Thermodynamic properties and entropy scaling law for diffusivity in soft spheres

Exchange-correlation bound states of the triplet soft-sphere fermions by path-integral Monte Carlo simulations

Path-integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin-resolved radial distribution functions of the strongly correlated soft-sphere quantum fermions. The obtained spin-resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr-Sommerfeld quantization condition, applied to the potential of the mean force corresponding to the same-spin radial distribution functions, allows to detect exchange-correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution.

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.

A comprehensive study of the thermal conductivity of the hard sphere fluid and solid by molecular dynamics simulation

This work reports a new set of hard sphere (HS) thermal conductivity coefficient, λ, data obtained by Molecular Dynamics (MD) computer simulation, over a density range covering the dilute fluid to near the close-packed solid, and for a large number of particles (up to N = 13 1072) and long simulation times. The N-dependence of the thermal conductivity is shown to be proportional to N-2/3 to a good approximation over a wide range of system sizes, which enabled λ values in the thermodynamic limit to be predicted accurately. The fluid and solid λ can be represented well by the Enskog theory (ET) formula, λE, times a density-dependent correction term, which is close to unity for the fluid and practically constant for the solid. The convergence of the MD λ data back towards ET in the metastable fluid starts just above the freezing density. For the HS solid and dense fluid it was found that the thermal conductivity is nearly linear in pressure, as has been observed experimentally for a number of solids. Simple excess entropy scaling over the higher density fluid phase region was found, and Rosenfeld's exponential relationship can be fitted to the simulation data for the solid to a high degree of accuracy. The simulation analysis has revealed a number of new trends in the behaviour of the HS thermal conductivity which could be useful in building more accurate models for heat conduction in experimental systems.

Thermodynamic and dynamical properties of the hard sphere system revisited by molecular dynamics simulation

Revised thermodynamic and dynamical properties of the hard sphere (HS) system are obtained from extensive molecular dynamics calculations carried out with large system sizes (number of particles, N) and long times. Accurate formulas for the compressibility factor of the HS solid and fluid branches are proposed, which represent the metastable region and take into account its divergence at close packing. Some basic second-order thermodynamic properties are obtained and a maximum in some of their derivatives in the metastable fluid region is found. The thermodynamic parameters associated with the melting-freezing transition have been determined to four digit accuracy, which generates accurate new values for the coexistence properties of the HS system. For the self-diffusion coefficient, D, it is shown that relatively large systems (N > 104) are required to achieve an accurate linear extrapolation of D to the infinite size limit with a D vs. N-1/3 plot. Moreover, it is found that there is a density dependence of the value of the slope in the linear regime. The density dependent correction becomes practically insignificant at higher densities and the hydrodynamic formula found in the literature is still accurate. However, with decreasing density the density dependence of the size correction cannot be neglected, which indicates that other sources of N-dependence, apart from those derived on purely hydrodynamic grounds, may also be important (and as yet unaccounted for). A detailed analytic representation of the density dependence of the HS self-diffusion coefficient and the HS viscosity, η, is given. It is shown that the HS viscosity near freezing and in the metastable region can be described well by the Krieger-Dougherty equation. Both D and η start to scale at high densities and in the metastable region in such a way that Dηp = const, where p ≃ 0.97, and D → 0 and η → ∞ at a packing fraction of 0.58, which coincides with some previous predictions of the HS glass transition density.

Perspective: Excess-entropy scaling

This article gives an overview of excess-entropy scaling, the 1977 discovery by Rosenfeld that entropy determines properties of liquids like viscosity, diffusion constant, and heat conductivity. We give examples from computer simulations confirming this intriguing connection between dynamics and thermodynamics, counterexamples, and experimental validations. Recent uses in application-related contexts are reviewed, and theories proposed for the origin of excess-entropy scaling are briefly summarized. It is shown that if two thermodynamic state points of a liquid have the same microscopic dynamics, they must have the same excess entropy. In this case, the potential-energy function exhibits a symmetry termed hidden scale invariance, stating that the ordering of the potential energies of configurations is maintained if these are scaled uniformly to a different density. This property leads to the isomorph theory, which provides a general framework for excess-entropy scaling and illuminates, in particular, why this does not apply rigorously and universally. It remains an open question whether all aspects of excess-entropy scaling and related regularities reflect hidden scale invariance in one form or other.

The EXP pair-potential system. II. Fluid phase isomorphs

This paper continues the investigation of the exponentially repulsive EXP pair-potential system of Paper I [A. K. Bacher et al., J. Chem. Phys. 149, 114501 (2018)] with a focus on isomorphs in the low-temperature gas and liquid phases. As expected from the EXP system's strong virial potential-energy correlations, the reduced-unit structure and dynamics are isomorph invariant to a good approximation. Three methods for generating isomorphs are compared: the small-step method that is exact in the limit of small density changes and two versions of the direct-isomorph-check method that allows for much larger density changes. Results from the latter two approximate methods are compared to those of the small-step method for each of the three isomorphs generated by 230 one percent density changes, covering one decade of density variation. Both approximate methods work well.

Thermodynamic curvature of soft-sphere fluids and solids

The influence of the strength of repulsion between particles on the thermodynamic curvature scalar R for the fluid and solid states is investigated for particles interacting with the inverse power (r^{-n}) potential, where r is the pair separation and 1/n is the softness. Exact results are obtained for R in certain limiting cases, and the R behavior determined for the systems in the fluid and solid phases. It is found that in such systems the thermodynamic curvature can be positive for very soft particles, negative for steeply repulsive (or large n) particles across almost the entire density range, and can change sign between negative and positive at a certain density. The relationship between R and the form of the interaction potential is more complex than previously suggested, and it may be that R is an indicator of the relative importance of energy and entropy contributions to the thermodynamic properties of the system.

Bending and Gaussian rigidities of confined soft spheres from second-order virial series

We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical, and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension γ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to γ(R) and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed.

Scaling of the dynamics of flexible Lennard-Jones chains: Effects of harmonic bonds

The previous paper [A. A. Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics, and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs." In particular, this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.

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.

Simplicity of condensed matter at its core: generic definition of a Roskilde-simple system

The isomorph theory is reformulated by defining Roskilde-simple systems by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. If the potential energy as a function of all particle coordinates is denoted by U(R), this requirement translates into U(Ra) < U(Rb) ⇒ U(λRa) < U(λRb). Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.

Density scaling and quasiuniversality of flow-event statistics for athermal plastic flows

Athermal steady-state plastic flows were simulated for the Kob-Andersen binary Lennard-Jones system and its repulsive version in which the sign of the attractive terms is changed to a plus. Properties evaluated include the distributions of energy drops, stress drops, and strain intervals between the flow events. We show that simulations at a single density in conjunction with an equilibrium-liquid simulation at the same density allow one to predict the plastic flow-event statistics at other densities. This is done by applying the recently established "hidden scale invariance" of simple liquids to the glass phase. The resulting scaling of flow-event properties reveals quasiuniversality, i.e., that the probability distributions of energy drops, stress drops, and strain intervals in properly reduced units are virtually independent of the microscopic pair potentials.