Bend-induced melting of the smectic-A phase: analogy to a type-I superconductor

Analogy between periodic patterns in thin smectic liquid crystal films and the intermediate state of superconductors

Spontaneous breaking of symmetry in liquid crystal (LC) films often reveals itself as a microscopic pattern of molecular alignment. In a smectic-A LC, the emergence of positional order at the transition from the nematic phase leads to periodic textures that can be used as optical microarrays, templates for soft lithography, and ordering matrices for the organization and manipulation of functional nanoparticles. While both 1d and 2d patterns have been obtained as a function of the LC film thickness and applied fields, the connection has not been made between pattern formation and the peculiar critical behavior of LCs at the nematic-smectic transition, still eluding a comprehensive theoretical explanation. In this article, we demonstrate that an intense bend distortion applied to the LC molecular director while cooling from the nematic phase produces a frustrated smectic phase with depressed transition temperature, and the characteristic 1d periodic texture previously observed in thin films and under applied electric fields. In light of De Gennes' analogy with the normal-superconductor transition of a metal, we identify the 1d texture as the equivalent of the intermediate state in type I superconductors. The bend distortion is analog to the magnetic field in metals and penetrates in the frustrated phase as an array of undercooled nematic domains, periodically intermixed with bend-free smectic-A domains. Our findings provide fundamental evidence for theories of the nematic-smectic transition, highlighting the deep connection between phase frustration and pattern formation, and perspectives on the design of functional smectic microarrays.

Observations of a streak texture in the hybrid-aligned smectic-C phase

A novel structure was observed below the smectic-A-smectic-C phase transition in a very thin open cell having an air interface above and enforced planar anchoring at the substrate below. The structure appears as periodic dark and light streaks running perpendicular to the oily streaks, which are present in the smectic-A phase [D. Coursault et al., Soft Matter, 2016, 12, 678]. These new streaks, which we call "soapy streaks", form by extending from one oily streak to the next in discrete steps, eliminating optical evidence at visible wavelengths of the oily streaks. At lower temperatures the streaks can undulate and exhibit a sawtooth-like structure; such a structure is chiral in two dimensions. A possible scenario for the origin of these streaks is presented.

Chiral oily streaks in a smectic-A liquid crystal

The liquid crystal octylcyanobiphenyl (8CB) was doped with the chiral agent CB15 and spin-coated onto a substrate treated for planar alignment of the director, resulting in a film of thickness several hundred nm in the smectic-A phase. In both doped and undoped samples, the competing boundary conditions - planar alignment at the substrate and vertical alignment at the free surface - cause the liquid crystal to break into a series of flattened hemicylinders to satisfy the boundary conditions. When viewed under an optical microscope with crossed polarizers, this structure results in a series of dark and light stripes ("oily streaks") of period ∼1 μm. In the absence of chiral dopant the stripes run perpendicular to the substrate's easy axis. However, when doped with chiral CB15 at concentrations up to c = 4 wt%, the stripe orientation rotates by a temperature-dependent angle φ with respect to the c = 0 stripe orientation, where φ increases monotonically with c. φ is largest just below the nematic - smectic-A transition temperature TNA and decreases with decreasing temperature. As the temperature is lowered, φ relaxes to a steady-state orientation close to zero within ∼1 °C of TNA. We suggest that the rotation phenomenon is a manifestation of the surface electroclinic effect: The rotation is due to the weak smectic order parameter and resulting large director tilt susceptibility with respect to the smectic layer normal near TNA, in conjunction with an effective surface electric field due to polar interactions between the liquid crystal and substrate.

Nanoscale alignment and optical nanoimaging of a birefringent liquid

An anisotropic nanopatterning method, based on a technique of atomic force microscopy (AFM) scribing of a thin polyimide film, is used to generate an alignment layer whose topography depends on the writing direction. Detailed experimental measurements are presented for the topographical anisotropy that arises when the polyimide alignment layer is scribed parallel and antiparallel to the AFM cantilever orientation. By means of a novel nanotomographic approach, the optical retardation δ of an alignable birefringent liquid that covers the scribed substrate is measured with unprecedented resolution of only a few tens of nanometers. In this technique a thin optical fiber is raster-scanned at several fixed heights inside the birefringent liquid, and the transmitted polarized light is collected downstream. The optical retardation δ from the fiber's tip to the polyimide interface was measured as a function of position x,y,z, with the results reflecting the spatially varying depth of the medium due to the polymer film surface topography. Theoretical calculations for δ are in excellent agreement with both the topographical and the high resolution nanoimaging experimental results obtained.

Diverging elasticity and director uniformation in a nanopatterned cell near the nematic-smectic-A phase transition

The stylus of an atomic force microscope is used to scribe herringbone patterns of various wavelengths into a polyimide-coated substrate. The patterns serve as a template for alignment of the liquid crystal octyloxycyanobiphenyl and impose a bend distortion in the liquid crystal in the vicinity of the herringbone apexes. The pretransitional behavior of the liquid crystal is observed by polarized microscopy as it is cooled through the nematic-smectic- A phase transition, facilitating direct visualization of the extrapolation length, which is related to the trade-off between elastic and anchoring forces. Just above the phase transition temperature the expulsion of bend deformation is observed and is shown to be in good quantitative agreement with continuum theory. Very close to the transition temperature a weak threshold behavior is observed, wherein the smectic- A phase forms a monodomain for short period herringbones, but breaks into multiple domains when the patterned period is large.

Equilibrium topology of the intermediate state in type-I superconductors of different shapes

A high-resolution magneto-optical technique was used to analyze flux patterns in the intermediate state of bulk Pb samples of various shapes - cones, hemispheres, and discs. Combined with the measurements of macroscopic magnetization, these results allowed studying the effect of bulk pinning and geometric barrier on the equilibrium structure of the intermediate state. Zero-bulk pinning discs and slabs show hysteretic behavior due to topological hysteresis - flux tubes on penetration and lamellae on flux exit. (Hemi)spheres and cones do not have a geometric barrier and show no hysteresis with flux tubes dominating the intermediate field region in both regimes. It is concluded that flux tubes represent the equilibrium topology of the intermediate state. Real-time video is available in the EPAPS Document No. E-PRLTAO-98-024726..