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Journal of Chemical Physics / Volume 136 / Issue 8 / COMMUNICATIONS
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J. Chem. Phys. 136, 081101 (2012); http://dx.doi.org/10.1063/1.3687921 (4 pages)

Communication: Fundamental measure theory for hard disks: Fluid and solid

Roland Roth1, Klaus Mecke1, and Martin Oettel2

1Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
2Institut für Physik, WA 331, Johannes-Gutenberg Universität Mainz, 55099 Germany

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(Received 13 January 2012; accepted 6 February 2012; published online 22 February 2012)

Two-dimensional hard-particle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semi-quantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for two-dimensional hard-disk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional.

© 2012 American Institute of Physics

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KEYWORDS and PACS

Keywords

density functional theory, equations of state

PACS

  • 64.10.+h

    General theory of equations of state and phase equilibria

  • 71.15.Mb

    Density functional theory, local density approximation, gradient and other corrections

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3687921

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
The pair correlation function g(r) in a hard-disk fluid with a packing fraction of η = 0.65. The results of the present functional (full line) are in excellent agreement with data from Monte Carlo simulations (symbols). Note that the difference between the result of the present functional and that of the Rosenfeld functional for hard-disks (dashed line) is large. The inset shows the difference between DFT and the simulations.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
The density profile ρ(x, z) in a unit cell of a hard-disk solid at a reservoir packing fraction of ηr = 0.75 resulting from a free minimization of the functional. We extend the solid by using periodic boundary conditions in both directions.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
The chemical potential βμ (dotted line) and the pressure βp (full line) of the crystal as a function of the packing fraction ηr, obtained from free minimization of the new functional. The thin lines are predictions of cell theory for the pressure (dashed line) and the chemical potential (dashed-dotted line) of a two-dimensional crystal20 and the symbols are computer simulation data for the pressure (squares) (Refs. 21 and 23) and the chemical potential (circles).20 There is still a moderate but clear deviation between the DFT results and both the cell theory prediction and the computer simulation. In the inset, we show the vacancy concentration nvac of the crystal. Note that for ηr < 0.7201 the crystal is metastable.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint


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