Generalization of the van der Waals Equation

Abstract

The generalized van der Waals equation of state for anisotropic liquids in porous media consists of two terms. One of them is based on the equation of state for hard spherocylinders in random porous media obtained from the scaled particle theory. The second term is expressed in terms of the mean value of attractive intermolecular interactions. The obtained equation is used for the investigation of the gas-liquid-nematic phase behavior of a molecular system depending on the anisotropy of molecule shapes, anisotropy of attractive intermolecular interactions, and porosity of a porous medium. It is shown that the anisotropic phase is formed by the anisotropy of attractive intermolecular interactions and by the anisotropy of molecular shapes. The anisotropy of molecular shapes shifts the phase diagram to lower densities and higher temperatures. The anisotropy of attractive interactions widens significantly the coexistence region between the isotropic and anisotropic phases and shifts it to the region of lower densities and higher temperatures. It is shown that, for sufficiently long spherocylinders, the liquid-gas transition is localized completely within the nematic region. For all the considered cases, the decrease of the porosity shifts the phase diagram to the region of lower densities and lower temperatures. K e y w o r d s: fluids in random porous media, gas-liquid-nematic phase transitions, van der Waals equation, scaled particle theory, hard spherocylinders.

On generalization of Van der Waals approach for isotropic-nematic fluid phase equilibria of anisotropic fluids in disordered porous medium

“…The generalized Van der Waals theory for anisotropic fluids was formulated by Cotter [30][31][32] and by the Gelbart group [33,34]. By combining the Onsager theory with the Van der Waals approach in the group of Jackson [15,25] for the attractive hard spherocylinders, four possible pairs of coexisting fluid phases were predicted, namely vapor-liquid, vapor-nematic, liquid-nematic and nematic-nematic phases.In our previous papers [35,36], the Van der Waals approach was generalized for the description of isotropic-nematic phase equilibria of anisotropic fluids in a disordered porous medium. For that case, the Madden-Glandt model [37] was used whereby a porous medium is presented as a quenched configuration of randomly distributed obstacles, for example the hard spheres in the simplest case.…”

“…For the description of this reference system, the scaled particle theory has been used for the last decade extending the description of a hard sphere fluid in a disordered porous medium [38][39][40][41][42][43][44][45] and generalized for the study of the influence of porous media on the isotropic-nematic transition in a hard spherocylinder fluid [36,46,47] in disordered porous media and in hard spherocylinder-hard sphere mixture in bulk [48] and in porous media [49].However, in our previous papers [35,36] for the treatment of attractive interaction in the generalized Van der Waals theory for anisotropic fluids in disordered porous media, we neglect the coupling between anisotropic repulsion and attractive parts in the anisotropic phase. In this paper we revise the theory presented in [35,36] and analyze the coupling between anisotropic and attractive parts in the treatment of attractive interaction in the generalized Van der Waals equation for anisotropic fluids in disordered porous media. In addition, we will use our previous results [47] for a hard spherocylinder fluid in a disordered porous medium obtained in the framework of the scaled particle theory with the Carnahan-Starling [50] and the Parsons-Lee [51,52] corrections in order to accurately describe the reference system at higher densities.…”

“…In our previous papers [35,36], the Van der Waals approach was generalized for the description of isotropic-nematic phase equilibria of anisotropic fluids in a disordered porous medium. For that case, the Madden-Glandt model [37] was used whereby a porous medium is presented as a quenched configuration of randomly distributed obstacles, for example the hard spheres in the simplest case.…”

“…In accordance with the Van der Waals picture in the considered approach a hard spherocylinder fluid in a disordered porous medium is considered as the reference system. For the description of this reference system, the scaled particle theory has been used for the last decade extending the description of a hard sphere fluid in a disordered porous medium [38][39][40][41][42][43][44][45] and generalized for the study of the influence of porous media on the isotropic-nematic transition in a hard spherocylinder fluid [36,46,47] in disordered porous media and in hard spherocylinder-hard sphere mixture in bulk [48] and in porous media [49].…”

“…However, in our previous papers [35,36] for the treatment of attractive interaction in the generalized Van der Waals theory for anisotropic fluids in disordered porous media, we neglect the coupling between anisotropic repulsion and attractive parts in the anisotropic phase. In this paper we revise the theory presented in [35,36] and analyze the coupling between anisotropic and attractive parts in the treatment of attractive interaction in the generalized Van der Waals equation for anisotropic fluids in disordered porous media.…”