We study the structure of numerically simulated hard sphere packings at different densities by investigating local tetrahedral configurations of the spheres. Clusters of tetrahedra adjacent by faces present relatively dense aggregates of spheres atypical for crystals. The number of spheres participating in such polytetrahedral configurations increases with densification of the packing, and at the Bernal's limiting density (the packing fraction around 0.64) all spheres of the packing become involved in such tetrahedra. Thus the polytetrahedral packing cannot provide further increase in the density, and alternative structural change (formation of crystalline nuclei) begins henceforth.

Anikeenko, A. V. and Medvedev, N. N. and Aste, Tomaso (2008) Structural and entropic insights into the nature of the random-close-packing limit. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 77 (3). ISSN 1063-651X. Disordered packings of equal sized spheres cannot be generated above the limiting density ͑fraction of volume occupied by the spheres͒ of Ӎ 0.64 without introducing some partial crystallization. The nature of this "random-close-packing" limit ͑RCP͒ is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of "quasiperfect tetrahedra" grows with the density up to a saturation fraction of ϳ30% reached at the RCP limit. At this limit the fraction of aggregate "polytetrahedral" structures ͑made of quasiperfect tetrahedra which share a common triangular face͒ reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the ͑extrapolated͒ limit K Ӎ 0.66. Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed. DOI

A generalized version of the Voronoi−Delaunay method is used to study relatively large intermolecular voids in a model of the hydrated DMPC bilayer, obtained from all-atom Monte Carlo simulation. Application of the original version of the method for molecular systems has been hampered by the fact that these systems geometrically represent ensembles of partially overlapping spheres of different radii. The generalized version of the method is based on using the additively weighed Voronoi diagram, representing the locus of spatial points being equally far from the surface rather than the center of the corresponding pair of atoms. This version of the Voronoi−Delaunay method can be readily used to reveal and analyze voids accessible for probes of different radii even in rather complex molecular systems. When the properties of the voids present in the simulated DMPC membrane are investigated, their shape, size, and orientation have been analyzed in detail in the different regions of the membrane located at different depths along the membrane normal axis. The characteristics of the voids are found to be different in different regions of the bilayer, namely (i) at the middle of the membrane, in the region of the hydrophobic lipid tails, (ii) in the region of the hydrophilic zwitterionic headgroups, and (iii) in the region of the bulklike water adjacent to the bilayer. The largest and oblong voids are found in the middle of the membrane, with a preferred orientation that is parallel to the bilayer normal axis. A clear correlation between the orientation of the voids and the orientation of the lipid chains is observed. In the bulk water region the fraction of the empty space is even higher than at the middle of the membrane; however, here the voids are distributed more uniformly. Finally, in the high-density region of the hydrophilic headgroups the voids are found, on average, smaller than in the other parts of the system.

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