Determination of the solid-fluid coexistence of the n - 6 Lennard-Jones system from free energy calculations

Vibrational model for thermal conductivity of Lennard-Jones fluids: Applicability domain and accuracy level

Exact mechanisms of thermal conductivity in liquids are not well understood, despite a rich research history. A vibrational model of energy transfer in dense simple liquids with soft pairwise interactions seems adequate to partially fill this gap. The purpose of the present paper is to define its applicability domain and to demonstrate how well it works within the identified applicability domain in the important case of the Lennard-Jones model system. The existing results from molecular dynamics simulations are used for this purpose. Additionally, we show that a freezing density scaling approach represents a very powerful tool to estimate the thermal conductivity coefficient across essentially the entire gas-liquid region of the phase diagram, including metastable regions. A simple practical expression serving this purpose is proposed.

Freezing density scaling of fluid transport properties: Application to liquified noble gases

A freezing density scaling of transport properties of the Lennard-Jones fluid is rationalized in terms of the Rosenfeld's excess entropy scaling and isomorph theory of Roskilde-simple systems. Then, it is demonstrated that the freezing density scaling operates reasonably well for viscosity and thermal conductivity coefficients of liquid argon, krypton, and xenon. Quasi-universality of the reduced transport coefficients at their minima and at freezing conditions is discussed. The magnitude of the thermal conductivity coefficient at the freezing point is shown to agree remarkably well with the prediction of the vibrational model of thermal transport in dense fluids.

Freezing Temperature and Density Scaling of Transport Coefficients

It is demonstrated that the freezing density scaling of transport coefficients in fluids, similar to the freezing temperature scaling, originates from the quasi-universal excess entropy scaling approach proposed by Rosenfeld. The freezing density scaling has a considerably wider applicability domain on the phase diagram of Lennard-Jones and related systems. As an illustration of its predictive power, we show that it reproduces with an excellent accuracy the shear viscosity coefficients of saturated liquid argon, krypton, xenon, and methane.

Gas–liquid crossover in the Lennard-Jones system

It is demonstrated that the crossover between gas- and liquid-like regions on the phase diagram of the Lennard-Jones system occurs at a fixed value of the density divided by its value at the freezing point, ρ/ ρfr ≃ 0.35. This definition is consistent with other definitions proposed recently. As a result, a very simple practical expression for the gas-to-liquid crossover line emerges.

Application of cell models to the melting and sublimation lines of the Lennard-Jones and related potential systems

Harmonic cell models (HCMs) are shown to predict the melting line of the Lennard-Jones (LJ) but not the sublimation line. In addition, even for the melting line, the HCMs are found to be physically unrealistic for inverse power potential systems near the hard-sphere limit, and for the Weeks-Chandler-Andersen system at extremely low temperatures. Despite this, the HCM accurately predicts the LJ mean-square displacement (MSD) from molecular-dynamics (MD) simulations along both lines after simple scaling corrections, to include the effects of anharmonicity and correlated dynamics of the atoms, are applied. Single caged atom molecular dynamics and Monte Carlo simulations provide further quantitative characterization of these additional effects, which go beyond harmonicity. The melting indicator and a modification of the cell model in a similar form are shown to be approximately constant along the melting line, which indicates an isomorph. The less well studied LJ sublimation line is shown not to be an isomorph, yet it still can be represented analytically very accurately by the relationship k_{B}T=aρ^{4}+bρ^{2}, where a and b are constants (k_{B} is Boltzmann's constant, T is the temperature, and ρ is the number density). This relationship has been found previously for the melting line, but the two constants have opposite signs for the sublimation and melting lines. This simple formula is also predicted using a nonharmonic static lattice expression for the pressure. The probability distribution function of the melting factor indicates departures from harmonic or Gaussian behavior in the lower wing. Nevertheless, the mean melting factor is shown to follow a simple MSD Debye-Waller factor dependence along both the melting and sublimation lines. This work combining HCM and MD simulations provides a comparison of the melting and sublimation lines of the LJ system, which could provide the foundations for a more unified statistical mechanical description of these two solid boundary lines.

