Computational Studies of the Effect of Dimensionality on Fluids and Freezing

Abstract

Here the effect of dimensionality on the classical statistical mechanics of fluids and melting is explored. In particular the effects of short range structure on the thermodynamic properties, including entropy, are highlighted. Theoretical understanding of freezing and the properties of fluids at high density remains an unsolved problem and current approaches are approximate and contain ad hoc elements. This work is predicated on the belief that investigations of these properties in dimensions other than three will provide useful insights. It has been shown that for a range of substances including sodium, argon, a number of alkali halides and Molecular Dynamics (MD) computer simulations of 3 dimensional systems, that the isochoric entropy change (the communal entropy) of melting is approximately equal to Rln 2. Here we extend the range of substances shown to exhibit this behavior to include krypton and xenon; systems with larger atomic radii, and hence systems of higher polarisability. While these 3 dimensional systems exhibit a communal entropy on melting of ≈ Rln 2, MD computer simulations of 2 dimensional systems find the communal entropy of melting to be zero. This suggests a dependence upon either dimensionality, or the geometry of the close-packed structure of the dimension in question. Here, using 3 dimensional molecular dynamics simulations we provide evidence that the magnitude (Rln 2) of the communal entropy of melting is geometric in origin, its source being the number of 'holes' per lattice site in the D - 1 dimensional close packed lattice structure. To further investigate this model we present the results of 4 dimensional molecular dynamics simulations on a soft-sphere system. The communal entropy of this system is found to be ≈ Rln 3, consistent with a geometric origin of the communal entropy and implying that the 4-D particles access sites in the local short-range structure which originate from both tetrahedral and octahedral holes in the close-packed 3 D lattice, from which the 4D close packed lattice is constructed by layering Density functional theory calculations on the same system generally concur with the MD calculations but highlight the need for corrections arising from triplet correlations.