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Observing and characterizing the complex ordering phenomena of liquidcrystals subjected to external constraints constitutes an ongoing challenge forchemists and physicists alike. To elucidate the delicate balance appearing whenthe intrinsic positional order of smectic liquid crystals comes into play, weperform Monte-Carlo simulations of rod-like particles in a range of cavitieswith a cylindrical symmetry. Based on recent insights into the topology ofsmectic orientational grain boundaries in two dimensions, we analyze theemerging three-dimensional defect structures from the perspective of tetraticsymmetry. Using an appropriate three-dimensional tetratic order parameterconstructed from the Steinhardt order parameters, we show that those grainboundaries can be interpreted as a pair of tetratic disclination lines that arelocated on the edges of the nematic domain boundary. Thereby, we shed light onthe fine structure of grain boundaries in three-dimensional confined smectics.

Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals