dimensionless structural relaxation times-spanning six decades as a function of temperature, density, and degree of confinement-collapse when plotted versus excess entropy. The data also collapse when plotted versus excess isochoric heat capacity, a behavior consistent with the existence of isomorphs in the bulk and confined states.

Impact of small-scale geometric roughness on wetting behavior.

We examine the extent to which small-scale geometric substrate roughness influences the wetting behavior of fluids at solid surfaces. Molecular simulation is used to construct roughness wetting diagrams wherein the progression of the contact angle is traced from the Cassie to Wenzel to impregnation regime with increasing substrate strength for a collection of systems with rectangularly shaped grooves. We focus on the evolution of these diagrams as the length scale of the substrate features approaches the size of a fluid molecule. When considering a series of wetting diagrams for substrates with fixed shape and variable feature periodicity, we find that the diagrams progressively shift away from a common curve as the substrate features become smaller than approximately 10 fluid diameters. It is at this length scale that the macroscopic models of Cassie and Wenzel become unreliable. Deviations from the macroscopic models are attributed to the manner in which the effective substrate-fluid interaction strength evolves with periodicity and the important role that confinement effects play for substrates with small periodicities.

Connection between thermodynamics and dynamics of simple fluids in highly attractive pores.

Using molecular simulations, we investigate the structural and diffusive dynamics properties of a model fluid in highly absorptive cylindrical pores. At subcritical temperatures, self-diffusivity displays three distinct regimes as a function of average pore density ρ: (1) a decrease in self-diffusivity with increasing ρ at low ρ, (2) constant self-diffusivity with respect to varying ρ at moderate density, and (3) a decrease in self-diffusivity with increasing ρ at high density. These regimes are closely linked to the thermodynamic properties of the fluid in the pore, specifically, the adsorption isotherm, isosteric heat of adsorption, and the density profile. We show that these three diffusivity regimes qualitatively correspond to three distinct adsorption regimes: monolayer formation, multilayer adsorption, and pore filling, respectively. In addition, we find that the self-diffusivity is a universal function of the local film density in the monolayer formation regime at subcritical temperatures. The results of this work suggest a potential means to estimate the self-diffusivity over a broad pressure range using a limited number of experiments.

Understanding wetting of immiscible liquids near a solid surface using molecular simulation.

We introduce Monte Carlo simulation methods for determining interfacial properties of fluids that exhibit bulk liquid-liquid immiscibility. An interface-potential-based approach, in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface, is utilized to deduce the wetting characteristics of these systems. We present a framework for implementing this general method within both the grand canonical and semigrand isobaric-isothermal ensembles. Tracking the evolution of interfacial properties along various thermodynamic paths is also examined. This task is accomplished by implementing variants of the expanded ensemble technique, which enables one to obtain components of the interface potential along a path of interest. We also discuss how these concepts are employed to calculate bulk liquid-liquid coexistence properties in an efficient manner. The computational strategies introduced here are applied to three model Lennard-Jones systems. For each system, we compile the evolution of the liquid-liquid surface tension and contact angle with temperature or pressure. For one of the model systems we compare our results with literature data. We also examine how interfacial properties evolve upon variation of the relative affinity of the fluid components for the substrate. Overall, we find that the approach pursued here is generally applicable and provides an efficient and precise means to calculate the bulk and interfacial properties of fluids that exhibit liquid-liquid immiscibility.

Monte Carlo simulation strategies to compute interfacial and bulk properties of binary fluid mixtures.

We introduce Monte Carlo simulation methods for determining interfacial properties of binary fluid mixtures. The interface potential approach, in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface, is utilized to deduce the wetting characteristics of a fluid mixture. The strategy described here provides an effective means to obtain the evolution of interfacial properties with the chemical composition of the fluid. This task is accomplished by implementing an activity fraction expanded ensemble technique, which allows one to obtain elements of the interface potential as a function of composition. We also show how this technique can be utilized to calculate bulk coexistence properties of fluid mixtures in an efficient manner. The computational strategies introduced here are applied to three model systems. One includes an argon-methane fluid mixture that is known to display simple behavior in the bulk. The second fluid model contains a size asymmetric mixture that exhibits azeotropy. The third model fluid is the well-studied size symmetric mixture that displays liquid-liquid-vapor phase coexistence. The techniques outlined here are used to compile the composition dependence of spreading and drying coefficients, liquid-vapor surface tension, and contact angle for these systems. We also compare our surface tension results with values estimated from predictive-style models that provide the surface tension of a fluid mixture in terms of pure component properties. Overall, we find that the general approach pursued here provides an efficient and precise means to calculate the bulk and wetting properties of fluid mixtures.

Communication: Phase behavior of materials with isotropic interactions designed by inverse strategies to favor diamond and simple cubic lattice ground states.

We use molecular simulation to construct equilibrium phase diagrams for two recently introduced model materials with isotropic, soft-repulsive pair interactions designed to favor diamond and simple cubic lattice ground states, respectively, over a wide range of densities [Jain et al., Soft Matter 9, 3866 (2013)]. We employ free energy based Monte Carlo simulation techniques to precisely trace the inter-crystal and fluid-crystal coexistence curves. We find that both model materials display rich polymorphic phase behavior featuring stable crystals corresponding to the target ground-state structures, as well as a variety of other crystalline (e.g., hexagonal and body-centered cubic) phases and multiple reentrant melting transitions.

