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In this paper we present a novel high-resolution multi-channel FPGA-based time-to-digital converter (TDC). We designed and implemented a complex electronic circuit on the FPGA, whose overall accuracy is several orders of magnitude greater than the accuracy of the FPGA used in digital mode. Our sensor device contains simple circuit elements that are cheap and easily accessible (Xilinx Spartan 3 and Spartan 6). Using our design, many channels (80-100 channels) can be implemented on a larger FPGA. The prototype of our TDC has been implemented and functionally verified by experiments and measurements. By a certified pulse generator 20 ps precision has been measured over the range of 3 ns. Using more precise clock signal this range may be extended. The achieved resolution is 5 ps. Its resolution, channel number and range can be configured dynamically, which makes it suitable for effective use in industrial purposes.

The recently discovered ferroelectric nematic (NF) liquid crystals (LC) have been reported to show an extraordinarily large value of the real part of the dielectric constant at low frequencies. However, it was argued by Clark et al in Physical Review Research 6, 013195 (2024) that what was measured was the capacitance of the insulating layer at LC/electrode surface and not that of the liquid crystal. Here we describe the results of dielectric spectroscopy measurements of an NF material in cells with variable thickness of the insulating layers. Our measurements quantitatively verify the model by Clark et al. Additionally, our measurements in cells with bare conducting indium tin oxide surface provide a crude estimate of epsilon perpendicular~100 in the NF phase., Comment: 17 pages, 6 figures, Presented in Workshop on Ferroelectric Nematic Liquid Crystals in Ljubljana

Freestanding slender fluid filaments of room temperature ferroelectric nematic liquid crystals are described. They are stabilized either by internal electric fields of bound charges formed due to polarization splay, or by external voltage applied between suspending wires. The phenomenon is similar to those observed in dielectric fluids, such as deionized water, except that in ferroelectric nematic materials the voltages required are 3 orders of magnitudes smaller and the aspect ratio is much higher. The observed ferroelectric fluid threads are not only unique and novel, but also offer measurements of basic physical quantities, such as the ferroelectric polarization and viscosity. Ferroelectric nematic fluid threads may have practical applications in nano-fluidic micron-size logic devices, switches, and relays., Comment: 18 pages, 5 figures

Studies of sessile droplets and fluid bridges of a ferroelectric nematic liquid crystal in externally applied electric fields are presented. It is found that above a threshold, the interface of the fluid with air undergoes a fingering instability or ramification, resembling to Rayleigh-type instability observed in charged droplets in electric fields or circular drop-type instabilities observed in ferromagnetic liquids in magnetic field. The frequency dependence of the threshold voltage was determined in various geometries. The nematic director and ferroelectric polarization direction was found to point along the tip of the fingers that appear to repel each other, indicating that the ferroelectric polarization is essentially parallel to the director. The results are interpreted in connection to the Rayleigh and circular drop-type instabilities.

The isotropic to ferroelectric nematic liquid transition had been theoretically studied over one hundred years ago, but its experimental studies are rare. Here we present polarizing optical microscopy studies and theoretical considerations of ferroelectric nematic liquid crystal droplets coexisting with the isotropic melt. We find that the droplets have flat pancake-like shapes that are thinner than the sample thickness as long as there is a room to increase the lateral droplet size. In the center of the droplets a wing shaped defect with low birefringence is present that moves perpendicular to a weak in-plane electric field, and then extends and splits in two at higher fields. Parallel to the defect motion and extension, the entire droplet drifts along the electric field with speed that is independent of the size of the droplet and is proportional to the amplitude of the electric field. After the field is increased above 1V/mm the entire droplet gets deformed and oscillates with the field. These observations led us to determine the polarization field and revealed the presence of a pair of positive and negative bound electric charge due to divergences of polarization around the defect volume.

A thermal gradient-induced circular motion of particles placed on ferroelectric nematic liquid crystal sessile drops is demonstrated and explained. Unlike hurricanes and tornadoes that are the prime examples for thermal motors and where turbulent flows are apparent, here the texture without tracer particles appears completely steady indicating laminar flow. We provide a simple model showing that the tangential arrangement of the ferroelectric polarization combined with the vertical thermal gradient and the pyroelectricity of the fluid drives the rotation of the tracer particles that become electrically charged in the fluid. These observations provide a fascinating example of the unique nature of fluid ferroelectric liquid crystals.

