The effect of magnetic nanoparticles upon the smectic-A to smectic-C* phase transition

We report on wide-angle X-ray scattering measurements along the smectic-A to chiral ferroelectric smectic-C* phase transition of the liquid crystal SCE9 and its mixture with maghemite magnetic nanoparticles of typical dimension 20 nm. The temperature profiles of the tilt angle are fitted by an extended mean-field model. Neither pre-transitional order effects nor variations in the SmA layer thickness are observed, indicating a rather negligible influence of these nanoparticles upon the molecular orientation at the smectic-A to smectic-C* phase transition of SCE9. These results are very different from what was observed for smaller CdSe nanoparticles (3.5 nm) where both a dilation of the smectic layers in the SmA phase and a crossover behaviour for the smectic-A to smectic-C* transition away from tricriticality have been observed for analogous concentrations.     

Landau theory for uniaxial nematic,biaxial nematic,uniaxial smectic-A,and biaxial smectic-A phases

We use the Landau theory of phase transitions to obtain the global phase diagram concerning the uniaxial nematic, biaxial nematic, uniaxial smectic-A and biaxial smectic-A phases. The transition between the biaxial nematic and biaxial smectic is continuous as well as the transition between the nematic phases and the transition between the smectic phases. The transition from uniaxial nematic and uniaxial smectic is continuous with a tricritical point. The tricritical point may be absent and the entire transition becomes continuous. The four phases meet at a tetracritical point.     

Graphene and liquid crystal mediated interactions

ABSTRACT

The two-dimensional graphene-honeycomb structure can interact with the liquid crystal’s (LC) benzene rings through π–π electron stacking. This LC–graphene interaction gives rise to a number of interesting physical and optical phenomena in the LC. In this paper, we present a combination of a review and original research of the exploration of novel themes of LC ordering at the nanoscale graphene surface and its macroscopic effects on the LC’s nematic and smectic phases. We show that monolayer graphene films impose planar alignment on the LC, creating pseudo-nematic domains (PNDs) at the surface of graphene. In a graphene-nematic suspension, these PNDs enhance the orientational order parameter, exhibiting a giant enhancement in the dielectric anisotropy of the LC. These anisotropic domains interact with the external electric field, resulting in a non-zero dielectric anisotropy in the isotropic phase as well. We also show that graphene flakes in an LC reduce the free ion concentration in the nematic media by an ion-trapping process. The reduction of mobile ions in the LC is found to have subsequent impacts on the LC’s rotational viscosity, allowing the nematic director to respond quicker on switching the electric field on and off. In a ferroelectric LC (smectic-C* phase), suspended graphene flakes enhance the spontaneous polarisation by improving the tilted smectic-C* ordering resulting from the π–π electron stacking. This effect accelerates the ferroelectric-switching phenomenon. Graphene can possess strain chirality due to a soft shear mode. This surface chirality of graphene can be transmitted into LC molecules exhibiting two types of chiral signatures in the LCs: an electroclinic effect (a polar tilt of the LC director perpendicular to, and linear in, an applied electric field) in the smectic-A phase, and a macroscopic helical twist of the LC director in the nematic phase. Finally, we show that a graphene-based LC cell can be fabricated without using any aligning layers and ITO electrodes. Graphene itself can be used as the electrodes as well as the aligning layers, obtaining an electro-optic effect of the LC inside the cell.     

Invited Lecture. Order-parameter theories of phase diagrams for antiferroelectric smectic-A phases

Using exact relations between Landau and molecular approaches, the symmetryinduced topologies of phase diagrams are studied for antiferroelectric smectic-A phases. In particular, the tricritical points are found for a large class of orderparameter theories of nematic-smectic A (-A₁, -A_d) and -A₂ (NA) phase transitions. These include generalizations to antiferroelectric smectic-A phases of McMillan and Meyer-Lubensky mean-field theories and the Ramakrishnan-Youssouff(RY) density-functional approach. The use of these different approaches allows study of influence of various couplings between nematic (orientational) and smectic (translational) degrees of freedom and polarization field, P₁ (cos θ), on various NA and AA phase transitions. From the results, it is of interest that the coupling between orientational degrees of freedom (P₄(cos θ) and density waves can destabilize the smectic-A phase at low temperatures-pointing to the existence of a nematic-smectic-A-reentrant-nematic phase transition. A possible relation of this result to A_d, C₂, C_d and [ctilde] phases is discussed. Some relations between Fourier components of correlation functions and order parameters at tricritical points are derived from the RY density-functional theory. Despite some limitations, the theory presented here seems to provide the simplest approach to study topologies of phase diagrams in molecular theories.     

