Chemistry - Nematic

In nematic liquid crystals the centers of gravity of molecules have no long-range order. The molecules tend to be parallel to a common axis, labeled by a unit vector (director) $\hat{\mathbf{n}}$ . Opposite orientations of the director are indistinquishible, even if the molecules are asymmetric. Hence, the nematic order parameter is a second-rank tensor

$Q_{\alpha\beta}=\frac{1}{2}\langle 3 n_\alpha n_\beta-\delta_{\alpha\beta}\rangle$

where

$n α$ are the components of a unit vector along the major symmetry axis of the molecules

The transition from the isotropic liquid state to the nematic phase is a (often weak) first order phase transition. The word nematic comes from the Greek νημα = thread. It refers to thread-like topological defects observed in nematics. They are called 'disclinations '. Hedgehog is the other type of topological defects in nematics.