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.

Stereochemical Rules Govern the Soft Self-Assembly of Achiral Compounds: Understanding the Heliconical Liquid-Crystalline Phases of Bent-Core Mesogens.

A series of bent-shaped 4-cyanoresorcinol bisterephthalates is reported. Some of these achiral compounds spontaneously form a short-pitch heliconical lamellar liquid-crystalline phase with incommensurate 3-layer pitch and the helix axis parallel to the layer normal. It is observed at the paraelectric-(anti)ferroelectric transition, if it coincides with the transition from random to uniform tilt and with the transition from anticlinic to synclinic tilt correlation of the molecules in the layers of the developing tilted smectic phase. For compounds with long chains the heliconical phase is only field-induced, but once formed it is stable in a distinct temperature range, even after switching off the field. The presence of the helix changes the phase properties and the switching mechanism from the naturally preferred rotation around the molecular long axis, which reverses the chirality, to a precession on a cone, which retains the chirality. These observations are explained by diastereomeric relations between two coexisting modes of superstructural chirality. One is the layer chirality, resulting from the combination of tilt and polar order, and the other one is the helical twist evolving between the layers. At lower temperature the helical structure is replaced by a non-tilted and ferreoelectric switching lamellar phase, providing an alternative non-chiral way for the transition from anticlinic to synclinic tilt.

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.

1,2,4-oxadiazole-based bent-core liquid crystals with cybotactic nematic phases.

Several series of bent-core mesogens derived from 3,5-diphenyl-1,2,4-oxadiazole with or without lateral groups and with different length terminal chains at both ends, and polycatenar molecules with three to six alkoxy chains are synthesized and their mesomorphic behaviour is investigated by polarizing microscopy, differential scanning calorimetry, X-ray diffraction (XRD), dielectric, electro-optical and second-harmonic generation (SHG) experiments. Most compounds exhibit broad regions of skewed cybotactic nematic (NcybC ) and tilted smectic (SmC) phases with a strong tilt of the aromatic cores (up to 63°), but non-tilted SmA and NcybA phases are also observed for a compound that has only one terminal chain. The XRD patterns of the nematic phases of most of the compounds investigated indicate a 2D periodicity with short correlation length in the magnetically aligned samples. This is of importance for the general interpretation of the small-angle XRD splitting patterns typically observed for aligned samples of bent-core nematic phases. In most nematic phases one current peak is observed in the half period of an applied electric field, though no coherent signal is found in the SHG experiments. Based on additional electro-optical and dielectric results, the nematic phases are considered to be cybotactic nematic phases with local polar order, and show a dielectric reorientation of the polar domains. Only chiral nematic phases (NcybC *), but not blue phases, are obtained for compounds with one or two chiral (3S)-3,7-dimethyloctyloxy tail(s).

Development of polar order and tilt in lamellar liquid crystalline phases of a bent-core mesogen.

A new bent-core mesogen combining a 4-cyanoresorcinol unit with two terephthalate based rod-like wings and terminated by two long alkyl chains, was synthesized and investigated by DSC, XRD, optical, electrooptical and dielectric methods. A series of liquid crystalline phases in the unique sequence SmA-SmA(P)-SmCPR-(M1/SmCPα)-SmCsPA-SmCPA-SmCaPA, mainly distinguished by the degree and mode of correlation of tilt and polar order, was observed. The development of polar order is associated with the emergence of a small tilt (<10°). With decreasing temperature the tilt changes from random (SmA) via synclinic to anticlinic, while the coherence length of the polar domains grows. This small tilt gives rise to an only weak layer coupling which is in competition with the polar coupling and this leads to new modes of self assembly in lamellar phases of bent-core mesogens, among them the SmCPR and the SmCPα phases. The SmCPR phase is an only slightly tilted biaxial smectic phase with randomized polar order and the SmCPα phase is a slightly tilted and antiferroelectric switching, but uniaxial smectic phase. For this phase a regular change of the in-plane polarization vector between the layers by an angle between >0° and <90° is proposed.

Understanding how junction resistances impact the conduction mechanism in nano-networks.

