An Equation of State for Real Fluids Based on the Lennard-Jones Potential

Sun, Tongfan; Teja, Amyn S.

doi:10.1021/jp9620476

Cited by 61 publications

(67 citation statements)

References 14 publications

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“…Comprehensive data of the higher virial coefficients over a wide range of temperatures is available only for simple atomic fluids, such as the square well, 6 and the Lennard-Jones. [7][8][9] For molecular fluids, however, only a few calculations of the third virial coefficients have been reported, [10][11][12][13] and very few less, if any, for higher order coefficients. Despite this lack of knowledge, the virial series of simple molecular fluids has attracted much attention recently.…”

Section: Introductionmentioning

confidence: 99%

Critical properties of molecular fluids from the virial series

MacDowell

Menduiña

Vega

et al. 2003

The Journal of Chemical Physics

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We present results for the fourth virial coefficient of quadrupolar Lennard-Jones diatomics for several quadrupole moments and elongations. The coefficients are employed to predict the critical properties from two different truncated virial series. The first one employs the exact second and third virial coefficients, calculated in our previous work. The second includes also the exact fourth virial coefficient as obtained in this work. It is found that the first method yields already fairly good predictions. The second method significantly improves on the first one, however, yielding good results for both the critical temperature and pressure. Particularly, when compared with predictions from perturbation theories available in the literature, the virial series to fourth order compares favorably for the critical temperature. The results suggest that the failure of perturbation theories to predict the critical temperature and pressure is not only related to the neglect of density fluctuations, but also to poor prediction of the virial coefficients.

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Section: Introductionmentioning

confidence: 99%

Critical properties of molecular fluids from the virial series

MacDowell

Menduiña

Vega

et al. 2003

The Journal of Chemical Physics

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“…This method has been applied more recently by Sun and Teja [11]. This method yielded results for the Lennard-Jones uid up to ®fth order in density.…”

Section: Introductionmentioning

confidence: 99%

“…This potential form has been seen in quite a large body of computational studies, and thus its properties are well known [3]. Another aspect of the LennardJones potential which makes it useful for this calculation is that it has been used for our purpose before by Barker and coworkers [6,7] and by Sun and Teja [11].…”

Section: Introductionmentioning

confidence: 99%

“…2 we show the formalism which we use to relate the radial distribution function, the integral equations, and the virial coecients. We outline the method used to calculate the bridge diagram, give a brief description of the analytic expansion of the virial coecients as used by Rowlinson [12], Barker and coworkers [6,7,8], and Sun and Teja [11] and conclude the section with a brief discussion of the equivalence of the two methods. Section 3 gives the results from our calculation, as well as a comparison of our results with those in the literature.…”

Section: Introductionmentioning

confidence: 99%

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A reexamination of virial coefficients of the Lennard-Jones fluid

Dyer

Perkyns

Pettitt

2001

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

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The fourth-order virial coecients have been calculated exactly to ®ve decimal places for pure¯uids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more signi®cance than was thought from previous studies, especially in the low-temperature range. This result was con®rmed by direct evaluation of the diagrams which construct the virial coecients, as given by Rowlinson, Barker, and coworkers. This calculation con®rmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These dierences, though minor at higher temperatures, can be seen to be more signi®cant at the lower temperature ranges.

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“…One is determined by Johnson et al [19] and the other by Sun and Teja [20]. These equations are determined by fitting procedure to the molecular simulation results.…”

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Monte Carlo simulations in multibaric–multithermal ensemble

Okumura

Okamoto

2004

Chemical Physics Letters

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We propose a new generalized-ensemble algorithm, which we refer to as the multibaricmultithermal Monte Carlo method. The multibaric-multithermal Monte Carlo simulations perform random walks widely both in volume space and in potential energy space. From only one simulation run, one can calculate isobaric-isothermal-ensemble averages at any pressure and any temperature. We test the effectiveness of this algorithm by applying it to the Lennard-Jones 12-6 potential system with 500 particles. It is found that a single simulation of the new method indeed gives accurate average quantities in isobaric-isothermal ensemble for a wide range of pressure and temperature.PACS numbers: 64.70. Fx, 02.70.Ns, 47.55.Dz Monte Carlo (MC) algorithm is one of the most widely used methods of computational physics. In order to realize desired statistical ensembles, corresponding MC techniques have been proposed [1,2,3,4,5]. The first MC simulation was performed in the canonical ensemble in 1953 [1]. This method is called the Metropolis algorithm and widely used. The canonical probability distribution P N V T (E) for potential energy E is given by the product of the density of states n(E) and the Boltzmann weight factor e −β0E :where β 0 is the inverse of the product of the Boltzmann constant k B and temperature T 0 at which simulations are performed. Since n(E) is a rapidly increasing function and the Boltzmann factor decreases exponentially, P N V T (E) is a bell-shaped distribution. The isobaric-isothermal MC simulation [2] is also extensively used. This is because most experiments are carried out under the constant pressure and constant temperature conditions. Both potential energy E and volume V fluctuate in this ensemble. The distribution P N P T (E, V ) for E and V is given byHere, the density of states n(E, V ) is given as a function of both E and V , and H is the "enthalpy":where P 0 is the pressure at which simulations are performed. This ensemble has bell-shaped distributions in both E and V . Besides the above physical ensembles, it is now almost a default to simulate in artificial, generalized ensembles so that the multiple-minima problem, or the broken ergodicity problem, in complex systems can be overcome (for a recent review, see Ref.[6]). The multicanonical algorithm [7,8] is one of the most well known such methods in generalized ensemble. In multicanonical ensemble, a non-Boltzmann weight factor W mc (E) is used. This multicanonical weight factor is characterized by a flat probability distribution P mc (E):and thus a free random walk is realized in the potential energy space. This enables the simulation to escape from any local-minimum-energy state and to sample the configurational space more widely than the conventional canonical MC algorithm. Another advantage is that one can obtain various canonical ensemble averages at any temperature from a * Electronic address: hokumura@ims.ac.jp † Electronic address: okamotoy@ims.ac.jp

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An Equation of State for Real Fluids Based on the Lennard-Jones Potential

Cited by 61 publications

References 14 publications

Critical properties of molecular fluids from the virial series

Critical properties of molecular fluids from the virial series

A reexamination of virial coefficients of the Lennard-Jones fluid

Monte Carlo simulations in multibaric–multithermal ensemble

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