Inherent structures, fragility, and jamming: Insights from quasi-one-dimensional hard disks

Yamchi, Mahdi Zaeifi; Ashwin, Sarah; Bowles, Richard K.

doi:10.1103/physreve.91.022301

Cited by 30 publications

(27 citation statements)

References 79 publications

(100 reference statements)

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“…Numerical simulations can be performed in any physical dimensions, and the range d = 1 − 12 was explored in that context. [146][147][148][149] Even the space topology can be varied. 150,151 One can study the effect of freezing a subset of particles with arbitrary geometries by means of computer simulations.…”

Section: Computer Simulations Of Glass-forming Liquidsmentioning

confidence: 99%

Configurational entropy of glass-forming liquids

Berthier

Ozawa

Scalliet

2019

The Journal of Chemical Physics

102

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The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, non-ambiguous, and experimentally-relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems. I. CONFIGURATIONAL ENTROPY AND GLASS FORMATION A. The glass transitionWhen a liquid is cooled, it can either form a crystal or avoid crystallization and become a supercooled liquid. In the latter case, the liquid remains structurally disordered, but its relaxation time increases so fast that there exists a temperature, called the glass temperature T g , below which structural relaxation takes such a long time that it becomes impossible to observe. The liquid is then trapped virtually forever in one of many possible structurally disordered states: this is the basic phenomenology of the glass transition. 1-4 Clearly, T g depends on the measurement timescale and shifts to lower temperatures for longer observation times. The experimental glass transition is not a genuine phase transition, as it is not defined independently of the observer.The rich phenomenology characterizing the approach to the glass transition has given rise to a thick literature. It is not our goal to review it, and we refer instead to previous articles. 1-9 There are convincing indications that the dynamic slowing down of supercooled liquids is accompanied by an increasingly collective relaxation dynamics. This is seen directly by the measurement of growing lengthscales for these dynamic heterogeneities, 10-12 or more indirectly by the growth of the apparent activation energy for structural relaxation, as seen in its non-Arrhenius temperature dependence. These observations suggest an interpretation of the experimental glass transition in terms of a generic, collective mechanism possibly controlled by a sharp phase transition. 13 'Solving the glass problem' thus amounts to identifying and obtaining direct experimental signatures about the fundamental nature and the mathematical des...

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Section: Computer Simulations Of Glass-forming Liquidsmentioning

confidence: 99%

Configurational entropy of glass-forming liquids

Berthier

Ozawa

Scalliet

2019

The Journal of Chemical Physics

102

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“…They also are of keen theoretical interest because they lend themselves to exact analytical treatments [6], and thus to insight into the nature of phase transitions in higher-dimensional systems. One way to partly bridge the gap between 1D and higher dimensions is to consider quasi-one-dimensional (q1D) models, which can be construed as strongly confined versions of higherdimensional systems (with a single unbounded dimension) [7][8][9][10][11][12]. These models further have experimental analogues in the trapping of fullerenes within nanotubes [13,14], the self-assembly of nanoparticles within cylindrical pores [15][16][17] and the formation of colloidal wires [18].…”

Section: Introductionmentioning

confidence: 99%

Correlation lengths in quasi-one-dimensional systems via transfer matrices

2018

Molecular Physics

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Using transfer matrices up to next-nearest-neighbour (NNN) interactions, we examine the structural correlations of quasi-one-dimensional systems of hard disks confined by two parallel lines and hard spheres confined in cylinders. Simulations have shown that the non-monotonic and non-smooth growth of the correlation length in these systems accompanies structural crossovers (Fu et al., Soft Matter, 2017, 13, 3296). Here, we identify the theoretical basis for these behaviour. In particular, we associate kinks in the growth of correlation lengths with eigenvalue crossing and splitting. Understanding the origin of such structural crossovers answers questions raised by earlier studies, and thus bridges the gap between theory and simulations for these reference models.arXiv:1804.00693v1 [cond-mat.soft]

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“…Its dependence on packing fraction is consistent with the general picture of a crossover from fragile glass behavior at low packing fractions to strong glass behavior at high packing fraction, which has been investigated previously in Refs. [2,4].…”

Section: Fig 1: (Color Online)mentioning

confidence: 99%

“…It has been frequently observed that disks moving in a narrow channel can provide useful insights into glassy behavior [1][2][3][4][5][6][7]. In a recent paper [6] two of us studied the static and dynamic properties of N disks of diameter σ, which move in a narrow channel consisting of two impenetrable walls (lines) spaced by a distance H d , such that 1 < H d /σ < 1 + √ 3/2 (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Glasslike behavior of a hard-disk fluid confined to a narrow channel

2016

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Disks moving in a narrow channel have many features in common with the glassy behavior of hard spheres in three dimensions. In this paper we study the caging behavior of the disks which sets in at characteristic packing fraction φ d . Four-point overlap functions similar to those studied when investigating dynamical heterogeneities have been determined from event driven molecular dynamics simulations and the time dependent dynamical length scale has been extracted from them. The dynamical length scale increases with time and, on the equilibration time scale, it is proportional to the static length scale associated with the zigzag ordering in the system, which grows rapidly above φ d . The structural features responsible for the onset of caging and the glassy behavior are easy to identify as they show up in the structure factor, which we have determined exactly from the transfer matrix approach.

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Inherent structures, fragility, and jamming: Insights from quasi-one-dimensional hard disks

Cited by 30 publications

References 79 publications

Configurational entropy of glass-forming liquids

Configurational entropy of glass-forming liquids

Correlation lengths in quasi-one-dimensional systems via transfer matrices

Glasslike behavior of a hard-disk fluid confined to a narrow channel

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