Calculation of inhomogeneous-fluid cluster expansions with application to the hard-sphere∕hard-wall system.

We examine the suitability of cluster expansion methods for the description of inhomogeneous fluids. In particular, we apply these methods to characterize the density profile, surface tension, and excess adsorption for a hard-sphere fluid near a hard wall. Coefficients for these series up to seventh order are evaluated by the Mayer-sampling Monte Carlo method. Comparison of the series to Monte Carlo simulations of these systems finds very good agreement up to bulk densities approaching the freezing point. This work indicates that knowledge of surface cluster integrals of inhomogeneous systems can be at least as useful as the bulk-phase virial expansions.

Efficiency Comparison of Single- and Multiple-Macrostate Grand Canonical Ensemble Transition-Matrix Monte Carlo Simulations.

Recent interest in parallelizing flat-histogram transition-matrix Monte Carlo simulations in the grand canonical ensemble, due to its demonstrated effectiveness in studying phase behavior, self-assembly and adsorption, has led to the most extreme case of single-macrostate simulations, where each macrostate is simulated independently with ghost particle insertions and deletions. Despite their use in several studies, no efficiency comparisons of these single-macrostate simulations have been made with multiple-macrostate simulations. We show that multiple-macrostate simulations are up to 3 orders of magnitude more efficient than single-macrostate simulations, which demonstrates the remarkable efficiency of flat-histogram biased insertions and deletions, even with low acceptance probabilities. Efficiency comparisons were made for supercritical fluids and vapor-liquid equilibrium of bulk Lennard-Jones and a three-site water model, self-assembling patchy trimer particles and adsorption of a Lennard-Jones fluid confined in a purely repulsive porous network, using the open source simulation toolkit FEASST. By directly comparing with a variety of Monte Carlo trial move sets, this efficiency loss in single-macrostate simulations is attributed to three related reasons. First, ghost particle insertions and deletions in single-macrostate simulations incur the same computational expense as grand canonical ensemble trials in multiple-macrostate simulations, yet ghost trials do not reap the sampling benefit from propagating the Markov chain to a new microstate. Second, single-macrostate simulations lack macrostate change trials that are biased by the self-consistently converging relative macrostate probability, which is a major component of flat histogram simulations. Third, limiting a Markov chain to a single macrostate reduces sampling possibilities. Existing parallelization methods for multiple-macrostate flat-histogram simulations are shown to be more efficient than parallel single-macrostate simulations by approximately an order of magnitude or more in all systems investigated.

Monte Carlo simulation methods for computing the wetting and drying properties of model systems.

We introduce general Monte Carlo simulation methods for determining the wetting and drying properties of model systems. We employ an interface-potential-based approach in which the interfacial properties of a system are related to the surface excess free energy of a thin fluid film in contact with a surface. Two versions of this approach are explored: a "spreading" method focused on the growth of a thin liquid film from a surface in a mother vapor and a "drying" method focused on the growth of a thin vapor film from a surface in a mother liquid. The former provides a direct measure of the spreading coefficient while the latter provides an analogous drying coefficient. When coupled with an independent measure of the liquid-vapor surface tension, these coefficients enable one to compute the contact angle. We also show how one can combine information gathered from application of the spreading and drying methods at a common state point to obtain direct measures of the contact angle and liquid-vapor surface tension. The computational strategies introduced here are applied to two model systems. One includes a monatomic Lennard-Jones fluid that interacts with a structureless substrate via a long-ranged substrate potential. The second model contains a monatomic Lennard-Jones fluid that interacts with an atomistically detailed substrate via a short-ranged potential. Expanded ensemble techniques are coupled with the interface potential approach to compile the temperature- and substrate strength-dependence of various interfacial properties for these systems. Overall, we find that the approach pursued here provides an efficient and precise means to calculate the wetting and drying properties of model systems.

Monte Carlo simulation strategies for computing the wetting properties of fluids at geometrically rough surfaces.

We introduce Monte Carlo simulation methods for determining the wetting properties of model systems at geometrically rough interfaces. The techniques described here enable one to calculate the macroscopic contact angle of a droplet that organizes in one of the three wetting states commonly observed for fluids at geometrically rough surfaces: the Cassie, Wenzel, and impregnation states. We adopt an interface potential approach in which the wetting properties of a system are related to the surface density dependence of the surface excess free energy of a thin liquid film in contact with the substrate. We first describe challenges and inefficiencies encountered when implementing a direct version of this approach to compute the properties of fluids at rough surfaces. Next, we detail a series of convenient thermodynamic paths that enable one to obtain free energy information at relevant surface densities over a wide range of temperatures and substrate strengths in an efficient manner. We then show how this information is assembled to construct complete wetting diagrams at a temperature of interest. The strategy pursued within this work is general and is expected to be applicable to a wide range of molecular systems. To demonstrate the utility of the approach, we present results for a Lennard-Jones fluid in contact with a substrate containing rectangular-shaped grooves characterized by feature sizes of order ten fluid diameters. For this particular fluid-substrate combination, we find that the macroscopic theories of Cassie and Wenzel provide a reasonable description of simulation data.