Packing fraction of a disk assembly randomly close packed on a plane

Williams, D.

doi:10.1103/physreve.57.7344

Cited by 20 publications

(16 citation statements)

References 7 publications

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“…For all r < 1, the typical packing fraction seen at large times ranges from 0.78 − 0.82 in two dimensions. This value is very close to 0.84, the packing fraction of random close packed structures seen in jamming of frictionless spherical particles [35]. For r = 1, the packing fraction is p-3 Zahera Jabeen and R. Rajesh and Purusattam Ray 9) and ( 10) with scaling exponent α = 1/3.…”

supporting

confidence: 68%

Universal scaling dynamics in a perturbed granular gas

2010

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We study the response of a granular system at rest to an instantaneous input of energy in a localised region. We present scaling arguments that show that, in d dimensions, the radius of the resulting disturbance increases with time t as t α , and the energy decreases as t −αd , where the exponent α = 1/(d + 1) is independent of the coefficient of restitution. We support our arguments with an exact calculation in one dimension and event driven molecular dynamic simulations of hard sphere particles in two and three dimensions.

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confidence: 68%

Universal scaling dynamics in a perturbed granular gas

2010

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“…1(c) was approximately 0.50, which is much smaller than the ϕ values for the two-dimensional (2D) closest-packing ( ϕ = 0.91) 15 and 2D random close-packing (0.81) of equal-sized spheres 16 . The smaller observed ϕ values may be partly attributed to the weak electrostatic repulsion between the silica particles, which afforded short gaps even at [NaCl] = 50 mM.…”

Section: Resultsmentioning

confidence: 78%

Particle Adsorption on Hydrogel Surfaces in Aqueous Media due to van der Waals Attraction

Sato

Aoyama

Yamanaka

et al. 2017

Sci Rep

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Particle adhesion onto hydrogels has recently attracted considerable attention because of the potential biomedical applications of the resultant materials. A variety of interactions have been taken advantage of for adsorption, including electrostatic forces, hydrophobic interactions and hydrogen bonding. In this study, we report significant adsorption of submicron-sized silica particles onto hydrogel surfaces in water, purely by van der Waals (vdW) attraction. The vdW forces enabled strong adhesions between dielectric materials in air. However, because the Hamaker constant decreases in water typically by a factor of approximately 1/100, it is not clear whether vdW attraction is the major driving force in aqueous settings. We investigated the adsorption of silica particles (diameter = 25–600 nm) on poly(acrylamide) and poly(dimethylacrylamide) gels using optical microscopy, under conditions where chemical and electrostatic adsorption is negligible. The quantity of adsorbed particles decreased on decreasing the Hamaker constant by varying the refractive indices of the particles and medium (ethyleneglycol/water), indicating that the adsorption is because of the vdW forces. The adsorption isotherm was discussed based on the adhesive contact model in consideration of the deformation of the gel surface. The present findings will advance the elucidation and development of adsorption in various types of soft materials.

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“…They argue that said tessellations do not actually occur in the 2d hard disc fluid, but that the densities at which the fluid to hexatic and hexatic to crystal transitions occur might be signatures of the existence of nearby tessellations that completely span the 2D space, i.e., ghost configurations that parallel the change in character of the solutions to the integral equation for the inhomogeneous density distribution function. Taking the same point of view, we note that Williams [34] has argued that a tessellation of 2D space with rhombuses that have average internal…”

Section: Discussionmentioning

confidence: 88%

Maximally random jamming of one-component and binary hard-disk fluids in two dimensions

Rice

2011

Phys. Rev. E

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We report calculations of the density of maximally random jamming of one-component and binary hard-disk fluids. The theoretical structure used provides a common framework for description of the hard-disk liquid-to-hexatic, the liquid-to-hexagonal crystal, and the liquid to maximally random jammed state transitions. Our analysis is based on locating a particular bifurcation of the solutions of the integral equation for the inhomogeneous single-particle density at the transition between different spatial structures. The bifurcation of solutions we study is initiated from the dense metastable fluid, and we associate it with the limit of stability of the fluid, which we identify with the transition from the metastable fluid to a maximally random jammed state. For the one-component hard-disk fluid the predicted packing fraction at which the metastable fluid to maximally random jammed state transition occurs is 0.84, in excellent agreement with the experimental value 0.84 ± 0.02. The corresponding analysis of the limit of stability of a binary hard-disk fluid with specified disk-diameter ratio and disk composition requires extra approximations in the representations of the direct correlation function, the equation of state, and the number of order parameters accounted for. Keeping only the order parameter identified with the largest peak in the structure factor of the highest-density regular lattice with the same disk- diameter ratio and disk composition as the binary fluid, the predicted density of maximally random jamming is found to be 0.84-0.87, depending on the equation of state used, and very weakly dependent on the ratio of disk diameters and the fluid composition, in agreement with both experimental data and computer simulation data.

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Packing fraction of a disk assembly randomly close packed on a plane

Cited by 20 publications

References 7 publications

Universal scaling dynamics in a perturbed granular gas

Universal scaling dynamics in a perturbed granular gas

Particle Adsorption on Hydrogel Surfaces in Aqueous Media due to van der Waals Attraction

Maximally random jamming of one-component and binary hard-disk fluids in two dimensions

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