Smectic phase

A smectic phase is a layered liquid crystal with periodic density or composition variation along one direction and fluid-like positional organization within a layer. A simple order-parameter profile is $\varphi (\mathbf{r})=A\cos ({\mathbf{q}}_0\cdot \mathbf{r})$, with layer spacing $2\pi /|{\mathbf{q}}_0|$.

Layer displacement and orientational fluctuations are additional degrees of freedom, so a fixed cosine is only the simplest mean profile. A smectic A phase has average molecular alignment along the layer normal; a smectic C phase has a tilted director. Scattering can reveal the preferred layer spacing and orientation through peaks near ${\mathbf{q}}_0$. The layer structure does not imply a full three-dimensional crystal lattice of fixed molecular positions.

A smectic C phase has layered positional order with the nematic director tilted away from the layer normal. The tilt supplies additional orientational information beyond the density modulation of a smectic phase.

A smectic A phase has layered positional order with the average molecular orientation along the layer normal. Molecular positions within each layer remain liquid-like. Its orientational axis is described by a nematic director.

A polar helical smectic has a vector order parameter of constant magnitude whose direction rotates at a nonzero wavevector. For an isotropic Brazovskii free energy, all constant rotations of the helical plane are degenerate until a longitudinal-gradient term such as $|\nabla \cdot \mathbf{p}{|}^2$ selects its orientation.