Computation of interfacial properties via grand canonical transition matrix Monte Carlo simulation

Measuring line tension: Thermodynamic integration during detachment of a molecular dynamics droplet

The contact line (CL) is where solid, liquid, and vapor phases meet, and Young's equation describes the macroscopic force balance of the interfacial tensions between these three phases. These interfacial tensions are related to the nanoscale stress inhomogeneity appearing around the interface, and for curved CLs, e.g., a three-dimensional droplet, another force known as the line tension must be included in Young's equation. The line tension has units of force, acting parallel to the CL, and is required to incorporate the extra stress inhomogeneity around the CL into the force balance. Considering this feature, Bey et al. [J. Chem. Phys. 152, 094707 (2020)] reported a mechanical approach to extract the value of line tension τℓ from molecular dynamics (MD) simulations. In this study, we show a novel thermodynamics interpretation of the line tension as the free energy per CL length, and based on this interpretation, through MD simulations of a quasi-static detachment process of a quasi-two-dimensional droplet from a solid surface, we obtained the value τℓ as a function of the contact angle. The simulation scheme is considered to be an extension of a thermodynamic integration method, previously used to calculate the solid-liquid and solid-vapor interfacial tensions through a detachment process, extended here to the three-phase system. The obtained value agreed well with the result by Bey et al. and showed the validity of thermodynamic integration at the three-phase interface.

Identifying pathways to metal-organic framework collapse during solvent activation with molecular simulations

Metal-organic framework (MOF) materials are a vast family of nanoporous solids with potential applications ranging from drug delivery to environmental remediation. Application of MOFs in these scenarios is hindered, however, by difficulties in MOF 'activation' after initial synthesis - removal of the synthesis solvent from the pores to make the pore space accessible - often leading to framework collapse if improperly performed. While experimental studies have correlated collapse to specific solvent properties and conditions, the mechanism of activation-collapse is currently unknown. Developing this understanding would enable researchers to create better activation protocols for MOFs, accelerating discovery and process intensification. To achieve this goal, we simulated solvent removal using grand-canonical Monte Carlo and free energy perturbation methods. By framing activation as a fluid desorption problem, we investigated activation processes in the isoreticular metal organic framework (IRMOF) family of MOFs for different solvents. We identified two pathways for solvent activation - the solvent either desorbs uniformly from each individual pore or forms coexisting phases during desorption. These mesophases in turn lead to large capillary stresses within the framework, corroborating experimental hypotheses for the cause of activation-collapse. Finally, we found that the activation energy of solvent removal increased with pore size and connectivity due to the increased stability of solvent mesophases, matching experimental findings. Using these simulations, it is possible to screen MOF activation procedures, enabling rapid identification of ideal solvents and conditions and thus enabling faster development of MOFs for practical applications.

Effect of shape anisotropy on the precipitation of dimeric nanoparticles

We use grand canonical transition matrix Monte Carlo simulations to study the precipitation of dimeric nanoparticles. The dimers are composed of two particles having different chemical features and separated by a fixed distance. The non-attractive and attractive parts of the dimer are modeled using hard-sphere and square-well potentials, respectively. The shape anisotropy is altered by changing the relative sizes of the two particles. We observe that the stability of the nanosuspension increases with the increase in the size of the non-attractive part of the dimer. The precipitates of dimers having larger non-attractive parts have lower packing densities, contain large cavities, and show evidence of self-assembly in the bulk and on the surface. We also use the results from our simulations and the classical nucleation theory to study the kinetics of precipitation. At a given temperature and relative supersaturation, the rate of homogeneous nucleation increases with the increase in the size of the non-attractive parts. Finally, we use an example to show how our results can guide the design of nanosuspensions containing chemically anisotropic dimers that are stable under particular conditions.

Emerging Trends of Computational Chemistry and Molecular Modeling in Froth Flotation: A Review

Froth flotation is the most versatile process in mineral beneficiation, extensively used to concentrate a wide range of minerals. This process comprises mixtures of more or less liberated minerals, water, air, and various chemical reagents, involving a series of intermingled multiphase physical and chemical phenomena in the aqueous environment. Today's main challenge facing the froth flotation process is to gain atomic-level insights into the properties of its inherent phenomena governing the process performance. While it is often challenging to determine these phenomena via trial-and-error experimentations, molecular modeling approaches not only elicit a deeper understanding of froth flotation but can also assist experimental studies in saving time and budget. Thanks to the rapid development of computer science and advances in high-performance computing (HPC) infrastructures, theoretical/computational chemistry has now matured enough to successfully and gainfully apply to tackle the challenges of complex systems. In mineral processing, however, advanced applications of computational chemistry are increasingly gaining ground and demonstrating merit in addressing these challenges. Accordingly, this contribution aims to encourage mineral scientists, especially those interested in rational reagent design, to become familiarized with the necessary concepts of molecular modeling and to apply similar strategies when studying and tailoring properties at the molecular level. This review also strives to deliver the state-of-the-art integration and application of molecular modeling in froth flotation studies to assist either active researchers in this field to disclose new directions for future research or newcomers to the field to initiate innovative works.

