Thermodynamic geometry of the Gaussian core model fluid

Abstract

The three-dimensional Gaussian core model (GCM) for soft-matter systems has repulsive interparticle interaction potential ϕ(r)=εexp[−(r/σ)2], with r the distance between a pair of atoms, and the positive constants ε and σ setting the energy and length scales, respectively. ϕ(r) is mostly soft in character, without the typical hard core present in fluid models. We work out the thermodynamic Ricci curvature scalar R for the GCM, with particular attention to the sign of R, which, based on previous results, is expected to be positive/negative for microscopic interactions repulsive/attractive. Over most of the thermodynamic phase space, R is found to be positive, with values of the order of σ3. However, for low densities and temperatures, the GCM potential takes on the character of a hard-sphere repulsive system, and R is found to have an anomalous negative sign. Such a sign was also found earlier in inverse power law potentials in the hard-sphere limit, and seems to be a persistent feature of hard-sphere models.