Random sequential addition of hard spheres in high Euclidean dimensions

Torquato, Salvatore; Uche, Obioma U.; Stillinger, Frank H.

doi:10.1103/physreve.74.061308

Cited by 146 publications

(107 citation statements)

References 42 publications

(136 reference statements)

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“…Usually mean coordination number is calculated for direct contact of particles, i.e., λ = 1.0 [4]. However with the RSA method used for the nonoverlapping fibres the cumulative coordination number attains zero when upper limit equals r/d = 1.0 [9,8]. Therefore, for the integral with such limit, the mean coordination number also goes to zero.…”

Section: Pair Distribution Function Methodsmentioning

confidence: 99%

“…Two cases were considered following suggestions found in the literature. In the first case the upper limit of the integral was assumed to be λ = 1.5 [7,11,14] and in the second case it was made equal to the distance corresponding to the location of the first minimum of the pair distribution function [9,2]. The numerical procedure for calculation PDF function follows the one suggested in literature [20,4].…”

Section: Pair Distribution Function Methodsmentioning

confidence: 99%

“…Statistical nature of the RSA causes that the probability of perfect contact between two particles goes to zero [9]. In effect typical coordination number calculation with direct contact condition is rather useless and to omit this problem specified neighbour radius is defined [9,14,8]. It is worth here to mention that the sequential analysis was initially introduced for particles in direct contact, and it is extended to more general case in this paper.…”

Section: Coordination Numbermentioning

confidence: 99%

“…It is calculated as an integral of the specified function called the pair distribution function in given integration limits [6][7][8]. Such integral may give valuable information about many processes, for instance about fluid-solid phase transition [9]. The coordination number is strongly coupled with behaviour of the PDF function.…”

Section: Coordination Numbermentioning

confidence: 99%

“…Therefore a problem appears how to define a distance for which one particle is considered as the neighbour of another particle. Statistical nature of the RSA causes that the probability of perfect contact between two particles goes to zero [9]. In effect typical coordination number calculation with direct contact condition is rather useless and to omit this problem specified neighbour radius is defined [9,14,8].…”

Section: Coordination Numbermentioning

confidence: 99%

See 4 more Smart Citations

Coordination number for random distribution of parallel fibres

Darnowski

Furmański

Domański

2017

Archives of Thermodynamics

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This paper presents the results of computer simulations carried out to determine coordination numbers for a system of parallel cylindrical fibres distributed at random in a circular matrix according to twodimensional pattern created by random sequential addition scheme. Two different methods to calculate coordination number were utilized and compared. The first method was based on integration of pair distribution function. The second method was the modified sequential analysis. The calculations following from ensemble average approach revealed that these two methods give very close results for the same neighbourhood area irrespective of the wide range of radii used for calculation.

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Section: Pair Distribution Function Methodsmentioning

confidence: 99%

Section: Pair Distribution Function Methodsmentioning

confidence: 99%

Section: Coordination Numbermentioning

confidence: 99%

Section: Coordination Numbermentioning

confidence: 99%

Section: Coordination Numbermentioning

confidence: 99%

See 3 more Smart Citations

Coordination number for random distribution of parallel fibres

Darnowski

Furmański

Domański

2017

Archives of Thermodynamics

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Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

Douglas

Freed

2016

Advances in Chemical Physics

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We explore the nature of glass-formation in variable spatial dimensionality (d) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established statistical mechanical model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the d → ∞ limit and that the fluid transforms upon sufficient cooling above a critical dimension near d = 8 into a dense amorphous state with a finite positive residual configurational entropy. Direct computations of the isothermal compressibility and thermal expansion coefficient, taken to be physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation.PACS numbers: 64.70.QGrowing evidence indicates that molecular packing plays an essential role in both the physics of crystallization [1][2][3][4][5] and glass-formation [6][7][8][9][10][11][12][13][14][15][16][17], prompting a consideration of variable spatial dimensionality (d) as a conceptual probe of these solidification processes. In particular, the "decorrelation principle", recently proposed by Torquato and Stillinger [18,19], states that unconstrained correlations in hard hyperspheres diminish with increasing d and vanish in the d → ∞ limit. Likewise, recent simulations [7][8][9] have indicated that certain often cited aspects of glass-formation, such as the dynamic heterogeneity and the decoupling between structural relaxation and diffusion, become diminished at elevated d. While prior studies [11][12][13][14][15] have focused mainly on how critical packing fractions associated with glass-formation in hard hyperspheres vary with d, little is known concerning the d dependence of the characteristic temperatures and fragility of glass-formation in molecular fluids. No prior work has considered complex fluids, such as polymeric liquids, where many molecular parameters may be tuned to control the nature of glass-formation.In this Letter, we consider the glass-formation of a model polymer glass-forming (GF) liquid in d dimensions. Our approach is based on the generalized entropy theory (GET) [20], which is a combination of the lattice cluster theory (LCT) [21] and the Adam-Gibbs (AG) theory [22] linking the configurational entropy s c (i.e., the entropy devoid of the vibrational component) to the structural relaxation time τ α . The LCT employs a ddimensional hypercubic lattice model, whose use facilitates the development of an expansion about the meanfield limit of infinite d. The LCT thus naturally provides * Contribution of the National Institute of Standards and Technology -Work not subject to copyright in the United States. † wsxu@uchicago.edu ‡ jack.douglas@nist.gov § freed@uchicago.edu a framework for considering the d dependence of polymer thermodynamic properties, thereby making the GET suitable for exploring glass-formation in d dimensions.As a primary result, we find that structural relaxation in the fluid st...

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Toward Hyperuniform Disorder via Self‐Assembly of Bidisperse Colloidal Patterns at an Electrode

Piechulla

Wehrspohn

Sprafke

2022

Adv Materials Inter

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While hyperuniform‐disordered patterns have been researched from a theoretical perspective for two decades, large scale experimental realizations remain scarce. In this work, as a potential route to overcome this issue, 2D patterns are evaluated that form through sedimentation of charged particles from a colloidal dispersion at an electrically conductive substrate. The particles are given a sufficient amount of time to form various morphologies and then locked in place irreversibly by setting attractive particle‐substrate potentials. The system can be interpreted as a 2D, however, comparisons to previous numerical works remain qualitative, as the latter do not consider the constant exchange of particles with the 3D bulk of the dispersion. For monodisperse colloids, depending on particle density, random sequential adsorption‐like, fluid, and crystalline phases are obtained, of which the fluid phase most effectively suppresses density fluctuations, or in terms of the hyperuniformity metric HS ≈ 8.7 × 10−3. For bidisperse colloids, the particle sizes tend to segregate at high density thereby reducing the ability of the system to suppress density fluctuations, which are explained within the framework of a eutectic system. The latter also provides hints that the degree of hyperuniformity can be increased by tuning the size distribution to the eutectic point.

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Random sequential addition of hard spheres in high Euclidean dimensions

Cited by 146 publications

References 42 publications

Coordination number for random distribution of parallel fibres

Coordination number for random distribution of parallel fibres

Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

Toward Hyperuniform Disorder via Self‐Assembly of Bidisperse Colloidal Patterns at an Electrode

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