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Voronoi glass-forming liquids: A structural study

C. Ruscher, J. Baschnagel, and J. Farago
Phys. Rev. E 97, 032132 – Published 27 March 2018
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  • INTRODUCTION
  • THE POLYDISPERSE VORONOI FLUID
  • GENERAL RESULTS ON THERMODYNAMICS
  • STRUCTURAL PROPERTIES
  • CONCLUSION
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We introduce a theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that the fluid, though sharing the global features of other models of fluids with soft interactions, has several unusual characteristics, which are investigated and discussed.

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    • Received 23 December 2017
    • Revised 13 February 2018

    DOI:https://doi.org/10.1103/PhysRevE.97.032132

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Glass transition
    1. Physical Systems
    Liquids
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    C. Ruscher, J. Baschnagel, and J. Farago*

    • Institut Charles Sadron, Université de Strasbourg, CNRS UPR 22, Strasbourg, France

    • *jean.farago@ics-cnrs.unistra.fr

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    Issue

    Vol. 97, Iss. 3 — March 2018

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    Images

    • Figure 1
      Figure 1

      Left: How a dividing plane is defined in the Voronoi-Laguerre tessellation. Two neighboring particles i and j, located at I and J, and having natural radii Ri and Rj, respectively, have Voronoi-Laguerre cells which share a common facet located in a plane normal in B to IJ (vertical bold line). The powers of B (or any point of the plane) with respect to i and j are equal. Note that the dividing plane is shifted, in accordance with intuition, toward the smaller particle. One has IB=ρijIJ with ρij=12[1+(Ri2−Rj2)/IJ2]. The figure shows also the distance AM, which represents the square root of the power of a point M with respect to I. Right: Typical sketch of a two-dimensional Voronoi-Laguerre tessellation. Dividing planes of neighboring particles are unchanged with respect to the ordinary Voronoi, but shift toward the smallest particles otherwise (dashed: dividing line for an ordinary Voronoi tessellation).

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    • Figure 2
      Figure 2

      Temperature dependence of (main) 〈Ep(m)〉/N (dashed green) and −〈Ep(a)〉/N (solid blue), and (inset) normalized distribution of particle energies ei for the large particles (see text for details). All temperatures collapse approximately on the Gaussian y=exp(−x2/2)/2π (black dotted). Note the small positive skewness.

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    • Figure 3
      Figure 3

      Blue circles: Mean potential energy per particle as a function of ξ2. The temperature is T=2. The black line is the best linear fit with slope −242. Green triangles: 〈Ep−12Ep(a)〉 as a function of ξ2 for T=2.

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    • Figure 4
      Figure 4

      Temperature dependence of Cve/N (red solid) and of the two components Cv(x)/N=N−1d〈Ep(x)〉/dT of the excess constant volume heat capacity Cve/N: dashed green, x=m; dash-dotted blue: x=a. Inset: Test of the “quadratic configurational entropy hypothesis” prediction for Cv(e). See text for details.

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    • Figure 5
      Figure 5

      Radial distribution functions of the Voronoi fluid. Main: for T=0.85 and N=8000,g11(r) (solid black), g12(r)=g21(r) (dashed purple), and g22(r) (dash-dotted light blue). Inset: g(r) for temperatures T=0.85 (solid blue), T=1.00 (dashed green), and T=2.00 (dash-dotted red).

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    • Figure 6
      Figure 6

      Static structure factors of the Voronoi fluid. Main: for T=0.85 and N=8000,S11(k) (solid black), S22(k) (dash-dotted light blue), and S(k) (thin solid ultramarine). The red circles show the “random Ansatz” S11A(k)=α1Smono(k)+1−α1 (see text for details). Inset: S12(k) for T=0.85 (solid purple) and the random Ansatz S12A(k)=α1α2[Smono(k)−1].

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    • Figure 7
      Figure 7

      Limiting case beyond which the right particle does not remain in its Voronoi cell.

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    • Figure 8
      Figure 8

      Variations of the bulk (K∞, blue circles) and shear (G∞, green triangles) moduli, normalized by the ideal gas shear modulus G∞id=T/v, with temperature. Dashed line: corresponding quantities for the monodisperse Voronoi fluid.

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    • Figure 9
      Figure 9

      Typical partial radial distribution functions (top) and partial structure factors (bottom) for a 80:20 mixture. The vertical bars are located at positions of maxima to highlight the property demonstrated in Appendix pp3. The nth maximum of g12 (resp. S12) is exactly halfway those of g11 and g12 (resp. S11 and S22).

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    • Figure 10
      Figure 10

      Solid blue: g(r). Dashed green: ∑j/j≠i〈δ(r−rij)[vi−v]〉. Monodisperse fluid at T=1.05. This figure shows that at each maximum (resp. minimum) of g(r) the dashed curve has a positive (resp. negative) slope.

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