The phase behavior, structure, and dynamics of rodlike mesogens with various flexibility using dissipative particle dynamics simulation

We present a systematic dissipative particle dynamics (DPD) study on the phase behavior, structure, and dynamics of rodlike mesogens. In addition to a rigid fused-bead-chain model with RATTLE constraint method, we also construct a semirigid model in which the flexibility is controlled by the bending constant of k(φ). Using this notation, the rigid model has an infinite bending constant of k(φ)=∞. Within the parameter space studied, both two kinds of models exhibit the nematic and smectic-A phases in addition to the isotropic and solid phases. All of the phase transitions are accompanied by the discontinuities in the thermodynamical, structural, and dynamical quantities and the hysteresis around the transition points, and are therefore first order. Note that the obtained solid state exhibits an in-layer tetragonal packing due to the high density. For the rigid model, the simulations show that the liquid crystal phases can be observed for mesogens with at least five beads and the nematic phase is the first one to appear. More importantly, the phase diagram of seven-bead-chain models is obtained as a function of k(φ) and temperature. It is found that decreasing the value of k(φ) reduces the anisotropy of molecular shape and the orientational ordering, and thereby shifts the liquid crystal phases to the lower temperature end of the phase diagram. Due to the different k(φ) dependence of phase transition temperatures, the nematic phase range exhibits a more marked narrowing than the smectic-A phase as k(φ) is reduced, implying that the flexibility has a destabilizing effect on the nematic and smectic-A phases. We also have investigated the anisotropic translational diffusion in liquid crystal phases and its temperature and flexibility dependence. In our study, we find that the phases formed, their statical and dynamic properties, as well as the transition properties are in close accord with those observations in real thermotropic liquid crystals. It is clear that both the rigid and semirigid models we used are valuable models with which to study the behavior of thermotropic liquid crystals using DPD algorithm.     

Understanding self-assembly of rod-coil copolymer in nanoslits

Rod-coil diblock copolymers are a special kind of molecule containing a rigid rod and a flexible part. We present a systematic study on self-assembly of the rod-coil copolymers in nanoslits using a hybrid density functional theory. The self-assembly of the rod-coil molecule is driven by the bulk concentration, and there exists a critical bulk concentration beyond which the rod-coil molecule self-assembled into ordered lamellar structures in the slit, otherwise it is in a disordered state. By monitoring the effect of the interaction (epsilon(TT)(*)) of molecular tail on the self-assembly, we found that in the nanoslit of H=13sigma, it is at epsilon(TT)(*)=8 rather than epsilon(TT)(*)=10 or epsilon(TT)(*)=12 that the minimal critical bulk concentration occurs. It may be because the strong tail-tail interaction leads to aggregation of the copolymer molecules in bulk phase, and the resulting supramolecular structures are fairly difficult to enter the slit due to the depletion effect. At a fixed slit, the structural evolution of the self-assembled film with the bulk concentration is observed, including trilayer and five-layer lamellar structures, smectic-A, smectic-C, and a mixture of smectic-A and smectic-C liquid crystal phases and so on. We found that the critical bulk concentration, corresponding to the disordered-ordered phase transition, greatly depends on the separation between two walls, and it changes periodically with the increase of the slit width. In addition, it is also found that the molecular flexibility is one of key factors determining the self-assembled structure in the slit, and the critical bulk density increases with the molecular flexibility.     

