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.

Equilibrium molecular dynamics evaluation of the solid-liquid friction coefficient: Role of timescales.

Solid-liquid friction plays a key role in nanofluidic systems. Following the pioneering work of Bocquet and Barrat, who proposed to extract the friction coefficient (FC) from the plateau of the Green-Kubo (GK) integral of the solid-liquid shear force autocorrelation, the so-called plateau problem has been identified when applying the method to finite-sized molecular dynamics simulations, e.g., with a liquid confined between parallel solid walls. A variety of approaches have been developed to overcome this problem. Here, we propose another method that is easy to implement, makes no assumptions about the time dependence of the friction kernel, does not require the hydrodynamic system width as an input, and is applicable to a wide range of interfaces. In this method, the FC is evaluated by fitting the GK integral for the timescale range where it slowly decays with time. The fitting function was derived based on an analytical solution of the hydrodynamics equations [Oga et al., Phys. Rev. Res. 3, L032019 (2021)], assuming that the timescales related to the friction kernel and the bulk viscous dissipation can be separated. By comparing the results with those of other GK-based methods and non-equilibrium molecular dynamics, we show that the FC is extracted with excellent accuracy by the present method, even in wettability regimes where other GK-based methods suffer from the plateau problem. Finally, the method is also applicable to grooved solid walls, where the GK integral displays complex behavior at short times.

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 the solid-fluid interfacial tensions depending on the substrate curvature: Young's equation holds for wetting around nanoscale cylinder.

By extending the theoretical framework derived in our previous study [Imaizumi et al., J. Chem. Phys. 153, 034701 (2020)], we successfully calculated the solid-liquid (SL) and solid-vapor (SV) interfacial tensions of a simple Lennard-Jones fluid around solid cylinders with nanometer-scale diameters from single equilibrium molecular dynamics systems in which a solid cylinder was vertically immersed into a liquid pool. The SL and SV interfacial tensions γSL - γS0 and γSV - γS0 relative to that for bare solid surface γS0, respectively, were obtained by simple force balance relations on fluid-containing control volumes set around the bottom and top ends of the solid cylinder, which are subject to the fluid stress and the force from the solid. The theoretical contact angle calculated by Young's equation using these interfacial tensions agreed well with the apparent contact angle estimated by the analytical solution to fit the meniscus shape, showing that Young's equation holds even for the menisci around solids with nanoscale curvature. We have also found that the curvature effect on the contact angle was surprisingly small while it was indeed large on the local forces exerted on the solid cylinder near the contact line. In addition, the present results showed that the curvature dependence of the SL and SV interfacial free energies, which are the interfacial tensions, is different from that of the corresponding interfacial potential energies.

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.

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 ρA 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 θapp was calculated from the droplet density distribution. The theoretical contact angle θYD and the apparent one θapp, both indicating the enhancement of wettability by an increase in ρA OH, presented good quantitative agreement, especially for non-hydroxylated and highly hydroxylated surfaces. On partially hydroxylated surfaces, in which θYD and θapp 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.

Wilhelmy equation revisited: A lightweight method to measure liquid-vapor, solid-liquid, and solid-vapor interfacial tensions from a single molecular dynamics simulation.

We have given theoretical expressions for the forces exerted on a so-called Wilhelmy plate, which we modeled as a quasi-2D flat and smooth solid plate immersed in a liquid pool of a simple liquid. All forces given by the theory, the local forces on the top, the contact line, and the bottom of the plate as well as the total force, showed an excellent agreement with the MD simulation results. The force expressions were derived by a purely mechanical approach, which is exact and ensures the force balance on the control volumes arbitrarily set in the system, and are valid as long as the solid-liquid (SL) and solid-vapor (SV) interactions can be described by mean-fields. In addition, we revealed that the local forces around the bottom and top of the solid plate can be related to the SL and SV interfacial tensions γSL and γSV, and this was verified through the comparison with the SL and SV works of adhesion obtained by the thermodynamic integration (TI). From these results, it has been confirmed that γSL and γSV as well as the liquid-vapor interfacial tension γLV can be extracted from a single equilibrium MD simulation without the computationally demanding calculation of the local stress distributions and the TI.

Extraction of the equilibrium pinning force on a contact line exerted from a wettability boundary of a solid surface through the connection between mechanical and thermodynamic routes.

