Nematic phase

Nematic phase for the hard 6x1x1 ellipsoid model.

The nematic phase has orientational order, but no positional order.

Discotic nematic phase

Discotic-nematic phase for the hard 6x6x1 ellipsoid model.

Dielectric tensor

In the uniaxial nematic phase, defining the z-axis to be parallel to the nematic axis, one has

${ϵ}_{\alpha \beta }=\left(\begin{array}{ccc}{ϵ}_{\mathrm{\perp }}& 0& 0\\ 0& {ϵ}_{\mathrm{\perp }}& 0\\ 0& 0& {ϵ}_{|}\end{array}\right)$

The anisotropy is defined as

$\mathrm{\Delta }ϵ={ϵ}_{|}-{ϵ}_{\mathrm{\perp }}$.

The response of a nematic liquid crystal to an external electric field depends on both the sign and the magnitude of $\mathrm{\Delta }ϵ$.

Biaxial nematic phase

1. Carl McBride and Enrique Lomba "Hard biaxial ellipsoids revisited: Numerical results", Fluid Phase Equilibria 255 pp. 37-45 (2007)
2. Roberto Berardi, Luca Muccioli, and Claudio Zannoni "Field response and switching times in biaxial nematics", Journal of Chemical Physics 128 024905 (2008)