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

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.Comment: 11 pages, 4 figure

Cluster expansion for the description of condensed state: crystalline cell approach

A well-known cluster expansion, which leads to virial expansion for the free energy of low density systems, is modified in such a way that it becomes applicable to the description of condensed state of matter. To this end, the averaging of individual clusters over the states of an ideal gas is replaced by the averaging over the states of a non-correlated crystal using single-particle cell potentials. As a result, we arrive at the expansion of the partition function in correlations on the basis of single-particle functions corresponding to the multiplicative approximation. The cell potentials defining these functions are found from the condition of the minimum of the remainder in the constructed decomposition.Comment: 16 page

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

The scaled particle theory (SPT) approximation is applied for the study of the influence of a porous medium on the isotropic-nematic transition in a hard spherocylinder fluid. Two new approaches are developed in order to improve the description in the case of small lengths of spherocylinders. In one of them, the so-called SPT-CS-PL approach, the Carnahan-Starling (CS) correction is introduced to improve the description of thermodynamic properties of the fluid, while the Parsons-Lee (PL) correction is introduced to improve the orientational ordering. The second approach, the so-called SPT-PL approach, is connected with generalization of the PL theory to anisotropic fluids in disordered porous media. The phase diagram is obtained from the bifurcation analysis of a nonlinear integral equation for the singlet distribution function and from the thermodynamic equilibrium conditions. The results obtained are compared with computer simulation data. Both ways and both approaches considerably improve the description in the case of spherocylinder fluids with smaller spherocylinder lengths. We did not find any significant differences between the results of the two developed approaches. We found that the bifurcation analysis slightly overestimates and the thermodynamical analysis underestimates the predictions of the computer simulation data. A porous medium shifts the phase diagram to smaller densities of the fluid and does not change the type of the transition.Comment: 13 pages, 5 figure

What is liquid in random porous media: the Barker-Henderson perturbation theory

We apply the Barker-Henderson (BH) perturbation theory to the study of a Lennard-Jones fluid confined in a random porous matrix formed by hard sphere particles. In order to describe the reference system needed in this perturbation scheme, the extension of the scaled particle theory (SPT) is used. The recent progress in the development of SPT approach for a hard sphere fluid in a hard sphere matrix allows us to obtain very accurate results for thermodynamic properties in such a system. Hence, we combine the BH perturbation theory with the SPT approach to derive expressions for the chemical potential and the pressure of a confined fluid. Using the obtained expressions, the liquid-vapour phase diagrams of a LJ fluid in HS matrix are built from the phase equilibrium conditions. Therefore, the effect of matrix porosity and a size of matrix particles is considered. It is shown that a decrease of matrix porosity lowers both the critical temperature and the critical density, while the phase diagram becomes narrower. An increase of a size of matrix particles leads to an increase of the critical temperature. From the comparison it is observed that the results obtained from the theory are in agreement with computer simulations. The approach proposed in the present study can be extended to the case of anisotropic fluid particles in HS matrices.Comment: 17 pages, 9 figure