 Nematic liquid crystal

A nematic liquid crystal has orientational order without a periodic three-dimensional lattice of molecular positions. Its local preferred axis is the nematic director $\mathbf{n}$, with $\mathbf{n}$ and $-\mathbf{n}$ representing the same physical alignment.

Because the two directions are equivalent, an ordinary vector average can vanish even in an aligned sample. A symmetric traceless nematic order parameter instead measures the alignment; a common convention is $Q_{ij}=S(n_i{n}_j-{\delta }_{ij}/3)$. Spatial variations produce nematic splay, nematic twist and nematic bend, while boundary anchoring constrains the texture. Optical transmission through polarizers can reveal director changes because aligned molecules generally respond differently along and across the axis. Such a texture measurement must be distinguished from direct imaging of fixed molecular positions.