Phase transitions study of the liquid crystal DIO with a ferroelectric nematic, a nematic, and an intermediate phase and of mixtures with the ferroelectric nematic compound RM734 by adiabatic scanning calorimetry.

High-resolution calorimetry has played a significant role in providing detailed information on phase transitions in liquid crystals. In particular, adiabatic scanning calorimetry (ASC), capable of providing simultaneous information on the temperature dependence of the specific enthalpy h(T) and on the specific heat capacity c_{p}(T), has proven to be an important tool to determine the order of transitions and render high-resolution information on pretransitional thermal behavior. Here we report on ASC results on the compound 2,3',4',5'-tetrafluoro[1,1'-biphenyl]-4-yl 2,6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate (DIO) and on mixtures with 4-[(4-nitrophenoxy)carbonyl]phenyl 2,4-dimethoxybenzoate (RM734). Both compounds exhibit a low-temperature ferroelectric nematic phase (N_{F}) and a high-temperature paraelectric nematic phase (N). However, in DIO these two phases are separated by an intermediate phase (N_{x}). From the detailed data of h(T) and c_{p}(T), we found that the intermediate phase was present in all the mixtures over the complete composition range, albeit with strongly decreasing temperature width for that phase with decreasing mole fraction of DIO (x_{DIO}). The x_{DIO} dependence on the transition temperatures for both transitions could be well described by a quadratic function. Both these transitions were weakly first order. The true latent heat of the N_{x}-N transition of DIO was as low as L=0.0075±0.0005J/g and L=0.23±0.03J/g for the N_{F}-N_{x} transition, which is about twice the previously reported value of 0.115 J/g for the N_{F}-N transition in RM734. In the mixtures both transition latent heats decrease gradually with decreasing x_{DIO}. At all the N_{x}-N transitions pretransition fluctuation effects are absent and these transitions are purely but very weakly first order. As in RM734 the transition from the N_{F} to the higher-temperature phase exhibits substantial pretransitional behavior, in particular, in the high-temperature phase. Power-law analysis of c_{p}(T) resulted in an effective critical exponent α=0.88±0.1 for DIO and this value decreased in the mixtures with decreasing x_{DIO} toward α=0.50±0.05 reported for RM734. Ideal mixture analysis of the phase diagram was consistent with ideal mixture behavior provided the total transition enthalpy change was used in the analysis.

The interplay between spatial and heliconical orientational order in twist-bend nematic materials.

The helical pitch formed by organic molecules, such as the α-helix of proteins, usually requires hydrogen bonding between chiral units and long-range positional order. It was recently found that certain liquid crystal oligomers can have a twist-bend nematic (NTB) phase with nanoscale heliconical structure without hydrogen bonding, molecular chirality or positional order. To understand the nature of this unique structure, here we present hard and resonant tender X-ray scattering studies of two novel sulfur containing dimer materials. We simultaneously measure the temperature dependences of the helical pitch and the correlation length of both the helical and positional order. In addition to an unexpected strong variation of the pitch with the length of the spacer connecting the monomer units, we find that at the transition to the NTB phase the positional correlation length drops. The helical structure was found not only in the NTB phase but observed even in the upper range of a smectic phase that forms just below the NTB state. The coexistence of smectic layering and the heliconical order indicates a layered (SmATB) phase wherein the rigid units of the dimers are tilted with respect to the smectic layer normal in order to accommodate the bent conformation of the dimers and the tilt direction rotates along the heliconical axis.

Soft modes of the dielectric response in the twist-bend nematic phase and identification of the transition to a nematic splay bend phase in the CBC7CB dimer.

The dielectric spectra of the twist-bend nematic phase (NTB) of (the bent-shaped) achiral liquid-crystal dimer 1''-,7''-bis(4-cyanobiphenyl-4'-yl)heptane (CB7CB) are studied for the determination of the different relaxation modes. Two molecular processes and one collective process were observed in the megahertz frequency range. Two molecular processes were assigned: one to the precessional rotation of the longitudinal components of the cyanobiphenyl groups and the second one to the spinning rotation of the transverse component of the CB7CB dimer. The peak, at a frequency of about 1 MHz, shows a peculiar temperature behavior at the NTB to N transition, reminiscent of the soft mode at the transition from the SmA to the SmC phase. This peak can be assigned to a collective fluctuation of the tilt angle of the coarse grained director N with respect to the pseudo-layer normal. This corresponds well with the electro-clinic effect observed as a response to an electric field in electro-optic experiments. The low frequency relaxation process, observed in the frequency range of 1 Hz-102 Hz can be identified as a Goldstone mode, related to long-scale fluctuation of the cone phase. The frequency drop of the mode on increasing the bias field is interpreted as unwinding of a helix and an indication of the formation of a field induced nematic splay bend phase (NSB). This finding is also confirmed by birefringence data in the presence of strong bias fields.

