Energetics of topographically designed Smectic-A oily streaks.

A thin Smectic-A liquid crystal (LC) film is deposited on a polymer vinyl alcohol-coated substrate that had been scribed with a uniform easy axis pattern over a square of side length L ≤ 85 µm. The small size of the patterned region facilitates material distribution to form either a hill (for a thin film) or divot (for a thick film) above the scribed square and having an oily streak (OS) texture. Optical profilometry measurements vs. film thickness suggest that the OS structure aims to adopt a preferred thickness z0 that depends on the nature of the molecule, the temperature, and the surface tension at the air interface. We present a phenomenological model that estimates the energy cost of the OS layer as its thickness deviates from z0.

Co-revolving topological defects in a nematic liquid crystal.

A patterned surface defect of strength m = +1 and its associated disclination lines can decompose into a pair of surface defects and disclination lines of strength m = +1/2. For a negative dielectric anisotropy liquid crystal subjected to an applied ac electric field E, these half-integer defects are observed to wobble azimuthally for E > than some threshold field and, for sufficiently large fields, to co-revolve antipodally around a central point approximately midway between the two defects. This behavior is elucidated experimentally as a function of applied field strength E and frequency ν, where the threshold field for full co-revolution scales as ν1/2. Concurrently, nematic electrohydrodynamic instabilities were investigated. A complete field vs. frequency "phase diagram" compellingly suggests that the induced fluctuations and eventual co-revolutions of the ordinarily static defects are coupled strongly to-and driven by-the presence of the hydrodynamic instability. The observed behaviour suggests a Lehmann-like mechanism that drives the co-revolution.

Spontaneous Anchoring-Mediated Topography of an Orientable Fluid.

A topography in a Newtonian fluid occurs if there is a disturbance near the surface. But what if there is no such disturbance? We show by optical profilometry that a thin nematic film resting on a topological-defect-patterned substrate can exhibit a hill or divot at the opposing free (air) interface in the absence of a topological disturbance at that interface. We propose a model that incorporates several material properties and that predicts the major experimental features. This work demonstrates the importance of, in particular, anisotropic surface interactions in the creation of a free-surface topography.

Transition from escaped to decomposed nematic defects, and vice versa.

An escaped radial director profile in a nematic liquid crystal cell can be transformed into a pair of strength m = +1/2 surface defects (and their associated disclination lines) at a threshold electric field. Analogously, a half-integer defect pair can be transformed at a threshold electric field into a director profile that escapes into the third dimension. These transitions were demonstrated experimentally and numerically, and are discussed in terms of topologically discontinuous and continuous pathways that connect the two states. Additionally, we note that the pair of disclination lines associated with the m = +1/2 surface defects were observed to co-rotate around a common point for a sufficiently large electric field at a sufficiently low frequency.

Electric field-driven reconfigurable multistable topological defect patterns.

Topological defects appear in symmetry breaking phase transitions and are ubiquitous throughout Nature. As an ideal testbed for their study, defect configurations in nematic liquid crystals (NLCs) could be exploited in a rich variety of technological applications. Here we report on robust theoretical and experimental investigations in which an external electric field is used to switch between pre-determined stable chargeless disclination patterns in a nematic cell, where the cell is sufficiently thick that the disclinations start and terminate at the same surface. The different defect configurations are stabilised by a master substrate that enforces a lattice of surface defects exhibiting zero total topological charge value. Theoretically, we model disclination configurations using a Landau-de Gennes phenomenological model. Experimentally, we enable diverse defect patterns by implementing an in-house-developed Atomic Force Measurement scribing method, where NLC configurations are monitored via polarised optical microscopy. We show numerically and experimentally that an "alphabet" of up to 18 unique line defect configurations can be stabilised in a 4x4 lattice of alternating s=±1 surface defects, which can be "rewired" multistably using appropriate field manipulation. Our proof-of-concept mechanism may lead to a variety of applications, such as multistable optical displays and rewirable nanowires. Our studies also are of interest from a fundamental perspective. We demonstrate that a chargeless line could simultaneously exhibit defect-antidefect properties. Consequently, a pair of such antiparallel disclinations exhibits an attractive interaction. For a sufficiently closely-spaced pair of substrate-pinned defects, this interaction could trigger rewiring, or annihilation if defects are depinned.