Smectic polymorphism in a series of three-ring enaminoketone compounds

Abstract

Liquid crystalline properties of 1 - (4′ - alkoxyphenylamino) - 3 - (4′ - hexyloxyphenyl)-prop-1-en-3-ones, from methoxy to heptadecyloxy, have been examined by optical, DSC, and X-ray methods. The phase diagram for the series exhibits a rich polymorphism of tilted smectic phases, for example, five mesophases were found for the hexyloxy derivative. A characteristic feature of the phase diagram is a gap in the crystal G phase area. For the heptyloxy homologue, a direct crystal H-smectic F phase transition was found; in the case of shorter as well as longer terminal substituents, the phase sequence crystal H–crystal G–smectic F is observed. Calorimetric and X-ray studies revealed the existence of a tricritical point on the crystal G–smectic F transition line.     

Phase Transition and Structural Investigations in 50.5, 50.6 and 50.7

Abstract

We report X-ray diffraction, density, ultrasonic velocity and refractive index studies in the N(p-n-pentyloxy benzylidene) p-n-alkylaniline compounds, viz. 50.5, 50.6 and 50.7. The nematic-smectic A (NA) transition is found to be weak first order in 50.6 while it is second order in 50.5 and 50.7. The salient features observed are cybotactic clusters in the nematic phase in all the compounds, molecular tilt which was inferred due to the end alkyl chains tilt causing orienta-tional disorder (smaller orientational order parameters ‘s’ than expected) in smectic A phase, smectic F phase and large tilt angle variation in smectic C phase in a small temperature range in 50.5. The observed results are discussed in the light of available data in other n0.m compounds.     

Optical and dielectric properties of antiferroelectric liquid crystals and their surface effects

Abstract

A detailed study of the dielectric and optical properties of the ferroelectric liquid crystal material (R)-4′-(3-methoxycarbonyl-2-propoxycarbonyl)phenyl 4-(4-(n-octyloxy)phenyl)benzoate (3MC2PCPOPB) has been carried out. It has been found that an anomalous temperature dependence of the dielectric constant in 3MC2PCPOPB is due to the antiferroelectric and ferrielectric properties. A T(temperature)-E(electric field) phase diagram has been obtained on the basis of the apparent tilt angle measurements. In a thin cell (< 3 μm), both ferroelectric and antiferroelectric domains are simultaneously observed over a wide temperature range, and the complete antiferroelectric phase does not appear even at low temperature. A characteristic texture in which boundary focal conics are aligned parallel to a smectic layer has been observed. The movement of the zig-zag defect line caused by the application of the voltage is also observed.     

The effect of chiral doping in achiral smectic liquid crystals on the de Vries characteristics: smectic layer thickness,electro-optics and birefringence

An addition of chiral dopant to two achiral smectic liquid crystals from a homologous series, by varying weight percentages with known low values of layer shrinkage, leads to chiral smectic-C* phase with a finite value of the spontaneous polarisation. The electro-optical response arising from changes in the induced apparent tilt angle brought about by a weak electric field in the SmA* phase gives rise to power law dependency on the reduced temperature. The critical exponent γ of the power law depends on the dopant concentration but its value is found to be greater than the typical value of 1.32. This implies that the short-range correlation extends from two dimensions to three dimensions in these materials in the SmA phase. The layer thickness of smectic layers in the guest–host system remains unaltered up to the 15 wt % addition of the chiral dopant to two achiral smectics. The system thus retains the low layer shrinkage of the achiral smectic as evidenced by measurements of the layer thickness from X-ray scattering and thickness measurements from optical interferometry. Results on the optical birefringence and the apparent tilt angle lead us to the conclusion of having successfully obtained chiral smectic materials for devices with de Vries characteristics by chiral doping.     

Liquid-crystal phase diagrams of binary mixtures of hard spherocylinders

We have built the liquid crystal phase diagram of several binary mixtures of freely rotating hard spherocylinders employing a second-order virial density functional theory with Parsons scaling, suitably generalized to deal with mixtures and smectic phases. The components have the same diameter and aspect ratio of moderate value, typical of many mesogens. Attention has been paid to smectic-smectic demixing and the types of arrangement that rods can adopt in layered phases. Results are shown to depend on the aspect ratio of the individual components and on the ratio of their lengths. Smectic phases are seen not to easily mix together at sufficiently high pressures. Layered phases where the longer rods are the majority component have a smectic-A structure. In the opposite case, a smectic-A(2) phase is obtained where the shorter particles populate the layers and the longer ones prefer to stay parallel to the latter in the interlayer region.     