Dielectric response of electric-field distortions of the twist-bend nematic phase for LC dimers.

Wide band dielectric spectroscopy of bent-shaped achiral liquid-crystal dimers 1″-n″-bis(4-cyanobiphenyl-4'-yl) n-alkanes (CBnCB n = 7, 9, 11) has been investigated in a frequency range 0.1 Hz-100 MHz using planar-aligned cells of sample thicknesses ranging from 2 to 10 (µm) over a temperature range that covers both nematic and twist bend nematic phases. Two peaks in the dielectric spectrum in the higher frequency range are assigned to the molecular relaxation processes. The peak at the highest frequency, ∼40 to 80 MHz, is assigned to an internal precessional rotation of a single unit of the dimer around the director. The mode in the next lower frequency range of 2-10 MHz is assigned to the spinning rotation of the dimer around its long axis. This involves fluctuations of the dipole moment of the bent-shaped conformation that is directed along its arrow direction of the bow shape formed by the dimer. The peak in the frequency range 100 kHz-1 MHz can be assigned to the collective fluctuations of the local director with reference to the helical axis of the NTB structure. The dependence of its frequency on temperature is reminiscent of the soft mode observed at the SmA* to SmC* phase transition. This result clearly corresponds to the electro-clinic effect-the response of the director to the applied electric field in an electro-optic experiment. The lowest frequency mode, observed in the frequency range of 0.1 Hz-100 Hz, is identified with the Goldstone mode. This mode is concerned with the long range azimuthal angle fluctuations of the local director. This leads to an alternating compression and expansion of the periodic structure of the NTB phase.

Proton and Deuterium NMR Study of the CBC9CB Dimer System.

Using proton and deuterium NMR spectroscopy, this work provides a description of the molecular orientational order of the mesogenic groups in both the Ntb and the classical nematic phase (N) of the liquid crystal dimer CB-C9-CB. The proton NMR data were collected at high field (7 T) with the nematic domains aligned by the field. Deuterium NMR data obtained from aligned samples at 11.7 T, published by Hoffmann , A. Soft Matter 2015 , 11 , 850 , were also considered in this study. Using the first-order perturbation theory, we carried out detailed simulations of the proton spectra from the terminal mesogenic groups along with the quadrupolar splittings from the carbon-deuterium bonds in the first chain positions, which allow for the determination of the Saupe order tensor for the mesogenic groups. We show that the main mechanism that induces the change of the 1H NMR spectrum and the quadrupolar splittings at the N-Ntb phase transition is the change of the orientation of the most ordered molecular frame (eigenframe of the Saupe tensor), along with the onset of the molecular biaxiality parameter, D. This orientation change is associated with the achiral symmetry breaking at the N-Ntb phase transition.

Molecular organization in the twist-bend nematic phase by resonant X-ray scattering at the Se K-edge and by SAXS, WAXS and GIXRD.

Using a magnetically aligned liquid crystal mixture containing a novel Se-labelled dimer and the difluoroterphenyl dimer DTC5C7, the twist-bend nematic phase (Ntb) was studied by the resonant scattering of hard X-rays and by conventional small and wide-angle X-ray scattering (SAXS, WAXS). Resonant diffraction spots indicated a helix with a 9-12 nm pitch in the Ntb phase and an unprecedentedly high helix orientation. This enabled deconvolution of global and local order parameters. These findings, combined with the simultaneously recorded resonant and non-resonant SAXS and WAXS data, allowed us to construct a locally layered molecular model of the Ntb phase, where the average twisted conformation of each molecule was idealised as a helical segment, matching the local heliconical director field. The dimers were found to be less bent in the Ntb phase than in their minimum energy conformation, and straightening further with increasing temperature. It is proposed that on further heating their low bend angle allows the transition to the normal nematic phase, where the molecules can freely move longitudinally, without the need to perform screw-like motion as in the Ntb phase. At the low-temperature end, the increasing molecular twist becomes unsustainable, leading to a transition to a smectic phase, where no twist is required.

Light scattering study of the "pseudo-layer" compression elastic constant in a twist-bend nematic liquid crystal.

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 Beff and average director splay constant K. The magnitude of K 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, Beff could differ substantially from the typical value of ∼106 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 Beff in the range 103-104 Pa. We show additionally that the temperature dependence of Beff 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.

Mesophase structure and behaviour in bulk and restricted geometry of a dimeric compound exhibiting a nematic-nematic transition.

