Pattern-Stabilized Decorated Polar Liquid-Crystal Fibers

Geometric frustration gives rise to new fundamental phenomena and is known to yield the formation of exotic states of matter, such as incommensurate crystals, modulated liquid-crystalline phases, and phases stabilized by defects. In this Letter, we present a detailed study of polar structure of freely suspended fluid filaments in a polarization modulated liquid-crystal phase. We show that a periodic pattern of polarization-splay stripes separated by defect boundaries and decorating smectic layers can stabilize the structure of fluid fibers against the Rayleigh-Plateau instability. The instability is suppressed by the resistance of the defect structure to a radial compression of the cylindrical fibers. Our results provide direct experimental observation of a link between the stability of the liquid fibers, internal polar order, and geometrical constraints. They open a new perspective on a wide range of fluid polar fiber materials.

Figure 1

Polarizing optical microscope (POM) images and molecular alignment in the PM-$\mathrm{Sm}CP$ phase. (a) texture of a $10\mathrm{\text{−}}\mu \mathrm{m}$-thick cell at the transition from the isotropic phase to the PM-$\mathrm{Sm}CP$ phase. (b) POM image of freestanding (in air) filaments in the PM-$\mathrm{Sm}CP$ phase ($T=155°\mathrm{C}$, image width 1.5 mm), the chemical formula of the compound is given in the inset. (c) Schemes of the director configuration (polarization modulated structure) in a single layer of the PM-$\mathrm{Sm}CP$ phase. The arrows indicate the direction of the molecular bows ($p$ director). (d) Schematic presentation of a filament bundle structure. The smectic layers form a concentric nested cylinder resulting in a nested-cylinder structure. The optical slow axis is aligned radially, perpendicular to the axis of the fiber.

Figure 2

SH generation in filaments. (a) Optical setup for SHG interferometry. In this geometry the SHG signal of the filament interferes with that of a quartz crystal constructively or destructively depending on the rotation angle of a thin glass plate, resulting in a fringe structure. (b) Temperature dependence of $p\mathrm{\text{−}}p$ and $s\mathrm{\text{−}}s$ components of SHG intensity (filament thickness $150\mu \mathrm{m}$). (c) SHG interferogram for SHG signal from a thick filament. Measurements on several other filaments of the same thickness show nearly the same phase, which means that the polar directional sense is the same in every filament.

Figure 3

SHG-interferometry microscopy. (a) Optical image of the fiber. (b) SHG image of the fiber. The SHG activity of the fibers indicates their polar nature. (c) SHG interferogram for each fiber. SHG microscopy interferometry technique allows us to determine the polar directional sense of each fiber. Opposite polar direction results in a phase shift of $\pi$. In our case one can differentiate between the fibers polarized in parallel or antiparallel directions with respect to the pulling direction.

Figure 4

Unstable and stable fibers made of concentric smectic layers. (a) A scheme of an unstable fiber without layer decoration. Any change of the radius is allowed with a help of materials flow from the meniscus. (b) Optical microscopy images of unstable filaments (dark images) upon the transition into the nonmodulated $\mathrm{Sm}CP$ phase (image width $600\mu \mathrm{m}$). (c) Polarization-splay stripes in two subsequent smectic layers in a fiber. A slight increase of the curvature radius $\delta r$ results in a deviation of the stripe width $\delta l$ from its equilibrium value.