Thermal analysis of hydrogen bonded benzoic acid liquid crystals

Novel homologous series of supramolecular hydrogen bonded liquid crystals have been investigated. Hydrogen bonds are formed between p-n octyloxy benzoic acid and various p-n alkyloxy benzoic acids whose carbon chain length varied from pentyl to dodecyl. These complexes are characterized by Fourier transform infrared spectroscopy, polarizing optical microscopy (POM), and differential scanning calorimetry (DSC). Phase diagram is constructed from POM and DSC data. The order of the phase transitions is determined by Navard and Cox ratio (N _R). Characteristic phases like nematic, smectic C, and smectic F are identified. A new smectic ordering observed in this series is investigated by constructing phase diagram obtained from two binary mixtures of the present homologs. Inter-digitation of lamellar layers is observed to be one of the reasons for the occurrence of new smectic ordering. Optical tilt angle in smectic C phase is fitted to a power law. The magnitude of exponent of the power law is found to concur with the Mean Field theory predicted value.     

A continuum description for cholesteric and nematic twist-bend phases based on symmetry considerations

ABSTRACT

The recently discovered twist-bend nematic phase, N_tb, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, n, on a conical helix with a tilt angle θ and helical pitch P. The stability of the N_tb phase has been recently demonstrated from the elastic point of view by extending the Frank elastic energy density of the nematic phase to include the symmetry element of the helical axis, t. In the present article, we investigate the influence of an external bulk field (magnetic or electric) on the N_tb phase. Using symmetry arguments we derive the expression for the flexoelectric polarisation in twist-bend nematic phases. We show that, besides the standard contribution related to the spatial variation of the nematic director, two new contributions connected with the existence of the helical axis appear. In the ground state, where the nematic deformation is a pure heliconical deformation, the new contribution vanishes identically, and the total flexoelectric polarisation is perpendicular to the nematic director. Furthermore, as an example, we study the role of an external magnetic field applied parallel to the helical axis for a material with positive magnetic susceptibility anisotropy. We show that the field modifies the range of values of the coupling parameter between the director and the helical axis, thus shifting the interval of values for which this coupling results in the N_tb phase.     

On the origin of high optical director tilt in a partially fluorinated orthoconic antiferroelectric liquid crystal mixture

We have investigated the orthoconic antiferroelectric liquid crystal mixture W107 by means of optical, X-ray and calorimetry measurements in order to assess the origin of the unusally high tilt angle between the optic axis and the smectic layer normal in this material. The optical birefringence increases strongly below the transition to the tilted phases, showing that the onset of tilt is coupled with a considerable increase in orientational order. The layer spacing in the smectic A* (SmA*) phase is notably smaller than the extended length of the molecules constituting the mixture, and the shrinkage in smectic C* (SmC*) and smectic C_a* (SmC_a*) is much less than the optical tilt angle would predict. These observations indicate that the tilting transition in W107 to a large extent follows the asymmetric de Vries diffuse cone model. The molecules are on average considerably tilted with respect to the layer normal already in the SmA* phase but the tilting directions are there randomly distributed, giving the phase its uniaxial characteristics. At the transition to the SmC* phase, the distribution is biased such that the molecular tilt already present in SmA* now gives a contribution to the macroscopic tilt angle. In addition, there is a certain increase of the average tilt angle, leading to a slightly smaller layer thickness in the tilted phases. Analysis of the wide angle scattering data show that the molecular tilt in SmC_a* is about 20° larger than in SmA*. The large optical tilt (45°) in the SmC_a* phase thus results from a combination of an increased average molecule tilt and a biasing of tilt direction fluctuations.     

Smectic networks obtained from twin LC epoxy monomers—mechanical deformation of the smectic networks

Deformation experiments were carried out for densely crosslinked smectic-like networks obtained from diepoxy monomers with twin mesogen architecture. For the initially unoriented smectic networks, the network could be aligned up to an orientation parameter of 0.35 by applying 8 MPa of external stress in the rubbery regime. X-ray diffraction measurements revealed that the deformed smectic network possesses both smectic-A like and smectic-C like structure. It is thought that after extension domains initially oriented parallel to the external stress displayed a smectic-A-like structure, whereas domains initially tilted with respect to the tensile direction showed a stress-induced smectic-C like structure. A smectic network oriented under a.c. electric fields with an orientation parameter of 0.4 had a smectic-A like structure and possessed linear elasticity in the rubbery regime. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 31–38, 1998     

