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

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.

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.

Computing the Work of Solid-Liquid Adhesion in Systems with Damped Coulomb Interactions via Molecular Dynamics: Approaches and Insights

Recently, the dry-surface method [Langmuir2016, 31, 8335−8345] has been developed to compute the work of adhesion of solid–liquid and other interfaces using molecular dynamics via thermodynamic integration. Unfortunately, when long-range Coulombic interactions are present in the interface, a special treatment is required, such as solving additional Poisson equations, which is usually not implemented in generic molecular dynamics software, or as fixing some groups of atoms in place, which is undesirable most of the time. In this work, we replace the long-range Coulombic interactions with damped Coulomb interactions, and explore several thermal integration paths. We demonstrate that regardless of the integration path, the same work of adhesion values are obtained as long as the path is reversible, but the numerical efficiency differs vastly. Simple scaling of the interactions is most efficient, requiring as little as 8 sampling points, followed by changing the Coulomb damping parameter, while modifying the Coulomb interaction cutoff length performs worst. We also demonstrate that switching long-range Coulombic interactions to damped ones results in a higher work of adhesion by about 10 mJ/m² because of slightly different liquid molecule orientation at the solid–liquid interface, and this value is mostly unchanged for surfaces with substantially different Coulombic interactions at the solid–liquid interface. Finally, even though it is possible to split the work of adhesion into van der Waals and Coulomb components, it is known that the specific per-component values are highly dependent on the integration path. We obtain an extreme case, which demonstrates that caution should be taken even when restricting to qualitative comparison.

Interaction between dilute water vapor and dodecane thiol ligated Au nanoparticles: Hydrated structure and pair potential of mean force

The interaction between two ligated nanoparticles depends on whether they are isolated or immersed in a liquid solvent. However, very little is known about the influence of solvent vapor on the interaction between two ligated nanoparticles. Recent experiments yield the surprising result that the cyclic exposure of solvent free suspended monolayers of dodecane thiol ligated gold nanoparticles (AuNPs) to water vapor and dry nitrogen generates reversible cyclic decreases and increases in Young's modulus of the monolayer, implying corresponding cyclic changes in the AuNP-AuNP interaction. We examine how water vapor interacts with an isolated dodecane thiol dressed AuNP and how water vapor affects the interaction between a pair of nanoparticles, using all-atom molecular-dynamics simulations. We find that there is condensation of water molecules onto the ligand shell of an AuNP in the form of clusters of 100-2000 molecules that partially cover the shell, with most of the water in a few large clusters. A water cluster bridges the AuNPs, with a sensibly constant number of water molecules for AuNP-AuNP separations from the edge-to-edge contact up to center-to-center separations of 100 Å. The wet AuNP-AuNP interaction has a slightly deeper and wider asymmetric well than does the dry interaction, a change that is qualitatively consistent with that implied by the observed water vapor induced change in Young's modulus of a monolayer of these AuNPs. We find that macroscopic analyses of water drop-deformable surface interactions and dynamics provide both guidance to understanding and qualitatively correct predictions of the phenomena observed in our simulations.

Nanoscale Wetting of Crystalline Cellulose

Cellulose possesses considerable potential for a wide range of sustainable applications. Nanocellulose-based material properties are primarily dependent on the structural surface characteristics of its crystalline planes. Experimental measurements of the affinity of crystalline nanocellulose surfaces with water are scarce and challenging to obtain. Therefore, the relative hydrophilicity of different cellulose allomorphs crystalline planes is often inferred from qualitative assessments of their surface and the exposition of polar groups to the solvent. This work investigates the relative hydrophilicity of cellulose surfaces using molecular dynamics simulations. The behavior of a water droplet laid on different crystal planes was used to determine their relative hydrophilicity. The water molecules fully spread onto highly hydrophilic surfaces. However, a water droplet placed on less hydrophilic surfaces equilibrates as an oblate spheroidal cap allowing the measurement of a contact angle. The results indicate that the Iα (010), Iα (11̅0), Iβ (010), and Iβ (110) faces, as well as the faces of human-made celluloses II and III_I (100), (11̅0), (010), and (110) are all highly hydrophilic. They all have a contact angle value inferior to 11°. Not unexpectedly, the Iα (001) and Iβ (100) surfaces are less hydrophilic with contact angles of 48 and 34°, respectively. However, the Iβ (11̅0) plane, often referred to as a hydrophilic surface, forms a contact angle of about 32°. The results are rationalized in terms of structure, exposure of hydroxyl groups to the solvent, and degree of cellulose-cellulose versus cellulose-water hydrogen bonds on each face. The simulations also show that the surface oxidation degree tunes the surface hydrophilicity in a nonlinear manner due to cooperative effects involving water-cellulose interactions. Our study helps us to understand how the degree of hydrophilicity of cellulose emerges from specific structural features of each crystalline surface.

