Equation of state for the Lennard–Jones fluid based on the perturbation theory

Betancourt-Cárdenas, Felix F.; Galicia‐Luna, Luis A.; Sandler, Stanley I.

doi:10.1016/j.fluid.2007.11.015

Cited by 19 publications

(30 citation statements)

References 49 publications

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“…The approximations inherent in Eqs. (13) and (14) have also been employed recently by Betancourt-Cardenas et al 91 to derive the perturbation terms in the Helmholtz energy expansion of the LJ fluid; this explains in part why these authors find discrepancies between their simulation data for the perturbation terms and the original values of Smith et al 92 An exact evaluation of the second-order term a 2 (fluctuation contribution) is much more difficult as it requires a knowledge of two-, three-, and four-body correlation functions of the reference system. 92 When the superposition approximation is used to evaluate the three-and four-body functions, the integrals may be evaluated numerically.…”

Section: New Saft-vr Mie Formulationmentioning

confidence: 99%

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

Lafitte

Apostolakou

Avendaño

et al. 2013

The Journal of Chemical Physics

437

735

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Section: New Saft-vr Mie Formulationmentioning

confidence: 99%

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

Lafitte

Apostolakou

Avendaño

et al. 2013

The Journal of Chemical Physics

437

735

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“…Betancourt-Cárdenas et al have proposed an equation of state for the LJ fluid based on a second order perturbation scheme for the excess free energy of the system at the same temperature and density as the ideal gas. 41 They then fit the free energy to a power series in the bulk volume fraction of the LJ fluid defined by the temperature-dependent effective hard-core diameter. We have used their results for the free energy of the LJ fluid including the first order perturbation.…”

Section: Theorymentioning

confidence: 99%

Structure of solvent-free grafted nanoparticles: Molecular dynamics and density-functional theory

Chremos

Panagiotopoulos

et al. 2011

The Journal of Chemical Physics

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The structure of solvent-free oligomer-grafted nanoparticles has been investigated using molecular dynamics simulations and density-functional theory. At low temperatures and moderate to high oligomer lengths, the qualitative features of the core particle pair probability, structure factor, and the oligomer brush configuration obtained from the simulations can be explained by a density-functional theory that incorporates the configurational entropy of the space-filling oligomers. In particular, the structure factor at small wave numbers attains a value much smaller than the corresponding hardsphere suspension, the first peak of the pair distribution function is enhanced due to entropic attractions among the particles, and the oligomer brush expands with decreasing particle volume fraction to fill the interstitial space. At higher temperatures, the simulations reveal effects that differ from the theory and are likely caused by steric repulsions of the expanded corona chains.

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“…Obviously, such empirical or semi-empirical approaches, beside to require a lot of experimental [1,2] or simulation data [5,6], forbidden molecular interpretation of results. On the other hand, theoretically based EOSs are very general and applicable for the entire family of systems obeying the given interparticle potential model [7,8,9,10,11,12,13,14,15,16].The most apparent progress toward EOS was made by applying principles of statistical mechanics. Integral equation [10,11], thermodynamic perturbation [9,12,13,14,15,16], and mean field theories [17] are the most common theoretical approaches to develop analytical EOS for simple fluids.…”

mentioning

confidence: 99%

“…On the other hand, theoretically based EOSs are very general and applicable for the entire family of systems obeying the given interparticle potential model [7,8,9,10,11,12,13,14,15,16].…”

mentioning

confidence: 99%

New criteria for the equation of state development: Simple model fluids

Duda¹,

Orea²

2008

Fluid Phase Equilibria

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Recently we have proposed (J. Chem. Phys. 128 (2008) 134508) a new rescaling of fluid density ρ by its critical value ρ 2/3 c to apply the corresponding states law for the attractive Yukawa fluids study. Analysis of precise simulation results allows us to generalize this concept to the case of simple fluids with different interparticle interactions, like Mie (n,m) and Sutherland pair potentials. It is shown, that there is a linear relationship between the critical pressure and critical temperature, as well as the critical density and inverse critical temperature for these frequently used pair potentials. As a consequence, the critical compressibility factor of these model fluids is close to its universal value measured experimentally for different real substances. PACS numbers:Equation of state (EOS) is of crucial importance to predict or correlate fluid thermodynamic properties [1,2,3]. Since van der Waals proposed the first version of his EOS [4], many modifications have been proposed, and today, there are numerous more accurate EOSs reported in the literature for describing the behavior of simple fluids and fluid mixtures. An improvement in the accuracy of analytical EOSs for the modeling of experimental data of real fluids is usually achieved, not by improving theoretical base, but by introducing empirical temperature functionalities in their parameters. Obviously, such empirical or semi-empirical approaches, beside to require a lot of experimental [1,2] or simulation data [5,6], forbidden molecular interpretation of results. On the other hand, theoretically based EOSs are very general and applicable for the entire family of systems obeying the given interparticle potential model [7,8,9,10,11,12,13,14,15,16].The most apparent progress toward EOS was made by applying principles of statistical mechanics. Integral equation [10,11], thermodynamic perturbation [9,12,13,14,15,16], and mean field theories [17] are the most common theoretical approaches to develop analytical EOS for simple fluids. The advantage of theoretically based EOS over their empirical counterparts is that they can be further improved by testing against computer simulations and later be used as a reference for perturbation theory calculations of bulk and interfacial properties of more complex fluids such as polymers and associating systems (i.e., hydrogen-bonding fluids) [18,19,20,21,22,23].Although last decades significant progress has been achieved in the development of theoretically based expressions for EOS, there is still a lack of equations that described PVT properties of simple fluids in wide range of thermodynamic parameters. Such precise analytical expression may be obtained if one has a set of universal criteria (as for example, corresponding states law [24,25,26]) or/and apply self-consistent integral equations [27].Recently, we have applied the corresponding states law for the hard core attractive Yukawa (HAY) fluid [26], and revealed that after a certain rescaling of fluid number density ρ the reduced surface tension and pressur...

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Equation of state for the Lennard–Jones fluid based on the perturbation theory

Cited by 19 publications

References 49 publications

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

Accurate statistical associating fluid theory for chain molecules formed from Mie segments

Structure of solvent-free grafted nanoparticles: Molecular dynamics and density-functional theory

New criteria for the equation of state development: Simple model fluids

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