Networks of nanowires, nanotubes, and nanosheets are important for many applications in printed electronics. However, the network conductivity and mobility are usually limited by the resistance between the particles, often referred to as the junction resistance. Minimising the junction resistance has proven to be challenging, partly because it is difficult to measure. Here, we develop a simple model for electrical conduction in networks of 1D or 2D nanomaterials that allows us to extract junction and nanoparticle resistances from particle-size-dependent DC network resistivity data. We find junction resistances in porous networks to scale with nanoparticle resistivity and vary from 5 Ω for silver nanosheets to 24 GΩ for WS2 nanosheets. Moreover, our model allows junction and nanoparticle resistances to be obtained simultaneously from AC impedance spectra of semiconducting nanosheet networks. Through our model, we use the impedance data to directly link the high mobility of aligned networks of electrochemically exfoliated MoS2 nanosheets (≈ 7 cm2 V-1 s-1) to low junction resistances of ∼2.3 MΩ. Temperature-dependent impedance measurements also allow us to comprehensively investigate transport mechanisms within the network and quantitatively differentiate intra-nanosheet phonon-limited bandlike transport from inter-nanosheet hopping.

Response to an applied electric field in an antiferroelectric 1/2 subphase: The role of thermal fluctuations.

The response to an applied electric field in the q_{T}=1/2 subphase of the MC881-MC452 binary mixture system is studied by using thick homeotropically aligned cells. In the ordinary antiferroelectric SmC_{A}^{*} and 1/2 (sub)phases, some nonplanar asymmetric distortions in the antiferroelectric unit cell structure produce induced polarization in the applied field direction, starts to unwind the helix from the beginning, and tends to align the averaged tilt plane direction parallel to the applied field. In the 1/2 subphase under consideration, however, the helix resists being deformed at the beginning and then the thresholdlike steep increase of birefringence Δn occurs in the transition from 1/2 to unwound SmC^{*} at a field of less than 0.5 V/µm; we conclude that the thermal fluctuations play an important role in promoting the director flip-flopping in a single layer under the applied field and bring about additional induced polarization, which counteracts the aforementioned ordinary induced one and prevents the helix from unwinding. This suggests that the Langevin-like director reorientation is the mechanism of the V-shaped switching which was actually observed in the thin films of Mitsui mixture [Phys. Rev. Lett. 87, 015701 (2001)0031-900710.1103/PhysRevLett.87.015701] and must have been used in prototyped thresholdless antiferroelectric liquid-crystal displays.

Variety of subphase emerging sequences, the frustration of three main phases, SmC_{A}

Prompted by the existence of biaxial subphases 1/4, 2/5, and 3/7 [Phys. Rev. E 96, 012701 (2017)2470-004510.1103/PhysRevE.96.012701], we reconsidered the three-phase frustration and the resulting degeneracy lifting by combining the phase diagram of SmC_{A}^{*}, SmC^{*}, and SmA with the discrete flexoelectric effect. We systematically calculated the phase diagrams and tried to understand the overall picture of the phenomena by means of a simple and intuitively clear way in terms of minimal number of parameters. The treatment naturally explains the highly distorted helical structures of the biaxial subphases as well as the microscopic helical short-pitch of SmC_{α}^{*} which increases or decreases accordingly with rising temperature. The regular subphase emerging sequence is SmC_{A}^{*}(SmC_{α}^{*})-1/4-1/3-2/5-3/7-1/2-SmC^{*}(SmC_{α}^{*}), where the subphases other than 1/3 and 1/2 may or may not emerge. At the same time, we can see a variety of irregular sequences; in particular, any one of the biaxial subphases may singly emerge between SmC_{A}^{*}(SmC_{α}^{*}) and (SmC^{*})SmC_{α}^{*}. Moreover, the experimentally confirmed extraordinary subphase emerging sequence SmC^{*}-1/2-SmC_{α}^{*} appears for particular parameter values. Contrastingly to these affirmative aspects, some calculated results are contradictory to the previously reported experimental results: the change from SmC_{A}^{*} and SmC^{*} to SmC_{α}^{*} is always continuous, the 6-layer 2/3 subphase is not stabilized, and the subphase emerging sequence SmC_{A}^{*}-1/3-SmC^{*} does not appear. The causes of inconsistency and how to resolve them were discussed in comparisons with experimental findings.

Dielectric study of a subphase stabilized in an exceptionally wide temperature range by a delicate balance of interlayer interactions and thermal fluctuations.

