Isotropic-nematic transition in a mixture of hard spheres and hard spherocylinders: scaled particle theory description

Abstract

The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the minimization of free energy, a nonlinear integral equation for the orientational singlet distribution function is formulated. An isotropic-nematic phase transition in this mixture is investigated from the bifurcation analysis of this equation. It is shown that with an increase of concentration of hard spheres, the total packing fraction of a mixture on phase boundaries slightly increases. The obtained results are compared with computer simulations data.

Scaled particle theory for a hard spherocylinder fluid in a disordered porous medium: Carnahan-Starling and Parsons-Lee corrections

“…where P is the pressure of the fluid, V s is the volume of the scaled particle, the multiplier 1/p 0 (λ s , α s ) appears due to an excluded volume confined by matrix particles and can be considered as a probability to find a cavity created by a scaled particle in the absence of fluid particles. The probability p 0 (λ s , α s ) is directly related to two different types of porosity introduced by us in [10,12,14,26]. The first one corresponds to the geometrical porosity where the coefficients of this expansion can be found from the continuity of the excess chemical potential given in (2.2) and (2.4), as well as from the corresponding derivatives ∂ µ ex s /∂λ s , ∂ µ ex s /∂α s , ∂ 2 µ ex s /∂α s ∂λ s and ∂ 2 µ ex s /∂λ 2 s .…”

“…The best one is the SPT2b approximation which was derived replacing φ by φ 0 everywhere in (2.18) except the first term. However, this term has a divergence at η 1 = φ and due to this, some other approximations were proposed in [11,12,14,26]. One of them called SPT2b1 can be obtained from the expression for the chemical potential in SPT2b approach by removing the divergence at η 1 = φ through the expansion of the logarithmic term in the SPT2b expression for the chemical potential as follows:…”

“…Recently the SPT was applied for the description of isotropic-nematic phase transition in a mixture of hard spheres and hard spherocylinders. By comparison with the corresponding computer simulation data [12][13][14] it was shown that the accuracy of the SPT description reduces with a decreasing length L 1 of spherocylinder. Such a bad accuracy of SPT description can be improved by CS correction.…”

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

“…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.…”

“…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].…”