A General Method for Calculating Solid/Liquid Interfacial Free Energies from Atomistic Simulations: Application to CaSO4.xH2O

We present a general method for computing interfacial free energies from atomistic simulations, which is particularly suitable for solid/liquid interfaces. Our method uses an Einstein crystal as a universal reference state and is more flexible than previous approaches. Surfaces with dipoles, complex reconstructions, and partially dissolved species are all easily accommodated within the framework. It may also be extended to calculating the relative free energies of different phases and other types of defect. We have applied our method to interfaces of bassanite and gypsum with water and obtained interfacial free energies of the order of 0.15 J/m2, of which approximately 50 % is due to entropic contributions. Our calculations of the interfacial free energy of NaCl with water obtained a value of 0.13 J/m2 of which only 19 % is from entropic contributions. We have also predicted equilibrium morphologies for bassanite and gypsum that compare well with experiments and previous calculations.

Effects of surface contamination on the interfacial properties of CO2/water/calcite systems

Understanding the wetting properties of reservoir rocks can be of great benefit for advanced applications such as the effective trapping and geological storage of CO₂. Despite their importance, not all mechanisms responsible for wetting mineral surfaces in subsurface environments are well understood. Factors such as temperature, pressure and salinity are often studied, achieving results with little unanimity; other possible factors are left somewhat unexplored. One such factor is the effect of contamination. In the present study, the effects of adding a non-aqueous organic contaminant, ethanol, on the CO₂-water interfacial tension (IFT) and the CO₂/water/calcite contact angle were investigated using molecular dynamics simulations. Within the conditions studied, relatively small amounts of ethanol cause a significant decrease in the CO₂-water IFTs, as well as a pronounced increase in the water-calcite-CO₂ three phase contact angle. The latter result is due to the decrease of the IFT between CO₂ and water and the strong adsorption of ethanol on the solid substrate. These findings could be helpful for explaining how impurities can affect experimental data and could lead to effective carbon sequestration strategies.

Classical statistical mechanics in the grand canonical ensemble

The methodology developed by Lustig for calculating thermodynamic properties in the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994)JCPSA60021-960610.1063/1.466446; Mol. Phys. 110, 3041 (2012)MOPHAM0026-897610.1080/00268976.2012.695032] is applied to derive rigorous expressions for thermodynamic properties of fluids in the grand canonical ensemble. All properties are expressed by phase-space functions, which are related to derivatives of the grand canonical potential with respect to the three independent variables of the ensemble: temperature, volume, and chemical potential. The phase-space functions contain ensemble averages of combinations of the number of particles, potential energy, and derivatives of the potential energy with respect to volume. In addition, expressions for the phase-space functions for temperature-dependent potentials are provided, which are required to account for quantum corrections semiclassically in classical simulations. Using the Lennard-Jones model fluid as a test case, the derived expressions are validated by Monte Carlo simulations. In contrast to expressions for the thermal expansion coefficient, the isothermal compressibility, and the thermal pressure coefficient from the literature, our expressions yield more reliable results for these properties, which agree well with a recent accurate equation of state for the Lennard-Jones model fluid. Moreover, they become equivalent to the corresponding expressions in the canonical ensemble in the thermodynamic limit.

Water on hydroxylated silica surfaces: Work of adhesion, interfacial entropy, and droplet wetting

In the last few years, much attention has been devoted to the control of the wettability properties of surfaces modified with functional groups. Molecular dynamics (MD) simulation is one of the powerful tools for microscopic analysis providing visual images and mean geometrical shapes of the contact line, e.g., of nanoscale droplets on solid surfaces, while profound understanding of wetting demands quantitative evaluation of the solid-liquid (SL) interfacial tension. In the present work, we examined the wetting of water on neutral and regular hydroxylated silica surfaces with five different area densities of OH groups ρ_A ^OH, ranging from a non-hydroxylated surface to a fully hydroxylated one through two theoretical methods: thermodynamic integration (TI) and MD simulations of quasi-two-dimensional equilibrium droplets. For the former, the work of adhesion needed to quasi-statically strip the water film off the solid surface was computed by the phantom wall TI scheme to evaluate the SL interfacial free energy, whereas for the latter, the apparent contact angle θ_app was calculated from the droplet density distribution. The theoretical contact angle θ_YD and the apparent one θ_app, both indicating the enhancement of wettability by an increase in ρ_A ^OH, presented good quantitative agreement, especially for non-hydroxylated and highly hydroxylated surfaces. On partially hydroxylated surfaces, in which θ_YD and θ_app slightly deviated, the Brownian motion of the droplet was suppressed, possibly due to the pinning of the contact line around the hydroxyl groups. Relations between work of adhesion, interfacial energy, and entropy loss were also analyzed, and their influence on the wettability was discussed.

