Loci of extrema of thermodynamic response functions for the Lennard–Jones fluid

Lines of extrema along isotherms and isobars for the residual isochoric heat capacity, the residual isobaric heat capacity, the isobaric thermal expansivity, and the isothermal compressibility of the Lennard–Jones fluid have been studied from popular equations of state due to Johnson et al. [Mol. Phys. 78, 591 (1993)], Kolafa and Nezbeda [Fluid Phase Equilib. 100, 1 (1994)], and Mecke et al. [Int. J. Thermophys. 17, 391 (1996)]. On depicting such loci in the pressure–temperature plane, the characteristic behaviour of thermodynamic response functions in the ideal-gas limit (at high enough temperatures or low enough pressures), the close-packed-fluid limit (at low enough temperatures or high enough pressures) as well as in the liquid, critical, and supercritical regions is identified. The present analysis is informative itself, but it also stimulates further work in order to tackle more complicated cases of study including associated fluids.     

Perturbation approach for equation of state for hard-sphere and Lennard–Jones pure fluids

In this paper we have established the equation of state (EOS) for liquids. The EOS was established for hard-sphere (HS) fluid along with Lennard–Jones (LJ) fluid incorporating perturbation techniques. The calculations are based on suitable axiomatic functional forms for surface tension S _m (r), r ≥ d/2 with intermolecular separation r, as a variable, and m is an arbitrary real number (pole). The results for βP/ρ from the present EOS thus obtained are compared with Percus-Yevick (PY), scaled particle theory (SPT), and Carnahan–Starling (CS). In addition, we have found a simple EOS for the HS fluid in the region which represents the simulation data accurately.     

Density functional study of the pressure tensor for inhomogeneous Lennard—Jones fluids

Based on classical density functional theory,an expression of the pressure tensor for inhomogeneous fluids is presented.This takes into account greater correlation between particles,especially for systems that are geometrically confined or involve an interface.The density and pressure components of Lennard-Jones fluids confined in hard and softened nano-cavities are calculated.A comparison between the results of this work and IK expression suggests that the agreement depends on temperature.The interfacial tension for hard sphere fluids agrees well with the Monte Carlo result when the bulk density is not too large.The results of the solid-fluid interfacial tension for Lennard-Jones fluids demonstrate that different types of external potentials modulate the interfacial tension in different manners.     

Structure of Lennard–Jones nanowires encapsulated by carbon nanotubes

Molecular dynamics simulations have been performed to investigate the structures of Lennard–Jones(LJ) nanowires(NWs) encapsulated in carbon nanotubes(CNTs). We find that the structures of NWs in a small CNT only adopt multi-shell motifs, while the structures of NWs in a larger CNT tend to adopt various motifs. Among these structures, three of them have not been reported previously. The phase boundaries among these structures are obtained regarding filling fractions, as well as the interaction between NWs and CNTs.     

The calculation of singular points in the supercritical region for a system with a Lennard—Jones interaction potential

In this work the positions of the critical point, the supercritical point, and the maximum fluctuation point in a supercritical isotherm were found for a system with the Lennard—Jones interaction potential. Virial coefficients and methods based on accelerated convergence of the perturbation-theory series, which are well known for such systems, were used. The results were compared with computer-simulation data. As has been established, if one uses the positively defined Weeks—Chandler—Andersen potential as a reference system, the calculated parameters tend monotonically to exact values as a function of the number of virial coefficients. This decomposition is favorably different from the virial one, where the aspiration is not monotonic. These results indicate that this method makes it possible to determine the positions of the three vertices of the supercritical triangle with an accuracy that is comparable to that of a simulated experiment.     

A new equation of state for associating Lennard–Jones fluids with two sites: small bond angle

ABSTRACT

We developed a new equation of state for Lennard–Jones spheres with two short-ranged, directional association sites. The theory is novel in that association is dependent on bond angle between the two sites, and formation of self-assembled linear and cyclic clusters is predicted in the model. The competition between ring and chain formations at various densities and temperatures is predicted by the theory and verified by Monte Carlo simulations. It was found that closed-loop structures become important at low temperatures and densities. Also, at fixed association energy, intensifying the Lennard–Jones energy reduces the extent of association in the fluid. The theory and simulation are in excellent agreement.     

