The Percus-Yevick approximation for quadrupolar molecular fluids.

The Percus-Yevick integral equation theory has been solved to study the equilibrium and structural properties of quadrupolar Gay-Berne fluids. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 have been considered. Molecules with length-to-breadth ratios 3.0 and 4.0 have been considered and results are reported for different densities, temperatures, and quadrupole moments. The values of pair correlation functions have been compared with the available computer simulation results.

Structure and freezing of fluids interacting via the Gay-Berne (n-6) potentials.

We have calculated the pair-correlation functions of a fluid interacting via the Gay-Berne (n-6) pair potentials using the Percus-Yevick integral equation theory and have shown how these correlations depend on the value of n that measures the sharpness of the repulsive core of the pair potential. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We have used two different versions of the theory known as the second order and the modified weighted-density-functional theory and examined the freezing of these fluids for 8< or =n< or =30 and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic A phases. For none of these cases smectic A phase was found to be stabilized though in some range of temperature for a given n it appeared as a metastable state. We have examined the variation of freezing parameters for the isotropic-nematic transition with temperature and n. We have also compared our results with simulation results wherever they are available. While we find that the density-functional theory is good to study the freezing transitions in such fluids the structural parameters found from the Percus-Yevick theory need to be improved particularly at high temperatures and lower values of n.

Pair correlation functions and a free energy functional for the nematic phase.

In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation (MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska [J. Mol. Liq. 82, 161 (1999)]. A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give a nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function h(x1,x2) connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories.

Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid.

We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 < or = x(0) < or = 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x(0) considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x(0). The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.