Coupled Monte Carlo and Molecular Dynamics Simulations on Interfacial Properties of Antifouling Polymer Membranes

We use molecular simulation to study the wetting behavior of antifouling polymer-tethered membranes. We obtain the interfacial properties (e.g., contact angle) of water at various temperatures for five polymer membranes, including a base polysulfone (PSF) membrane and four other PSF membranes grafted with antifouling polymers (two poly(ethylene glycol) (PEG) tethers and two zwitterionic tethers). We implement a coupled Monte Carlo (MC)/molecular dynamics (MD) approach to determine the interface potentials of water on the membrane surfaces in an efficient manner. Within this method, short MC and MD simulations are performed in cycles to collect the surface excess free energy of a thin water film on polymer membrane surfaces. Simulation results show that the grafting of zwitterionic tethers provides a more significant enhancement in the hydrophilicity of the PSF membrane than that of the PEG tethers. Water completely wets the surface of zwitterionic polymer membranes.

Computation of solid-fluid interfacial free energy in molecular systems using thermodynamic integration

In this article, we present two methods based on thermodynamic integration for computing solid-fluid interfacial free energy for a molecular system. As a representative system, we choose two crystal polymorphs of orcinol (5-methylbenzene-1,3-diol) as the solid phase and chloroform and nitromethane as the liquid phase. The computed values of the interfacial free energy are then used in combination with the classical nucleation theory to predict solvent induced polymorph selectivity during crystallization of orcinol from solution.

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.

Characterizing surface wetting and interfacial properties using enhanced sampling (SWIPES)

We introduce an accurate and efficient method for characterizing surface wetting and interfacial properties, such as the contact angle made by a liquid droplet on a solid surface, and the vapor-liquid surface tension of a fluid. The method makes use of molecular simulations in conjunction with the indirect umbrella sampling technique to systematically wet the surface and estimate the corresponding free energy. To illustrate the method, we study the wetting of a family of Lennard-Jones surfaces by water. For surfaces with a wide range of attractions for water, we estimate contact angles using our method, and compare them with contact angles obtained using droplet shapes. Notably, our method is able to capture the transition from partial to complete wetting as surface-water attractions are increased. Moreover, the method is straightforward to implement and is computationally efficient, providing accurate contact angle estimates in roughly 5 nanoseconds of simulation time.

On the equilibrium contact angle of sessile liquid drops from molecular dynamics simulations

We present a new methodology to estimate the contact angles of sessile drops from molecular simulations by using the Gaussian convolution method of Willard and Chandler [J. Phys. Chem. B 114, 1954-1958 (2010)] to calculate the coarse-grained density from atomic coordinates. The iso-density contour with average coarse-grained density value equal to half of the bulk liquid density is identified as the average liquid-vapor (LV) interface. Angles between the unit normal vectors to the average LV interface and unit normal vector to the solid surface, as a function of the distance normal to the solid surface, are calculated. The cosines of these angles are extrapolated to the three-phase contact line to estimate the sessile drop contact angle. The proposed methodology, which is relatively easy to implement, is systematically applied to three systems: (i) a Lennard-Jones (LJ) drop on a featureless LJ 9-3 surface; (ii) an SPC/E water drop on a featureless LJ 9-3 surface; and (iii) an SPC/E water drop on a graphite surface. The sessile drop contact angles estimated with our methodology for the first two systems are shown to be in good agreement with the angles predicted from Young's equation. The interfacial tensions required for this equation are computed by employing the test-area perturbation method for the corresponding planar interfaces. Our findings suggest that the widely adopted spherical-cap approximation should be used with caution, as it could take a long time for a sessile drop to relax to a spherical shape, of the order of 100 ns, especially for water molecules initiated in a lattice configuration on a solid surface. But even though a water drop can take a long time to reach the spherical shape, we find that the contact angle is well established much faster and the drop evolves toward the spherical shape following a constant-contact-angle relaxation dynamics. Making use of this observation, our methodology allows a good estimation of the sessile drop contact angle values even for moderate system sizes (with, e.g., 4000 molecules), without the need for long simulation times to reach the spherical shape.

