Equation of state of a multicomponent<i>d</i>-dimensional hard-sphere fluid

Santos, Andrés; Yuste, S. B.; Haro, M. López de

doi:10.1080/00268979909482932

Cited by 69 publications

(103 citation statements)

References 16 publications

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“…There are several modified equations of state for multi-component mixtures in the literature, which require the knowledge of the equation of state for a one-component system [155]. First, we consider Santos et al's equation of state, based on the Carnahan-Starling equation of state: …”

Section: Polydisperse Systemsmentioning

confidence: 99%

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Microstructure and macroscopic properties of polydisperse systems of hard spheres

Ogarko¹

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Section: Polydisperse Systemsmentioning

confidence: 99%

“…There exists no unique equation of state, valid for the intermediate densities, where the system changes from the disordered to the ordered state, since the system displays hysteresis and rate-dependence; for various theoretical approaches see Refs. [116,[151][152][153][154][155][156][157][158][159][160] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Microstructure and macroscopic properties of polydisperse systems of hard spheres

Ogarko¹

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“…The comparison with other EOS for the mixture available in the literature indicated that their proposal does the best job with respect to the Monte Carlo data. Among these other EOS for the binary mixture, only the one introduced by us a few years ago [3] also shares with Barrio and Solana's EOS the fact that it may be expessed in terms of the EOS for a single component system. What we want to point out here is that the comparison made in Ref.…”

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confidence: 99%

“…The EOS for the mixture, consistent with a given EOS for a single component system that we introduced recently reads [3] …”

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Equation of state of additive hard-disk fluid mixtures: A critical analysis of two recent proposals

2002

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A flaw in the comparison between two different theoretical equations of state for a binary mixture of additive hard disks and Monte Carlo results, as recently reported in C. Barrio and J. R. Solana, Phys. Rev. E 63, 011201 (2001), is pointed out. It is found that both proposals, which require the equation of state of the single component system as input, lead to comparable accuracy but the one advocated by us [A. Santos, S. B. Yuste, and M. López de Haro, Mol. Phys. 96, 1 (1999)] is simpler and complies with the exact limit in which the small disks are point particles.In a recent paper, Barrio and Solana [1] proposed an equation of state (EOS) for a binary mixture of additive hard disks. Such an equation reproduces the (known) exact second and third virial coefficients of the mixture and may be expressed in terms of the EOS of a single component system. They also performed Monte Carlo simulations and found that their recipe was very accurate provided an accurate EOS for the single component system (in their case it was the EOS proposed by Woodcock [2]) was taken as input. The comparison with other EOS for the mixture available in the literature indicated that their proposal does the best job with respect to the Monte Carlo data. Among these other EOS for the binary mixture, only the one introduced by us a few years ago [3] also shares with Barrio and Solana's EOS the fact that it may be expessed in terms of the EOS for a single component system. What we want to point out here is that the comparison made in Ref.[1] is flawed by the fact that it was not performed by taking the same EOS for the single component system in both proposals.Let us consider a binary mixture of additive hard disks of diameters σ 1 and σ 2 . The total number density is ρ, the mole fractions are x 1 and x 2 = 1 − x 1 , and the packing fraction is η = π 4 ρ σ 2 , where σ n ≡ 2 i=1 x i σ n i . Let Z = p/ρk B T denote the compressibility factor, p being the pressure, T the absolute temperature, and k B the Boltzmann constant. Then, Barrio and Solana's EOS for a binary mixture of hard disks, Z BS m (η), may be written in terms of a given EOS for a single component system, Z s (η), aswhere ξ ≡ σ 2 / σ 2 and β is adjusted as to reproduce the exact third virial coefficient for the mixture B 3 , namely β = B 3 (π/4) 2 σ 2 2 (1 + ξ) − b 3 2 .Here, b 3 = 4(4/3 − √ 3/π) is the reduced third virial coefficient for the single component system while B 3 is given by [4]

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Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

Haro

Yuste

Santos

2008

Theory and Simulation of Hard-Sphere Fluids and Related Systems

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An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically consistent formulation, thus improving and extending the known analytical results of the Percus-Yevick theory. Approximate expressions for the contact values of the radial distribution functions and the corresponding analytical equations of state are also discussed. Extensions of this methodology to related systems, such as sticky hard spheres and squarewell fluids, as well as its use in connection with the perturbation theory of fluids are briefly addressed.

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Equation of state of a multicomponentd-dimensional hard-sphere fluid

Cited by 69 publications

References 16 publications

Microstructure and macroscopic properties of polydisperse systems of hard spheres

Microstructure and macroscopic properties of polydisperse systems of hard spheres

Equation of state of additive hard-disk fluid mixtures: A critical analysis of two recent proposals

Alternative Approaches to the Equilibrium Properties of Hard-Sphere Liquids

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