Ferroelectric nematic liquid crystals represent not only interesting fundamental science, but they also hold promise for storage capacitors with high power density or new information display technology having sub-millisecond switching. In this work we describe the synthesis and measurements of the physical properties of a new highly polar ferroelectric nematic compound, 4-nitrophenyl 4-[(2,4-dimethoxylbenzoyl)oxy]-2-fluorobenzoate (RT11001). The dipole moment of this material (along the long molecular axis) is calculated to exceed 11.5 Debye. We employ a wide range of physical characterization methods including differential scanning calorimetry (DSC), mass density measurement, optical birefringence, polarizing optical microscopy (POM), electric current analysis, and electro-optical switching, to show that RT11001 has three distinct ferroelectric states, F1, F2 and F3. F1 is purely orientationally ordered ferroelectric nematic phase (NF), F2 has a ferroelectric nematic with possibly short-range hexagonal order normal to the director (NhF), and we conjecture that F3 has a long-range hexagonal order normal to the director (ColhF)., Comment: 31 pages, 10 figures

The nanostructure of two novel sulfur containing dimer materials has been investigated experimentally by hard and by resonant tender X-ray scattering techniques. On cooling the dimers through the nematic to twist-bend nematic (N-NTB) phase transition, the correlation length associated with short-range positional order drops, while the heliconical orientational order becomes more correlated. The heliconical pitch shows a stronger temperature dependence near the N-NTB transition than observed in previously studied dimers, such as the CBnCB series of compounds. We explain both this strong variation and the dependence of the heliconical pitch on the length of the spacer connecting the monomer units by taking into account a temperature dependent molecular bend and intermolecular overlap. and. The heliconical structure is observed even in the upper 3-4{\deg}C range of the smectic phase that forms just below the NTB state. The coexistence of smectic layering and the heliconical order indicates a SmCTB -type phase where the rigid units of the dimers are tilted with respect to the layer normal in order to accommodate the bent conformation of the dimers, but the tilt direction rotates along the heliconical axis. This is potentially similar to the SmCTB phase reported by Abberley et al (Nat. Commun. 2018, 9, 228) below a SmA phase., Comment: 24 pages, 7 figures

We synthesized the liquid crystal dimer and trimer members of a series of flexible linear oligomers and characterized their microscopic and nanoscopic properties using resonant soft x-ray scattering and a number of other experimental techniques. On the microscopic scale, the twist-bend phases of the dimer and trimer appear essentially identical. However, while the liquid crystal dimer exhibits a temperature-dependent variation of its twist-bend helical pitch varying from 100 - 170 {\AA} on heating, the trimer exhibits an essentially temperature-independent pitch of 66 {\AA}, significantly shorter than those reported for other twist-bend forming materials in the literature. We attribute this to a specific combination of intrinsic conformational bend of the trimer molecules and a sterically favorable intercalation of the trimers over a commensurate fraction (two-thirds) of the molecular length. We develop a geometric model of the twist-bend phase for these materials with the molecules arranging into helical chain structures, and we fully determine their respective geometric parameters., Comment: supplemental information included

A third order real tensor is called a piezoelectric-type tensor if it is partially symmetric with respect to its last two indices. The piezoelectric tensor is a piezoelectric-type tensor of dimension three. We introduce C-eigenvalues and C-eigenvectors for piezoelectric-type tensors. Here, "C" names after Curie brothers, who first discovered the piezoelectric effect. We show that C-eigenvalues always exist, they are invariant under orthonormal transformations, and for a piezoelectric-type tensor, the largest C-eigenvalue and its C-eigenvectors form the best rank-one piezoelectric-type approximation of that tensor. This means that for the piezoelectric tensor, its largest C-eigenvalue determines the highest piezoelectric coupling constant. We further show that for the piezoelectric tensor, the largest C-eigenvalue corresponds to the electric displacement vector with the largest $2$-norm in the piezoelectric effect under unit uniaxial stress, and the strain tensor with the largest $2$-norm in the converse piezoelectric effect under unit electric field vector. Thus, C-eigenvalues and C-eigenvectors have concrete physical meanings in piezoelectric effect and converse piezoelectric effect. Finally, we apply C-eigenvalues and associated C-eigenvectors for various piezoelectric crystals with different symmetries.

