The critical temperature and properties of real gas from low order perturbed virial expansions

Krejčí, Jan; Nezbeda, Ivó

doi:10.1016/j.fluid.2011.10.005

Cited by 9 publications

(5 citation statements)

References 32 publications

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“…Two thermodynamic theories have been tested: the "perturbed virial expansion" of Nezbeda and co-workers [35][36][37], which in the present case is based on the difference between the virial expansions of hard spheres and dipolar hard spheres (truncated at the third virial coefficient); and the "logarithmic free energy" theory of the current authors, in which the virial expansion of the Helmholtz free energy is resummed in to a logarithmic form. For λ 2 it was shown that the logarithmic free energy theory is superior.…”

Section: Discussionmentioning

confidence: 99%

“…Numerical results are obtained using the Mayer-sampling method introduced by Singh and Kofke [34]. Next, the analytical results are incorporated in to various virial-type expressions for the thermodynamic functions, including the so-called perturbed virial expansion (PVE) developed by Nezbeda and co-workers [35][36][37], and the present authors' LFE theory [24]. The theoretical results for the equation of state are compared critically against Monte Carlo (MC) simulation results, and it is demonstrated that the LFE theory is superior for DHSs in an applied magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamics of ferrofluids in applied magnetic fields

2013

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The thermodynamic properties of ferrofluids in applied magnetic fields are examined using theory and computer simulation. The dipolar hard sphere model is used. The second and third virial coefficients (B 2 and B 3 ) are evaluated as functions of the dipolar coupling constant λ, and the Langevin parameter α. The formula for B 3 for a system in an applied field is different from that in the zero-field case, and a derivation is presented. The formulas are compared to results from Mayer-sampling calculations, and the trends with increasing λ and α are examined. Very good agreement between theory and computation is demonstrated for the realistic values λ 2. The analytical formulas for the virial coefficients are incorporated in to various forms of virial expansion, designed to minimize the effects of truncation. The theoretical results for the equation of state are compared against results from Monte Carlo simulations. In all cases, the so-called logarithmic free energy theory is seen to be superior. In this theory, the virial expansion of the Helmholtz free energy is re-summed in to a logarithmic function. Its success is due to the approximate representation of high-order terms in the virial expansion, while retaining the exact low-concentration behavior. The theory also yields the magnetization, and a comparison with simulation results and a competing modified mean-field theory shows excellent agreement. Finally, the putative field-dependent critical parameters for the condensation transition are obtained and compared against existing simulation results for the Stockmayer fluid. Dipolar hard spheres do not undergo the transition, but the presence of isotropic attractions, as in the Stockmayer fluid, gives rise to condensation even in zero field. A comparison of the relative changes in critical parameters with increasing field strength shows excellent agreement between theory and simulation, showing that the theoretical treatment of the dipolar interactions is robust.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermodynamics of ferrofluids in applied magnetic fields

2013

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“…2-Yukawa and EXP6 fluids give an estimate of the critical temperature obtained using the common virial expansion and the perturbed virial expansion of the 2nd order [13,14]; in the perturbed expansion we used the fluid of hard spheres of diameter σ as the reference. As we see, the perturbed method provides a very good estimate which further confirms its superiority over the common virial expansion.…”

Section: -5mentioning

confidence: 99%

Virial coefficients and vapor-liquid equilibria of the EXP6 and 2-Yukawa fluids

Krejčí¹,

Nezbeda²,

Melnyk³

et al. 2011

Condens. Matter Phys.

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“…Ghatee et al 43 predicted the T c of ionic liquids from surface tension at liquid−vapor equilibrium and developed a correlation of T c with the interaction energy. Nezbeda estimated the T c by the second virial coefficient 44 and low order perturbed virial expansions; 45 both of the results were superior to the common virial expansion. In addition, the Gibbs ensemble Monte Carlo (GEMC) simulations, the Wang−Landau simulations, and the grand canonical ensemble were also used to estimate the T c by Nath, 46 Desgranges, 47 and Lai 48 (and their co-workers), respectively.…”

Section: ■ Introductionmentioning

confidence: 99%

The New Method for Correlation and Prediction of Thermophysical Properties of Fluids. Critical Temperature

Zuo²,

et al. 2017

J. Chem. Eng. Data

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On the basis of the linear free energy relationships theory and thermodynamics formulas, a new method predicting critical temperature (T c) of pure fluids is proposed for the first time. Sixteen homologues of 616 substances have been regressed and correlation equations between T c and molecular descriptors are obtained. The mean relative deviations of the 16 equations are from 0.01% to 2.73%, and most of them are under 2%. In addition, the squared correlation coefficients are from 0.90 to 0.98. Moreover, the equations are tested through cross-validation by the leave-one-out procedure and most of the squared correlation coefficients are greater than 0.90. The results reveal that the equations exhibit better effect with simple form of equation, high prediction accuracy, and definitude theory meaning. This study successfully combines macroscopic physical properties of fluids with their molecular microstructure and breaks through the experimental or theoretical application scope, perfecting calculation of critical temperature for pure liquids.

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The critical temperature and properties of real gas from low order perturbed virial expansions

Cited by 9 publications

References 32 publications

Thermodynamics of ferrofluids in applied magnetic fields

Thermodynamics of ferrofluids in applied magnetic fields

Virial coefficients and vapor-liquid equilibria of the EXP6 and 2-Yukawa fluids

The New Method for Correlation and Prediction of Thermophysical Properties of Fluids. Critical Temperature

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