The Effect of Mesogenic Coronas on the Type and Anisotropy of Gold Nanoparticle Superlattices: When Can the Tail Wag the Dog?

The correlation between the size of nanoparticles, the structure and shape of mesogenic ligands and the ensuing assembly behaviour is not really understood. Closer inspection shows very surprising features. Here, 2- and 4-nm gold nanoparticles (NPs) were synthesized, and grafted with a forked ligand containing two rod-like mesogens in its branches: one cholesterol, the other with azobenzene. The 4-nm NPs also contained n-hexylthiol as co-ligand. They were found to form a FCC cubic superlattice, whereas the 2-nm NPs form hexagonal HCP with weak birefringence, hence with partially oriented ligands. The structures were compared with those of related systems containing a range of different azobenzene-to-cholesterol ratios, all giving body-centred tetragonal superlattices with various degrees of anisotropy. Geometric analysis is presented in terms of the asphericity of the NPs' surroundings, requirement for space-filling and structural anisotropy. Some general rules are derived to help design the soft corona around the NPs in order to obtain superlattices with the desired structure and anisotropy.

Dipole-dipole correlations in the nematic phases of symmetric cyanobiphenyl dimers and their binary mixtures with 5CB.

We report on the temperature dependence of birefringence and of the static dielectric permittivity tensor in a series of binary mixtures between the symmetric, bent-shaped, 1'',9''-bis(4-cyanobiphenyl-4'-yl)nonane (CB9CB) dimer and the monomeric nematogen 5CB. In the studied composition range the mixtures exhibit two nematic phases with distinct birefringence and dielectric features. Birefringence measurements are used to estimate the temperature dependence of the tilt between the axis defining the nanoscale helical modulation of the low temperature nematic phase with the (local) direction of the maximal alignment of the cyanobiphenyl units. Planar as well as magnetically and/or electrically aligned samples are used to measure the perpendicular and parallel components of the dielectric permittivity in both nematic phases. A self-consistent molecular field theory that takes into account flexibility and symmetry of the constituent mesogens is introduced for the calculation of order parameters and intra-molecular orientational dipolar correlations of the flexible dimers as a function of temperature/concentration. Utilising the tilt angle, as calculated from the birefringence measurements, and the predictions of the molecular theory, dielectric permittivity is modelled in the framework of the anisotropic version of the Kirkwood-Fröhlich theory. Using the inter-molecular Kirkwood correlation factors as adjustable parameters, excellent agreement between theory and permittivity measurements across the whole temperature range and composition of the mixtures is obtained. The importance of the orientational, intra- and inter-molecular, dipolar correlations, their relative impact on the static dielectric properties, as well as their connection with the local structure of the nematic phases of bent-shaped bimesogens, is discussed.

Spontaneous mirror symmetry breaking and chiral segregation in the achiral ferronematic compound DIO.

An achiral compound, DIO, known to exhibit three nematic phases namely N, NX and NF, is studied by polarizing microscopy and electro-optics for different surface conditions in confinement. The high temperature N phase assigned initially as a conventional nematic phase, shows two additional unusual features: the optical activity and the linear electro-optic response related to the polar nature of this phase. An appearance of chiral domains is explained by the spontaneous symmetry breaking arising from the saddle-splay elasticity and followed by the formation of helical domains of the opposite chirality. This is the first example of helical segregation observed in calamitic non-chiral molecules in the nematic phase. As reported previously, the ferronematic NF shows strong polar azimuthal surface interaction energy which stabilizes a homogeneous structure in planar aligned LC cells rubbed parallel and exhibits a twisted structure in cells with antiparallel buffing. The transmission spectra are simulated using Berreman's 4 × 4 matrix method. The observed agreement between the experimental and the simulated spectra quantitatively confirms the presence of twisted structures in antiparallel rubbed cells.

Dynamic phase measurement of fast liquid crystal phase modulators.

We present dynamic time-resolved measurements of a multi-pixel analog liquid crystal phase modulator driven at a 1 kHz frame rate. A heterodyne interferometer is used to interrogate two pixels independently and simultaneously, to deconvolve phase modulation with a wide bandwidth. The root mean squared optical phase error within a 30 Hz to 25 kHz bandwidth is <0.5° and the crosstalk rejection is 50 dB. Measurements are shown for a custom-built device with a flexoelectro-optic chiral nematic liquid crystal. However, the technique is applicable to many different types of optical phase modulators and spatial light modulators.

Study of the Experimental and Simulated Vibrational Spectra Together with Conformational Analysis of Thioether Cyanobiphenyl-Based Liquid Crystal Dimers.

Infrared spectroscopy (IR) and quantum chemistry calculations that are based on the density functional theory (DFT) have been used to study the structure and molecular interactions of the nematic and twist-bend phases of thioether-linked dimers. Infrared absorbance measurements were conducted in a polarized beam for a homogeneously aligned sample in order to obtain more details about the orientation of the vibrational transition dipole moments. The distributions to investigate the structure and conformation of the molecule dihedral angle were calculated. The calculated spectrum was compared with the experimental infrared spectra and as a result, detailed vibrational assignments are reported.

How Do Intermolecular Interactions Evolve at the Nematic to Twist-Bent Phase Transition?

Polarized beam infrared (IR) spectroscopy provides valuable information on changes in the orientation of samples in nematic phases, especially on the role of intermolecular interactions in forming the periodically modulated twist-bent phase. Infrared absorbance measurements and quantum chemistry calculations based on the density functional theory (DFT) were performed to investigate the structure and how the molecules interact in the nematic (N) and twist-bend (NTB) phases of thioether dimers. The nematic twist-bend phase observed significant changes in the mean IR absorbance. On cooling, the transition from the N phase to the NTB phase was found to be accompanied by a marked decrease in absorbance for longitudinal dipoles. Then, with further cooling, the absorbance of the transverse dipoles increased, indicating that transverse dipoles became correlated in parallel. To investigate the influence of the closest neighbors, DFT calculations were performed. As a result of the optimization of the molecular cores system, we observed changes in the square of the transition dipoles, which well corresponds to absorbance changes observed in the IR spectra. Interactions of molecules dominated by pairing were observed, as well as the axial shift of the core to each other.

Molecular biaxiality determines the helical structure - infrared measurements of the molecular order in the nematic twist-bend phase of difluoro terphenyl dimer.

Fourier-transform infrared polarized spectroscopy was employed, to obtain the three components of the infrared absorbance for a series of bent-shaped dimers containing double fluorinated terphenyl core (DTC5Cn, n = 5, 7, 9, 11). The data were used to calculate both uniaxial and biaxial order parameters, for various molecular groups of dimers. The molecule bend was estimated based on the observed differences between the uniaxial order parameters for the terphenyl core and central hydrocarbon linker. The orientational order, distinctly reverses its monotonic trend of increase to decrease at the transition temperature, from the uniaxial nematic to the twist-bend nematic phase as result of the director tilt in latter/(twist-bend) phase. The molecular biaxiality, which is negligible in the nematic phase, starts increasing on entering the twist-bend nematic phase, following a sin-square relationships with the tilt angle. The local director curvature is found to be controlled by the molecular biaxiality parameter.

Analog modulation by the flexoelectric effect in liquid crystals.

We have solved the long-standing problems of stability and hysteresis, and we are able to obtain the homogeneous uniform lying helix structure in polymer-free cholesteric liquid crystals. This is instrumental for the present work to demonstrate the analog modulation at high speed and high precision. The device is configured for the transverse field switching wherein the substrate surface is flat. In addition to the response time of 10 ms at room temperature, we have obtained the R-squared and the adjusted R-squared as a measure of true sine wave for the sinusoidal responding transmissions from 1 Hz to 100 kHz that are all greater than 0.9993. In a Michelson interferometer, the phase shift at wavelength 633 nm after two passes has been measured to be equal to about $\pi /{9}$π/9 at 4.6 V/µm for the chiral-doped nematic mixtures E7.