The chiral smectic phases of calamitic liquid crystals, SmC^{*} and SmC_{A}^{*}, are characterized by the synclinic ferroelectric F ordering and the anticlinic antiferroelectric A ordering in adjacent layers. Various states with mixed A and F orderings are degenerate at the frustrated phase-transition point. The degeneracy lifting is commonly caused by the long-range interlayer interactions (LRILIs), producing a series of biaxial subphases specified by a relative ratio of both orderings, q_{T}=[F]/([A]+[F]). Sandhya et al. [Phys. Rev. E 87, 012502 (2013)PLEEE81539-375510.1103/PhysRevE.87.012502] established, however, the importance of thermal fluctuations in the degeneracy lifting in some binary mixtures of MC881 and MC452. They observed the most intriguing interplay of thermal fluctuations and LRILIs in the stabilization of an apparently single subphase. Since no other detailed experimental study of the subphase has so far been made, we carry out its dielectric investigations and clarify the following five points: (1) the subphase is surely a single phase from ≈80^{∘}C down to room temperature; (2) the imaginary part of complex permittivity ε^{″} shows the weak antiphase mode and hence it must be antiferroelectric q_{T}=1/2; (3) ε^{″} becomes much stronger above ≈80^{∘}C, indicating the emergence of ferroelectric and/or ferrielectric states; (4) the dielectric amplitude gradually increases at least just above the 1/2 subphase, suggesting it be due to a continuous increase of q_{T}; and (5) at low temperatures the antiphase relaxation mode shows irregularities that indicate the important role played by the cooperative motion of the layer undulation as well as of the director tilting.

Unexpected electric-field-induced antiferroelectric liquid crystal phase in the SmC_{α}

The unique nanometer-sized helical structure in SmC_{α}^{*} may sometimes evolve continuously to the micrometer-sized one in SmC^{*}; conceivably ferroelectric SmC_{α}^{*} is to be unwound by an applied electric field. By drawing electric-field-induced birefringence contours in the field-temperature phase diagram and by studying the superlattice structure of the field-induced subphase with resonant x-ray scattering, we established that an applied field unexpectedly stabilizes the well-known antiferroelectric four-layer biaxial subphase as well as the other prototypal ferrielectric three-layer one in the SmC_{α}^{*} temperature range; the effective long-range interlayer interaction due to the discrete flexoelectric effect actually plays an important role in stabilizing not only the biaxial subphases but also the optically uniaxial SmC_{α}^{*} subphase, contrary to the notion that the competition between the direct interactions of the nearest-neighbor layers and those of the next-nearest-neighbor layers should be required for the nanometer-sized helical structure.

Resonant x-ray scattering observation of transitional subphases during the electric-field-induced phase transition in a mixture of Se-containing chiral smectic liquid crystals.

Using resonant x-ray scattering techniques, transitional subphases during the electric-field-induced phase transition of a mixture of Se-containing chiral liquid crystals, 80% AS657 and 20% AS620, in a planar-aligned cell geometry were investigated, where the prototypical phase sequence SmC_{A}^{*}-SmC_{γ}^{*}-AF-SmC^{*} was observed; the transitional subphases were formed during the transition from the three-layer periodicity phase to the ferroelectric phase. In the lower-temperature range where the three-layer SmCγ^{*} phase appeared under the low electric field, nine- and six-layer subphases and a "streak" pattern appeared in sequence after the transition from the SmCγ^{*} phase with increasing applied electric field; the ferroelectric phase was realized. In the higher-temperature range where the four-layer AF phase appeared under a low electric field, the AF phase changed to a three-layer phase at the medium electric field. The twelve-, nine-, and six-layer subphases subsequently appeared in sequence, and finally the ferroelectric phase was generated with increasing electric field. The molecular arrangements of the field-induced subphases, especially the newly found nine-layer periodicity phase, was analyzed. The successive field-induced phase transition of the present results was compared with that of our previous results for pure Se-containing and Br-containing liquid crystals, and the relation to the three-layer ferrielectric phase was discussed.

Formation and development of nanometer-sized cybotactic clusters in bent-core nematic liquid crystalline compounds.

Two homologue achiral bent-core liquid crystals (LCs), BCN66 and BCN84, in their nematic phases are studied by dielectric spectroscopy in the frequency range 10 Hz-10 MHz. In each of these compounds, two relaxation processes are identified and assigned to (i) collective dynamics of molecules in nanometer-sized cybotactic clusters and (ii) individual molecular relaxations, in the ascending order of frequency of the probe field. The temperature and the bias electric field dependence of the dielectric strength and relaxation frequency for these processes are shown to give rise to sharpness in cluster boundaries, increased size and volume fraction in the LC nematic phase. The effect of the bias field on the LC cell is similar to reducing its temperature; both variables increase the cluster size and volume fraction and give rise to sharp cluster boundaries. The findings confirm that dielectric spectroscopy is a powerful and an extremely useful technique to provide a deeper understanding of the mechanism of cybotactic cluster formation in the isotropic liquid and the nematic phase of LCs as a function of temperature and the bias field.

