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

Abstract

A generalized Van der Waals approach is developed for anisotropic fluids in disordered porous media. As the reference system a hard spherocylinder fluid in a disordered porous medium is considered and described in the framework of the scaled particle theory with the Carnahan-Starling and Parsons-Lee corrections. The attractive part of interaction is treated in the framework of the mean field approximation in which due to orientational dependence of the excluded volume of two spherocylinders, a coupling between attractive and repulsive contributions is found. We focus on spherocylinder fluids with sufficiently long particle lengths for which the nematicnematic transition was established. It is shown that these two nematic phases have different densities and are characterized by different orientational ordering. Strong influence of the type of interparticle attraction on the phase behaviour of anisotropic fluids in disordered porous media is established. Three simple models for this purpose are considered, namely a model with the Lennard-Jones anisotropic attraction, a model with modified Lennard-Jones attraction and a model with anisotropic square-well potential. For all considered models, the phase diagram shifts to the region of lower densities and lower temperatures as the porosity decreases.cylinders when the length of a spherocylinder L 1 → ∞ and the diameter D 1 → 0 in such a way that the non-dimensional concentration C 1 = πρ 1 L 2 1 D 1 /4 is fixed, where ρ 1 = N 1 /V, N 1 is the number of spherocylinders, V is the volume of the system [16]. The application of the scaled particle theory (SPT) previously developed for a hard-sphere fluid [18,19] provides an efficient way to incorporate higher order contributions neglected in the Onsager theory [20][21][22].Another mechanism of formation of liquid crystalline matter can be connected with anisotropic attraction usually treated in molecular mean-field approaches such as the Maier-Saupe theory [23,24]. In this approach, the orientationally dependent attractive interactions are considered as the key to the orientational order in thermotropic liquid crystals controlled by the temperature. In many cases, anisotropic fluids exhibit simultaneously lyotropic and thermotropic behaviour, which can be presented in concentration-temperature phase diagrams [15,25]. Due to this, both repulsive and attractive interactions between particles should be taken into account. This leads to the Van der Waals picture of fluids [26] in which the hard molecular core is treated as the reference system that determines the fluid structure while the attractions are incorporated by the perturbation way [27][28][29]. 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-nemat...

Diffusion of hard sphere fluids in disordered porous media: Enskog theory description

“…The developed SPT2 approach was generalized for fluids of anisotropic particles [20,21], for a hard sphere mixture [22] and for a mixture of hard sphere and anisotropic particles [23,24] in disordered porous media. The obtained results for the models considered were also used as the reference system taking into account attractive [24,25], associative [26] and Coulombic [27][28][29] interactions.…”

Effects of porous media on the phase behaviour of polypeptide solutions

“…As was discussed in [30], the van der Waals approximation corresponds to the first order of thermodynamic perturbation theory, if for the pair function of the reference system we use the approximation…”

“…is the contribution from the repulsive part of the interaction. The coefficient 𝛿 = 3/8 is due to the Parsons-Lee correction [25,26], which we introduced in [30]. The contribution from the attractive part of the interaction…”

“…This is the purpose of the present work. The theoretical basis of the work is based on the works [28][29][30], in which the generalization of van der Waals equation on anisotropic fluids in porous media is given. In contrast to [20], the orientational ordering in the system is described through a corresponding integral equation for the singlet distribution function, which is found by minimizing the free energy functional of the system and its numerical solution on the basis of generalization [31].…”

Clustering effects on the diffusion of patchy colloids in disordered porous media

“…The SPT2 approach was generalized for fluids of anisotropic particles [17,18], for a hard sphere mixture [19], for a mixture of hard spheres and anisotropic particles [20] in disordered porous media. The obtained results were also used as a reference system to take into account the attractive [21,22], the associative [2] and Coulomb [23][24][25][26][27] interactions. The SPT2 approach is useful not only for the description of thermodynamic properties, but it can be also applied for the description of the static structure of hard sphere fluids in disordered porous media.…”