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.

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).

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.

Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra.

All hard, convex shapes are conjectured by Ulam to pack more densely than spheres, which have a maximum packing fraction of phi = pi/ radical18 approximately 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction. For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with phi = 0.7786 (ref. 4), which was subsequently compressed numerically to phi = 0.7820 (ref. 5), while compressing with different initial conditions led to phi = 0.8230 (ref. 6). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, which can be compressed to a packing fraction of phi = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is phi = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to phi = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Mode delocalization in 1D photonic crystal lasers.

We have investigated the formation of in-bandgap delocalized modes due to random lattice disorder as determined from the longitudinal mode spacing in a distributed Bragg laser. We were able to measure the penetration depth, and from transfer matrix simulations, determine how the localization length is altered for disordered lattices. Transfer matrix simulations and studies of the ensemble average were able to connect the gap delocalized modes to localized modes outside of the gap as expected from consideration of Anderson localization, as well as identify the controlling parameters.

Direct measurement of surface-induced orientational order parameter profile above the nematic-isotropic phase transition temperature.

The spatial and temperature dependence of the surface-induced orientational order parameter S(z,T) was determined in the isotropic phase. An optical fiber was immersed in a thin liquid crystal layer and the retardation was measured as a function of the fiber's height above the surface, from which the model-independent S(z,T) was deduced with resolution

Patterning-induced surface chirality and modulation of director twist in a nematic cell.

A substrate coated with a polyimide alignment layer is scribed bidirectionally with the stylus of an atomic force microscope to create an easy axis for liquid-crystal orientation. The resulting noncentrosymmetric topography breaks two-dimensional inversion symmetry and results in a spatial amplitude modulation of an imposed twisted nematic state. This is observed optically as spatially periodic light and dark stripes. When the alignment layer is scribed unidirectionally the centrosymmetric topography maintains inversion symmetry, and no stripes are observed. The appearance of the twist modulation is consistent with a chiral term in the free energy.

Polar-horizontal versus polar-vertical reverse-tilt-domain walls: influence of a pretilt angle below the nematic-isotropic phase transition.

On cooling through the isotropic-to-nematic phase transition in a cell whose substrates induce a large pretilt angle theta0 from the vertical direction, but with no preferential azimuthal orientation, tilt domains appear. The boundary walls between reverse tilt domains are found to be bendlike and twistlike when theta0(T=TNI) is sufficiently large just below the isotropic-nematic phase transition temperature TNI--i.e., for a nearly planar orientation. Here the director becomes planar approximately midway through the wall, and we refer to this type of wall as "polar horizontal," which is topologically stable. However, if theta0(T=TNI) is sufficiently small just below TNI--i.e., closer to vertical orientation--a splay like and twistlike domain wall obtains, where the director is vertically oriented approximately midway through the wall; we refer to this type of wall as "polar vertical," whose stability depends on the anchoring. On cooling through the nematic phase, the pretilt angle theta0 decreases, with the director aligning closer to the vertical orientation. Nevertheless, the structures of both types of domain walls remain unchanged on variation of theta0 with temperature owing to topological constraints and also are unchanged after the application and removal of a large electric field. We examine the structure of domain walls for the liquid crystal ZLI-4330 (Merck) as a function of pretilt angle theta0(T=TNI) and calculate a critical value theta0c(T=TNI) of the pretilt angle just below TNI for which the predominance of domain walls crosses over from polar horizontal to polar vertical.

Naturally occurring reverse tilt domains in a high-pretilt alignment nematic liquid crystal.

A cell whose substrates were coated with the polyamic acid SE1211 (Nissan Chemical Industries) and baked at high temperatures was filled with a nematic liquid crystal in the isotropic phase. On cooling into the nematic phase, naturally occurring and temporally and thermally robust reverse tilt domains separated by thin filamentlike walls were observed. The properties of these structures are reported.

Comment on "Pushing the hyperpolarizability to the limit".

It is shown that energy/length scaling complicates maximizing the first hyperpolarizability of a single electron as a function of the potential. A more transparent formula for this hyperpolarizability is given. Examining this formula demonstrates that Zhou et al.(1) have not proved that modulated conjugation results in large hyperpolarizability.

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

Using an atomic force microscope to nanopattern a substrate for liquid crystal alignment, a bend distortion is imposed on a liquid crystal. In regions of large bend the smectic-A phase melts into the nematic phase, and the width of the melted region is measured as a function of temperature. The results are consistent with type-I superconducting (nematic-smectic-A) behavior, wherein a large magnetic field (bend or twist distortion) induces an order to disorder transition. A model that accounts for non-mean-field behavior is presented.