Definite existence of subphases with eight- and ten-layer unit cells as studied by complementary methods, electric-field-induced birefringence and microbeam resonant x-ray scattering.

A mixture of two selenium-containing compounds, 80 wt. % AS657 and 20 wt. % AS620, are studied with two complementary methods, electric-field-induced birefringence (EFIB) and microbeam resonant x-ray scattering (µRXS). The mixture shows the typical phase sequence of Sm-C_{A}^{*}-1/3-1/2-Sm-C^{*}-Sm-C_{α}^{*}-Sm-A, where 1/3 and 1/2 are two prototypal ferrielectric and antiferroelectric subphases with three- and four-layer unit cells, respectively. Here we designate the subphase as its q_{T} number defined by the ratio of [F]/([F]+[A]), where [F] and [A] are the numbers of synclinic ferroelectric and anticlinic antiferroelectric orderings in the unit cell, respectively. The electric field vs temperature phase diagram with EFIB contours indicates the emergence of three additional subphases, an antiferroelectric one between Sm-C_{A}^{*} and 1/3 and antiferroelectric and apparently ferrielectric ones between 1/3 and 1/2. The simplest probable q_{T}'s for these additional subphases are 1/4, 2/5, and 3/7, respectively, in the order of increasing temperature. The µRXS profiles indicate that antiferroelectric 1/4 and 2/5 approximately have the eight-layer (FAAAFAAA) and ten-layer (FAFAAFAFAA) Ising unit cells, respectively. The remaining subphase may be ferrielectric 3/7 with a seven-layer unit cell, although the evidence is partial. These experimental results are compared with the phenomenological Landau model [P. V. Dolganov and E. I. Kats, Liq. Cryst. Rev. 1, 127 (2014)2168-039610.1080/21680396.2013.869667] and the quasimolecular model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)1063-651X10.1103/PhysRevE.68.051703].

Experimental demonstration, using polarized Raman and infrared spectroscopy, that both conventional and de Vries smectic-A phases may exist in smectic liquid crystals with a first-order A-C* transition.

Two models exist for the orientational distribution of the long molecular axes in smectic-A liquid crystals: the conventional unimodal distribution and the "cone-shaped" de Vries distribution. The de Vries hypothesis provides a plausible picture of how, at a molecular level, a first-order Sm-A to Sm-C* transition may occur, especially if there is little or no concomitant shrinkage of the layer spacing. This work investigates two materials with such transitions: C7 and TSiKN65. The azimuthal distribution of in-layer directors is probed using IR and polarized Raman spectroscopy, which allows us to obtain orientational order parameters. In C7, we observe a discontinuous change in the order parameter, the magnitude of which is small compared with the corresponding change in the in-layer director tilt angle Theta . Assuming that the smectic-A liquid crystal is of the de Vries type, we calculate the Theta required to reproduce the apparent order parameter app, obtained from IR, by using the true order parameter , obtained from polarized Raman scattering. The results indicate that, for C7, the tilt angle so calculated is much smaller than that in the Sm-C* angle and hence de Vries behavior may not be the appropriate explanation in this case. Conversely, we find that TSiKN65 shows a different behavior to C7, which can be explained in terms of the de Vries concept. Thus, we conclude that either type of distribution may exist in Sm-A phases which undergo a first-order transition to the Sm-C* phase. We also discuss the changes in the smectic layer spacing and the orientational order parameters across the Sm-A-Sm-C* phase transition, together with changes in birefringence with applied electric field.

Transitional subphases near the electric-field-induced phase transition to the ferroelectric phase in Se-containing chiral smectic liquid crystals observed by resonant x-ray scattering.

Resonant x-ray scattering experiments revealed transitional subphases near the electric-field-induced phase transition of a Se-containing chiral liquid crystal in a planar aligned cell geometry. In the lower-temperature range (Sm-C_{A}^{*} and three-layer periodicity Sm-C_{γ}^{*} phases), the six-layer periodicity subphase appeared with increasing electric field during the field-induced transition from Sm-C_{γ}^{*} to Sm-C^{*}. In the higher-temperature range [four-layer periodicity antiferroelectric (AF) phase], the peak positions of the three-layer satellites shifted to those of the four-layer satellites and then the satellites corresponding to the five- through seven-layer periodicity appeared in sequence. Near the AF to Sm-C_{α}^{*} phase transition temperature, the layer periodicity increased with applied field. The molecular configurations of the subphases near the field-induced transition are discussed based on the Ising, distorted clock, and perfect clock models.