We present structural studies of a dimeric compound composed of a central heptyl spacer linking two mesogens consisting of terphenyl units at which two adjacent fluoro groups are attached to each central ring. The terminal rings are linked to pentyl chains as terminal groups. The material exhibits a nematic-nematic transition and a low temperature modulated phase. The higher temperature nematic phase was found to exhibit an anomaly of the bend elastic constant similar to that of the dimers with N-Ntb phase sequence, and the physical properties of the low-temperature nematic phase are similar to those of the known Ntb materials. The structure of the low-temperature modulated smectic/columnar phase is described together with its ability to form freely suspended films and fibres. The relation of the modulated structure to the fibre formation and to the appearance of the labyrinthine instability in freely-suspended films is discussed.

Anomalous Increase in Nematic-Isotropic Transition Temperature in Dimer Molecules Induced by a Magnetic Field.

We have determined the nematic-isotropic transition temperature as a function of an 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 15 K when subjected to a 22 T 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.

Thermal optical non-linearity of nematic mesophase enhanced by gold nanoparticles--an experimental and numerical investigation.

In this work the mechanisms leading to the enhancement of optical nonlinearity of nematic liquid crystalline material through localized heating by doping the liquid crystals (LCs) with gold nanoparticles (GNPs) are investigated. We present some experimental and theoretical results on the effect of voltage and nanoparticle concentration on the nonlinear response of GNP-LC suspensions. The optical nonlinearity of these systems is characterized by diffraction measurements and the second order nonlinear refractive index, n2, is used to compare systems with different configurations and operating conditions. A theoretical model based on heat diffusion that takes into account the intensity and finite size of the incident beam, the nanoparticle concentration dependent absorbance of GNP doped LC systems and the presence of bounding substrates is developed and validated. We use the model to discuss the possibilities of further enhancing the optical nonlinearity.

Second harmonic light scattering induced by defects in the twist-bend nematic phase of liquid crystal dimers.

The nematic twist-bend (NTB) 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 NTB 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 NTB 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, NTB-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 NTB 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.

Similarities and differences between molecular order in the nematic and twist-bend nematic phases of a symmetric liquid crystal dimer.

The order parameter, Szz, where z is the para axis of the difluoroterphenyl groups in DTC5C9, has been obtained from chemical shift anisotropies measured by (13)C - {(1)H} NMR experiments at temperatures throughout the nematic, NU, and twist-bend nematic, NTB, phases shown by this compound. The order parameter temperature profiles are unusual in having a maximum value in the NU phase and then decreasing until the NTB phase is reached. There is a small discontinuity (∼2%) in Szz at TNNTB and then a gradual decrease until a new phase appears. This behaviour is interpreted as revealing a temperature-dependent tilting of local directors in both phases away from the applied magnetic field direction. In the enantiomorphic twist-bend phase this tilt is consistent with the structure of the phase as a helical arrangement of local directors, whilst in the high-temperature non-chiral nematic the tilt must involve a non-chiral arrangement. It is proposed that in both phases the tilting of directors has a common origin in the bent shape of the molecules.

The stabilisation of the Nx phase in mixtures.

The phase behaviour of mixtures between two symmetric dimers, CBC9CB and the ether-linked analogue CBOC9OCB was investigated by Polarizing Optical Microscopy (POM), Differential Scanning Calorimetry (DSC) and X-Ray Diffraction (XRD) studies. The dimeric constituents are fully miscible and the construction of a temperature-composition phase diagram reveals a surprising amplification of the stability of the Nx phase in compositions of up to 37 wt% of CBOC9OCB in CBC9CB. The origin for this enhancement of stability is discussed and an explanation based on chiral recognition is developed.

Nematic twist-bend phase with nanoscale modulation of molecular orientation.

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. Here 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).

Capacitance and optical studies of elastic and dielectric properties in an organosiloxane tetrapode exhibiting a N(B) phase.

Biaxial (N(B)) and uniaxial nematic (N(U)) phase behavior was detected and confirmed for an organosiloxane tetrapode material using capacitance and birefringence measurements. Elastic constants, permittivities at two distinct low frequencies, and birefringencies were determined as a function of temperature over both the N(U) and the N(B) phase ranges. The N(U)-N(B) transition is clearly observed in the birefringencies and conoscopy data. A temperature dependent cross-over frequency is also detected in this material for the permittivities, allowing the electrical switching of both planar and homeotropic aligned samples.

Light-induced changes of the refractive indices in a colloid of gold nanoparticles in a nematic liquid crystal.

