Percus-Yevick integral equation theory for athermal hard-sphere chains.

Chiew, Yee C.

doi:10.1080/00268979100101251

Cited by 139 publications

(75 citation statements)

References 14 publications

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“…The perturbed hard-sphere-chain (PHSC) equation of state uses the modified Chiew equation of state for hard-sphere chains (Chiew, 1990;Song, et aI., 1993a) as the reference system, a van der Waals type perturbation term and the Song-Mason method (Song and Mason, 1989) 18 Table I. Pair potential parameters used to determine universal functions in Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…A particularly elegant, yet simple, method has been presented by Chiew (1990) who solved the Percus-Yevick integral equation coupled with chain connectivity for hard-sphere chains and mixtures. Analytical equations of state were obtained.…”

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confidence: 99%

“…There have been many attempts to develop analytical equations of state for molecular fluids from statistical-mechanical theories; a few examples include the generalized van der Waals , equations (Rigby, 1972;Svejda and Kohler, 1983), the chain-of-rotators equation (Chien, et al, 1978), the perturbed-hard-chain equation (Beret and Prausnitz,1975b;Donohue and Prausnitz, 1978), and the statistical-mechanical perturbation equations (Song and Mason, 1989;1990;Sowers and Sandler, 1992). Although many of the details are different, these theoretically-based equations of state share a common premise first suggested by van der Waals over one hundred years ago, namely, that the structure of a molecular fluid is determined primarily by repulsive forces; therefore, fluids of athermal hard bodies (spherical or non-spherical) can serve as useful reference systems.…”

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confidence: 99%

“…When comparing the above equations of state, Rodgers (1993) notes that the LF EOS and the Flory EOS provide the least accurate correlation of polymer pVT properties. 2 During the last 10 years, there has been increased interest in developing analytical EOS for fluids with chain-like molecules based on a relatively simple model: athermal hard-sphere chains, where a chain molecule is modeled by a series of freely-jointed tangent hard spheres (Boublik, 1989;Boublik, et al, 1990;Chapman, et aI., 1988;Chiew, 1990;Dickman and Hall, 1986;Honnell and Hall, 1989;Wertheim, 1987). A hard-sphere chain EOS can be used as the reference system in place of the hard-sphere reference used in most equations of state for simple spherical fluids.…”

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confidence: 99%

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A Perturbed Hard-Sphere-Chain Equation of State for Normal Fluids and Polymers

Song¹,

Lambert²,

Prausnitz³

1994

Ind. Eng. Chem. Res.

195

181

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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A Perturbed Hard-Sphere-Chain Equation of State for Normal Fluids and Polymers

Song¹,

Lambert²,

Prausnitz³

1994

Ind. Eng. Chem. Res.

195

181

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“…Firstly, it requires analytical expressions for the pair correlation functions of the hard-chain fluid that are reliable over the entire range of density and chain length parameter. These expressions can be obtained from integral-equation theories for monomers and short chains 40,41,42,43,44 . However, because of non-trivial correlations due to excluded volume effects, such expressions become less accurate for long chains and polymers, where for instance m can be of order 10 3 and larger.…”

Section: B Attractive Interactionsmentioning

confidence: 99%

A global investigation of phase equilibria using the perturbed-chain statistical-associating-fluid-theory approach

Yelash

Müller

Paul

et al. 2005

The Journal of Chemical Physics

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The recently developed Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) is investigated for a wide range of model parameters including the parameter m representing the chain length and the thermodynamic temperature T and pressure p. This approach is based upon the first-order thermodynamic perturbation theory for chain molecules developed by Wertheim [ M.S. Wertheim, J. Stat. Phys. 35, 19-46 (1984); ibid. 42, 459-492 (1986) Chem. Phys. 47, 4714 (1967)]. We systematically study a hierarchy of models which are based on the PC-SAFT approach using analytical model calculations and Monte Carlo simulations. For one-component systems we find that the analytical model in contrast to the simulation results exhibits two phase-separation regions in addition to the common gas-liquid coexistence region: One phase separation occurs at high density and low temperature. The second demixing takes place at low density and high temperature where usually the ideal gas phase is expected in the phase diagram. These phenomena, which are referred to as "liquid-liquid" and "gas-gas" equilibria, give rise to multiple critical points in one-component systems, as well as to critical end points (CEP) and equilibria of three fluid phases, which can usually be found in multicomponent mixtures only. Furthermore, it is shown that the "liquid-liquid" demixing in this model is not a consequence of a "softened" repulsive interaction as assumed in the theoretical derivation of the model. Experimental data for the melt density of polybutadiene with molecular mass M w = 45000 g/mol are correlated here using the PC-SAFT equation. It is shown that the discrepancies in modeling the polymer density at ambient temperature and high pressure can be traced back to the "liquid-liquid" phase separation predicted by the equation of state at low temperatures. This investigation provides a basis for understanding possible inaccuracies or even unexpected phase behavior which can occur in engineering applications of the PC-SAFT model aiming at predicting properties of macromolecular substances.

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