By molecular dynamics (MD) simulations, we investigated the effects of chemical inhomogeniety of a wall surface on the equilibrium pinning behavior of a contact line (CL) of solid (S), liquid (L), and vapor (V) phases. We analyzed a quasi-two-dimensional LV-meniscus of Lennard-Jones fluid formed between two parallel flat solid walls, where the CL was located around the wetting boundary (WB) between lyophilic and lyophobic areas of the wall surface. Based on the relationship between the wall-tangential stress integral at the SL or SV interface and the corresponding thermodynamic work of adhesion WSL or WSV shown in our previous study [Y. Yamaguchi et al., J. Chem. Phys. 150, 044701 (2019)], the mechanical balance on the fluid around the CL was successfully described by the relation among WSL, WSV, the apparent contact angle, and the pinning force. In addition, the depinning force needed to move the CL across the WB was estimated as the difference between WSL values at lyophilic and lyophobic areas. Since the works of adhesion WSL and WSV can be easily calculated independently in simple systems through the thermodynamics integration, such a connection between the mechanical and thermodynamic routes provides a possible pathway toward the understanding of wetting including CL-pinning without the need of computationally demanding calculation of the local stress distributions.

Interpretation of Young's equation for a liquid droplet on a flat and smooth solid surface: Mechanical and thermodynamic routes with a simple Lennard-Jones liquid.

In this study, we carried out molecular dynamics simulations of a cylindrical Lennard-Jones droplet on a flat and smooth solid surface and showed that Young's equation as the relation among solid-liquid, solid-vapor, and liquid-vapor interfacial tensions γSL, γSV, and γLV, respectively, was applicable only under a very restricted condition. Using the fluid stress-tensor distribution, we examined the force balance in the surface-lateral direction exerted on a rectangular control volume set around the contact line. As the mechanical route, the fluid stress integrals along the two control surfaces normal to the solid-fluid interface were theoretically connected with γSL and γSV relative to the solid-vacuum interfacial tension γS0 by Bakker's equation extended to solid-related interfaces via a thought experiment, for which the position of the solid-fluid interface plane was defined at the limit that the fluid molecules could reach. On the other hand, the fluid stress integral along the control surface lateral to the solid-fluid interface was connected with γLV by the Young-Laplace equation. Through this connection, we showed that Young's equation was valid for a system in which the net lateral force exerted on the fluid molecules from the solid surface was zero around the contact line. Furthermore, we compared γSL - γS0 and γSV - γS0 obtained by the mechanical route with the solid-liquid and solid-vapor works of adhesion obtained by the dry-surface method as one of the thermodynamic routes and showed that both routes resulted in a good agreement. In addition, the contact angle predicted by Young's equation with these interfacial tensions corresponded well to the apparent droplet contact angle determined by using the previously defined position of the solid-fluid interface plane; however, our theoretical derivation indicated that this correspondence was achieved because the zero-lateral force condition was satisfied in the present system with a flat and smooth solid surface. These results indicated that the contact angle should be predicted not only by the interfacial tensions but also by the pinning force exerted around the contact line.

Shear force measurement of the hydrodynamic wall position in molecular dynamics.

Flows in nanofluidic systems are strongly affected by liquid-solid slip, which is quantified by the slip length and by the position where the slip boundary condition applies. Here, we show that the viscosity, slip length, and hydrodynamic wall position (HWP) can be accurately determined from a single molecular dynamics (MD) simulation of a Poiseuille flow, after identifying a relation between the HWP and the wall shear stress in that configuration. From this relation, we deduce that in gravity-driven flows, the HWP identifies with the Gibbs dividing plane of the liquid-vacuum density profile. Simulations of a generic Lennard-Jones liquid confined between parallel frozen walls show that the HWP for a pressure-driven flow is also close to the Gibbs dividing plane (measured at equilibrium), which therefore provides an inexpensive estimate of the HWP, going beyond the common practice of assuming a given position for the hydrodynamic wall. For instance, we show that the HWP depends on the wettability of the surface, an effect usually neglected in MD studies of liquid-solid slip. Overall, the method introduced in this article is simple, fast, and accurate and could be applied to a large variety of systems of interest for nanofluidic applications.

Molecular dynamics analysis of the influence of Coulomb and van der Waals interactions on the work of adhesion at the solid-liquid interface.