Excess entropy and Stokes-Einstein relation in simple fluids

The Stokes-Einstein (SE) relation between the self-diffusion and shear viscosity coefficients operates in sufficiently dense liquids not too far from the liquid-solid phase transition. By considering four simple model systems with very different pairwise interaction potentials (Lennard-Jones, Coulomb, Debye-Hückel or screened Coulomb, and the hard sphere limit) we identify where exactly on the respective phase diagrams the SE relation holds. It appears that the reduced excess entropy s_{ex} can be used as a suitable indicator of the validity of the SE relation. In all cases considered the onset of SE relation validity occurs at approximately s_{ex}≲-2. In addition, we demonstrate that the line separating gaslike and liquidlike fluid behaviours on the phase diagram is roughly characterized by s_{ex}≃-1.

Entropy of simple fluids with repulsive interactions near freezing

Among different thermodynamic properties of liquids, the entropy is one of the hardest quantities to estimate. Therefore, the development of models allowing accurate estimations of the entropy for different mechanisms of interatomic interactions represents an important problem. Here, we propose a method for estimating the excess entropy of simple liquids not too far from the liquid-solid phase transition. The method represents a variant of cell theory, which particularly emphasizes relations between liquid state thermodynamics and collective modes properties. The method is applied to calculate the excess entropy of inverse-power-law fluids with ∝r^-n repulsive interactions. The covered range of potential softness is extremely wide, including the very soft Coulomb (n = 1) case, much steeper n = 6 and n = 12 cases, and the opposite hard-sphere interaction limit (n = ∞). An overall reasonably good agreement between the method's outcome and existing "exact" results is documented at sufficiently high fluid densities. Its applicability condition can be conveniently formulated in terms of the excess entropy itself. The method is also applied to the Lennard-Jones potential but demonstrates considerably lower accuracy in this case. Our results should be relevant to a broad range of liquid systems that can be described with isotropic repulsive interactions, including liquid metals, macromolecular systems, globular proteins, and colloidal suspensions.

Transport properties of Lennard-Jones fluids: Freezing density scaling along isotherms

It is demonstrated that properly reduced transport coefficients (self-diffusion, shear viscosity, and thermal conductivity) of Lennard-Jones fluids along isotherms exhibit quasi-universal scaling on the density divided by its value at the freezing point. Moreover, this scaling is closely related to the density scaling of transport coefficients of hard-sphere fluids. The Stokes-Einstein relation without the hydrodynamic diameter is valid in the dense fluid regime. The lower density boundary of its validity can serve as a practical demarcation line between gaslike and liquidlike regimes.

Sound Velocities of Generalized Lennard-Jones (n - 6) Fluids Near Freezing

In a recent paper [S. Khrapak, Molecules 25, 3498 (2020)], the longitudinal and transverse sound velocities of a conventional Lennard-Jones system at the liquid-solid coexistence were calculated. It was shown that the sound velocities remain almost invariant along the liquid-solid coexistence boundary lines and that their magnitudes are comparable with those of repulsive soft-sphere and hard-sphere models at the fluid-solid phase transition. This implies that attraction does not considerably affect the magnitude of the sound velocities at the fluid-solid phase transition. This paper provides further evidence to this by examining the generalized Lennard-Jones (n - 6) fluids with n ranging from 12 to 7 and demonstrating that the steepness of the repulsive term has only a minor effect on the magnitude of the sound velocities. Nevertheless, these minor trends are identified and discussed.

