Pankaj Mishra

Pair Correlation Functions in Nematics: Free-Energy Functional and Isotropic-Nematic Transition

We develop a free-energy functional for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function. These correlation functions are found by solving the Ornstein-Zernike equation with the Percus-Yevick closure relation. The method developed here gives the pair correlation functions in the ordered phase with features that agree well with the results found by computer simulations. The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can be extended to study other ordered phases such as smectics and crystalline solids.

Effect of confinement on coil-globule transition

The equilibrium thermodynamic properties of a linear polymer chain confined to a space between two impenetrable walls (lines) at a distance D under various solvent conditions have been studied using series analysis and exact enumeration technique. We have calculated the end-to-end distance of polymer chain, which shows a nonmonotonic behavior with inter wall separation D. The density distribution profile shows a maxima at a particular value of (D=)D*. Around this D*, our results show that the collapse transition occurs at higher temperature as compared to its bulk value of 2d and 3d. The variation of theta-temperature with D shows a re-entrance behavior. We also calculate the force of compression exerted by the walls (lines) on the polymer.

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.