Defocused orientation and position imaging (DOPI) of myosin V.

The centroid of a fluorophore can be determined within approximately 1.5-nm accuracy from its focused image through fluorescence imaging with one-nanometer accuracy (FIONA). If, instead, the sample is moved away from the focus, the point-spread-function depends on both the position and 3D orientation of the fluorophore, which can be calculated by defocused orientation and position imaging (DOPI). DOPI does not always yield position accurately, but it is possible to switch back and forth between focused and defocused imaging, thereby getting the centroid and the orientation with precision. We have measured the 3D orientation and stepping behavior of single bifunctional rhodamine probes attached to one of the calmodulins of the light-chain domain (LCD) of myosin V as myosin V moves along actin. Concomitant with large and small steps, the LCD rotates and then dwells in the leading and trailing position, respectively. The probe angle relative to the barbed end of the actin (beta) averaged 128 degrees while the LCD was in the leading state and 57 degrees in the trailing state. The angular difference of 71 degrees represents rotation of LCD around the bound motor domain and is consistent with a 37-nm forward step size of myosin V. When beta changes, the probe rotates +/-27 degrees azimuthally around actin and then rotates back again on the next step. Our results remove degeneracy in angles and the appearance of nontilting lever arms that were reported.

Effect of flexible bimesogen dopant on the stability of the anticlinic liquid-crystal phase.

Small quantities of the floppy bimesogen di(4PPB5)3Si were dissolved in an anticlinic liquid crystal consisting of a mixture of left-handed and right-handed TFMHPOBC, with enantiomer excess X=0.2 . The bimesogen dopant was found to promote anticlinic order with an anticlinic interaction coefficient per molecule udopant smaller than, but of the same order as, that of the rigid bent-core dopant P-7PIMB. For both dopants udopant was found to be much larger than that due to a pair of TFMHPOBC molecules in adjacent layers. The results are examined in terms of both the flexibility of the group linking the two legs of each dopant, as well as their chemical structure.

Twist elasticity and anchoring in a lamellar nematic phase.

Electro-optic measurements were performed on a lamellar nematic phase in which the mesogenic moieties lie in lamellae that are separated by partially perfluorinated side groups. The twist elastic constant K22, viscosity gamma(1), and the quadratic and quartic anchoring strength coefficients are reported. K22 and gamma(1) are found to be considerably smaller than that of typical three-dimensional nematics. The small K22 is due to the greatly weakened interactions between the spatially separated lamellae.

Light scattering investigation above the nematic-smectic-A phase transition in binary mixtures of calamitic and bent-core mesogens.

Quasielastic light scattering measurements were performed in the nematic phase of mixtures consisting of the calamitic mesogen 8OCB doped with small concentrations of the bent-core molecule P-7PIMB. It was found that the regular part of the bend elastic constant decreases strongly with dopant concentration X. Close to the nematic-smectic-A phase transition temperature, the divergent part of the bend elastic constant, which is proportional to the bare correlation length xi(0)(||) parallel to the layer normal, also decreases rapidly with X. The effect of the dopant on xi(0)(||) is examined in brief theoretically.

Apparent tricritical behavior at a nearly second-order nematic-isotropic phase transition of a cyclic liquid crystalline trimer.

The cyclic liquid crystalline trimer TPB-(c)9(3) was investigated by optical retardation and Fréedericksz techniques within a few tens of millikelvins of the superheating limit of the nearly second-order nematic-isotropic phase transition. Both the optical retardation and the Fréedericksz bend threshold voltage are in good agreement with tricritical behavior for the transition.

Nematic liquid-crystal polarization gratings by modification of surface alignment.

The stylus of an atomic force microscope is used to scribe preferred directions for liquid-crystal alignment on a polyimide-coated substrate. The opposing substrate that comprises the liquid-crystal cell is rubbed unidirectionally, resulting in a twisted nematic structure associated with each micrometer-sized pixel. The polarization of light entering from the uniformly rubbed substrate rotates with the nematic director by a different amount in each pixel, and each of the two emerging polarization eigenmodes interferes separately. Two examples are discussed: a square grating that allows only odd-order diffraction peaks and a grating that combines rotation with optical retardation to simulate a blazed grating for circularly polarized light. The gratings can be electrically switched if used with semitransparent electrodes.