Dynamic response of large tilt-angle flexoelectro-optic liquid crystal modulators.

We present here the first time-resolved tilt-angle and retardance measurements for large-tilt (>45°) flexoelectro-optic liquid crystal modulators. These devices have potential for next generation fast switching (>1 kHz), 0-2π analog phase spatial light modulators (SLMs), with applications in optical beamsteering, microscopy and micromachining. The chiral nematic device used consisted of a mixture of CBC7CB and the chiral dopant R5011 in a nominally 5 µm-thick cell, aligned in the uniform lying helix mode. As the device is dynamically switched over angles of ± 54°, retardance changes of up to 0.17λ are observed. Furthermore, the time-resolved measurements reveal an asymmetry in the tilt in the optic-axis depending on the polarity of the applied electric field. The change in the optic-axis exhibits a pattern dependence, whereby it is determined by both the pulse history and the applied field. This pattern dependence results in tilt-angle errors of up to 8.8°, which could manifest as phase errors as large as 35.2° in potential SLMs. These time domain measurements may allow correction of these deterministic errors, to realize practical devices.

1H NMR study of molecular order and dynamics in the liquid crystal CB-C9-CB.

Molecular order and dynamics of the CB-C9-CB liquid crystalline dimer exhibiting the nematic (N) and the twist bend nematic (Ntb) phases were investigated by proton NMR spectroscopy, using fields of 0.78 T and 7.04 T, and relaxometry. The first relaxometry experiments for a very wide Larmor frequency domain (8 kHz-300 MHz) on this system, using a combination of standard and fast field cycling NMR techniques, were performed. The spectroscopy results in the Ntb phase allowed us to probe the local molecular orientation relative to the Ntb helix axis. The relaxation data were analyzed considering order director fluctuations (ODF), molecular self-diffusion (SD) and local molecular rotations/reorientations (R) relaxation mechanisms. Global fits of theoretical relaxation models, as a function of temperature and Larmor frequency, for the phases under investigation, allowed for the determination of rotational correlation times, diffusion coefficients, viscoelastic parameters, correlation lengths and activation energies (in the case of thermally activated mechanisms). A clear difference between the structures of the N and Ntb phases was detected from the results of proton spin-lattice relaxation through distinct temperature and frequency dependencies' signatures of the collective modes. Significant pre-transitional effects were observed at the N-Ntb phase transition both from relaxometry and spectroscopy data. The experimental results correlate to data and models for comparable liquid crystalline systems.

Pretransitional behavior of viscoelastic parameters at the nematic to twist-bend nematic phase transition in flexible n-mers.

We report dynamic light scattering measurements of the orientational (Frank) elastic constants and associated viscosities among a homologous series of a liquid crystalline dimer, trimer, and tetramer exhibiting a uniaxial nematic (N) to twist-bend nematic (NTB) phase transition. The elastic constants for director splay (K11), twist (K22) and bend (K33) exhibit the relations K11 > K22 > K33 and K11/K22 > 2 over the bulk of the N phase. Their behavior near the N-NTB transition shows dependency on the parity of the number (n) of the rigid mesomorphic units in the flexible n-mers. Namely, the bend constant K33 in the dimer and tetramer turns upward and starts increasing close to the transition, following a monotonic decrease through most of the N phases. In contrast, K33 for the trimer flattens off just above the transition and shows no pretransitional enhancement. The twist constant K22 increases pretransitionally in both even and odd n-mers, but more weakly so in the trimer, while K11 increases steadily on cooling without evidence of pretransitional behavior in any n-mer. The viscosities associated with pure splay, twist-dominated twist-bend, and pure bend fluctuations in the N phase are comparable in magnitude to those of rod-like monomers. All three viscosities increase with decreasing temperature, but the bend viscosity in particular grows sharply near the N-NTB transition. The N-NTB pretransitional behavior is shown to be in qualitative agreement with the predictions of a coarse-grained theory, which models the NTB phase as a "pseudo-layered" structure with the symmetry (but not the mass density wave) of a smectic-A* phase.

Flexoelectro-optic liquid crystal analog phase-only modulator with a 2π range and 1 kHz switching.