Structure and Contact Angle in Sessile Droplets of Binary Mixtures of Lennard-Jones Chains: A Molecular Dynamics Study

Molecular dynamics simulations were carried out to investigate cylindrical droplets consisting of binary mixtures of Lennard-Jones (LJ) fluids in contact with a solid substrate. The droplets are composed of mixtures of the monomeric LJ fluid plus linear-tangent chains of 2, 10, 20, and 30 segments per chain that interact through a harmonic potential and the spherically truncated and shifted potential Lennard-Jones. The solid surface was modeled as a semi-infinite platinum substrate with an FCC structure that interacts with the fluid by means of a LJ 9-3 potential. We place emphasis on the effect of mixing a monomeric LJ fluid with heavy components on the contact angle and on the droplet structure, especially in the liquid-solid region. The density profiles of the droplets reveal a strong discrete layering of the fluid in the vicinity of the solid-liquid interface. The layering is more pronounced at low temperatures and for mixtures of short chains (symmetric mixtures). The ordering of the fluid was much less intense for fluids of long chains (asymmetric mixtures), and some cases even show gas enrichment at the solid-liquid interface. Enrichment at the vapor-liquid interfaces and density inversion can also be observed. However, these effects are not as marked as in planar interfaces. The contact angle between the droplet and the substrate is calculated by fitting an ellipse to the vapor-liquid interface defined by the Gibbs dividing surface. In general, an increment in the concentration of the heavy component and a reduction of the temperature resulted in an increase of the contact angle, which in turn disfavored the wetting of the droplet.

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.

Surface thermodynamics at the nanoscale

Fluid interfaces with nanoscale radii of curvature are generating great interest, both for their applications and as tools to probe our fundamental understanding. One important question is what is the smallest radius of curvature at which the three main thermodynamic combined equilibrium equations are valid: the Kelvin equation for the effect of curvature on vapor pressure, the Gibbs-Thomson equation for the curvature-induced freezing point depression, and the Ostwald-Freundlich equation for the curvature-induced increase in solubility. The objective of this Perspective is to provide conceptual, molecular modeling, and experimental support for the validity of these thermodynamic combined equilibrium equations down to the smallest interfacial radii of curvature. Important concepts underpinning thermodynamics, including ensemble averaging and Gibbs's treatment of bulk phase heterogeneities in the region of an interface, give reason to believe that these equations might be valid to smaller scales than was previously thought. There is significant molecular modeling and experimental support for all three of the Kelvin equation, the Gibbs-Thomson equation, and the Ostwald-Freundlich equation for interfacial radii of curvature from 1 to 4 nm. There is even evidence of sub-nanometer quantitative accuracy for the Kelvin equation and the Gibbs-Thomson equation.

Understanding the asymmetry between advancing and receding microscopic contact angles

By means of molecular dynamics simulation, the advancing and receding microscopic contact angles were analyzed for a shear flow of two mono-atomic fluids confined between parallel non-polar solid walls. We defined the microscopic dynamic contact angle based on the coarse-grained microscopic density distribution of the fluids (the instantaneous interface method [Willard and Chandler, J. Phys. Chem. B, 2010, 114, 1954-1958]) near the moving contact line. We have found that the asymmetric change of fluid density near the wall with respect to the moving contact line results in a different dependence between the advancing and receding contact angles on the contact line velocity in a system where the two fluids across the interface have unequal wettability to the solid wall. This difference between the advancing and receding contact angles leads to different flow resistance caused by the advancing and receding contact lines, which should have impact on the industrial applications of the fine fluid transportation with contact lines.

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.