Simple Lennard-Jones Fluid Research Articles

(Invited) Nanoscale Wetting and Its Connection with Macroscopic Young's Equation

Wetting plays a key role in the cleaning process to remove impurities as one of the essential processes for the fabrication of semiconductor device, where cleaning of trenches with water, replacement with IPA (isopropyl-alcohol) and its removal are iteratively carried out. This process is still required upon recent reduction of the line width under 10 nm; however, this size is already at the border of the continuum limit where the theories of fluid mechanics can be applied. The authors adopted molecular dynamics (MD) simulations to examine the liquid behavior, especially regarding wetting at the nanoscale with respect to simple Lennard-Jones fluid [1-3], water [4,5], methanol as well as IPA as the liquids [6,7], while simple non-polar crystal [1-3,6], silica partially terminated with OH as the solids [4,5,7]. In these series of studies, we have shown how the solid-liquid, solid-vapor and liquid-vapor interfacial tensions can be defined in nanoscale to be consistent with Young’s equation as the macroscopic description about wetting.In the presentation, we will discuss how the interfacial tensions as the free energy can be properly calculated by MD simulations from mechanical and thermodynamic viewpoints.[1] Y. Yamaguchi, H. Kusudo, D. Surblys, T. Omori and G. Kikugawa, J. Chem. Phys. 150 (2019), 044701.[2] H. Kusudo, T. Omori, Y. Yamaguchi, J. Chem. Phys. 151 (2019), 154501.[3] Y. Imaizumi, T. Omori, H. Kusudo, C. Bistafa, Y. Yamaguchi, J. Chem. Phys., 153 (2020), 034701.[4] D. Surblys, F. Leroy, Y. Yamaguchi, F. Mueller-Plathe, J. Chem. Phys. 148 (2018), 134707.[5] C. Bistafa, D. Surblys, H. Kusudo, Y. Yamaguchi, J. Chem. Phys., 155 (2021), 064703.[6] D. Surblys, Y. Yamaguchi, K. Kuroda, M. Kagawa, T. Nakajima, and H. Fujimura, J. Chem. Phys. 140 (2014), 034505.[7] Y. Yamaguchi, S. Nakaoka, T. Hayashi, M. Kawakami, D. Yano, ECS Trans. 92 (2019), 87.

Optimal Replica-Exchange Molecular Simulations in Combination with Evolution Strategies.

We have incorporated Evolution Strategies into the Replica-Exchange Monte Carlo simulation method to predict the phase behavior of several example fluids. The replica-exchange method allows one system to exchange temperatures with its neighbors to search for the most stable structure relatively efficiently in a single simulation. However, if the temperature intervals of the replicas are not positioned carefully, there is an issue that local exchange does not occur. Our results for a simple Lennard-Jones fluid and the liquid-crystal Yukawa model demonstrate the utility of the approach when compared to conventional methods. When Evolution Strategies were applied to the Replica-Exchange Monte Carlo simulation, the problem of a significant localized decrease in exchange probability near the phase transition was avoided. By obtaining the optimal temperature intervals, the system efficiently traverses a broader parameter space with a small number of replicas. This is equivalent to accelerating molecular simulations with limited computational resources and can be useful when attempting to predict the phase behavior of complex 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.

Simulation of shock induced vapor condensation flows in the Lennard-Jones fluid by microscopic and continuum models

The vapor condensation onto a thin liquid film, induced by the reflection of a weak shock wave, is studied by molecular dynamics atomistic simulations of a simple Lennard-Jones fluid. Molecular dynamics results provide reference flowfields for two models. The first one adopts a hybrid continuum-kinetic description in which the liquid phase is described by hydrodynamic equations, whereas the vapor is described by the Boltzmann equation. The structureless liquid–vapor interface is replaced by a classical kinetic boundary condition. The second model is based on the diffuse interface full continuum description of the Lennard-Jones fluid liquid, vapor, and interface regions. For both models, the required fluid thermodynamic and transport properties have been prescribed according to those of the Lennard-Jones fluid. Not unexpectedly, the results show that the continuum-kinetic model provides a good description of molecular dynamics results when the vapor is close to ideal conditions, increasingly deviating from reference data when the vapor non-ideality increases. The opposite behavior is found for the diffuse interface model. It is observed that flow conditions exist where both models fail to provide a reasonably accurate description of reference flow properties.

