Molecular dynamics analysis of multiphase interfaces based on in situ extraction of the pressure distribution of a liquid droplet on a solid surface

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.

Molecular Dynamics Study of the Microscopic Mechanical Balance at the Three-Phase Contact Line of Interfacial Nanobubble

This study reveals the microscopic mechanical balance at the three-phase contact line (TPCL) of an interfacial nanobubble on a substrate with a wettability pattern using molecular dynamics simulations. The apparent contact angle was compared to that evaluated using Young's equation, in which the interfacial tensions were computed using a mechanical route. The comparison was conducted by changing the wettability of the substrate from hydrophilic to neutral while maintaining a hydrophobic region in the center of the substrate. When the wettability pattern pins the TPCL at the wettability boundary, the contact angle computed by Young's equation is larger than the apparent contact angle because a pinning force exists in the inward direction of the nanobubble. Conversely, on the surfaces where the wettability pattern does not pin the TPCL, the contact angle computed by Young's equation agrees with the apparent contact angle because the pinning force disappears. The distribution of principal stresses around the TPCL, which was visualized for the first time in this study, indicates that large compressive principal stresses exist between the liquid phase and the solid substrate interface, which pin the TPCL at the surface wettability boundary, and that the maximum principal stress occurs in the inward direction of the nanobubbles at the TPCL. The normalized pinning force estimated from the maximum principal stress is equivalent to that measured experimentally.

The receding contact line cools down during dynamic wetting

When a contact line (CL)-where a liquid-vapor interface meets a substrate-is put into motion, it is well known that the contact angle differs between advancing and receding CLs. Using non-equilibrium molecular dynamics simulations, we reveal another intriguing distinction between advancing and receding CLs: while temperature increases at an advancing CL-as expected from viscous dissipation, we show that temperature can drop at a receding CL. Detailed quantitative analysis based on the macroscopic energy balance around the dynamic CL showed that the internal energy change of the fluid due to the change of the potential field along the pathline out of the solid-liquid interface induced a remarkable temperature drop around the receding CL, in a manner similar to latent heat upon phase changes. This result provides new insights for modeling the dynamic CL, and the framework for heat transport analysis introduced here can be applied to a wide range of nanofluidic systems.

Quantifying interfacial tensions of surface nanobubbles: How far can Young's equation explain?

Nanobubbles at solid-liquid interfaces play a key role in various physicochemical phenomena and it is crucial to understand their unique properties. However, little is known about their interfacial tensions due to the lack of reliable calculation methods. Based on mechanical and thermodynamic insights, we quantified for the first time the liquid-gas, solid-liquid, and solid-gas interfacial tensions of submicron-sized nitrogen bubbles at graphite-water interfaces using molecular dynamics (MD) analysis. It was revealed that Young's equation holds even for nanobubbles with different radii. We found that the liquid-gas and solid-liquid interfacial tensions were not largely affected by the gas density inside the nanobubbles. In contrast, the size effect on the solid-gas interfacial tension was observed, namely, the value dramatically decreased upon an increase in the gas density due to gas adsorption on the solid surface. However, our quantitative evaluation also revealed that the gas density effect on the contact angles is negligible when the footprint radius is larger than 50 nm, which is a typical range observed in experiments, and thus the flat shape and stabilization of submicron-sized surface bubbles observed in experiments cannot be explained only by the changes in interfacial tensions due to the van der Waals interaction-induced gas adsorption, namely by Young's equation without introducing the pinning effect. Based on our analysis, it was clarified that additional factors such as the differences in the studied systems are needed to explain the unresolved open issues - a satisfactory explanation for the nanobubbles in MD simulations being ultradense, non-flat, and stable without pinning.

Local stress tensor calculation by the method-of-plane in microscopic systems with macroscopic flow: A formulation based on the velocity distribution function

In this work, we developed a calculation method of local stress tensor applicable to non-equilibrium molecular dynamics (NEMD) systems, which evaluates the macroscopic momentum advection and the kinetic term of the stress in the framework of the Method-of-Plane (MoP), in a consistent way to guarantee the mass and momentum conservation. From the relation between the macroscopic velocity distribution function and the microscopic molecular passage across a fixed control plane, we derived a method to calculate the basic properties of the macroscopic momentum conservation law including the density, the velocity, the momentum flux, and the two terms of the stress tensor, i.e., the interaction and the kinetic terms, defined on a surface with a finite area. Any component of the streaming velocity can be obtained on a control surface, which enables the separation of the kinetic momentum flux into the advection and stress terms in the framework of MoP, and this enables strict satisfaction of the mass and momentum conservation for an arbitrary closed control volume (CV) set in NEMD systems. We validated the present method through the extraction of the density, velocity, and stress distributions in a quasi-one-dimensional steady-state Couette flow system and in a quasi-2D steady-state NEMD system with a moving contact line. We showed that with the present MoP, in contrast to the volume average method, the conservation law was satisfied even for a CV set around the moving contact line, which was located in a strongly inhomogeneous region.

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.

