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How does translational symmetry change when a nematic liquid crystal becomes a smectic liquid crystal?
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liquid crystal
Figure 1: Arrangements of molecules.
In the nematic phase, all translational symmetries are continuous, meaning molecule positions are disordered in all three spatial directions.1
As a substance transitions from the nematic to the smectic phase, this symmetry changes through a process of symmetry breaking. Specifically, the continuous translational symmetry is broken along one independent direction, resulting in the formation of layers. Within these layers, the substance retains continuous translational symmetry in the remaining two directions, allowing molecules to remain mobile and disordered in those planes.1