Third virial coefficient of nonpolar gases from accurate binary potentials and ternary forces

Abstract

An explicit model for the third virial coefficient C(T) is presented, based on accurate binary interactions plus three-body forces; its predictions are compared to experimental data for 15 fluids (argon, krypton, xenon, nitrogen, oxygen, fluorine, carbon monoxide, carbon dioxide, perfluoromethane, methane, ethene, ethane, propane, n-butane, and n-pentane). Three-body interactions are represented by the Axilrod–Teller–Muto (ATM) triple-dipole potential, while the binary potential profile is systematically varied using approximate non-conformal (ANC) potentials. Non-conformality affects significantly both two- and three-body contributions to C(T). A formula for C(T) of ANC+ATM systems is obtained in terms of all interaction parameters; the three-body contribution is proportional to the parameter ν of the ATM potential while its temperature dependence is proportional to that of a reference fluid (argon). The ANC+ATM model reproduces C(T) within experimental error for most of the fluids considered, with a small negative deviation in some cases, which may be ascribed to the need of a complement to the ATM term.

Ab initio development of generalized Lennard-Jones (Mie) force fields for predictions of thermodynamic properties in advanced molecular-based SAFT equations of state

“…where rij is the center-of-mass distance between species i and j, γ i , γ j , and γ k are the interior angles of the triangle formed by the three species i, j and k, respectively, and ν is referred to as the AT coefficient; this denotes the magnitude of the three-body interactions. They are available a priori for a range of species; in our work, these were obtained either from ab initio calculations 82,83 (in the case of noble gases) or estimated from third virial coefficients 84 (in the case of methane). We note that the AT coefficient for methane and other molecular species can also be obtained from ab initio calculations, e.g., Hellmann obtained the AT coefficient for carbon dioxide in this manner.…”

“…53 Although both types 13 ) using experimental data, by mapping potentials determined by Hellmann and co-workers, 44 and by mapping ab initio DLPNO-CCSD(T)/TZ (QC) calculations; these mapped potentials denoted by the suffix "-Mie." The AT coefficient, ν, is taken from the literature; 84 the cell relating to the AT coefficient is left blank when the AT correction is not employed. of simulations for thermodynamic properties of helium have been carried out by Sesé, 101,102 these were performed for thermodynamic states at much higher density than those considered in our current work.…”

Ecuación de estado virial de esferas suaves

“…En esta etapa del proyecto se eligió la construcción de una EDE virial para el sistema de esferas suaves ANC, debido a los antecedentes que se tiene de los potenciales ANC ( [2], [3], [4], [5], [6]). La importancia de la EDE virial es que tiene una fundamentación teórica rigurosa de la mecánica estadística, que provee relaciones entre los coeficientes viriales y las interacciones entre las moléculas.…”

“…Por otra parte, existen ecuaciones de estado para sistemas repulsivos tales como: las esferas suaves WCA, Lennard-Jones repulsivo, que se usan como sistema de referencia pero no explora el efecto de la no conformalidad; las esferas suaves de potencia inversa, donde sí se estudia la no conformalidad de los potenciales y pueden usarse como sistemas de referencia [32]. Ahora bien, en las esferas suaves ANC se estudia el efecto de la no conformalidad de los potenciales y además, debido a los antecedentes de los potenciales ANC ( [2], [3], [4], [5], [6]), son una buena opción como sistema de referencia en la teoría de perturbaciones.…”

“…Los potenciales ANC han mostrado que son capaces de reproducir, dentro del error experimental, propiedades termodinámicas de más de sesenta sustancias en la fase gaseosa. En específico, el segundo y tercer coeficiente virial de sustancias puras y algunas de sus mezclas ( [2], [3], [4], [5], [6]). Así pues, si se quiere construir una EDE para los sistemas ANC, un camino es obtener antes la EDE de las esferas suaves ANC.…”