The 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 \PY integral equation theory and have shown how these correlations depend on the value of n which 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 $8 \leq n \leq 30$ 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 \PY theory need to be improved particularly at high temperatures and lower values of $n$.Comment: 21 Pages (in RevTex4), 6 GIF and 4 Postscript format Fig

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. $\bf 82$, 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 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 $h({\bf x_1},{\bf x_2})$ 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.Comment: 27 pages, 11 figures, Accepted in J. Chem. Phy

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 $3.0\leq x_0\leq 4.0$ 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 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.Comment: 15 pages, 6 figure

Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order

Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted with respect to the smectic layer normal. As in the previous papers of the series (Phys. Rev. A {\bf 45}, 974 (1992), E {\bf 49}, 501, (1994)) the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalised spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self- consistently. We estimate the value of elastic constants using reasonable guess for the order and structural- parameters.Comment: 31 pages; 1 Fig. in GIF format, To be appear in Phys. Rev.

Density-functional theory of the nematic phase: results for a system of hard ellipsoids of revolution

A second-order density-functional theory is used to study the isotropic-nematic transition in a system of hard ellipsoids of revolution. The direct pair-correlation functions of the coexisting isotropic liquid that enter in the theory as input information are obtained from solving the Ornstein-Zernike equation using the Percus-Yevick closure relation. The spherical harmonic expansion coefficients of the correlation functions obtained from this solution are in good agreement with those found from computer simulations. We find that a system spontaneously transforms to a nematic phase when the structural parameter denoted by c<SUP>Λ</SUP><SUB>22</SUB><SUP>(0)</SUP> attains a value close to 4.40. This value of c<SUP>Λ</SUP><SUB>22</SUB><SUP>(0)</SUP> depends, although very weakly, on the value of the length-to-width ratio of the molecules. The transition parameters we found are in very good agreement with the results generated by computer simulations. By using the harmonic coefficients of the direct pair-correlation functions, we have calculated the Frank elastic constants of the nematic phase

Thermodynamically self-consistent integral-equation theory for pair-correlation functions of a molecular fluid

We propose a "mixed" integral equation for the pair correlation function of molecular fluids which interpolates between the hypernetted-chain and Percus-Yevick approximations. Thermodynamic consistency between the virial and compressibility equation of state is achieved by varying a single parameter in a suitably chosen mixing function. The integral equation proposed here generalizes the suggestion by Rogers and Young [Phys. Rev. A 30, 999 (1984)] to an angle-dependent pair potential. When compared to available computer simulation data, the equation is found to yield excellent results for both the thermodynamic properties and the pair-correlation functions

Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids

The Percus-Yevick (PY) integral equation has been solved for two model fluids: (i) a fluid of hard ellipsoids of a revolution represented by a Gaussian overlap model, and (ii) a fluid the molecules of which interact via a Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] model potential. The method used involves an expansion of angle dependent functions appearing in the integral equation in terms of spherical harmonics. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures, and lengths to width ratios of the molecules. We have compared our results with those of computer simulations wherever they are available. We find that the PY theory gives reasonable values of the harmonic coefficients for both fluids at all fluid densities when all terms involving the index l up to six in the expansion are considered. For the Gay-Berne fluid we have developed a perturbation expansion for a calculation of the structure and thermodynamic properties of the isotropic phase