Critical properties of molecular fluids from the virial series

MacDowell, Luis G.; Menduiña, C.; Vega, Carlos; Miguel, Enrique de

doi:10.1063/1.1622373

Cited by 18 publications

(12 citation statements)

References 36 publications

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“…It has been known for some time that the virial series is able to provide a good estimate for the critical temperature . The virial series has also been shown to predict values for the critical pressure that are very close to simulation data and experiments .…”

Section: Introductionmentioning

confidence: 61%

Critical isotherms from virial series using asymptotically consistent approximants

et al. 2014

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The low-density equation of state of a fluid along its critical isotherm is considered. An asymptotically consistent approximant is formed having the correct leading-order scaling behavior near the vapor-liquid critical point, while retaining the correct low-density behavior as expressed by the virial equation of state. The formulation is demonstrated for the Lennard-Jones fluid, and models for helium, water, and n-alkanes. The ability of the approximant to augment virial series predictions of critical properties is explored, both in conjunction with and in the absence of criticalproperty data obtained by other means. Given estimates of the critical point from molecular simulation or experiment, the approximant can refine the critical pressure or density by ensuring that the critical isotherm remains well-behaved from low density to the critical region. Alternatively, when applied in the absence of other data, the approximant remedies a consistent underestimation of the critical density when computed from the virial series alone. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 3336-3349, 2014 Keywords: virial equation of state, critical phenomena, crossover, approximant, Lennard-Jones P c . When solved using a sufficiently high-order virial series, these predictions for T c and P c are often close to simulation data and/or experiments, but those for q c are consistently about 10% too low in such a comparison. 4,8 Underestimation of the critical density by the virial series is connected to the nonclassical behavior of real fluids at the critical point, for which critical scaling laws assert that q c is a branch-point singularity of the function P(q) along the critical isotherm. In the context of critical phenomena, the molar In this section, critical isotherms are constructed using given values of the critical density q c , critical pressure P c , Values are given in Lennard-Jones units. Virial coefficients are from Schultz et al. 5 q c,AJ is the corrected critical density given by the smallest positive root of (7), which takes the following as inputs: d 5 4.789; P c , q c , and T c as predicted by the virial series at each order J (given above); and the corresponding virial coefficients (taken from an interpolation). Numbers in parentheses specify the 68% uncertainty on the last digit, propagated from uncertainty in the virial coefficients (with the exception of the simulation values). a Predicted using (7) with P c,sim , T c,sim , and the first seven virial coefficients taken at T c,sim (from an interpolation) as inputs.

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Section: Introductionmentioning

confidence: 61%

Critical isotherms from virial series using asymptotically consistent approximants

et al. 2014

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“…On the other hand, numerical integration based method is used by Vega and co-workers [21,22,24,25] to calculate second, third and fourth virial coefficients of the two-center Lennard-Jones molecules embedded with point quadrupole and dipole moments.…”

Section: Introductionmentioning

confidence: 99%

Virial coefficients of hard-core attractive Yukawa fluids

Naresh

Singh

2009

Fluid Phase Equilibria

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“…However, in implementing Eq. (8) the method of MacDowell et al, 32 was followed in that the molecular centers were embedded with hard spheres to avoid computer over°ow in evaluating the Boltzmann factor. Figure 6 compares a number of di®erent corrections to the classical second volumetric virial coe±cient of nitrogen.…”

Section: Resultsmentioning

confidence: 99%

Virial coefficients of nitrogen from a quadrupolar site–site potential function

Monago

Otobrise

2016

J. Theor. Comput. Chem.

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This work describes a procedure for the numerical calculation of third virial coe±cients of simple linear molecules. The method is applied to nitrogen using a site-site model pair-potential and the triple dipole term. Values of volumetric and acoustic second and third virial coe±cients of nitrogen are reported over a wide range of temperature and compared with experimental data of several authors. The e®ect of including the quadrupole-quadrupole energy to the pair potential is investigated and the results suggest that the contributions of the quadrupole moment to second and third virial coe±cients are non-negligible at low temperatures.

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Critical properties of molecular fluids from the virial series

Cited by 18 publications

References 36 publications

Critical isotherms from virial series using asymptotically consistent approximants

Critical isotherms from virial series using asymptotically consistent approximants

Virial coefficients of hard-core attractive Yukawa fluids

Virial coefficients of nitrogen from a quadrupolar site–site potential function

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