In searching for novel photoactive liquid crystals, we have synthesized a series of five-ring pyridine-based bent-core compounds bearing different substituents at the peripheral phenyl rings (CH3O, Cl and NO2). Their mesomorphic behaviour has been investigated by polarizing optical microscopy, differential scanning calorimetry and X-ray scattering, and then compared with the unsubstituted parent compound. The introduction of the methoxy groups at the peripheral phenyl rings of the bent core results in a non-mesomorphic compound, whereas the chloro- and nitro-substituted compounds form enantiotropic B1-like phases. Significant changes of the textures and transition temperatures of the mesophase have been observed under UV light. The presented investigation of the mesomorphic properties of the synthesized compounds, coupled with analysis of the molecular packing of the related three-ring compounds, will help to design self-organized molecules suitable for UV indicators., Comment: 9 pages, 8 figures, revised version appeared in New Journal of Chemistry

The nematic twist-bend (TB) phase, exhibited by certain achiral thermotropic liquid crystalline (LC) dimers, features a nanometer-scale, heliconical rotation of the average molecular long axis (director) with equally probable left- and right-handed domains. On meso to macroscopic scales, the TB phase may be considered as a stack of equivalent slabs or "pseudo-layers", each one helical pitch in thickness. The long wavelength fluctuation modes should then be analogous to those of a smectic-A phase, and in particular the hydrodynamic mode combining "layer" compression and bending ought to be characterized by an effective layer compression elastic constant $B_{eff}$ and average director splay constant $K_1^{eff}$. The magnitude of $K_1^{eff}$ is expected to be similar to the splay constant of an ordinary nematic LC, but due to the absence of a true mass density wave, $B_{eff}$ could differ substantially from the typical value of $\sim 10^6$ Pa in a conventional smectic-A. Here we report the results of a dynamic light scattering study, which confirms the "pseudo-layer" structure of the TB phase with $B_{eff}$ in the range $\sim 10^3-10^4$ Pa. We show additionally that the temperature dependence of $B_{eff}$ at the TB to nematic transition is accurately described by a coarse-grained free energy density, which is based on a Landau-deGennes expansion in terms of a heli-polar order parameter that characterizes the TB state and is linearly coupled to bend distortion of the director., Comment: 9 pages, 7 figures

The nematic twist-bend ($\mathrm{N_{TB}}$) phase, exhibited by certain thermotropic liquid crystalline (LC) dimers, represents a new orientationally ordered mesophase -- the first distinct nematic variant discovered in many years. The $\mathrm{N_{TB}}$ phase is distinguished by a heliconical winding of the average molecular long axis (director) with a remarkably short (nanoscale) pitch and, in systems of achiral dimers, with an equal probability to form right- and left-handed domains. The $\mathrm{N_{TB}}$ structure thus provides another fascinating example of spontaneous chiral symmetry breaking in nature. The order parameter driving the formation of the heliconical state has been theoretically conjectured to be a polarization field, deriving from the bent conformation of the dimers, that rotates helically with the same nanoscale pitch as the director field. It therefore presents a significant challenge for experimental detection. Here we report a second harmonic light scattering (SHLS) study on two achiral, $\mathrm{N_{TB}}$-forming LCs, which is sensitive to the polarization field due to micron-scale distortion of the helical structure associated with naturally-occurring textural defects. These defects are parabolic focal conics of smectic-like "pseudo-layers", defined by planes of equivalent phase in a coarse-grained description of the $\mathrm{N_{TB}}$ state. Our SHLS data are explained by a coarse-grained free energy density that combines a Landau-deGennes expansion of the polarization field, the elastic energy of a nematic, and a linear coupling between the two.

We have determined the nematic-isotropic transition temperature as a function of applied magnetic field in three different thermotropic liquid crystalline dimers. These molecules are comprised of two rigid calamitic moieties joined end to end by flexible spacers with odd numbers of methylene groups. They show an unprecedented magnetic field enhancement of nematic order in that the transition temperature is increased by up to 15K when subjected to 22T magnetic field. The increase is conjectured to be caused by a magnetic field-induced decrease of the average bend angle in the aliphatic spacers connecting the rigid mesogenic units of the dimers.

