Fundamental-measure density functional for the fluid of aligned hard hexagons: New insights in fundamental measure theory

Abstract

In this article we obtain a fundamental measure functional for the model of aligned hard hexagons in the plane. Our aim is not just to provide a functional for a new, admittedly academic, model, but to investigate the structure of fundamental measure theory. A model of aligned hard hexagons has similarities with the hard disk model. Both share "lost cases", i.e. admit configurations of three particles in which there is pairwise overlap but not triple overlap. These configurations are known to be problematic for fundamental measure functionals, which are not able to capture their contribution correctly. This failure lies in the inability of these functionals to yield a correct low density limit of the third order direct correlation function. Here we derive the functional by projecting aligned hard cubes on the plane x+y+z=0. The correct dimensional crossover behavior of these functionals permits us to follow this strategy. The functional of aligned hard cubes, however, does not have lost cases, so neither had the resulting functional for aligned hard hexagons. The latter exhibits, in fact, a peculiar structure as compared to the one for hard disks. It depends on a uniparametric family of weighted densities through a new term not appearing in the functional for hard disks. Apart from studying the freezing of this system, we discuss the implications of the functional structure for new developments of fundamental measure theory.

arXiv comment10 pages, 9 figures, uses RevTeX4

References in corpus (15)

• Dimensional crossover of the fundamental-measure functional for parallel hard cubes
• Fluid mixtures of parallel hard cubes
• Density functional theory for colloidal mixtures of hard platelets, rods, and spheres
• Close to the edge of Fundamental Measure Theory: density functional for hard sphere mixtures
• Fundamental measure theory for lattice fluids with hard core interactions
• A density functional theory for general hard-core lattice gases
• Phase behavior of hard-core lattice gases: A Fundamental Measure approach
• Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model
• Fundamental measure theory for mixtures of parallel hard cubes. II. Phase behavior of the one-component fluid and of the binary mixture
• Rosenfeld functional for non-additive hard spheres
• Bulk and wetting phenomena in a colloidal mixture of hard spheres and platelets
• Density functional theory for nearest-neighbor exclusion lattice gasses in two and three dimensions
• Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media
• Cluster density functional theory for lattice models based on the theory of Mobius functions
• Lattice density functional for colloid-polymer mixtures: Multi-occupancy versus Highlander version

Cited by in corpus (2)

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