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

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.

Chasing the Critical Wetting Transition. An Effective Interface Potential Method

Wettablity is one of the important characteristics defining a given surface. Here we show that the effective interface potential method of determining the wetting temperature, originally proposed by MacDowell and Müller for the surfaces exhibiting the first order wetting transition, can also be used to estimate the wetting temperature of the second order (continuous) wetting transition. Some selected other methods of determination of the wetting temperature are also 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.

A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids

Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry, and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover previously unrecognized classes of surface phase diagram which differ from that established for simple lattice models and often assumed to be universal. The differences relate both to the topology of the phase diagram and to the nature of the transitions, with a remarkable feature being a difference between drying and wetting transitions which persists even in the approach to the bulk critical point. Most experimental and simulational studies of liquids at a substrate belong to one of these previously unrecognized classes. We predict that while there appears to be nothing particularly special about water with regard to its wetting and drying behavior, superhydrophobic behavior should be more readily observable in experiments conducted at high temperatures than at room temperature.

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.

Monte Carlo simulation of cylinders with short-range attractions

Cylindrical or rod-like particles are promising materials for the applications of fillers in nanocomposite materials and additives to control rheological properties of colloidal suspensions. Recent advances in particle synthesis allows for cylinders to be manufactured with short-ranged attractions to study the gelation as a function of packing fraction, aspect ratio and attraction strength. In order to aid in the analysis of small-angle scattering experiments of rod-like particles, computer simulation methods were used to model these particles with specialized Monte Carlo algorithms and tabular superquadric potentials. The attractive interaction between neighboring rods increases with the amount of locally-accessible surface area, thus leading to patchy-like interactions. We characterize the clustering and percolation of cylinders as the attractive interaction increases from the homogenous fluid at relatively low attraction strength, for a variety of aspect ratios and packing fractions. Comparisons with the experimental scattering results are also presented, which are in agreement.

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.

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.

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.

Depletion-driven crystallization of cubic colloids sedimented on a surface

Cubic colloids, sedimented on a surface and immersed in a solution of depletant molecules, were modeled with a family of shapes which smoothly varies from squares to circles. Using Wang-Landau simulations with expanded ensembles, we observe the formation of rhombic lattices, square lattices, hexagonal lattices, and a fluid phase. This systematic investigation includes locating transitions between all combinations of the three lattice structures upon changing the shape and transitions between the fluid and crystal upon changing the depletant concentration. The rhombic lattice deforms smoothly between square-like and hexagonal-like angles, depending on both the shape and the depletant concentration. Our results on the effect of the depletant concentration, depletant size, and colloid shape to influence the stability of the fluid and the lattice structures may help guide experimental studies with recently synthesized cubic colloids.

Critical Drying of Liquids

We report a detailed simulation and classical density functional theory study of the drying transition in a realistic model fluid at a smooth substrate. This transition (in which the contact angle θ→180°) is shown to be critical for both short-ranged and long-ranged substrate-fluid interaction potentials. In the latter case critical drying occurs at exactly zero attractive substrate strength. This observation permits the accurate elucidation of the character of the transition via a finite-size scaling analysis of the density probability function. We find that the critical exponent ν_{∥} that controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall, is over twice as large as predicted by mean field and renormalization group calculations. We suggest a reason for the discrepancy. Our findings shed new light on fluctuation phenomena in fluids near hydrophobic and solvophobic interfaces.

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.

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.

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.