A molecular dynamics study of the atomic-level surface structural phase diagram for the existence form of nanobubbles and its influence in a dynamic system

The nucleation of nanobubbles was studied through molecular dynamics (MD) simulations. The wettability and surface atomic-level structural features of the substrate were found to play a role in a ternary (solid, liquid, and gas) system that was composed of only simple Lennard-Jones fluids. The simulation first revealed that surface nanobubbles form only on a hydrophobic substrate, while for a hydrophilic substrate, bulk nanobubbles are formed in the liquid. Second, the existence form of nanobubbles and some behavioral characteristics strongly depend on the surface structural features. Specifically, we deduced the phase diagram of the nanobubbles with respect to the critical structural parameters and then defined a critical region for the formation of surface nanobubbles: cap-shaped surface nanobubbles can stably form above the upper critical line but not below the lower critical line; the contact angle decreases as the parameter value increases. Finally, the existence of nanobubbles was found to affect the dynamic properties of the system.

(Invited) Molecular Dynamics Analysis on the Behavior of Water and Alcohol Liquids on a OH-Terminated SiO2 Surface

Cleaning process to remove impurities is one of the essential processes for the fabrication of semiconductor device, where cleaning of trenches with water, replacement with IPA (isopropyl-alcohol) and its removal are iteratively carried out, and this process is still required upon recent reduction of the line width under 10 nm. This size is already at the border of the continuum limit where the theories of fluid mechanics can be applied. Hence, the authors adopted molecular dynamics (MD) simulations to examine the liquid behavior, especially wetting behavior and solid-liquid friction at the nanoscale with respect to simple Lennard-Jones fluid, water, methanol as well as IPA as the liquids, whereas simple non-polar crystal and silica as the solids [1-8]. In these studies, we have shown that surprisingly the liquid behavior even around this continuum border was qualitatively not remarkably different from that expected from a macroscopic point of view. On the other hand, the physical properties of liquids in the so-called adsorption layers formed in the vicinity of the solid typically of a few molecular diameters, are different from those in bulk, and their effects should be extracted and properly connected to the macroscopic scale, e.g. as a boundary condition to predict the liquid behavior. In the presentation, we will discuss about the MD simulation results of liquid infiltration into a nanoscale slit, effects of gas molecules in the slit as well the diffusion of water and alcohol molecules on OH-terminated silica surfaces. In addition, the replacement procedure of adsorbed water/alcohol by bulk alcohol/water liquid will be discussed. [1] Y. Yamaguchi, H. Kusudo, D. Surblys, T. Omori and G. Kikugawa, J. Chem. Phys. 150 (2019), 044701. [2] D. Surblys, F. Leroy, Y. Yamaguchi, F. Mueller-Plathe, J. Chem. Phys. 148 (2018), 134707. [3] S. Nakaoka, Y. Yamaguchi, T. Omori, L. Joly, Mechanical Engineering Lett. 3 (2017), 17-00422. [4] S. Nakaoka, Y. Yamaguchi, T. Omori, L. Joly, J. Chem. Phys. 146 (2017), 174702. [5] S. Nakaoka, Y. Yamaguchi, T. Omori, M. Kagawa, T. Nakajima, H. Fujimura, Phys. Rev. E 92 (2015), 022402. [6] S. Nishida, D. Surblys, Y. Yamaguchi , K. Kuroda, M. Kagawa, T. Nakajima and H. Fujimura, J. Chem. Phys. 140 (2014), 074707. [7] D. Surblys, Y. Yamaguchi , K. Kuroda, T. Nakajima and H. Fujimura, J. Chem. Phys. 140 (2014), 034505. [8] Y. Yamaguchi, M. Kawakami, D. Yano, Jpn. J. Multiphase Flow 32-2 (2018), 218 (in Japanese).

