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PACKING OF DISKS ON A TWO DIMENSIONAL CAVITY WITH DILUTED PINS

Wellington Castro Ferreira ; Valdemiro da Paz Brito 1 ; José Pimentel de Lima 1 ; Marcelo Andrade de Filgueiras Gomes
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The physics of two-dimensional systems have fascinating behavior, and can also be surprisingly different from physics in three dimensions. This has stimulated the study of statistical properties of several systems such as monolayer packing configurations of a string of beads [1], as well as, two-dimensional systems involving hard discs on a flat cell. These systems have been subject of continued interest in physics, because they have connections with many problems, as e.g. in the study of elastic and inelastic deformation of polymers, and the study of fundamental properties of condensed matter, including structural phase transitions, among others. In this contribution it is investigated the problem of the packing of hard discs on a two dimensional cell with fixed cylindrical pins which are obstacles with a much smaller diameter than the disks. The cell consists of two rectangular sheets of acrylic separated by a thickness that allows to accommodate only a single layer of discs. More than two hundred configurations of such packing were analyzed and grouped by considering the density of pins and the nature of their distribution (square lattice or random lattice), all them obtained in the limit of maximum packing density. Working with the digitized image of each configuration, the centroid of each disk was determined. The packing of disks was analyzed as a function of the number of obstacles and it was represented as configurations of Wigner-Seitz (WS) cells. We found that the cellular structure of packaged discs follows a statistical description already described by Weaire and Rivier [2], in the partial characterization of random structures in two dimensions in several aspects as, the distributions of angles and the number of sides of the WS cells. The distribution of sides for the WS cells was analyzed and compared with the Shackelford-Masaryk hypothesis, and we also found that the arguments of Buechner et al. [3] do not apply to this study to explain the lognormal distribution proposed in [3]. Additionally we verified a reasonable agreement with the Aboav's law [4]. The pair correlation function was calculated for the centroid of the discs and the results suggest the characterization of the properties of the system in periodic, hexatic and random regimes, which depend of the density of pins.

[1] Brito,V.P., Castro,W.S., Coelho,A.S.O., Gomes,M.A.F., Physica A, 342(2004)419.
[2] Weaire,D.; Rivier,N. Soap, Contemporary Physics, 25(1984)59.
[3] Buechner,C., Schlexer,P, Lichtenstein,L, Stuckenholz,S, Heyde, and Freund,H-J, Z. Phys. Chem, 228(2014)587.
[4] Hilhorst,H.J. Journal Physics A, 39(2006)7227.