Electric field-induced crossover from 3D to 2D topological defects in a nematic liquid crystal: experimental verification.

A substrate was patterned with two pairs of half-integer strength topological defects, (+1/2, +1/2) and (+1/2, -1/2). In a sufficiently thick cell, a disclination line runs in an arch above the substrate connecting the two half integer defects within each pair. The director around the disclination line for the like-sign pair must rotate in 3D, whereas for the opposite-sign defect pair the director lies in the xy-plane parallel to the substrate. For a negative dielectric anisotropy nematic, an electric field applied normal to the substrate drives the director into the xy-plane, forcing the arch of the disclination line of the like-sign pair to become extended along the z-axis. For sufficiently large field the arch splits, resulting in two nearly parallel disclination lines traversing the cell from one substrate to the other. The opposite-sign defect pair is largely unaffected by the electric field as the director already lies in the xy-plane. Experimental results are presented, which are consistent with numerical simulations.

Nematic topological defects positionally controlled by geometry and external fields.

Using a Landau-de Gennes approach, we study the impact of confinement topology, geometry and external fields on the spatial positioning of nematic topological defects (TDs). In quasi two-dimensional systems we demonstrate that a confinement-enforced total topological charge of m > 1/2 decays into elementary TDs bearing a charge of m = 1/2. These assemble close to the bounding substrate to enable essentially bulk-like uniform nematic ordering in the central part of a system. This effect is reminiscent of the Faraday cavity phenomenon in electrostatics. We observe that in certain confinement geometries, varying the correlation length size of the order parameter could trigger a global rotation of an assembly of TDs. Finally, we show that an external electric field could be used to drag the boojum fingertip towards the interior of the confinement cell. Assemblies of TDs could be exploited as traps for appropriate nanoparticles, opening several opportunities for the development of functional nanodevices.

Decomposition vs. escape of topological defects in a nematic liquid crystal.

Nematic cells patterned with square arrays of strength m = ±1 topological defects were examined as a function of cell thickness (3 < h < 7.5 µm), temperature, and applied voltage. Thicker cells tend to exhibit an escape or partial escape of the nematic director as a means of mitigating the elastic energy cost near the defect cores, whereas thinner cells tend to favor splitting of the integer defects into pairs of half-integer strength defects. On heating the sample into the isotropic phase and cooling back into the nematic, some apparently split defects can reappear as unsplit integer defects, or vice versa. This is consistent with the system's symmetry, which requires a first order transition between the two relaxation mechanisms.

Decomposition of strongly charged topological defects.

We study decomposition of geometrically enforced nematic topological defects bearing relatively large defect strengths m in effectively two-dimensional planar systems. Theoretically, defect cores are analyzed within the mesoscopic Landau-de Gennes approach in terms of the tensor nematic order parameter. We demonstrate a robust tendency of defect decomposition into elementary units where two qualitatively different scenarios imposing total defect strengths on a nematic region are employed. Some theoretical predictions are verified experimentally, where arrays of defects bearing charges m=±1 and even m=±2 are enforced within a plane-parallel nematic cell using an atomic force microscopy scribing method.

Influence of a dispersion of magnetic and nonmagnetic nanoparticles on the magnetic Fredericksz transition of the liquid crystal 5CB.

