Defects in a TGBA phase: a theoretical approach

Following our experimental observations of disclination lines in freely suspended droplets and free-standing films (Yu.A. Nastishin et al., Eur. Phys. J. E 5 353 (2001)), topological defects of the twist grain boundary (TGBA) phase are considered according to two aspects: topological and energetical. There are two classes of line defects, disclinations (as in the cholesteric (N*) phase and the liquid vortices phase (NL*), relating to the directors tripod symmetries) and dispirations (relating to the translation-rotation symmetries); there are no topological point defects. Differences between N*, NL* and TGBA disclinations are physical, not topological. The absence of focal conic domains in the TGBA phase is an immediate consequence of the materialization of the helical axis (along the chi-director); the same feature, coupled to the trend to parallelism of the smectic layers, accounts for the predominance of lambda-lines. Finally, the presence of defects akin to developable domains is explained in the frame of the least curvature model, that requires the introduction of a third type of defects: the densities of edge dislocations of the smectic layers.