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

Abstract

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 coe%cients of the correla-

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

“…We found that, with these number of harmonics, self consistent iterative solution of OZ and PY converges up to the accuracy of 10 À5 in the range of density of our interest. The numerical procedure for solving Equations (16) and (21) is the same as discussed in [27].…”

“…It has now become a standard model to study various phenomenon and properties of Liquid-crystalline phases, [11] anisotropic colloids [12] and liquid crystalline polymers through computer simulation [12][13][14][15][16][17][18][19][20][21][22] and also theoretically. [23][24][25][26][27] In this paper, our objective is to study the liquid crystalline phase transitions and the topology of the phase diagram of a system of highly elongated (κ ' 10) model ellipsoidal conjugated oligomers using the density functional theory (DFT) of freezing. [28,29] Pair correlation functions needed as input information in DFT have been calculated using the Percus-Yevick (PY) integral equation theory at a grid of temperature and density.…”

The direct correlation functions of hard Gaussian overlap and hard ellipsoidal fluids

“…Many works [18,23,31] have been done to solve the OZ equation for hard convex body [32] fluids. As mentioned in Section 1, the hard ellipsoids of revolution model may provide useful reference systems to investigate realistic systems.…”

“…Baus and coworkers formulated the other simple approximation for the DCF which decouples the radial part from the angular part [10]. Ram and Singh [23] have revisited the work of Singh and Singh [24] and solved Ornestein-Zernike (OZ) equation. They used the PY closure relation and found the spherical harmonic expansion coefficients of the HE DCFs.…”

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

“…[13] and determined the values of c To solve (7)- (8) we first set up linear equations for h (n) l 1 l 2 lm 1 m 2 m (r) and c (n) l 1 l 2 lm 1 m 2 m (r) using the expansions of eqn. (9) and (10).…”