A long time ago, Brochard and de Gennes predicted the possibility of significantly decreasing the critical magnetic field of the Fredericksz transition (the magnetic Fredericksz threshold) in a mixture of nematic liquid crystals and ferromagnetic particles, the so-called ferronematics. This phenomenon is rarely measured to be large, due to soft homeotropic anchoring induced at the nanoparticle surface. Here we present an optical study of the magnetic Fredericksz transition combined with a light scattering study of the classical nematic liquid crystal: the pentylcyanobiphenyl (5CB), doped with 6 nm diameter magnetic and nonmagnetic nanoparticles. Surprisingly, for both nanoparticles, we observe at room temperature a net decrease of the threshold field of the Fredericksz transition at low nanoparticle concentrations, which appears associated with a coating of the nanoparticles by a brush of polydimethylsiloxane copolymer chains inducing planar anchoring of the director on the nanoparticle surface. Moreover, the magnetic Fredericksz threshold exhibits nonmonotonic behavior as a function of the nanoparticle concentration for both types of nanoparticles, first decreasing down to a value from 23% to 31% below that of pure 5CB, then increasing with a further increase of nanoparticle concentration. This is interpreted as an aggregation starting at around 0.02 weight fraction that consumes more isolated nanoparticles than those introduced when the concentration is increased above c=0.05 weight fraction (volume fraction 3.5×10^{-2}). This shows the larger effect of isolated nanoparticles on the threshold with respect to aggregates. From dynamic light scattering measurements we deduced that, if the decrease of the magnetic threshold when the nanoparticle concentration increases is similar for both kinds of nanoparticles, the origin of this decrease is different for magnetic and nonmagnetic nanoparticles. For nonmagnetic nanoparticles, the behavior may be associated with a decrease of the elastic constant due to weak planar anchoring. For magnetic nanoparticles there are non-negligible local magnetic interactions between liquid crystal molecules and magnetic nanoparticles, leading to an increase of the average order parameter. This magnetic interaction thus favors an easier liquid crystal director rotation in the presence of external magnetic field, able to reorient the magnetic moments of the nanoparticles along with the molecules.

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.

Electroclinic effect in a chiral paranematic liquid-crystal layer above the bulk nematic-to-isotropic transition temperature.

Electroclinic measurements are reported for two chiral liquid crystals above their bulk chiral isotropic-nematic phase transition temperatures. It is found that an applied electric field E induces a rotation θ [∝Ε] of the director in the very thin paranematic layers that are induced by the cell's two planar-aligning substrates. The magnitude of the electroclinic coefficient dθ/dE close to the transition temperature is comparable to that of a bulk chiral nematic, as well as to that of a parasmectic region above a bulk isotropic-to-chiral smectic-A phase. However, dθ/dE in the paranematic layer varies much more slowly with temperature than in the parasmectic phase, and its relaxation time is slower by more than three orders of magnitude than that of the bulk chiral nematic electroclinic effect.

Creating arbitrary arrays of two-dimensional topological defects.

An atomic force microscope was used to scribe a polyimide-coated substrate with complex patterns that serve as an alignment template for a nematic liquid crystal. By employing a sufficiently large density of scribe lines, two-dimensional topological defect arrays of arbitrary defect strength were patterned on the substrate. When used as the master surface of a liquid crystal cell, in which the opposing slave surface is treated for planar degenerate alignment, the liquid crystal adopts the pattern's alignment with a disclination line emanating at the defect core on one surface and terminating at the other surface.

Optical imaging of liquid crystals at the nanoscale.

The instrumentation associated with near-field scanning optical microscopy (NSOM) can be exploited to provide three-dimensional structure and dynamic information about liquid crystals at scales not possible with diffraction-limited tools. This Minireview focuses on our use of NSOM techniques to probe spatial variations of the nematic director and the nematic orientational order parameter on length scales as small as a few nanometers.

Nematic molecular core flexibility and chiral induction.

Electroclinic measurements, in which an applied electric field E induces a rotation Δθ ([proportional]E) of the liquid crystal director about the electric field axis in a chiral environment, were performed on several configurationally achiral liquid crystals in the presence of an imposed helical director profile. This imposed twist establishes a chiral symmetry environment for the liquid crystal. It was observed that a conformationally racemic mesogen possessing a flexible phenyl benzoate core exhibits a measurable electroclinic response in the nematic phase. On the other hand, when the phenyl benzoate mesogen is mixed with a mesogen containing a rigid, conformationally achiral core (fluorenone), or with a racemic dopant with an axially chiral core that mimics a mesogen having rigid right- and left-handed conformations (2,2'-spirobiindan-1,1'-dione), the magnitudes of the electroclinic responses were found to decrease sharply, apparently going to zero when extrapolated to the pure 2,2'-spirobiindan-1,1'-dione or fluorenone limit. (Note that neither of these additives possesses a nematic phase.). The results suggest that the flexibility of the core and its ability to deracemize conformationally in order to compensate the elastic energy cost of the imposed twist is the primary mechanism behind the observed electroclinic response.

