Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

Аникеенко, А. В.; Medvedev, N. N.; Bezrukov, Alexander; Stoyan, Dietrich

doi:10.1016/j.jnoncrysol.2007.05.113

Cited by 20 publications

(30 citation statements)

References 27 publications

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“…The cyclic twinned structures that appear in event-driven MD simulations of crystallization of monoatomic hard spheres [16] consist of partially or fully developed cyclic sector twins with a pseudo-fivefold rotation axis, resembling those in [1,22,23]. In our structures, between three and five such sectors can be resolved.…”

Section: Morphology Of Twins In Systems Of Monoatomic Hard Spheresmentioning

confidence: 78%

“…The peaks in the bond angle and torsion angle distributions stem from the most probable three-sphere (bond angle) and four-sphere (bond torsion) arrangements. These most probable arrangements have been positively correlated [43] with simple configurations of three or four consecutive spheres obtained by placing them on the vertices of one or two tetrahedra that share an edge or a face [22,23].…”

Section: Calculation Of Entropic Loss Using Rotational Isomeric Statementioning

confidence: 99%

“…As mandated by the pseudo fivefold symmetry, spheres along the axis have a fivefold symmetric environment. The structure along the axis can also be viewed as a linear array of parallel stacked pentagons, or a pile of pentagonal bipyramids, as in [1,23,29] closely related to the Bagley structure [30].…”

Section: Morphology Of Twins In Systems Of Monoatomic Hard Spheresmentioning

confidence: 99%

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Twinning of Polymer Crystals Suppressed by Entropy

Karayiannis¹,

Foteinopoulou²,

Laso³

2014

Symmetry

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Abstract:We propose an entropic argument as partial explanation of the observed scarcity of twinned structures in crystalline samples of synthetic organic polymeric materials. Polymeric molecules possess a much larger number of conformational degrees of freedom than low molecular weight substances. The preferred conformations of polymer chains in the bulk of a single crystal are often incompatible with the conformations imposed by the symmetry of a growth twin, both at the composition surfaces and in the twin axis. We calculate the differences in conformational entropy between chains in single crystals and chains in twinned crystals, and find that the reduction in chain conformational entropy in the twin is sufficient to make the single crystal the stable thermodynamic phase. The formation of cyclic twins in molecular dynamics simulations of chains of hard spheres must thus be attributed to kinetic factors. In more realistic polymers this entropic contribution to the free energy can be canceled or dominated by nonbonded and torsional energetics.

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Section: Morphology Of Twins In Systems Of Monoatomic Hard Spheresmentioning

confidence: 78%

Section: Calculation Of Entropic Loss Using Rotational Isomeric Statementioning

confidence: 99%

Section: Morphology Of Twins In Systems Of Monoatomic Hard Spheresmentioning

confidence: 99%

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Twinning of Polymer Crystals Suppressed by Entropy

Karayiannis¹,

Foteinopoulou²,

Laso³

2014

Symmetry

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“…Simulations using anisotropic potentials suggest that local arrangements of sites with pentagonal symmetry are locally favored, thereby causing frustration in the crystallization of glasses [18]. Fivefolds have also been reported to occur in crystal phases [19] and in dense random packings [20] of hard spheres. However, their role in the morphology and dynamics of athermal crystals remains unknown.…”

Section: Introductionmentioning

confidence: 99%

Fivefold symmetry as an inhibitor to hard-sphere crystallization

et al. 2011

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Through molecular simulations we investigate the dynamics of crystallization of hard spheres of uniform size from dense amorphous states and the role that hidden structures in an otherwise disordered medium might have on it. It is shown that short-range order in the form of sites with fivefold symmetry acts as a powerful inhibitor to crystal growth. Fivefold sites not only retard crystallization, but can self-assemble into organized structures that arrest crystallization at high densities or lead to the formation of defects in a crystal. The latter effect can be understood in terms of a random polyhedral model.

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“…The distinguishing feature is the absence of twinned structures in polymer systems [72]. In computer simulations, packings of single hard spheres often form quite perfect tetrahedral clusters which tend to aggregate in pentatwins [73]. The entropic conformational entropy loss associated with twinning in polymeric systems rises the entropic barrier to the extent that individual crystals with single or multiple stacking directions and abundant defects are observed predominantly in simulations.…”

Section: Introductionmentioning

confidence: 99%

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Benito

Karayiannis

Laso

2018

Preprint

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Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

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Observation of fivefold symmetry structures in computer models of dense packing of hard spheres

Cited by 20 publications

References 27 publications

Twinning of Polymer Crystals Suppressed by Entropy

Twinning of Polymer Crystals Suppressed by Entropy

Fivefold symmetry as an inhibitor to hard-sphere crystallization

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

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