Thermodynamics of condensed matter with strong pressure-energy correlations

We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, $T=f(s)h(\rho)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(\rho)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{\"u}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(\rho)=\sum_nC_n\rho^{n/3}$ in which the only non-zero terms are those appearing in the pair potential expanded as $v(r)=\sum_n v_n r^{-n}$. Molecular dynamics simulations of Lennard-Jones type systems confirm the theory

Estimating the density-scaling exponent of a monatomic liquid from its pair potential

This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for the density-scaling exponent directly in terms of the pair potential. The second conjecture is a refined version of this, which involves the most likely nearest-neighbor distance determined from the pair-correlation function. The two conjectures for the density-scaling exponent are tested by simulations of three systems, one of which is the standard Lennard-Jones liquid. While both expressions give qualitatively correct results, the second expression is more accurate

Isomorphs in the phase diagram of a model liquid without inverse power law repulsion

It is demonstrated by molecular dynamics simulations that liquids interacting via the Buckingham potential are strongly correlating, i.e., have regions of their phase diagram where constant-volume equilibrium fluctuations in the virial and potential energy are strongly correlated. A binary Buckingham liquid is cooled to a viscous phase and shown to have isomorphs, which are curves in the phase diagram along which structure and dynamics in appropriate units are invariant to a good approximation. To test this, the radial distribution function, and both the incoherent and coherent intermediate scattering function are calculated. The results are shown to reflect a hidden scale invariance; despite its exponential repulsion the Buckingham potential is well approximated by an inverse power-law plus a linear term in the region of the first peak of the radial distribution function. As a consequence the dynamics of the viscous Buckingham liquid is mimicked by a corresponding model with purely repulsive inverse-power-law interactions. The results presented here closely resemble earlier results for Lennard-Jones type liquids, demonstrating that the existence of strong correlations and isomorphs does not depend critically on the mathematical form of the repulsion being an inverse power law.Comment: 7 pages, 9 figure

Scaling of viscous dynamics in simple liquids:theory, simulation and experiment

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density to some power over temperature. We show that power-law density scaling breaks down for larger density variations than usually studied. This is demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture and two molecular models, as well as by experimental results for two van der Waals liquids. A more general form of density scaling is derived, which is consistent with results for all the systems studied. An analytical expression for the scaling function for liquids of particles interacting via generalized Lennard-Jones potentials is derived and shown to agree very well with simulations. This effectively reduces the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.Comment: 7 pages, 5 figure

Do the repulsive and attractive pair forces play separate roles for the physics of liquids?

Abstract According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force

Statistical mechanics of Roskilde liquids: Configurational adiabats, specific heat contours, and density dependence of the scaling exponent

We derive exact results for the rate of change of thermodynamic quantities, in particular the configurational specific heat at constant volume, $C_V$, along configurational adiabats (curves of constant excess entropy $S_{\textrm{ex}}$). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. Their slope in a double logarithmic representation of the density-temperature phase diagram, $\gamma$ can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where $\gamma$ increases (decreases) with density, the contours of $C_V$ have smaller (larger) slope than configurational adiabats. We clarify also the connection between $\gamma$ and the pair potential. A fluctuation formula for the slope of the $C_V$-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid and the Girifalco fluid. The sign of $d\gamma/d\rho$ is thus a third key parameter in characterizing Roskilde liquids, after $\gamma$ and the virial-potential energy correlation coefficient $R$. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient along adiabats and $C_V$-contours, finding it more invariant along adiabats

Do the repulsive and attractive pair forces play separate roles for the physics of liquids?

According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force

RUMD: A general purpose molecular dynamics package optimized to utilize GPU hardware down to a few thousand particles

RUMD is a general purpose, high-performance molecular dynamics (MD) simulation package running on graphical processing units (GPU's). RUMD addresses the challenge of utilizing the many-core nature of modern GPU hardware when simulating small to medium system sizes (roughly from a few thousand up to hundred thousand particles). It has a performance that is comparable to other GPU-MD codes at large system sizes and substantially better at smaller sizes.RUMD is open-source and consists of a library written in C++ and the CUDA extension to C, an easy-to-use Python interface, and a set of tools for set-up and post-simulation data analysis. The paper describes RUMD's main features, optimizations and performance benchmarks.Comment: 22 pages. Resubmission to SciPost Physic