Abstract
Liquids displaying strong virial-potential energy correlations conform to an approximate density scaling of their structural and dynamical observables. This scaling property does not extend to the entire phase diagram, in general. The validity of the scaling can be quantified by a correlation coefficient. In this work a simple scheme to predict the correlation coefficient and the density-scaling exponent is presented. Although this scheme is exact only in the dilute gas regime or in high dimension d, a comparison with results from molecular dynamics simulations in d=1 to 4 shows that it reproduces well the behavior of generalized Lennard-Jones systems in a large portion of the fluid phase.
Highlights
The density-scaling exponent is not the only relevant state-point dependent quantity in the isomorph theory: it is paired with the virial potential-energy correlation coefficient R ∈ [−1, 1], the value of which indicates whether or not density scaling is satisfied in the proximity of the state point in question
In the third section we present the analytic approximation which is compared in the fourth section to molecular dynamics simulations in two, three, and four dimensions, over a wide range of temperatures and densities
We have introduced a set of simplified equations to compute the virial-potential energy correlation coefficient R and the density-scaling exponent γ, valid in any dimension and for any pair potential in the isotropic liquid phase
Summary
The past 20 years have developed an increasing interest in the so-called density-scaling approach. The density-scaling exponent is not the only relevant state-point dependent quantity in the isomorph theory: it is paired with the virial potential-energy correlation coefficient R ∈ [−1, 1], the value of which indicates whether or not density scaling is satisfied in the proximity of the state point in question. We devise a simple low-density approximation for the density-scaling exponent and the virial-potential energy correlation coefficient, and compare it to computer simulations, with very good agreement As this approximation becomes exact in the limit of infinite dimension, we connect these results to the recent finding that isomorph invariance is exactly achieved for a large class of potentials as d → ∞, beyond the Euler-homogeneous ones like IPLs, in the liquid and glass phases [27].
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