Characteristic Curves of the Lennard-Jones Fluid

Equations of state based on intermolecular potentials are often developed about the Lennard-Jones (LJ) potential. Many of such EOS have been proposed in the past. In this work, 20 LJ EOS were examined regarding their performance on Brown's characteristic curves and characteristic state points. Brown's characteristic curves are directly related to the virial coefficients at specific state points, which can be computed exactly from the intermolecular potential. Therefore, also the second and third virial coefficient of the LJ fluid were investigated. This approach allows a comparison of available LJ EOS at extreme conditions. Physically based, empirical, and semi-theoretical LJ EOS were examined. Most investigated LJ EOS exhibit some unphysical artifacts.

Sound Velocities of Lennard-Jones Systems Near the Liquid-Solid Phase Transition

Longitudinal and transverse sound velocities of Lennard-Jones systems are calculated at the liquid-solid coexistence using the additivity principle. The results are shown to agree well with the "exact" values obtained from their relations to excess energy and pressure. Some consequences, in particular in the context of the Lindemann's melting rule and Stokes-Einstein relation between the self-diffusion and viscosity coefficients, are discussed. Comparison with available experimental data on the sound velocities of solid argon at melting conditions is provided.

The Lennard-Jones melting line and isomorphism

The location of the melting line (ML) of the Lennard-Jones (LJ) system and its associated physical properties are investigated using molecular dynamics computer simulation. The radial distribution function and the behavior of the repulsive and attractive parts of the potential energy indicate that the ML is not a single isomorph, but the isomorphic state evolves gradually with temperature, i.e., it is only "locally isomorphic." The state point dependence of the unitless isomorphic number, X̃, for a range of static and dynamical properties of the LJ system in the solid and fluid states, and for fluid argon, are also reported. The quantity X̃ typically varies most with state point in the vicinity of the triple point and approaches a plateau in the high density (temperature) limit along the ML.

Fluid-solid transition in simple systems using density functional theory

A free energy functional for a crystal which contains both the symmetry-conserved and symmetry-broken parts of the direct pair correlation function has been used to investigate the fluid-solid transition in systems interacting via purely repulsive Weeks-Chandler-Anderson Lennard-Jones potential and the full Lennard-Jones potential. The results found for freezing parameters for the fluid-face centred cubic crystal transition are in very good agreement with simulation results. It is shown that although the contribution made by the symmetry broken part to the grand thermodynamic potential at the freezing point is small compared to that of the symmetry conserving part, its role is crucial in stabilizing the crystalline structure and on values of the freezing parameters.

A unified approach to computation of solid and liquid free energy to revisit the solid-fluid equilibrium of Lennard-Jones chains

Liquid free energies are computed by integration along a path from a reference system of known free energy, using a strong localization potential. A particular choice of localization pathway is introduced, convenient for use in molecular dynamics codes, and which achieves accurate results without the need to include the identity-swap or relocation Monte Carlo moves used in previous studies. Moreover, an adaptive timestep is introduced to attain the reference system. Furthermore, a center-of-mass correction that is different from previous studies and phase-independent is incorporated. The resulting scheme allows computation of both solid and liquid free energies with only minor differences in simulation protocol. This is used to re-visit solid-liquid equilibrium in a system of short semi-flexible Lennard-Jones chain molecules. The computed melting curve is demonstrated to be consistent with direct co-existence simulations and computed hysteresis loops, provided that an entropic term arising from unsampled solid states is included.

Direct calculation of the solid-liquid Gibbs free energy difference in a single equilibrium simulation

Computing phase diagrams of model systems is an essential part of computational condensed matter physics. In this paper, we discuss in detail the interface pinning (IP) method for calculation of the Gibbs free energy difference between a solid and a liquid. This is done in a single equilibrium simulation by applying a harmonic field that biases the system towards two-phase configurations. The Gibbs free energy difference between the phases is determined from the average force that the applied field exerts on the system. As a test system, we study the Lennard-Jones model. It is shown that the coexistence line can be computed efficiently to a high precision when the IP method is combined with the Newton-Raphson method for finding roots. Statistical and systematic errors are investigated. Advantages and drawbacks of the IP method are discussed. The high pressure part of the temperature-density coexistence region is outlined by isomorphs.