We investigated the solid-liquid work of adhesion of water on a model silica surface by molecular dynamics simulations, where a methodology previously developed to determine the work of adhesion through thermodynamic integration was extended to a system with long-range electrostatic interactions between solid and liquid. In agreement with previous studies, the work of adhesion increased when the magnitude of the surface polarity was increased. On the other hand, we found that when comparing two systems with and without solid-liquid electrostatic interactions, which were set to have approximately the same total solid-liquid interfacial energy, former had a significantly smaller work of adhesion and a broader distribution in the interfacial energies, which has not been previously reported in detail. This was explained by the entropy contribution to the adhesion free energy; i.e., the former with a broader energy distribution had a larger interfacial entropy than the latter. While the entropy contribution to the work of adhesion has already been known, as a work of adhesion itself is free energy, these results indicate that, contrary to common belief, wetting behavior such as the contact angle is not only governed by the interfacial energy but also significantly affected by the interfacial entropy. Finally, a new interpretation of interfacial entropy in the context of solid-liquid energy variance was offered, from which a fast way to qualitatively estimate the work of adhesion was also presented.

LED-CT Scan for pH Distribution on a Cross-Section of Cell Culture Medium.

In cell culture, the pH of the culture medium is one of the most important conditions. However, the culture medium may have non-uniform pH distribution due to activities of cells and changes in the environment. Although it is possible to measure the pH distribution with an existing pH meter using distributed electrodes, the method involves direct contact with the medium and would greatly increase the risk of contamination. Here in this paper, we propose a computed tomography (CT) scan for measuring pH distribution using the color change of phenol red with a light-emitting diode (LED) light source. Using the principle of CT scan, we can measure pH distribution without contacting culture medium, and thus, decrease the risk of contamination. We have developed the device with a LED, an array of photo receivers and a rotation mechanism. The system is firstly calibrated with different shapes of wooden objects that do not pass light, we succeeded in obtaining their 3D topographies. The system was also used for measuring a culture medium with two different pH values, it was possible to obtain a pH distribution that clearly shows the boundary.

Molecular dynamics analysis of the friction between a water-methanol liquid mixture and a non-polar solid crystal surface.

We performed molecular dynamics analysis of the momentum transfer at the solid-liquid interface for a water-methanol liquid mixture between parallel non-polar solid walls in order to understand the strong decrease of the friction coefficient (FC) induced by the methanol adsorption at the surface observed in our previous work [S. Nakaoka et al., Phys. Rev. E 92, 022402 (2015)]. In particular, we extracted the individual contributions of water and methanol molecules to the total FC and found that the molecular FC for methanol was larger than that for water. We further showed that the reduction of the total solid-liquid FC upon the increase of the methanol molar fraction in the first adsorption layer occurred as a result of a decrease in the molecular number density as well as a decrease in the molecular FCs of both molecules. Analysis of the molecular orientation revealed that the decrease of the molecular FC of methanol resulted from changes of the contact feature onto the solid surface. Specifically, methanol molecules near the solid surface had their C-O bond parallel to the surface with both CH3 and O sites contacting the solid at low methanol molar fraction, while they had their C-O bond outward from the surface with only the CH3 site contacting the solid at higher methanol molar fraction. The mechanisms discussed in this work could be used to search for alternative water additives to further reduce the solid-liquid friction.

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.

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.

Molecular dynamics analysis of the velocity slip of a water and methanol liquid mixture.

The effect of methanol mixing on a nanoscale water flow was examined by using nonequilibrium molecular dynamics simulations of a Couette-type flow between nonpolarized smooth solid surfaces. Water and methanol molecules were uniformly mixed in the bulk, whereas at the solid-liquid interface methanol molecules showed a tendency to be adsorbed on the solid surface. Similar to a macroscale Couette flow, the shear stress exerted on the solid surface was equal to the shear stress in the liquid, showing that the mechanical balance holds in nanoscale. In addition, the shear stress in the liquid bulk was equal to the viscous stress which is a product of viscosity and velocity gradient. When more methanol molecules were adsorbed on the solid surface, the friction coefficient (FC) between solid and liquid was largely reduced with a small amount of methanol and that led to a remarkable decrease of the shear stress. The cause of the FC reduction was investigated in terms of the local rotational diffusion coefficient (RDC) near the solid surface, and it was shown that different from an existing model, the FC and local RDC were not simply inversely proportional to each other in the mixture system because the solid-liquid interfacial state was more complex.

New serotype of mutans streptococci isolated from pig oral cavity.

Gram-positive streptococcal mutans-like strains, but with clearly different colony formation than S. orisuis on Mitis Salivarius agar, were isolated from the pig oral cavity and identified by 16S rRNA sequencing, G+C content, DNA-DNA homology and extensive biochemical and serological testing. The phenotypic data showed that the strains were similar to S. orisuis except for susceptibility to bacitracin. DNA-DNA homology between the isolates and S. orisuis was 72~81%. However, serological data showed that they have a different sero-specific antigen from S. orisuis and other mutans streptococci. A new serotype, designated p, strains are classified in a serovar of S. orisuis, one of mutans streptococci.