It was shown that irradiation of a nematic liquid crystal doped with metal nanoparticles in the visible near the plasmon resonance band led to strong thermal changes of the refractive indices. The effect was studied by recording of dynamic optical gratings in the colloid. Nanoparticles "worked" as effective nano-heaters in a matrix causing the order parameter decrease around the particles. A large nonlinearity parameter (n (2) ≈ 10(-2) cm(2)/kW and fast response (≈ 0.7 ms), with no detectable particles' aggregation and excellent photo- thermo-stability make these colloids potentially attractive nonlinear optical media. Application of a dynamic holography technique allowed measuring the coefficients of thermal conductivity of the liquid crystal along the director k (||) = (0.4 ± 0.02) W m(-1)K(-1) and perpendicular to the director k (⊥) = (0.2 ± 0.01) W m(-1)K(-1).

Biaxial order and a rotation of the minor director in the nematic phase of an organo-siloxane tetrapode by the electric field.

Biaxiality in the nematic phase for a liquid crystalline tetrapode made up of organo-siloxanes mesogens is investigated using polarized infrared spectroscopy. An ordering of the minor director for the homeotropically aligned sample is found to depend on the amplitude of the in-plane electric field. On increasing the in-plane electric field, the minor director, lying initially along the rubbing direction, rotates to the direction of the applied field. The scalar order parameters of the second rank tensor are found to depend significantly on the strength of the electric field. A most significant increase is found in the nematic order parameter and in the parameter that characterizes the phase biaxiality.

Phase structure and molecular dynamics of liquid-crystalline side-on organosiloxane tetrapodes.

X-ray diffraction and proton NMR relaxation measurements were carried out on two liquid-crystalline organosiloxane tetrapodes with side-on mesogenic groups, exhibiting nematic and smectic- C phases, and on a monomeric analog. Packing models for the mesophases exhibited by these systems are proposed on the basis of x-ray diffraction data. As a consequence of microsegregation, the aromatic cores are packed in between two sublayers formed by a mixture of interdigitated aliphatic and siloxane chains. The mixed sublayers are characteristic for the tetrapodes with side-on mesogenic groups presented in this work and have not been observed in tetrapodes with terminally attached mesogens. The tilt angle in the smectic- C phase is found very large, i.e., approximately 61 degrees -62 degrees . Notably, smectic- C clusters are present also in the whole temperature range of the nematic phase. NMR relaxometry yields T(1)-1 dispersions clearly different from those of conventional calamitics. The influence of molecular tendency to form interdigitated structures is evidenced by frequency-dependent relaxation rate in the isotropic phase-indicating the presence of ordered clusters far above the phase transition-and by the diminished role of molecular self-diffusion in ordered phases. Nematiclike director fluctuations are the dominating relaxation mechanism whereas the translational displacements are strongly hindered by the interdigitation of dendrimer arms.

Detecting columnar deformations in a supermesogenic octapode by proton NMR relaxometry.

We used proton ( (1)H nuclear magnetic relaxation (NMR) dispersions to study the molecular dynamics in the isotropic phase and mesophases (nematic and columnar hexagonal) of a supermesogenic octapode formed by laterally connecting calamitic mesogens to an inorganic silsesquioxane cube through flexible spacers. The dispersions of the spin-lattice relaxation time (T(1)) are interpreted through relaxation mechanisms used for the study of molecular dynamics in low-molar-mass liquid crystals but adapted to the case of liquid crystalline supermolecules. At high frequencies (above 10MHz) the behaviour of the T(1) with the Larmor frequency is similar for all phases and is ascribed to local reorientations and/or rotations. At intermediate and low frequencies (below 10MHz) our results show notable differences in the T(1) behaviour with respect to the mesophases. The nematic (N) and isotropic (Iso) phases' low-frequency results are similar and are interpreted for both phases in terms of order director fluctuations (ODF), revealing that even in the isotropic phase local nematic order is detected by proton NMR relaxometry. Local nematic order in the Iso phase is interpreted in terms of the presence of nematic cybotactic clusters induced by the interdigitation of mesogens that is promoted by the silsesquioxane octapode molecular structure. In the columnar hexagonal (Col (h) phase, the T(1) dispersions show that elastic columnar deformations (ECD) dominate the nuclear magnetic relaxation below 10MHz. This result shows that the columnar packing of the octapode clearly restricts the collective fluctuations of the mesogenic units inspite of their local nematic order.

Spontaneous periodic deformations in nonchiral planar-aligned bimesogens with a nematic-nematic transition and a negative elastic constant.

Hydrocarbon linked mesogenic dimers are found to exhibit an additional nematic phase below the conventional uniaxial nematic phase as confirmed by x-ray diffraction. The phase produces unusual periodic stripe domains in planar cells. The stripes are found to be parallel to the rubbing direction (in rubbed cells) with a well-defined period equal to double the cell gap. The stripes appear without external electromagnetic field, temperature or thickness gradients, rubbing or hybrid alignment treatments. Simple modeling proposes a negative sign for at least one of the two elastic constants: splay and twist, as a necessary condition for the observed pattern.