Labyrinthine instability

Interplay between polarity and chirality in partially ordered systems such as liquid crystals gives rise to a diversity of states and morphologies. In contrast to the well known chiral liquid crystalline phases of rod-like molecules, phases with bent-core mesogens present a considerably bigger richness of behavior due their intrinsic sterically induced polar order which can appear without tilt of the molecules and, as a result, they represent the first liquid system where a spontaneous breaking of achiral symmetry has been observed. It gives rise to new classes of patterns and new properties in external fields (complex switching behavior including chirality switching), which is potentially useful in designing new controllable materials.
In free-standing liquid crystalline films, the molecular layers are aligned parallel to the film surface. Areas of different thickness have sharp boundaries enclosed by edge dislocations. Line-tension of the boundaries minimizes their length. If the film thickness is comparable with the wave length of visible light, the layer steps and islands can be easily detected by their reflection color. In polarization modulated phase, the director (direction of the molecular bows) exhibits a spontaneous splay. Such a splayed director field is incompatible with the extended geometry of the flat film and favors formation of stripes separated by defect lines (director discontinuity).
A spontaneous director splay introduces a linear divergence term into the free energy density, which results in a negative line-tension of the defect lines. Upon cooling the film from the non-modulated into the polarization modulated state, the layer dislocations become unstable and start growing. Initial fingering stage leads to a 1D modulated structure which turns into a complex labyrinthine pattern. The labyrinth growth is limited by the volume energy which dominates at small stripe widths. Labyrinthine state possesses a local ferroelectric structure within the stripes and a global antiferroelectric organisation of the stripes.
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Labyrinthine patterns of layer dislocations in freely suspended films in the polarisation-modulated smectic phase.

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