Effective long-range interlayer interactions and electric-field-induced subphases in ferrielectric liquid crystals.

Microbeam resonant x-ray scattering experiments recently revealed the sequential emergence of electric-field-induced subphases (stable states) with exceptionally large unit cells consisting of 12 and 15 smectic layers. We explain the emergence of the field-induced subphases by the quasimolecular model based on the Emelyanenko-Osipov long-range interlayer interactions (LRILIs) together with our primitive way of understanding the frustration in clinicity using the q_{E} number defined as q_{E}=|[R]-[L]|/([R]+[L]); here [R] and [L] refer to the numbers of smectic layers with directors tilted to the right and to the left, respectively, in the unit cell of a field-induced subphase. We show that the model actually stabilizes the field-induced subphases with characteristic composite unit cells consisting of several blocks, each of which is originally a ferrielectric three-layer unit cell stabilized by the LRILIs, but some of which would be modified to become ferroelectric by an applied electric field. In a similar line of thought, we also try to understand the puzzling electric-field-induced birefringence data in terms of the LRILIs.

Spontaneous helix formation in non-chiral bent-core liquid crystals with fast linear electro-optic effect.

Liquid crystals (LCs) represent one of the foundations of modern communication and photonic technologies. Present display technologies are based mainly on nematic LCs, which suffer from limited response time for use in active colour sequential displays and limited image grey scale. Herein we report the first observation of a spontaneously formed helix in a polar tilted smectic LC phase (SmC phase) of achiral bent-core (BC) molecules with the axis of helix lying parallel to the layer normal and a pitch much shorter than the optical wavelength. This new phase shows fast (∼30 µs) grey-scale switching due to the deformation of the helix by the electric field. Even more importantly, defect-free alignment is easily achieved for the first time for a BC mesogen, thus providing potential use in large-scale devices with fast linear and thresholdless electro-optical response.

Fractional rotational diffusion of rigid dipoles in an asymmetrical double-well potential.

The longitudinal and transverse components of the complex dielectric susceptibility tensor of an assembly of dipolar molecules rotating in an asymmetric double-well potential are evaluated using a fractional rotational diffusion equation (based on the diffusion limit of a fractal time random walk) for the distribution function of orientations of the molecules on the surface of the unit sphere. The calculation is the fractional analog of the Debye theory of orientational relaxation in the presence of external and mean field potentials (excluding inertial effects). Exact and approximate (based on the exponential separation for normal diffusion of the time scales of the intrawell and overbarrier relaxation processes associated with the bistable potential) solutions for the dielectric dispersion and absorption spectra are obtained. It is shown that a knowledge of the characteristic relaxation times for normal rotational diffusion is sufficient to predict accurately the anomalous dielectric relaxation behavior of the system for all time scales of interest. The model explains the anomalous (Cole-Cole-like) relaxation of complex dipolar systems, where the anomalous exponent differs from unity (corresponding to the normal dielectric relaxation), i.e., the relaxation process is characterized by a broad distribution of relaxation times (e.g., in glass-forming liquids).

Evidence for de Vries structure in a smectic-A liquid crystal observed by polarized Raman scattering.

The second- and fourth-order apparent orientational order parameters of the core part of the molecule P2 (app) and P4 (app) , have been measured by polarized vibrational Raman spectroscopy for a homogeneously aligned ferroelectric smectic liquid crystal with three dimethyl siloxane groups in the achiral terminal chain, which shows de Vries-type phenomena, i.e., very large electroclinic effect in the smectic- A (Sm-A) phase and a negligible layer contraction at the phase transition between the Sm-A and Sm- C(*) phases. The apparent orientational order parameters of the rigid core part of the molecule are extremely small both with and without the external electric field in Sm-A . These results provide evidence for the existence of the de Vries Sm-A phase, where the local molecular director is tilted at a large angle.

A liquid crystalline phase with uniform tilt, local polar order and capability of symmetry breaking.

A new liquid crystalline (LC) phase with uniform tilt, local polar order and capability of symmetry breaking is found for a bent-core mesogen combining a 4-cyanoresorcinol unit with two azobenzene wings. The combination of local polar order and long range synclinic tilt in this SmC(s)P(R) phase leads, under special conditions, to macroscopic domains with opposite chirality, though the molecules themselves are achiral.