Step 1: Understanding the Concept:
The question asks how molecular mobility is described in the smectic phase of a liquid crystal.
Step 2: Key Formula or Approach:
Liquid crystal phases are ranked by how much positional and rotational order their molecules keep compared to a fully ordered solid crystal. The smectic phase keeps more order than the nematic phase because its molecules are arranged in distinct layers, not just pointing the same direction.
Step 3: Detailed Explanation:
Within each smectic layer, molecules can still slide past each other, giving them mobility within the plane of the layer, which counts as motion in two directions. They are not free to drift between layers the way molecules in an ordinary liquid would move in three dimensions. On top of this sliding motion, each molecule can rotate about its own long axis, since nothing in the layered packing stops that spin. Put together, this gives the smectic phase its signature description: mobility confined to two directions within a layer, plus rotation about one axis.
Step 4: Final Answer:
Smectic liquid crystals show mobility in two directions along with rotation about one axis.