Polar smectic subphases: Phase diagrams, structures and X-ray scattering

We analyze a discrete phenomenological model accounting for phase transitions and structures of polar Smectic-C* liquid-crystalline phases. The model predicts a sequence of phases observed in experiment: antiferroelectric SmC _A ^* –ferrielectric SmC _FI1 ^* –antiferroelectric SmC _FI2 ^* (three-and four-layer periodic, respectively)–incommensurate SmC _α ^* –SmA. We find that, in the three-layer SmC _FI1 ^* structure, both the phase and the module of the order parameter (tilt angle) differ in smectic layers. This modulation of the tilt angle (and therefore of the layer spacing d) must lead to X-ray diffraction at the wave vectors Q _s =2πs/d(s=n±1/3) even for the nonresonant scattering.     

Molecular-statistical approach to a behavior of ferroelectric,antiferroelectric and ferrielectric smectic phases in the electric field

The fundamental theoretical approach derived in A.V. Emelyanenko et al., Phys. Rev. E 74, 011705 (2006) is complemented by a consideration of the influence of the homogeneous electric field on Sm- C _A ^* , biaxial intermediate phases, and Sm-C ^* . The crucial role of the induced polarization is investigated for the first time. The evolution of any tilted smectic phase in the electric field is found to meet the two thresholds. The first threshold corresponds to the unwinding process, and the second one corresponds to the phase transition into the bi-domain structure of Sm-C ^* , where the tilt plane has some contribution either along or against the electric field, while the average direction may still be perpendicular to the electric field. The tilt plane in the monodomain (conventional) structure preceding the second threshold is the same in every unwound phase, and is perpendicular to the electric field. No 3D distortion in Sm- C _A ^* is predicted on application of the electric field. The entire electric-field-temperature phase diagrams including the possibility of existence of the maximal number of tilted smectic phases are plotted and compared with the experimental ones. The numerical calculations in the framework of this fundamental study are done with help of AFLC Phase Diagram Plotter software developed by the author and available at his web page.     

Anticlinic-synclinic transitions in superthin free-standing smectic films

Anticlinic-synclinic transition was studied in superthin smectic films using polarized light reflected microscopy. The measurements were made in a compound exhibiting the mC _FI1 ^* subphase in a narrow temperature interval between antiferroelectric C _A ^* and ferroelectric SmC* phases. In films, we observed series of transitions with numbers increasing with increasing film thickness. Surface ordering leads to increasing transition temperatures with decreasing film thickness and to change of orientation of the molecular tilt plane in layers. Succession of transitions results from competition between the surface and the bulk ordering. We found that line string defects may form in a film, their orientation and collective behavior resulting from elastic deformation of molecular ordering.     

Theoretical investigation of antiferroelectric (SmCA) subphases by hydrodynamical approach

We provide a hydrodynamical approach utilizing time dependent Landau-Ginzburg model (L-G) and the Cahn-Hilliard model (C-H) to investigate antiferroelectric liquid crystals (AFLCs) exhibiting different chiral phases between paraelectric smectic A (SmA^?) phase and antiferroelectric smectic C_A^? phase (SmC_A^?). Introducing conserved and non-conserved order parameters in C-H and L-G models, we have predicted the appearance of a chiral smectic C (SmC^?) phase and a ferrielectric SmC_FI1^? phase (three layers SmC_A^?) in an antiferroelectric phase sequence. The three layers periodicity for SmC_FI1^? phase is studied in detail with a non-uniform layer interactions among smectic layers with strong experimental support. Finally, we provide some theoretical basis for the non-uniformity of our proposed layer interactions.     

Refractive index and orientational order parameter of a polar–polar binary system showing induced smectic Ad and re-entrant nematic phases

Refractive index measurements have been done on a polar–polar binary system, 4-cyanophenyl [4′(4″-n-heptylphenyl)] benzoate (7CPB)?+?4-cyanophenyl-4-nonylbenzoate (9.CN), exhibiting nematic–smectic A_d–re-entrant nematic phase sequence using thin prism technique. From refractive index as well as density data, the polarizability anisotropy in the mesomorphic state has been calculated from the standard Vuks model and the orientational order parameter (?P ₂?) values have been determined. By measuring the refractive indices and density in the solid phase, the validity of the Haller's extrapolation method for systems having higher order phases has been verified. The temperature variation of the density, birefringence, and ?P ₂? values at the nematic–smectic A_d and smectic A_d–re-entrant nematic transitions for all the mixtures are found to be continuous. The experimental ?P ₂? values have been compared with our previous X-ray data and also those calculated from the Luckhurst and Timimi model.     

