Jokhan Ram

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.

Perturbation theory for fluids of non-spherical molecules in the presence of three-body forces

The application of perturbation theory to a fluid of non-spherical molecules of arbitrary symmetry is considered. The influence of a large number of angle-dependent pair interactions and three-body non-additive interactions on the Helmholtz free energy and on the pair and triplet distribution functions, in some cases through the third order of the perturbation theory, is evaluated. Explicit expressions are given for the Helmholtz free energy for molecules possessing axial and tetrahedral symmetries in terms of molecular parameters and the reference systems pair and triplet distribution functions. The contributions of the various terms discussed in this paper are expected to be substantial at low temperatures for a real fluid.

Evaluation of the SSC/LHNC, SSCF and PY approximations for short ranged, anisotropic potentials

Three approximations for the orientational correlation function of molecular fluids—the single super chain/linearized hypernetted chain (SSC/LHNC), single super chain f-expansion (SSCF) and Percus-Yevick (PY) approximation—are evaluated in the dense liquid state for a fluid inter-acting with short ranged anisotropic interactions. These interactions are prototypical of the forces that determine the non-spherical shape of symmetric linear molecules. We find that SSC/LHNC is very poor, failing to predict many of the structural features present in the Monte Carlo (MC) simulation results. The PY and SSCF approximations produce much better results; however, neither approximation is completely satisfactory.

Effects of molecular elongation on liquid crystalline phase behaviour: isotropic–nematic transition

We present the density-functional approach to study the isotropic–nematic transitions and calculate the values of freezing parameters of the Gay–Berne liquid crystal model, concentrating on the effects of varying the molecular elongation, x0. For this, we have solved the Percus–Yevick integral equation theory to calculate the pair-correlation functions of a fluid the molecules of which interact via a Gay–Berne pair potential. These results have been used in the density-functional theory as an input to locate the isotropic–nematic transition and calculate freezing parameters for a range of length-to-width parameters 3.0⩽x0⩽4.0 at reduced temperatures 0.95 and 1.25. We observed that as x0 is increased, the isotropic–nematic transition is seen to move to lower density at a given temperature. We find that the density-functional theory is good to study the freezing transitions in such fluids. We have also compared our results with computer simulation results wherever they are available.

On the quantum corrections to the virial coefficients of the equation of state of a fluid

The first quantum correction to the virial coefficients of the equation of state of a fluid is derived in the presence of a weak three-body potential ϕ(i, j, k). Results for the third and fourth virial coefficients are given. Representing the potential energy of interaction of a pair and a triplet, by the Lennard-Jones (12-6) model and the triple dipole dispersion potential model of Axilrod and Teller, the first quantum correction to the third virial coefficient is calculated for many values of T*. The theoretical result is compared with the experimental data of helium.

On the quantum corrections to the radial distribution function and to the thermodynamic properties of fluids

Defining the radial distribution function g(r) as the ratio of two configurational integrals of the Slater sum, the first quantum correction to the radial distribution function has been derived. This result has been used to obtain the first quantum correction to the thermodynamic properties of fluids. The cluster integrals appearing in the density expansion of g(r) have been discussed. It has been found that additional diagrams appear, in each order of density, in the radial distribution function due to the quantum correction. Numerical values of the first few cluster integrals have been evaluated using a gaussian model and the results discussed. Equations relating the three-body distribution function with two-body distribution functions and the first quantum correction term with the classical distribution functions have been derived.

Structure and freezing of a fluid of long elongated molecules

The pair correlation functions of a fluid of long elongated molecules interacting via the Gay-Berne pair potential are calculated using the Percus-Yevick integral equation theory. Numerical accuracy has been examined by considering a large number of spherical harmonic coefficients for each orientation-dependent functions for a system of molecules having a length-to-breadth ratio equal to 4.4 at different densities and temperatures. The pair correlation functions of the isotropic fluid found from the Percus-Yevick theory have been used in the density-functional theory to locate the isotropic-nematic, isotropic-smectic A and nematic-smectic A transitions. It is found that at low temperatures the fluid freezes directly into the smectic A phase on increasing the density. The nematic phase is found to stabilize in between the isotropic and smectic A phases only at high temperatures and high densities. The calculated phase diagram is in good qualitative agreement with computer simulation results.

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

Abstract.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 ⩽ x0 ⩽ 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 x0 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 x0. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement.

Integral equation theory for molecular fluids: effect of quadrupolar interactions

The Percus–Yevick (PY) and the hypernetted chain (HNC) integral equations have been solved for fluids of hard ellipsoids of a revolution represented by a hard Gaussian overlap model and for fluids of quadrupolar hard Gaussian overlap model. The structural and thermodynamic properties of the isotropic phase are discussed in detail. Ellipsoids with length-to-width ratios of 1.792, 3.0, 4.0 and 5.0 are considered and results are reported for different densities and quadrupole moments. It is shown that both the HNC and PY theories are in reasonable agreement with the computer simulation results.