Is Random Close Packing of Spheres Well Defined?

Torquato, Salvatore; Truskett, Thomas M.; Debenedetti, Pablo G.

doi:10.1103/physrevlett.84.2064

Cited by 1,257 publications

(1,251 citation statements)

References 9 publications

(11 reference statements)

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“…3 (determined for 310 nm spheres) for SiO 2 unsupported membrane derived from the sol with pH 2.7. Random close packing with a distribution of particle sizes typically yields a porosity of 0.36 [19]. The H-K pore sizes determined for the unsupported membranes consolidated from the 5 nm sphere sols with pH 2.7 and pH 3.5 compared quite well with the geometrically calculated throat sizes of about 0.77 nm for close packed structures.…”

Section: Particle Size and Pore Structure Determinationsupporting

confidence: 63%

Preparation of particulate/polymeric sol–gel derived microporous silica membranes and determination of their gas permeation properties

Topuz

Çiftçioğlu

2010

Journal of Membrane Science

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a b s t r a c tMonodisperse silica sols with well-defined spherical particles ranging in size from 5 to 310 nm were prepared through Stober process. Both particulate and polymeric sol-gel routes were employed for the preparation of stable silica sols. The use of polymeric species in combination with particulate silica spheres may allow the design of predefined membrane pore structures with high thermal stability by cubic/random/close packing of monodisperse spherical particles incorporated into the polymeric network. The size and volume content of spheres were varied in order to modify the consolidation behaviour of 2-structural silica membranes which would enhance the thermal stability. The low shrinkage level for sphere loaded 2-structural systems compared to the pure polymeric counterparts might be explained by the decrease in the structural free energy of the polymeric/particulate 2-structural system. The thermal stability of the microporous membranes may thus be improved by incorporating particulates into the polymeric network through the formation of a lower extent of thermally induced microcrack formation. The N 2 permeation through 90 nm silica sphere added silica membranes remained constant when they were heat treated in the 250-400 • C range indicating the stability of the pore network.

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Section: Particle Size and Pore Structure Determinationsupporting

confidence: 63%

Preparation of particulate/polymeric sol–gel derived microporous silica membranes and determination of their gas permeation properties

Topuz

Çiftçioğlu

2010

Journal of Membrane Science

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“…For all of the order parameters discussed here, the cutoff radius is defined by the first minimum in the pair correlation function, in this case 1.45a. Q 6 is approximately 0.575 for a perfect fcc crystal; for jammed structures, it can exhibit a large range of values less than about 0.37 [34]. The full distribution of Q 6 for our model glass is shown for several ages as well as an initial melt state in Fig.…”

Section: Structural Evolutionmentioning

confidence: 99%

Simulations of aging and plastic deformation in polymer glasses

Warren

Rottler

2007

Phys. Rev. E

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We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation timescales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that the entire distribution of relaxation times scales identically with age. Despite large changes in mobility, we observe comparatively little structural change except for a weak logarithmic increase in the degree of short-range order that may be correlated to an observed decrease in aging with increasing load.

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“…Putting the question this way, we immediately run into difficulties because by considering different degrees of crystallinity, we can obtain a continuum of denser packings [49]. The random models studied here allow us to avoid -at least to fix ideas -the conceptual complication of crystallization, and to concentrate on the glassy aspects [45].…”

Section: The J-pointmentioning

confidence: 99%

Landscape analysis of constraint satisfaction problems

2007

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We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A 'benchmark' algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the 'clustering' and in some cases even the 'thermodynamic' transitions. This point has a simple geometric meaning and can be in principle determined with standard Statistical Mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph three and four-coloring problem. For Packing problems the present discussion allows to better characterize the 'J-point', proposed as a systematic definition of Random Close Packing [1], and to place it in the context of other theories of glasses.

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Is Random Close Packing of Spheres Well Defined?

Cited by 1,257 publications

References 9 publications

Preparation of particulate/polymeric sol–gel derived microporous silica membranes and determination of their gas permeation properties

Preparation of particulate/polymeric sol–gel derived microporous silica membranes and determination of their gas permeation properties

Simulations of aging and plastic deformation in polymer glasses

Landscape analysis of constraint satisfaction problems

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