Influence of pressure on the electric-field-induced phase transitions in liquid crystals

Within the framework of Landau-de-Gennes formulation, we analyse the effect of pressure on electric-field-induced phase transitions in a liquid crystal which shows spontaneously an isotropic-smectic A transition. Inferring from the experimental pressure dependences on the layer spacing in smectic A phase, as well as the nematic-smectic A metastable temperature T^*_AN, we incorporated the pressure dependence in the free energy through (the surface energy term) and the coupling between the quadrupolar nematic ordering Q_ij and the smectic order parameter ψ. From the S-T phase diagram, we found that the stability of field-induced nematic phase increases with pressure, whereas the discontinuity of the transition decreases. Also, the region where paranematic phase transits directly to smectic A phase increases with pressure.     

Macroscopic properties of smectic liquid crystals

We discuss the macroscopic behavior of smectic C_G liquid crystals. Smectic C_G is the most general tilted smectic phase that is fluid in the layers. It is characterized by global C₁ symmetry. Consequently, it is ferroelectric, pyroelectric and piezoelectric, opening up a number of possible applications for such a phase. As smectic C_G-phase has a macroscopic hand due to its structure, it is a natural candidate to explain the recent experimental observations of left and right-handed helices in a system composed of achiral molecules. We also discuss critically to what extent smectic C_G could be important for liquid crystalline phases formed by banana-shaped molecules. Phase transitions involving a smectic C_G phase and defects of its in-plane director are briefly discussed. Received: 25 March 1998 / Revised: 15 June 1998 / Accepted: 15 July 1998     

Extension of the resonant scattering technique to liquid crystals without resonant element

We report X-ray resonant scattering experiments performed on the prototype liquid-crystalline compound MHPOBC doped with a chemical probe containing a resonant atom (selenium). We determined directly for the first time the microscopic 3- and 4-layer structure of the ferrielectric subphases ( SmC_FI1^* and SmC_FI2^*) present in MHPOBC. Despite the low fraction of the selenium probe, the resonant signal is strong enough to allow an unambiguous determination of the basic structure of the ferrielectric subphases. These experiments demonstrate that the resonant scattering technique can be extended to liquid crystalline materials without resonant element and may stimulate new studies. A non-resonant Bragg reflection was also found in the SmC_FI1^* phase in pure MHPOBC, consistent with the 3-layer distorted model, but never detected before.     

Symmetries and induced effects in bilayer and multilayer antiferroelectric and ferrielectric liquid crystal phases

The stable antiferroelectric and ferrielectric smectic phases which may arise below a chiral SmA* phase are investigated theoretically. The symmetry and physical properties of the bilayer and multilayer configurations are worked out. Antiferroelectric and ferrielectric bilayer and multilayer configurations, possessing an induced spontaneous ferroelectric polarization component perpendicular to the smectic layers, are shown to take place, as the result of a nonlinear piezoelectric effect. These states of low polar symmetries occur when the angle between the inlayer projections of the dipoles and the director of the molecules is different from 90 degrees.     

Temperature-and field-induced transitions in free-standing films of an antiferroelectric liquid crystal

Thin free-standing films of a compound with the smectic-C _A ^* and smectic-C _α ^* phases were investigated by means of depolarized microscopy and optical reflectivity. In thin films, the smectic phase sequence C _A ^* ?C_α/*?A is replaced by a series of temperature-and field-induced transitions into states with the coplanar orientation of molecular tilt planes. Transitions are accompanied by a change in the direction of the electric polarization with respect to the tilt plane of molecules. The coplanar structure of these states is consistent with the Ising model.     

Smectic phases in hard particle mixtures: Koda's theory

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this ‘smectic demixing’ transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. [T. Koda, M. Numajiri, S. Ikeda, J. Phys. Jap., 65, 3551 (1996)] have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids and sphero-ellipsoids.     

Primitive ideals of C q [SL(3)]

The primitive ideals of the Hopf algebraC _q [SL(3)] are classified. In particular it is shown that the orbits in PrimC _q [SL(3)] under the action of the representation groupH C ^*×C ^* are parameterized naturally byW×W, whereW is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals ofC _q [SL(3)] and symplectic leaves of the associated Poisson algebraic groupSL(3,C).Partially supported by a grant from the N.S.A.     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Anisotropy of Interfaces in an Ordered HCP Binary Alloy

A multiple-order-parameter mean-field theory of ordering on a binary hexagonal- close-packed (HCP) crystal structure is developed, and adapted to provide a continuum formulation that incorporates the underlying symmetries of the HCP crystal in both the bulk and gradient energy terms of the free energy. The work is an extension of the previous treatment by Braun et al. [Phil. Trans. Roy. Soc. Lond. A 355:1787 (1997)] of order–disorder transitions on a face-centered-cubic crystal (FCC) lattice. The theory is used to compute the orientation dependence of the structure and energy of interphase and antiphase boundaries in ordering to the Cd₃Mg and CdMg structures, which are the HCP analogs of Cu₃Au and CuAu structures in FCC. As in the corresponding FCC case, the multiple order parameters do not form a vector. Anisotropy is a natural consequence of the underlying crystal symmetries and the multiple-order-parameter continuum formation presented here. The isotropy transverse to the sixfold axis expected for a scalar order parameter is not found.     