Size effect on boundary condition at solid-liquid interface in microchannel

The heat transfer in microchannel has attracted considerable attention due to many important applications in biology, chemistry, physics and engineering. When the fluid size shrinks to nanoscale, the energy transport of micro-system is significantly different from the conventional case. It is of great significance to study the size effect on heat transfer in a micro-system. However, there is a large size gap between existing molecular dynamics simulation and experimental measurement, in which the size effect on solid-liquid interfacial thermal resistance is rarely involved. Non-equilibrium molecular dynamics simulation is performed to investigate the heat transfer through the solid-liquid interface. Simple Lennard-Jones (LJ) fluid is simulated as the ultra-thin liquid film in a non-equilibrium simulation system. The liquid film is confined in a nanochannel composed of two solid surfaces. The potential function between solid and liquid atom is represented by a modified LJ function to control the solid-liquid interfaces of different surface wettabilities. We examine the size effect on temperature jump and thermal resistance at the solid-liquid interface. The fluid number density and temperature distribution in the perpendicular direction of solid wall are evaluated. It is found that the liquid atoms near wall are arranged as a solid-like structure. Particularly in the small channel, liquid atoms confined in the channel are affected by two solid walls. However, with the increase of channel height, the liquid atoms in the middle channel move freely, leading to the decrease of the size effect. The simulation results show that the dependence of thermal resistance on microchannel height exhibits two regimes: (i) monotonically increasing dependence for the small channel and (ii) keeping constant thermal resistance for the large channel. These two distinct trends can be explained by phonon vibrational density of states (VDOS) of solid wall and liquid. For the small channel, a stronger confinement of liquid leads to a weaker mismatch in VDOS of solid wall and liquid, thus resulting in a smaller thermal resistance. Whereas, for the large channel, the vibrational coupling between the solid and the liquid atom remains unchanged and the size effect is negligible. The size thresholds of the two regimes of the thermal resistance are both sensitive to the liquid-solid interaction strength, which decreases with solid-liquid interaction increasing. Furthermore, with the increase of the microchannel height, the temperature jump at the solid-liquid interface monotonically decreases and eventually approaches to the non-jump temperature boundary on a macroscopic scale. These findings may help to understand the mechanism of temperature boundary conditions on a microscopic scale and a macroscopic scale and provide a theoretical support for manufacturing new nano-devices.

Comparison of iterative inverse coarse-graining methods

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics.

We present a new multiscale simulation methodology for coupling a region with atomistic detail simulated via molecular dynamics (MD) to a numerical solution of the fluctuating Navier-Stokes equations obtained from smoothed dissipative particle dynamics (SDPD). In this approach, chemical potential gradients emerge due to differences in resolution within the total system and are reduced by introducing a pairwise thermodynamic force inside the buffer region between the two domains where particles change from MD to SDPD types. When combined with a multi-resolution SDPD approach, such as the one proposed by Kulkarni et al. [J. Chem. Phys. 138, 234105 (2013)], this method makes it possible to systematically couple atomistic models to arbitrarily coarse continuum domains modeled as SDPD fluids with varying resolution. We test this technique by showing that it correctly reproduces thermodynamic properties across the entire simulation domain for a simple Lennard-Jones fluid. Furthermore, we demonstrate that this approach is also suitable for non-equilibrium problems by applying it to simulations of the start up of shear flow. The robustness of the method is illustrated with two different flow scenarios in which shear forces act in directions parallel and perpendicular to the interface separating the continuum and atomistic domains. In both cases, we obtain the correct transient velocity profile. We also perform a triple-scale shear flow simulation where we include two SDPD regions with different resolutions in addition to a MD domain, illustrating the feasibility of a three-scale coupling.

The critical compressibility factor value: associative fluids and liquid alkali metals.

We show how to obtain the critical compressibility factor Z(c) for simple and associative Lennard-Jones fluids using the critical characteristics of the Ising model on different lattices. The results show that low values of critical compressibility factor are correlated with the associative properties of fluids in critical region and can be obtained on the basis of the results for the Ising model on lattices with more than one atom per cell. An explanation for the results on the critical point line of the Lennard-Jones fluids and liquid metals is proposed within the global isomorphism approach.

