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Abstract
Results from molecular dynamics simulations of two viscous molecular model liquids--the Lewis-Wahnström model of orthoterphenyl and an asymmetric dumbbell model--are reported. We demonstrate that the liquids have a "hidden" approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-law (IPL) potentials, the radial distribution functions are accurately reproduced by the IPL's, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation. IPL scaling of the dynamics also applies--with the scaling exponent predicted by the equilibrium fluctuations. In contrast, the equation of state does not obey the IPL scaling. We argue that our results are general for van der Waals liquids, but do not apply, e.g., for hydrogen-bonded liquids.
Highlights
A phenomenon is scale invariant if it has no characteristic length or time
We demonstrate that the liquids have a “hidden” approximate scale invariance: equilibrium potential energy fluctuations are accurately described by inverse power-lawIPLpotentials, the radial distribution functions are accurately reproduced by the IPL’s, and the radial distribution functions obey the IPL predicted scaling properties to a good approximation
It was recently shown2–4͔ that several model liquids exhibit strong correlations between the equilibrium fluctuations of the potential energy U and the virial Wdefining the contribution to pressure coming from the intermolecular interactions via pV = NkBT + W
Summary
A phenomenon is scale invariant if it has no characteristic length or time. Scale invariance emerged as a paradigm in the early 1970s following the tremendous successes of the theory of critical phenomena. Even dynamical properties are simple, e.g., the relaxation time may be written as. The predicted equation of state does not fit data for real fluids, and IPL liquids do not have low-pressure liquid states. Both problems derive from the absence of molecular attractions; these define the spatial scale of one intermolecular distance at low and moderate pressure. In this paper we demonstrate by example that there is a “hidden” approximate scale invariance in a large class of liquids, the van der Waals liquids. Several properties of IPL liquids apply to van der Waals liquids, leading to a number of experimentally testable predictions
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