We present a flexoelectro-optic liquid crystal (LC) analog phase modulator with >2π phase range at a 1 kHz switching frequency. The chiral nematic LC mixture consists of the bimesogen CBC7CB with chiral dopant R5011, aligned in the uniform lying helix mode. The mixture exhibits >±π/4 rotation of the optic axis for a drive voltage of ±21.5 V (E=±4.5 V µm-1). The rotation of the optic axis is converted into a phase modulation with the aid of a reflective device configuration incorporating a ∼5 µm LC cell, a polarizer, two quarter-wave plates, and a mirror. The residual amplitude modulation is found to be <23%. This flexoelectro-optic phase modulator combination has the potential to enable analog spatial light modulators with very fast frame rates suitable for a range of applications.

Tuning selective reflection of light by surface anchoring in cholesteric cells with oblique helicoidal structures.

Selective reflection of light by oblique helicoidal cholesteric (ChOH) can be tuned in a very broad spectral range by an applied electric field. In this Letter, we demonstrate that the peak wavelength of the selective reflection can be controlled by the surface alignment of the director in sandwich cells. The peak wavelength is blue-shifted when the surface alignment is perpendicular to the bounding plates and red-shifted when it is planar. The effect is explained by the electric field redistribution within the cell caused by a spatially varying heliconical ChOH structure. The observed phenomenon can be used in sensing applications.

Dynamic calorimetry and XRD studies of the nematic and twist-bend nematic phase transitions in a series of dimers with increasing spacer length.

A modulated and conventional DSC study of the transitions between the twist-bend nematic (Ntb), regular nematic (N) and isotropic liquid (Iso) phases was performed on a series of difluoroterphenyl-based dimers with (CH2)n spacers; n = 5, 7, 9, 11. The enthalpy of Ntb-N transition decreases steeply with increasing n, while that of the N-Iso transition increases with n; hence, the greatest effect of increasing n is a lowering N phase enthalpy. Based on past and present X-ray scattering experiments, we estimate the average molecular conformation in the Ntb phase and perform torsion energy calculations on the spacer. From this, the lowering enthalpy of the N phase is attributed to the decreasing torsional energy cost of bringing the two terphenyls from an inclined twisted conformation in the Ntb phase, to almost parallel in the N phase. With increasing n the C-C bonds of the spacers twist less away from their trans conformation, thereby reducing the overall torsion energy of the N phase. It is speculated that the nearly continuous nature of the Ntb-N transition in n = 11 dimer is associated with the divergence of the helical pitch toward infinity which is intercepted by a final jump at the very weak (0.01 J g-1) first-order transition. Small-angle X-ray scattering results suggest similar local cybotactic layering in both nematic phases, with four sublayers, i.e. tails, mesogens, spacers, mesogens.

Characterization of the Submicrometer Hierarchy Levels in the Twist-Bend Nematic Phase with Nanometric Helices via Photopolymerization. Explanation for the Sign Reversal in the Polar Response.

Photopolymerization of a reactive mesogen mixed with a mesogenic dimer, shown to exhibit the twist-bend nematic phase (NTB), reveals the complex structure of the self-deformation patterns observed in planar cells. The polymerized reactive mesogen retains the structure formed by liquid crystalline molecules in the twist bend phase, thus enabling its observation by scanning electron microscopy (SEM). Hierarchical ordering scales ranging from tens of nanometers to micrometers are imaged in detail. Submicron features, anticipated from earlier X-ray experiments, are visualized directly. In the self-deformation stripes formed in the NTB phase, the average director field is found tilted in the cell plane by an angle of up to 45° from the cell rubbing direction. This tilt explains the sign inversion being observed in the electro-optical studies.

Added Alkane Allows Thermal Thinning of Supramolecular Columns by Forming Superlattice-An X-ray and Neutron Study.