Evaluation of the work of adhesion at the interface between a surface-modified metal oxide and an organic solvent using molecular dynamics simulations

Advancing the practical applications of surface-modified nanoparticles requires that their dispersion in solvents can be controlled. The degree of dispersion depends on the affinity between surface-modified nanoparticles and solvents, which can be quantified using the work of adhesion at the interface. Herein, the affinity between a surface-modified inorganic solid and an organic solvent was evaluated by calculating the work of adhesion at the interface. The phantom-wall method, which is a thermodynamic route for evaluating the work of adhesion at an interface using molecular dynamics simulations, was applied to the decanoic acid-modified Al₂O₃/hexane interface. Molecular dynamics simulations were performed for flat interface systems to focus on the interactions between substances that affect the affinity on the surface. As a result, the surface coverage of decanoic acid was found to affect the work of adhesion, with a maximum value of 45.66 ± 0.75 mJ/m² at a surface coverage of 75%. An analysis of the mass density profiles of Al₂O₃, decanoic acid, and hexane in the vicinity of the interface showed that the increase in the work of adhesion with the surface coverage was due to the penetration of hexane molecules into the decanoic acid layer on the Al₂O₃ surface. At a surface coverage of 75%, some hexane molecules were trapped in the layer of oriented decanoic acid molecules. These results suggested that the interfacial affinity can be enhanced by controlling the surface modification so that the solvent can penetrate the layer of the modifier.

Size dependent influence of contact line pinning on wetting of nano-textured/patterned silica surfaces

Wetting behavior on a heterogeneous surface undergoes contact angle hysteresis as the droplet stabilized at a metastable state with a contact angle significantly different from its equilibrium value due to contact line pinning. However, there is a lack of consensus on how to calculate the influence of pinning forces. In general, the pinning effect can be characterized as (i) microscopic behavior when a droplet is pinned and the contact angle increases/decreases as the droplet volume increases/decreases and (ii) macroscopic behavior as the pinning effects decrease and ultimately, disappear with the increase of the droplet size. The current work studied both behaviors using molecular dynamics (MD) simulation with more than 300 different size water droplets on silica surfaces with three different patterns across two different wetting conditions. Results showed that the contact angle increases linearly with increasing droplet volume through the microscopic behavior, while the droplet is pinned on top of a certain number of patterns. When we normalized the droplet size with the corresponding pattern size, we observed a "wetting similarity" that linear microscopic contact angle variations over different size heterogeneities continuously line up. This shows that the pinning force remains constant and the resulting pinning effects are scalable by the size ratio between the droplet and pattern, independent of the size-scale. The slope of these microscopic linear variations decreases with an increase in the droplet size as observed through the macroscopic behavior. We further found a universal behavior in the variation of the corresponding pinning forces, independent of the wetting condition. In macroscopic behavior, pinning effects become negligible and the contact angle reaches the equilibrium value of the corresponding surface when the diameter of the free-standing droplet is approximately equal to 24 times the size of the surface structure. We found that the pinning effect is scalable with the droplet volume, not the size of the droplet base.

Large effect of lateral box size in molecular dynamics simulations of liquid-solid friction

Molecular dynamics simulations are a powerful tool to characterize liquid-solid friction. A slab configuration with periodic boundary conditions in the lateral dimensions is commonly used, where the measured friction coefficient could be affected by the finite lateral size of the simulation box. Here we show that for a very wetting liquid close to its melting temperature, strong finite size effects can persist up to large box sizes along the flow direction, typically ∼30 particle diameters. We relate the observed decrease of friction in small boxes to changes in the structure of the first adsorbed layer, which becomes less commensurable with the wall structure. Although these effects disappear for lower wetting cases or at higher temperatures, we suggest that the possible effect of the finite lateral box size on the friction coefficient should not be automatically set aside when exploring unknown systems.

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.

Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study

The question of the effect of surface heterogeneities on the evaporation of liquid droplets from solid surfaces is addressed through nonequilibrium molecular dynamics simulations. The mechanism behind contact line pinning which is still unclear is discussed in detail on the nanoscale. Model systems with the Lennard-Jones interaction potential were employed to study the evaporation of nanometer-sized cylindrical droplets from a flat surface. The heterogeneity of the surface was modeled through alternating stripes of equal width but two chemical types. The first type leads to a contact angle of 67°, and the other leads to a contact angle of 115°. The stripe width was varied between 2 and 20 liquid-particle diameters. On the surface with the narrowest stripes, evaporation occurred at constant contact angle as if the surface was homogeneous, with a value of the contact angle as predicted by the regular Cassie-Baxter equation. When the width was increased, the contact angle oscillated during evaporation between two boundaries whose values depend on the stripe width. The evaporation behavior was thus found to be a direct signature of the typical size of the surface heterogeneity domains. The contact angle both at equilibrium and during evaporation could be predicted from a local Cassie-Baxter equation in which the surface composition within a distance of seven fluid-particle diameters around the contact line was considered, confirming the local nature of the interactions that drive the wetting behavior of droplets. More importantly, we propose a nanoscale explanation of pinning during evaporation. Pinning should be interpreted as a drastic slowdown of the contact line dynamics rather than a complete immobilization of it during a transition between two contact angle boundaries.