A modified Langevin-Debye model for investigating the electro-optic behaviour of de Vries smectic liquid crystals

An external electric field applied across a planar-aligned cell in Smectic A* phase of de Vries smectic liquid crystal induces director redistribution over a cone, resulting in a substantial increase in the birefringence and the apparent optical tilt angle. Such an electro-optic response is modelled by Shen et al. [Y. Shen et al., Phys. Rev. E 88, 062504 (2013)], who modified their previous hollow cone with a diffuse cone model by introducing the molecular distribution function limited over a range of tilt angles, that lie in between θ_min and θ_max. The limits in these two tilt angles are assumed to be temperature independent though the tilt angle in between the two values can be temperature dependent. However, the high resolution measurements of birefringence and the layer thickness indicate the presence of temperature dependent diffuse cone angle in SmA* phase.. In the proposed model, we replace θ_min by θ_T, a temperature dependent fitting parameter and the change shows that a better fit of the experimental data to the model is obtained. We determine the temperature dependence of θ_min and show that this angle increases as SmA* to SmC* phase transition temperature is approached.     

Stable frustrated phases in chiral liquid crystals derived from optically active (R)- and (S)-3-ethylmercapto-2-methylpropionic acids

Highly optically pure (R)- and (S)-3-ethylmercapto-2-methylpropionic acids were synthesized by using optically active (D)- and (L)-2,10-camphorsultams as chiral auxiliaries, respectively. Their derivatives, (R)- and (S)-EMMPNmB (m=6-12), were prepared for investigation. Microscopic texture observations demonstrated that the materials possess three stable frustrated phases: BP, TGB_A* and TGB_C* phases. Interestingly, it was found that the N* phase behaves as an intermediary phase between BP and TGB_A* phases in a rather narrow temperature range (calc. 0.5-1.4°C). A study of the racemic mixture, (±)-EMMPNmB (m=10), indicated that the chirality of the molecule could suppress the formation of smectic phases in the heating process. An increase of alkyl chain length favoured the formation of the TGB phases particularly, in accompaniment with a change of TGB phases from monotropic to enantiotropic. Moderate maximum P _S values (calc. 14-19 nC cm^-2) and apparent tilt angle (calc. 20°) were obtained for the TGB_C* phase in a surface stabilized ferroelectric liquid crystal geometry.     

The influence of double bonds in the terminal chain of 2-ring compounds on the physical properties of S*c mixtures

Abstract

We present the properties of S*_c mixtures containing new 2-ring 5-n-alkyl-2-(4-n-alkenyloxyphenyl)pyridines and pyrimidines with systematically varying positions and configurations of the double bond Trans configurations at odd positions (counting the number of atoms from the core including the oxygen and the first carbon atom of the double bond) suppress the S_A phase, increase the S*_c tilt angle, Θ, and the spontaneous polarization, P _s, and lead to long switching times τ. Cis configurations at even positions suppress the nematic phase in favour of smectic phases, decrease Θ and P _s, and shorten τ. Other positional configurational combinations strongly reduce the clearing point. Furthermore, our results indicate that the preferred conformation of the alkenyloxy chain consists of alternating cis and trans units.     

The phase diagram of fullerene C60 at high temperatures and pressures

Experimental and literature data were used to calculate the Gibbs energies of polymerized C₆₀ phases and construct the equilibrium T-p phase diagram of fullerene C₆₀ at temperatures from 0 to 1000 K and pressures from 0 to 8 GPa. The diagram contains stability regions of the orthorhombic, tetragonal, and rhombohedral polymerized C₆₀ phases and primitive cubic (PC) and face-centered cubic (FCC) nonpolymerized C₆₀ phases. The orthorhombic phase (linear polymer) is an equilibrium phase at 298 K and 1 bar and in the adjacent region. The equilibrium line observed experimentally (FCC C₆₀—orthorhombic phase) is well described by the phase diagram. The optimum temperatures and pressures of the synthesis of polymerized phases are determined by kinetic rather than thermodynamic parameters.