Nanocapillarity and Liquid Bridge-Mediated Force between Colloidal Nanoparticles

In this work, we probe the concept of interface tension for ultrathin adsorbed liquid films on the nanoscale by studying the surface fluctuations of films down to the monolayer. Our results show that the spectrum of film height fluctuations of a liquid-vapor surface may be extended to ultrathin films provided we take into account the interactions of the substrate with the surface. Global fluctuations of the film height are described in terms of disjoining pressure, whereas surface deformations that are proportional to the interface area are accounted for by a film thickness-dependent surface tension. As a proof of concept, we model the capillary forces between colloidal nanoparticles held together by liquid bridges. Our results indicate that the classical equations for capillarity follow very precisely down to the nanoscale provided we account for the film height dependence of the surface tension.

Structure and Interfacial Tension of a Hard-Rod Fluid in Planar Confinement

The structural properties and interfacial tension of a fluid of rodlike hard-spherocylinder particles in contact with hard structureless flat walls are studied by means of Monte Carlo simulation. The calculated surface tension between the rod fluid and the substrate is characterized by a nonmonotonic trend as a function of the bulk concentration (density) over the range of isotropic bulk concentrations. As suggested by earlier theoretical studies, a surface-ordering scenario is confirmed by our simulations: the local orientational order close to the wall changes from uniaxial to biaxial nematic when the bulk concentration reaches about 85% of the value at the onset of the isotropic-nematic phase transition. The surface ordering coincides with a wetting transition whereby the hard wall is wetted by a nematic film. Accurate values of the fluid-solid surface tension, the adsorption, and the average particle-wall contact distance are reported (over a broad range of densities into the dense nematic region for the first time), which can serve as a useful benchmark for future theoretical and experimental studies on confined rod fluids. The simulation data are supplemented with predictions from second-virial density functional theory, which are in good qualitative agreement with the simulation results.

Water-Mediated Interactions between Hydrophilic and Hydrophobic Surfaces

All surfaces in water experience at short separations hydration repulsion or hydrophobic attraction, depending on the surface polarity. These interactions dominate the more long-ranged electrostatic and van der Waals interactions and are ubiquitous in biological and colloidal systems. Despite their importance in all scenarios where the surface separation is in the nanometer range, the origin of these hydration interactions is still unclear. Using atomistic solvent-explicit molecular dynamics simulations, we analyze the interaction free energies of charge-neutral model surfaces with different elastic and water-binding properties. The surface polarity is shown to be the most important parameter that not only determines the hydration properties and thereby the water contact angle of a single surface but also the surface-surface interaction and whether two surfaces attract or repel. Elastic properties of the surfaces are less important. On the basis of surface contact angles and surface-surface binding affinities, we construct a universal interaction diagram featuring three different interaction regimes-hydration repulsion, cavitation-induced attraction-and for intermediate surface polarities-dry adhesion. On the basis of scaling arguments and perturbation theory, we establish simple combination rules that predict the interaction behavior for combinations of dissimilar surfaces.

From hydration repulsion to dry adhesion between asymmetric hydrophilic and hydrophobic surfaces

Using all-atom molecular dynamics (MD) simulations at constant water chemical potential in combination with basic theoretical arguments, we study hydration-induced interactions between two overall charge-neutral yet polar planar surfaces with different wetting properties. Whether the water film between the two surfaces becomes unstable below a threshold separation and cavitation gives rise to long-range attraction, depends on the sum of the two individual surface contact angles. Consequently, cavitation-induced attraction also occurs for a mildly hydrophilic surface interacting with a very hydrophobic surface. If both surfaces are very hydrophilic, hydration repulsion dominates at small separations and direct attractive force contribution can-if strong enough-give rise to wet adhesion in this case. In between the regimes of cavitation-induced attraction and hydration repulsion we find a narrow range of contact angle combinations where the surfaces adhere at contact in the absence of cavitation. This dry adhesion regime is driven by direct surface-surface interactions. We derive simple laws for the cavitation transition as well as for the transition between hydration repulsion and dry adhesion, which favorably compare with simulation results in a generic adhesion state diagram as a function of the two surface contact angles.