We report a dynamic light scattering study of the fluctuation modes in a thermotropic liquid crystalline mixture of monomer and dimer compounds that exhibits the twist-bend nematic ($\mathrm{N_{TB}}$) phase. The results reveal a spectrum of overdamped fluctuations that includes two nonhydrodynamic and one hydrodynamic mode in the $\mathrm{N_{TB}}$ phase, and a single nonhydrodynamic plus two hydrodynamic modes (the usual nematic optic axis or director fluctuations) in the higher temperature, uniaxial nematic phase. The properties of these fluctuations and the conditions for their observation are comprehensively explained by a Landau-deGennes expansion of the free energy density in terms of heliconical director and helical polarization fields that characterize the $\mathrm{N_{TB}}$ structure, with the latter serving as the primary order parameter. A "coarse-graining" approximation simplifies the theoretical analysis, and enables us to demonstrate quantitative agreement between the calculated and experimentally determined temperature dependence of the mode relaxation rates., Comment: 14 pages and 8 figures

We report on the first direct nanoscale imaging of elementary edge dislocations in a thermotropic chiral smectic C liquid crystal with the Burgers vector equal to one smectic layer spacing d. We find two different types of dislocation profiles. In the dislocation of type A, the layers deformations lack mirror symmetry with respect to the plane perpendicular to the Burgers vector; the dislocation core size is on the order of d. In the dislocation of type S, the core is strongly anisotropic, extending along the Burgers vector over distances much larger (by a factor of 4) than d. The difference is attributed to a different orientation of the molecular tilt plane with respect to the dislocation axis; the asymmetric layers distortions are observed when the molecular tilt plane is perpendicular to the axis and the split S core is observed when the molecules are tilted along the line.

We present magneto-optic measurements on two materials that form the recently discovered twist-bend nematic (Ntb) phase. This intriguing state of matter represents a new fluid phase that is orientationally anisotropic in three directions and also exhibits translational order with periodicity several times larger than the molecular size. NTB materials may also spontaneously form a visible, macroscopic stripe texture. We show that the optical stripe texture can be persistently inhibited by a magnetic field, and a 25T external magnetic field depresses the N-Ntb phase transition temperature by almost 1 degree C. We propose a quantitative mechanism to account for this shift and suggest a Helfrich-Hurault-type mechanism for the optical stripe formation., Comment: 12 pages, 4 figures

We briefly review the literature of linear electromechanical effects of soft materials, especially in synthetic and biological polymers and liquid crystals (LCs). First we describe results on direct and converse piezoelectricity, and then we discuss a linear coupling between bending and electric polarization, which maybe called bending piezoelectricity, or flexoelectricity., Comment: 13 pages, 2 figures, 1 table

In search for novel nematic materials, a laterally linked H-shaped liquid crystal dimer have been synthesized and characterized. The distinct feature of the material is a very broad temperature range (about 50 oC) of the nematic phase, which is in contrast with other reported H-dimers that show predominantly smectic phases. The material exhibits interesting textural features at the scale of nanometers (presence of smectic clusters) and at the macroscopic scales. Namely, at a certain temperature, the flat samples of the material show occurrence of domain walls. These domain walls are caused by the surface anchoring transition and separate regions with differently tilted director. Both above and below this transition temperature the material represents a uniaxial nematic, as confirmed by the studies of defects in flat samples and samples with colloidal inclusions, freely suspended drops, X-ray diffraction and transmission electron microscopy., Comment: 30 pages (including Supplementary Information), 7 Figures

A state of matter in which molecules show a long-range orientational order and no positional order is called a nematic liquid crystal. The best known and most widely used (for example, in modern displays) is the uniaxial nematic, with the rod-like molecules aligned along a single axis, called the director. When the molecules are chiral, the director twists in space, drawing a right-angle helicoid and remaining perpendicular to the helix axis; the structure is called a chiral nematic. In this work, using transmission electron and optical microscopy, we experimentally demonstrate a new nematic order, formed by achiral molecules, in which the director follows an oblique helicoid, maintaining a constant oblique angle with the helix axis and experiencing twist and bend. The oblique helicoids have a nanoscale pitch. The new twist-bend nematic represents a structural link between the uniaxial nematic (no tilt) and a chiral nematic (helicoids with right-angle tilt)., Comment: 31 pages: 8 Figures and Supplementary Information with 3 Figures