Equation of State for Hard Spheres and Their Mixtures in the Isotropic, Metastable, and Random Close-Packed Regions

Waziri, Saidu M.; Hamad, Esam Z.

doi:10.1021/ie060204+

Cited by 7 publications

(8 citation statements)

References 29 publications

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“…5, the constant c in eqn (8) must be in the range of 1 r c r 4. Apparently, eqn (8) degenerates into eqn (7) when c = 1. For many practical applications, m = 15-20 would be adequate if c is properly chosen.…”

Section: The Limiting Behavior Of Predicted Virial Coefficientsmentioning

confidence: 99%

“…The discussion in last section suggests that the contribution of higher-order terms not used in the truncated virial equation can be approximately described by adding a simple factor (1 À cZ) À1 (c Z 1) to the last term. The resulting EOS is has the form of eqn (8). By continuous use of the following relation…”

Section: Prediction Of Compressibility Factorsmentioning

confidence: 99%

“…1 For example, the hard sphere system can be present as stable fluid, metastable fluid, [2][3][4] solids (body-center or face-center cubic crystals), 3,5 glassy state, 6 and random close-packed state. 3,7,8 Similarly, the hard disk system also has several states, such as fluid, hexatic phase, 9 solid phase, 10,11 glassy state, 12 random jammed packing 7 or random close packing. 13 On the other hand, it is well accepted that the structural features of real systems are determined primarily by the repulsive intermolecular potential.…”

Section: Introductionmentioning

confidence: 99%

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High-order virial coefficients and equation of state for hard sphere and hard disk systems

2009

Phys. Chem. Chem. Phys.

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A very simple and accurate approach is proposed to predict the high-order virial coefficients of hard spheres and hard disks. In the approach, the nth virial coefficient B(n) is expressed as the sum of n(D-1) and a remainder, where D is the spatial dimension of the system. When n > or = 3, the remainders of the virials can be accurately expressed with Padé-type functions of n. The maximum deviations of predicted B(5)-B(10) for the two systems are only 0.0209%-0.0044% and 0.0390%-0.0525%, respectively, which are much better than the numerous existing approaches. The virial equation based on the predicted virials diverges when packing fraction eta = 1. With the predicted virials, the compressibility factors of hard sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to eta = 0.545. The compressibility factors of hard disk fluid can be predicted very accurately up to eta = 0.63. The simulated B(7) and B(10) for hard spheres are found to be inconsistent with the other known virials and therefore they are modified as 53.2467 and 105.042, respectively.

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Section: The Limiting Behavior Of Predicted Virial Coefficientsmentioning

confidence: 99%

Section: Prediction Of Compressibility Factorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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High-order virial coefficients and equation of state for hard sphere and hard disk systems

2009

Phys. Chem. Chem. Phys.

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“…Concentration-induced transitions are not limited to glass transitions and can also include liquid−liquid phase transitions and gel formation . Although such phase behavior can be sensitive to the details of the molecules, a basic understanding of the mechanisms associated with these transitions can be can be achieved from studies of hard-sphere systems. ,,− …”

Section: Introductionmentioning

confidence: 99%

“…In the case of binary mixtures of hard spheres of size ratio q , entropic effects alone can give rise to phase separation and gel formation when q is sufficiently small. ,− By contrast, for q sufficiently close to unity, systems can exhibit a simultaneous arrest of both phases or formation of a double glass. For these systems, mode coupling theory (MCT) has been used to determine values of the combined volume fraction, ϕ m , where the system transitions to a state where the dynamics are dominated by cooperative phenomena .…”

Section: Introductionmentioning

confidence: 99%

Molecular Mixture as an Effective Single-Component System

Larsen

Zukoski

2011

J. Phys. Chem. B

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Colloidal systems exhibit a dramatic slowdown in particle dynamics at high concentrations. The study of the concentration-induced glass transition in these systems has been greatly simplified by treating the colloidal phase as an effective single component in a viscous continuum. We seek to apply an effective single-component approach to molecular systems by investigating a material that also exhibits a dramatic slowdown as the relative concentration of two components change. Our system is a binary mixture of ethanol and citric acid, in which the size ratio of the particles is 0.7. We measure the temperature and concentration dependence of the self-diffusivity of both components using pulse-gradient NMR. We model our data with an elementary free volume model and show that the self-diffusivity of both components depends on the properties of an effective single component. The particle size of the effective single component is the number-averaged size of the two components. Our results demonstrate that mixtures can be used to study the effect of particle size on glassy dynamics and are therefore useful for understanding systems that are intermediate between molecular and colloidal.

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