Dry-Surface Simulation Method for the Determination of the Work of Adhesion of Solid-Liquid Interfaces

We introduce a methodology, referred to as the dry-surface method, to calculate the work of adhesion of heterogeneous solid-liquid interfaces by molecular simulation. This method employs a straightforward thermodynamic integration approach to calculate the work of adhesion as the reversible work to turn off the attractive part of the actual solid-liquid interaction potential. It is formulated in such a way that it may be used either to evaluate the ability of force fields to reproduce reference values of the work of adhesion or to optimize force-field parameters with reference values of the work of adhesion as target quantities. The methodology is tested in the case of water on a generic model of nonpolar substrates with the structure of gold. It is validated through a quantitative comparison to phantom-wall calculations and against a previous characterization of the thermodynamics of the gold-water interface. It is found that the work of adhesion of water on nonpolar substrates is a nonlinear function of the microscopic solid-liquid interaction energy parameter. We also comment on the ability of mean-field approaches to predict the work of adhesion of water on nonpolar substrates. In addition, we discuss in detail the information on the solid-liquid interfacial thermodynamics delivered by the phantom-wall approach. We show that phantom-wall calculations yield the solid-liquid interfacial tension relative to the solid surface tension rather than the absolute solid-liquid interfacial tension as previously believed.

Disjoining pressure and the film-height-dependent surface tension of thin liquid films: new insight from capillary wave fluctuations

In this paper we review simulation and experimental studies of thermal capillary wave fluctuations as an ideal means for probing the underlying disjoining pressure and surface tensions, and more generally, fine details of the Interfacial Hamiltonian Model. We discuss recent simulation results that reveal a film-height-dependent surface tension not accounted for in the classical Interfacial Hamiltonian Model. We show how this observation may be explained bottom-up from sound principles of statistical thermodynamics and discuss some of its implications.

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.

What is the contact angle of water on graphene?

Although experimental and theoretical studies have addressed the question of the wetting properties of graphene, the actual value of the contact angle of water on an isolated graphene monolayer remains unknown. While recent experimental literature indicates that the contact angle of water on graphite is in the range 90-95°, it has been suggested that the contact angle on graphene may either be as high as 127° or moderately enhanced in comparison with graphite. With the support of classical molecular dynamics simulations using empirical force-fields, we develop an argumentation to show that the value of 127° is an unrealistic estimate and that a value of the order of 95-100° should be expected. Our study establishes a connection between the variation of the work of adhesion of water on graphene-based surfaces and the interaction potential between individual water molecules and these surfaces. We show that a variation of the contact angle from 90° on graphite to 127° on graphene would imply that both of the first two carbon layers of graphite contribute approximately the same interaction energy with water. Such a situation is incompatible with the short-range nature of the interaction between water and this substrate. We also show that the interaction potential energy between water and the graphene-based substrates is the main contribution to the work of adhesion of water with a relative magnitude that is independent of the number of graphene layers. We introduce the idea that the remaining contribution is entropic in nature and is connected to the fluctuations in the water-substrate interaction energy.

Can dynamic contact angle be measured using molecular modeling?

A method is presented for determining the dynamic contact angle at the three-phase contact between a solid, a liquid, and a vapor under an applied force, using molecular simulation. The method is demonstrated using a Lennard-Jones fluid in contact with a cylindrical shell of the fcc Lennard-Jones solid. Advancing and receding contact angles and the contact angle hysteresis are reported for the first time by this approach. The increase in force required to wet fully an array of solid cylinders (robustness) with decreasing separation distance between cylinders is evaluated. The dynamic contact angle is characterized by partial slipping of the three phase contact line when a force is applied.

Sensitivity of nucleation phenomena on range of interaction potential

Theoretical and computational investigations of nucleation have been plagued by the sensitivity of the phase diagram to the range of the interaction potential. As the surface tension depends strongly on the range of interaction potential and as the classical nucleation theory (CNT) predicts the free energy barrier to be directly proportional to the cube of the surface tension, one expects a strong sensitivity of nucleation barrier to the range of the potential; however, CNT leaves many aspects unexplored. We find for gas-liquid nucleation in Lennard-Jones system that on increasing the range of interaction the kinetic spinodal (KS) (where the mechanism of nucleation changes from activated to barrierless) shifts deeper into the metastable region. Therefore the system remains metastable for larger value of supersaturation and this allows one to explore the high metastable region without encountering the KS. On increasing the range of interaction, both the critical cluster size and pre-critical minima in the free energy surface of kth largest cluster, at respective kinetic spinodals, shift towards smaller cluster size. In order to separate surface tension contribution to the increase in the barrier from other non-trivial factors, we introduce a new scaling form for surface tension and use it to capture both the temperature and the interaction range dependence of surface tension. Surprisingly, we find only a weak non-trivial contribution from other factors to the free energy barrier of nucleation.