Geometry of the Structure of Monatomic Liquids

Bernal, J. D.

doi:10.1038/185068a0

Cited by 792 publications

(301 citation statements)

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“…In this sense, the idea of the MRJ state has replaced the mathematically ill-defined notion of random close packing [1]. Nearly half-a-century ago these systems were thought to describe the disordered structure of liquids [3], but it is now known that three-dimensional MRJ monodisperse sphere packings possess unusual quasi-long-range (QLR) pair correlations decaying as r −4 [4]. This property is markedly different from typical liquids, in which pair correlations decay exponentially fast [2,5,6].…”

Section: Introductionmentioning

confidence: 99%

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

2011

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Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales. Previous work on maximally random strictly jammed sphere packings in three dimensions has shown that these systems are hyperuniform and possess unusual quasi-long-range pair correlations decaying as r −4 , resulting in anomalous logarithmic growth in the number variance. However, recent work on maximally random jammed sphere packings with a size distribution has suggested that such quasi-long-range correlations and hyperuniformity are not universal among jammed hard-particle systems. In this paper we show that such systems are indeed hyperuniform with signature quasi-long-range correlations by characterizing the more general local-volume-fraction fluctuations. We argue that the regularity of the void space induced by the constraints of saturation and strict jamming overcomes the local inhomogeneity of the disk centers to induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic behavior in the spectral density, resulting in quasi-long-range spatial correlations scaling with r −(d+1) in d Euclidean space dimensions. A numerical and analytical analysis of the pore-size distribution for a binary MRJ system in addition to a local characterization of the n-particle loops governing the void space surrounding the inclusions is presented in support of our argument. This paper is the first part of a series of two papers considering the relationships among hyperuniformity, jamming, and regularity of the void space in hard-particle packings.

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Section: Introductionmentioning

confidence: 99%

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

2011

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“…Starting from the seminal works of Bernal and co-workers in the late 1950s, a wealth of knowledge has been obtained over the years on the structural evolution of random sphere packings with increasing volume fraction cp (Bernal, 1959(Bernal, , 1960Bernal and Finney, 1967;Bernal and Mason, 1960;Scott et al, 1962). It is now widely accepted that the densest possible random packings in a 3D space, generated through different experimental setups and/ or modelling protocols, are characterized by densities in the vicinity of q> MR¡ ~ 0.64, subject to different generation protocols and conditions Anikeenko et al, 2008;Aste, 2005;Aste et al, 2005;Finney, 1970;Jullien et al, 1996;Scott and Kilgour, 1969;Tian et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Foteinopoulou

Karayiannis

Laso

2015

Chemical Engineering Science

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HIGHLIGHTS• Identification of the maximally random jammed state for polymer packings.• Molecular simulation of the phase transition in hard-sphere chains.• Molecular modelling of the effect of confinement in densely-packed athermal polymers.• Numerical calculation of the topological constraints in polymeric systems.• First-principles calculation of the scaling regimes in flexible polymers. ABSTRACTWe review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder-order transition). In addition, we observe how these properties are affected by confinement realized by fiat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

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“…Although significant progress has been made and provided insights into the atomic-level structure and short-to-mediumrange order in glasses [3][4][5][6][7][8][9][10][11][12][13][14] , the way of leading to the mediumrange order is still unclear [5][6][7][8][9][10] . Does a universal rule exist that nature follows to construct a glass structure as what has been discovered for crystals?…”

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confidence: 99%

Hidden topological order and its correlation with glass-forming ability in metallic glasses

Wang

et al. 2015

Nat Commun

117

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Unlike the well-defined long-range periodic order that characterizes crystals, so far the inherent atomic packing mode in glassy solids remains mysterious. Based on molecular dynamics simulations, here we find medium-range atomic packing orders in metallic glasses, which are hidden in the diffraction data in terms of structure factors or pair correlation functions. The analysis of the hidden orders in various metallic glasses indicates that the glassy and crystalline solids share a nontrivial structural homology in short-to-medium range, and the hidden orders are formulated by inheriting partial crystalline orders during glass formation. As the number of chemical components increases, more hidden orders are often developed in a metallic glass and entangled topologically. We use this phenomenon to explain the geometric frustration in glass formation and the glass-forming ability of metallic alloys.

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Geometry of the Structure of Monatomic Liquids

Cited by 792 publications

References 5 publications

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

Hidden topological order and its correlation with glass-forming ability in metallic glasses

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