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 γ of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for γ directly in terms of the pair potential. The second conjecture is a refined version of this involving the most likely nearest-neighbor distance determined from the pair-correlation function. The conjectures 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 is more accurate.

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, CV, along configurational adiabats (curves of constant excess entropy Sex). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. The slope of the isomorphs in a double logarithmic representation of the density-temperature phase diagram, γ, can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where γ increases (decreases) with density, the contours of CV have smaller (larger) slope than configurational adiabats. We clarify also the connection between γ and the pair potential. A fluctuation formula for the slope of the CV-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 dγ∕dρ is thus a third key parameter in characterizing Roskilde liquids, after γ 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 CV-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.

Communication: 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(ρ). This implies that (1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by h(ρ)/T = Const., (2) the density-scaling exponent is a function of density only, and (3) a Grüneisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has h(ρ) = ∑(n)C(n)ρ(n/3) in which the only non-zero terms are those appearing in the pair potential expanded as ν(r) = ∑(n)ν(n)r(-n). Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.