Effects of molecular geometry on liquid crystalline phase behaviour: isotropic-nematic transition

The effects of range and geometry of a simple attractive square-well on the phase diagram of hard ellipsoids and hard spherocylinders is systematically studied using a simple van der Waals type theory. The orientational single particle distribution function is approximated using the Onsager trial function. The quantitative errors introduced by this are thought to be considerably smaller than the use of the van der Waals approximation, which has been shown to give qualitatively correct phase diagrams for similar models. The phase diagrams obtained for hard ellipsoids and hard spherocylinders of aspect ratios ranging between 3 and 10 with a variety of square-well attractions are found to fall into three general types. The first type shows liquid-vapour coexistence and an isotropic-nematic transition, which meet at a liquid-vapour-nematic triple point. The second type shows a marked widening of the isotropic-nematic biphasic region which pre-empts the liquid-vapour coexistence. The final phase diagram shows a strong destabilization of the nematic phase with respect to the isotropic, which results in a shift of the phase transition to higher densities and pressures as the temperature is lowered.