Nematic
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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) <math>\hat{\mathbf{n}}<math>. Opposite orientations of the director are indistinquishible, even if the molecules are asymmetric. Hence, the nematic order parameter is a second-rank tensor
- <math>Q_{\alpha\beta}=\frac{1}{2}\langle 3 n_\alpha n_\beta-\delta_{\alpha\beta}\rangle<math>
where
<math>n_\alpha<math> 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.