Twisted-grain-boundary (TGB) phases: nanostructured liquid-crystal analogue of Abrikosov vortex lattices

Twisted-grain-boundary (TGB) phases shown by some liquid-crystalline materials have properties common to those of both smectic and cholesteric phases. Following analogy between liquid crystals and super conductors proposed by de Gennes [Solid State Commun., 10, 753 (1972)], Renn and Lubensky [Phys. Rev. A, 38, 2132 (1988)] theoretically predicted a chiral analog of the smectic A (SmA*) phase, which is now known as TGBA phase. The TGBA phase was experimentally observed for the first time by Goodby et al. [Nature, 337, 449 (1989)] in the chiral homologous series of ferroelectric liquid-crystal material R- and S-1-methylheptyl 4′-[(4′′-n-alkoxyphenyl)propionoyloxy]-biphenyl-4-carboxylates (nP₁M₇), with n?=?13,14,15. Since then, more than a hundred pure and mixed systems showing TGBA phase have been found. Later, Renn derived a mean-field phase diagram based on the chiral Chen-Lubensky model, and predicted two more TGB phases, namely TGBC and TGBC?. These two phases have also been experimentally observed in many systems, and in a few, the phase diagram is similar to that predicted by Renn. Unlike the TGBA phase, several theoretical models have been proposed for TGBC and TGBC? phases, and it remains to be ascertained whether all the types of proposed TGBC/TGBC? structures experimentally exist. A review of the theoretically predicted and experimentally observed TGB phases is given in the present article. Some recently observed novel optical textures of the TGB phases are also reported.     

Anomalous Ortho-to-Para Ratio of Nuclear Spin Isomers of H2O at Low Temperatures

A theoretical model proposed for nuclear spin isomers of H₂O molecules located inside the C₆₀ fullerene explains an anomalously high stability of ortho-H₂O isomers detected in the experiments reported in [B. Meier et al., Nature Commun. 6, 8112 (2015)] at a temperature of T = 5 K.

     

Phase transitions in nanocomposites of hydrogen-bonded dimeric liquid crystals with mesogenic and non-mesogenic components

Microtextural polarization, phase transitions, and electro-optical effects are studied in a series of nanocomposites, grown by mixing alkyloxybenzoic acids (nOBAs), displaying hydrogen-bonded dimeric liquid crystal (LC) state, with non-mesogens (single-walled carbon nanotubes (SWCNTs), perfluorooctanoic acid) or mesogens (bent-core LC compound D14F3). Each of the studied nanocomposites, in which the nOBA serves as a matrix, forms complexes with bent-shaped dimeric, caused by the interaction between the dopant structural units and the dimer rings. This feature, coordinated with the surface anchoring, bulk and electrical effects, leads to drastic reduction of the LC system symmetry. As a result, transitions from achiral (characteristic for the pristine nOBA) to chiral states (including ferroelectric smectic C with C₂ symmetry and ferroelectric smectic C_G with the lowest C₁ triclinic one) take place. The functionalization of the SWCNTs causes drastic increase of the ferroelectricity.     

Nonlinear repolarization processes in ferroelectric liquid-crystal thin films

The dynamics of spontaneous polarization switching of the ferroelectric smectic C* in a variable electric field are examined theoretically and experimentally with the help of polarized light scattering. The observed effect of quasiresonant scattering both in freely suspended smectic films and in ordinary electro-optical cells is interpreted within the framework of the nonlinear model of isolated movable kinks in the director orientation distribution. It is shown that the maximum of the scattering intensity at the characteristic frequency of the applied electric field disappears at low temperatures and for small thicknesses of the smectic film. The dependence of the “resonant” frequency on the electric field amplitude, the proximity to the phase transition temperature, the film thickness and thickness of the ferroelectric domains, and also various material parameters is found. Estimates are made of such important characteristics as the dielectric anisotropy, viscosity, and elasticity of the smectic films. The effect of film thickness on the density distribution of the polar anisotropy energy in the film and on the corresponding shape of the moving orientation front within the film are discussed. Zh. éksp. Teor. Fiz. 111, 919–937 (March 1997)     

Phase transitions in PbZr0.72Sn0.28O3 single crystals studied by Raman spectroscopy

ABSTRACT

Raman light scattering measurements in the temperature range from 80 to 830 K were performed on a PbZr_0.72Sn_0.28O₃ single crystal. The frequencies of the Raman lines were analyzed and discussed in terms of the sequence of structural phase transitions. It was found that Raman spectrum displays important changes near 440, 480 and 493 K. The incorporation of more than 25 mol% of Sn⁴⁺ ions into the structure of PbZrO₃ enhances polar fluctuations above T_C as compared to the less Sn-doped crystals. These fluctuations lead to appearance of a ferroelastic intermediate phase below T_C. It is demonstrated that the structural phase transformation in PbZr_0.72Sn_0.28O₃ can be considered as the result of softening of a number of modes.