Surface topography and rotational symmetry breaking.

The surface electroclinic effect, which is a rotation of the molecular director in the substrate plane proportional to an electric field E applied normal to the substrate, requires both a chiral environment and C(2) (or lower) rotational symmetry about E. The two symmetries typically are created in tandem by manipulating the surface topography, a process that conflates their effects. Here we use a pair of rubbed polymer-coated substrates in a twist geometry to obtain our main result, viz., that the strengths of two symmetries, in this case the rub-induced breaking of C(∞) rotational symmetry and chiral symmetry, can be separated and quantified. Experimentally we observe that the strength of the reduced rotational symmetry arising from the rub-induced scratches, which is proportional to the electroclinic response, scales linearly with the induced topographical rms roughness and increases with increasing rubbing strength of the polymer. Our results also suggest that the azimuthal anchoring strength coefficient is relatively insensitive to the strength of the rubbing.

Macroscopic torsional strain and induced molecular conformational deracemization.

A macroscopic helical twist is imposed on an achiral nematic liquid crystal by controlling the azimuthal alignment directions at the two substrates. On application of an electric field the director rotates in the substrate plane. This electroclinic effect, which requires the presence of chirality, is strongest at the two substrates and increases with increasing imposed twist distortion. We present a simple model involving a trade-off among bulk elastic energy, surface anchoring energy, and deracemization entropy that suggests the large equilibrium director rotation induces a deracemization of chiral conformations in the molecules-effectively "top-down" chiral induction-quantitatively consistent with experiment.

Nematic electroclinic effect in a carbon-nanotube-doped achiral liquid crystal.

A small quantity of carbon nanotubes (CNTs) dispersed in an achiral liquid crystal (LC) matrix transmits chirality a short distance into the LC, and the LC+CNT mixture is found to exhibit a bulklike electroclinic effect in the nematic phase. The magnitude of the effect increases rapidly on cooling, showing significant pretransitional behavior on approaching the nematic-smectic-A transition temperature (T(NA)) from above. The variation of the electroclinic coefficient is negligible over the frequency range 100 Hz to 100 kHz in the in the nematic phase well above T(NA) and in the smectic-A phase, whereas the electroclinic coefficient falls off significantly with increasing frequency just above T(NA).

Direct visualization and measurement of the extrapolation length on cooling toward the nematic-smectic-A phase transition temperature.

A herringbone "easy axis" pattern is scribed into a polyimide alignment layer for liquid-crystal orientation using the stylus of an atomic force microscope. Owing to the liquid crystal's bend elasticity K33 , the nematic director is unable to follow the sharp turn in the scribed easy axis, but instead relaxes over an extrapolation length L=K33/W2φ, where W2φ is the quadratic azimuthal anchoring strength coefficient. By immersing a tapered optical fiber into the liquid crystal, illuminating the fiber with polarized light, and scanning the fiber close to the substrate, a visualization and direct measurement of L are obtained on approaching the nematic-smectic- A phase transition temperature T NA from above. L is found to exhibit a sharp pretransitional increase near T NA, consistent with a diverging bend elastic constant.

Mechanically generated surface chirality at the nanoscale.

A substrate coated with an achiral polyimide alignment layer was scribed bidirectionally with the stylus of an atomic force microscope to create an easy axis for liquid crystal orientation. The resulting noncentrosymmetric topography resulted in a chiral surface that manifests itself at the molecular level. To show this unambiguously, a planar-aligned negative dielectric aniostropy achiral nematic liquid crystal was placed in contact with the surface and subjected to an electric field E. The nematic director was found to undergo an azimuthal rotation approximately linear in E. This so-called "surface electroclinic effect" is a signature of surface chirality and was not observed when the polyimide was treated for a centrosymmetric topography, and therefore was nonchiral.