Interfacial thermal conductance and thermal accommodation coefficient of evaporating thin liquid films: A molecular dynamics study

Molecular dynamics (MD) simulations were carried out in this study to investigate the effect of solid–gas binding strength and surface coverage on the interfacial thermal conductance and thermal accommodation coefficient of evaporating liquid films. Simple Lennard–Jones fluids were simulated in a cubic domain, which consisted of an upper platinum wall and a lower platinum wall, with argon fluid in between. Both the equilibrium molecular dynamics (EMD) and the non-equilibrium molecular dynamics (NEMD) simulated the evaporation and condensation of the liquid films properly. In addition, the thermal conductance and accommodation coefficient increased with the increase in the binding strength. To further analyze the effects of inter-molecular forces and movements on heat transfer, the surface coverage and interaction time of the absorbed liquid atoms were measured with respect to various binding strengths. It is found that binding strength has an important role in forming the absorption layers that reduces the temperature jump and enhances the heat transfer performance.

Local viscosity of a fluid confined in a narrow pore

In this paper, molecular dynamics simulations of a simple Lennard-Jones fluid confined in narrow slit pores and undergoing shear have been performed. The aim is to investigate the effects of density inhomogeneities at the fluid-solid interfaces on the shear viscosity profiles. It has been found that the local viscosity was varying strongly with the distance from the solid walls for both dilute and dense fluid states with oscillations correlated to the density ones. To describe the computed viscosity profiles, we propose a scheme that uses the local average density model, combined with an adequate weight function, for the configurational viscosity and a semiempirical model for the translational viscosity. It is shown that the proposed approach is able to provide viscosity profiles in good agreement with those coming from simulations for different pore widths and for different fluid states (dilute to dense).

Grand canonical-like molecular dynamics simulations: Application to anisotropic mass diffusion in a nanoporous medium

In this work, we describe two grand canonical-like molecular dynamics approaches to investigate mass diffusion phenomenon of a simple Lennard-Jones fluid confined between solid surfaces and in direct contact with reservoirs. In the first method, the density is used as the control variable in the reservoir whereas it is the pressure in the second method. Both methods provide consistent results, however, the constant density approach is the most efficient with respect to the computational time and implementation. Then, employing the constant density approach, we have studied the transient behavior of the diffusion process associated with the migration of one fluid into another one confined between parallel solid walls. Results have shown that the evolution of molar fraction of the invading fluid follows roughly a 1D diffusion model when the solid phase is weakly or moderately adsorbent with a characteristic time increasing when the pore width decreases. However, when the adsorption is high and the pore width small (i.e., below ten molecular sizes), the apparent mass diffusion in the adsorbed layer is reduced compared to that in the center of the slit pore. Hence, this mass diffusion process becomes a two-dimension phenomenon that must take into account an effective mass diffusion coefficient varying locally.

Diffusive Shielding Stabilizes Bulk Nanobubble Clusters

Using molecular dynamics, we study the nucleation and stability of bulk nanobubble clusters. We study the formation, growth, and final size of bulk nanobubbles. We find that, as long as the bubble-bubble interspacing is small enough, bulk nanobubbles are stable against dissolution. Simple diffusion calculations provide an excellent match with the simulation results, giving insight into the reason for the stability: nanobubbles in a cluster of bulk nanobubbles protect each other from diffusion by a shielding effect.

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where “surface fields” may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.

Curvature dependence of surface free energy of liquid drops and bubbles: A simulation study

We study the excess free energy due to phase coexistence of fluids by Monte Carlo simulations using successive umbrella sampling in finite L×L×L boxes with periodic boundary conditions. Both the vapor-liquid phase coexistence of a simple Lennard-Jones fluid and the coexistence between A-rich and B-rich phases of a symmetric binary (AB) Lennard-Jones mixture are studied, varying the density ρ in the simple fluid or the relative concentration x(A) of A in the binary mixture, respectively. The character of phase coexistence changes from a spherical droplet (or bubble) of the minority phase (near the coexistence curve) to a cylindrical droplet (or bubble) and finally (in the center of the miscibility gap) to a slablike configuration of two parallel flat interfaces. Extending the analysis of Schrader et al., [Phys. Rev. E 79, 061104 (2009)], we extract the surface free energy γ(R) of both spherical and cylindrical droplets and bubbles in the vapor-liquid case and present evidence that for R→∞ the leading order (Tolman) correction for droplets has sign opposite to the case of bubbles, consistent with the Tolman length being independent on the sign of curvature. For the symmetric binary mixture, the expected nonexistence of the Tolman length is confirmed. In all cases and for a range of radii R relevant for nucleation theory, γ(R) deviates strongly from γ(∞) which can be accounted for by a term of order γ(∞)/γ(R)-1∝R(-2). Our results for the simple Lennard-Jones fluid are also compared to results from density functional theory, and we find qualitative agreement in the behavior of γ(R) as well as in the sign and magnitude of the Tolman length.