We report a columnar superlattice formed by blends of dendron-like Li 3,4,5-tris(n-alkoxy)benzoates with n-alkanes. Without the alkane, the wedge-shaped molecules form liquid crystal columns with 3 dendrons in a supramolecular disk. The same structure exists in the blend, but on heating one dendron is expelled from the disks in every third column and is replaced by the alkane. This superlattice of unequal columns is confirmed by complementary X-ray and neutron diffraction studies. Lateral thermal expansion of dendrons normally leads to the expulsion of excess molecules from the column, reducing the column diameter. However, in the already narrow columns of pure Li salt, expulsion of one of only three dendrons in a disk is not viable. The added alkane facilitates the expulsion, as it replaces the missing dendron. Replacing the alkane with a functional compound can potentially lead to active nanoarrays with relatively large periodicity by using only small molecules.

Helically Twisted Chiral Arrays of Gold Nanoparticles Coated with a Cholesterol Mesogen.

Gold nanoparticles have been prepared and surface-functionalized with a 1:1 molar mixture of a hexylthiol ligand and a chiral mesogenic ligand consisting of a cholesterylbenzoate attached via an undecylthiol spacer. Grazing incidence X-ray diffraction showed that upon annealing a columnar liquid crystal (LC) structure develops with the nanoparticles forming strings on a regular oblique 2d lattice. Synchrotron radiation circular dichroism is substantially enhanced upon the isotropic-LC transition. In the proposed structural model, layers of Au columns rotate by a small angle relative to their neighbors, with the columns winding around a helical axis. The work demonstrates that it is possible to obtain chiral LC superstructures from nanoparticles coated with chiral mesogen without the addition of a separate LC or chiral dopants. The results provide direction in the development of plasmonic metamaterials interacting selectively with circularly polarized light.

On the structure of the Nx phase of symmetric dimers: inferences from NMR.

NMR measurements on a selectively deuterated liquid crystal dimer CB-C9-CB, exhibiting two nematic phases, show that the molecules in the lower temperature nematic phase, N(X), experience a chiral environment and are ordered about a uniformly oriented director throughout the macroscopic sample. The results are contrasted with previous interpretations that suggested a twist-bend spatial variation of the director. A structural picture is proposed wherein the molecules are packed into highly correlated chiral assemblies.

Surface alignment, anchoring transitions, optical properties, and topological defects in the thermotropic nematic phase of organo-siloxane tetrapodes.

We perform optical, surface anchoring, and textural studies of an organo-siloxane "tetrapode" material in the broad temperature range of the nematic phase. The optical, structural, and topological features are compatible with the uniaxial nematic order rather than with the biaxial nematic order, in the entire nematic temperature range -25 °C < T < 46 °C studied. For homeotropic alignment, the material experiences surface anchoring transition, but the director can be realigned into an optically uniaxial texture by applying a sufficiently strong electric field. The topological features of textures in cylindrical capillaries, in spherical droplets and around colloidal inclusions are consistent with the uniaxial character of the long-range nematic order. In particular, we observe isolated surface point defects - boojums and bulk point defects - hedgehogs that can exist only in the uniaxial nematic liquid crystal.

Comparative Study of the Optical and Dielectric Anisotropy of a Difluoroterphenyl Dimer and Trimer Forming Two Nematic Phases.

We present a comparative study of the optical and dielectric anisotropy of a laterally fluorinated liquid crystal dimer and its homologous trimer, both exhibiting two nematic phases. In the high-temperature nematic phase, both oligomers exhibit positive optical anisotropy with similar magnitude, which, however, is lower in comparison with the optical anisotropy of the monomer. In the same temperature range, the dielectric permittivity along and perpendicular to the nematic director, measured on magnetically aligned samples, reveals negative dielectric anisotropy for both oligomers, which saturates as the temperature approaches the N-N phase transition temperature. Comparison of the dielectric anisotropies of the oligomers with the corresponding anisotropy of the monomer indicates a systematic variation of its magnitude with the number of the linked mesogenic units. Results are compared with the corresponding anisotropies of the cyanobiphenyl dimers, the archetypal compounds with two nematic phases, and are discussed in terms of the dipolar structure of the mesogens and the dipolar correlations in their nematic phases.