Linear hard sphere models Virial coefficients and equation of state

Vega, Carlos; Lago, S.; Garzón, B.

doi:10.1080/00268979400100874

Cited by 26 publications

(27 citation statements)

References 41 publications

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“…In practice, this extrapolation is carried out using Padé approximants, which reproduce the first few virial coefficients of the isotropic fluid. [36][37][38] The virial coefficients of the HGO fluid have been computed numerically up to the fifth order 39 for a number of elongations ranging from ϭ1.5 to ϭ10. The form considered for the compressibility factor is usually…”

Section: Choice Of Reference Isotropic Fluidmentioning

confidence: 99%

The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation

Padilla¹,

Velasco²

1997

The Journal of Chemical Physics

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The isotropic-nematic phase transition in a fluid of moderately long molecules interacting via a hard Gaussian overlap potential is studied using the decoupling approximation and computer simulation. Molecules of length-to-breadth ratios equal to 3 and 5, thought to set the relevant range of molecular elongations in real nematic liquid crystals, are considered. The results of the theory ͑pressure, order parameter, and location of the phase transition͒ and of several of its extensions, are compared with those from computer simulation, and their relative accuracy assessed. We first study the standard decoupling approximation, a resummed Onsager virial expansion where only the ͑exact͒ second virial coefficient, B 2 , is retained, and consider two different mappings to perform the resummation: a fluid of equivalent hard spheres and the isotropic phase of the hard Gaussian overlap fluid. Whereas the former mapping predicts a phase transition already in qualitative agreement with simulation, the mapping to the isotropic phase predicts a transition in closer agreement with the simulation result, shifting the location of the transition to lower pressures. However, the transition is overestimated in both cases, which seems to indicate a poor representation of angular correlations. In order to incorporate higher-order correlations, an approximate method is proposed to evaluate the B 3 and B 4 virial coefficients in the nematic phase numerically. This new information allows us to address two points: ͑i͒ the convergence of the virial series for short molecules, and ͑ii͒ the performance of extended decoupling approximation theories, incorporating the third and the fourth virial coefficients. As expected, inclusion of the high-order virial coefficients improves the results of the corresponding truncated virial expansion for the largest elongation considered, and provides quantitative agreement with the simulations, indicating a fast convergence of the virial series. The standard decoupling approximation provides results of similar accuracy. Also, the extended decoupling approximation including B 3 improves these results, though the extension to B 4 degrades the coexistence data slightly, which might indicate that the latter misrepresents to some extent the importance of angular correlations. In contrast, for molecules with a length-to-breadth ratio of 3, the truncated virial expansion is still inaccurate, whereas the extended decoupling approximation theories perform better, providing almost quantitative agreement with the simulations. As a result of our findings, we conclude that in order to improve the standard decoupling approximation for fluids of short molecules, it is essential to resum the virial series using knowledge of the B 3 virial coefficient and also the B 4 coefficient for the shortest molecules forming nematic phases. © 1997 American Institute of Physics. ͓S0021-9606͑97͒50524-1͔

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Section: Choice Of Reference Isotropic Fluidmentioning

confidence: 99%

The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation

Padilla¹,

Velasco²

1997

The Journal of Chemical Physics

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“…(5) to calculate the (isotropic) second virial coefficient of hard linear tangent sphere chains of chain length ranging from 2 to 10, one finds a near exact agreement (deviation at worst 0.02%) with Monte Carlo data. 40,42 To extend Eq. (12) to rod-coil molecules, it is instructive to examine the behavior of the excluded volume as a function of the rigidity parameter χ R .…”

Section: A Pure Componentsmentioning

confidence: 99%

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Westen

Vlugt

Groß

2012

The Journal of Chemical Physics

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Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin (γ ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].

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“…The solid lines represent generalized Flory-dimer predictions; the points represent Monte Carlo results 44. …”

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Equations of State and Virial Coefficients for Rigid Linear Chains

and

Honnell

1996

J. Phys. Chem.

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The study of isotropic-nematic phase transition in a system of rodlike molecules requires an accurate equation of state for the isotropic phase. In this paper, generalized Flory-dimer (GF-D) theory is extended to fluids composed of rigid linear chains, and its predictions of the compressibility factor and virial coefficients are compared with simulation results available in the literature. A simplified equation of state is derived which eliminates the need to evaluate exclusion volumes. Compressibility factor predictions for linear tangent hardsphere (LTHS) trimers, linear fused hard-sphere (LFHS) trimers, LTHS tetramers, and planar T-and Y-shaped tangent hard-sphere tetramers are in excellent agreement with simulation results. For LFHS 6-mers and 8-mers, with the ratio of bond length l to hard-sphere diameter d of 0.5, GF-D predictions are in good agreement with simulation results only for volume fractions less than about 0.4. At higher densities, GF-D theory first underpredicts and then slightly overpredicts the compressibility factor for both LFHS 6-mers and 8-mers. However, the modified Wertheim equation of state overpredicts the compressibility factor over the entire density range for these fluids. For LFHS 8-mers (l/d ) 0.6), the agreement between GF-D predictions and simulation results is good only up to a volume fraction of about 0.33, after which the theory overpredicts the compressibility factor. This breakdown is attributed to an isotropic-nematic phase transition. Examination of the virial coefficients for LTHS chains and LFHS (l/d ) 0.5) chains reveals that GF-D theory benefits from a cancellation of errors caused by overprediction and underprediction of the individual virial coefficients.

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Linear hard sphere models Virial coefficients and equation of state

Cited by 26 publications

References 41 publications

The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation

The isotropic–nematic transition for the hard Gaussian overlap fluid: Testing the decoupling approximation

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Equations of State and Virial Coefficients for Rigid Linear Chains

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