A critical behavior of the Lennard–Jones dimeric fluid in two-dimensions.: A Monte Carlo study

Monte Carlo simulation with hyper-parallel tempering, the histogram reweighting and finite-size scaling techniques are used to explore the critical behavior of Lennard-Jones fluids of dimers in the two-dimensional system. The dimers are built of two distinct segments. The critical parameters for selected types of dimers are estimated. We analyze the influence of the bond length and differences in the chemical nature of segments on the critical parameters. The results can be used to predict the critical parameters of dimers whose molecular parameters are known.     

Interface mixing behaviour of Lennard–Jones FCC (100) thin film

A modified Monte Carlo method combined with quenched molecular dynamics simulation is used to determine mixing energetics and concentration profiles at interface for systems containing mono-and bilayers of adatoms adsorbed on FCC (100) crystal surface. The systems under consideration are constructed via Lennard–Jones potential at temperatures near 0 K. For systems with monolayer of adatoms, intermixing at the interface becomes preferable with increasing magnitude of the potential well-depth ratio of adatom to substrate atom. The increasing tendency of intermixing is linearly enhanced when the adatom becomes smaller than the substrate atom, otherwise, the intermixing trend is non-linear and weaker. For systems with bilayers of adatoms, complex development of concentration profile is observed along with increasing magnitude of the potential well-depth ratio and atomic size difference between adatom and substrate atom. This behaviour is related to the interplay between contributions of asymmetric bond interaction and relaxation to minimise the total energy of the system.     

Vapour–liquid phase equilibrium and surface tension of fully flexible Lennard–Jones chains

We report measurements of the vapour–liquid coexistence densities and surface tension of fully flexible Lennard–Jones chain molecules ranging in length from 4 to 60 beads. We demonstrate that the surface tension for all chain lengths collapses to a single master curve when plotted according to the universal parachor correlation. We find a universal parachor exponent 3.79 ± 0.05 for conditions close to the critical point, with a deviation observed for the longest chains far below the critical point.     

Lieb–Robinson Bounds for the Toda Lattice

We establish locality estimates, known as Lieb–Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb–Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems.     

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.     

Calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function in the interface zone

A detailed study is presented of the calculation of the surface tension and the surface energy of Lennard–Jones fluids from the radial distribution function and the density profile. To do so, a modification is made to Lekner and Henderson's statistical mechanics approach by introducing two simple analytical expressions for the radial distribution function of the interface zone. In these expressions the radial distribution functions of the liquid and vapour phases are weighted via step or exponential variations. The well- known exponential model for the density profile in the interface zone is considered. Finally, results are compared with values from experiment, from computer simulation and from relevant theoretical developments. It is shown that the use of the proposed radial distribution function in the interface zone represents a significant improvement in applying Lekner and Henderson's approach.     

Molecular dynamics study of roughness and stress evolution using a Lennard–Jones potential

A three-dimensional molecular dynamics (MD) simulation is proposed to study the film growth, roughness and stress evolution during atom deposition on the (100) plane of a fcc regular crystal. We use the cubic system with an x–y periodic boundary condition. At the bottom we have an atomic surface and at the top a reflecting wall. The model uses the Lennard-Jones potential to describe the interatomic forces. The simulation results show that the film grows with the Volmer–Weber mode and exhibits specific curve shape of the stress evolution. The mean biaxial stress obtained during the simulation attains a local tension maximum at a coverage of two monolayers. The stress in the normal direction is smaller than the biaxial stress. The main contribution to the stress in the film arises from the first monolayer. The curves describing roughness possess maximum values at the same substrate coverage. The dependence of the roughness on the temperature is examined.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Convergence of the Graph Allen–Cahn Scheme

Journal of Statistical Physics - The graph Laplacian and the graph cut problem are closely related to Markov random fields, and have many applications in clustering and image segmentation. The...