Multilayer approximation for a confined fluid in a slit pore

A simple Lennard-Jones fluid confined in a slit nanopore with hard walls is studied on the basis of a multilayer structured model. Each layer is homogeneous and parallel to the walls of the pore. The Helmholtz energy of this system is constructed following van der Waals-like approximations, with the advantage that the model geometry permits to obtain analytical expressions for the integrals involved. Being the multilayer system in thermodynamic equilibrium, a system of non-linear equations is obtained for the densities and widths of the layers. A numerical solution of the equations gives the density profile and the longitudinal pressures. The results are compared with Monte Carlo simulations and with experimental data for Nitrogen, showing very good agreement.Received: 23 December 2009, Accepted: 24 February 2010; Edited by: D. A. Stariolo; DOI: 10.4279/PIP.020002

A transferable coarse-grained potential to study the structure of confined, supercritical Lennard-Jones fluids

In this paper, we develop a transferable coarse-grained interatomic potential to study the structure of simple (spherical and nonpolar) Lennard-Jones (LJ) fluids confined at supercritical temperatures. The potential is used in empirical potential based quasicontinuum theory, [A. V. Raghunathan et al., J. Chem. Phys. 127, 174701 (2007)] to study the structure of three simple LJ fluids (oxygen, methane, and argon) confined in slitlike geometries. The results obtained using the coarse-grained interatomic potential are found to be in good agreement with those predicted by equilibrium molecular dynamics simulations.

On the evaporation rate of ultra-thin liquid film at the nanostructured surface: A molecular dynamics study

Molecular dynamic (MD) simulations have been carried out to study the effect of the nanostructures on the evaporation rate of the ultra-thin liquid film at the solid surface. Simple Lennard-Jones (LJ) fluids are simulated as the ultra-thin liquid film in the non-equilibrium simulation system. The liquid film is confined in a nanochannel composed of two solid surfaces designed with nanostructures in a shape of molecular-scale unevenness. The potential function between solid and liquid molecules is represented by a modified LJ function to conduct the solid–liquid interfaces of different surface wettability. For the steady non-equilibrium MD simulation, the liquid film is subjected to the steady heat flux passing through the nanostructured surfaces. It is found that the interface thermal resistance decreases at the nanostructured surface and apparent heat transfer enhancement is achieved due to the surface area increment. For the unsteady non-equilibrium MD simulation, the vapor has been sandwiched between the liquid films in contact with the nanostructured surfaces of high and low temperature respectively. It is found that the evaporation rate of the ultra-thin liquid film has a larger value than that of the flat surface when the film thickness is larger than that of the adsorbed layer.

Evaluation of the Cox Equation to Derive Dynamic Contact Angle at Nanopores Imbibition: A Molecular Dynamics Study

Molecular dynamics (MD) simulation is employed to simulate the imbibition of a designed nanopore by a fluid. The fluid is considered as a simple Lennard-Jones (LJ) fluid. For this system (i.e., LJ fluid and nanopore), the length of imbibition as a function of time for various interactions between the fluid and the pore wall is recorded. In almost all cases, the kinetics of imbibition is successfully described with the Lucas-Washburn (LW) equation. However, the deviation from the LW equation is observed in some cases. This nonconformity is contributed to the neglecting of the dynamic contact angle (DCA) in the LW equation. A hydrodynamic model (i.e., the Cox equation) is taken into consideration to calculate the DCA. It is demonstrated that the LW equation together with the Cox equation is able to justify the simulation results for those cases, which are not in good agreement with the simple LW equation. Further investigation on the MD simulation data reveals that the Cox equation is only appropriate to derive the DCA at small capillary numbers. This finding is in consonance with the theoretical background of this equation as well as experimental work.