Novel approach to study liquid crystal phase transitions using Legendre moments

A novel approach is proposed to investigate the phase transitions of cholesteric liquid crystals using the Legendre moments. The textures of cholesteric liquid crystals (cholesteryl butyrate, cholesteryl n-valerate, cholesteryl decanoate, and cholesteryl myristate) are captured as a function of temperature using high-resolution camera attached to the arthroscopic mode of polarizing optical microscope with hot stage. A recurrence formula is used to compute the Legendre moments of the liquid crystal textures based on the Legendre polynomial using MATLAB software. The abrupt change in the values of Legendre moments as a function of temperature gives the phase transitions of liquid crystals. The investigated transition temperatures of cholesteric liquid crystals are compared with other techniques.     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.     

Costa ribeiro effect in some cholesteryl esters

In this paper we confirm the existence of the thermodielectric effect at phase transitions of some cholesteryl esters (cholesteryl chloride, cholesteryl nonanoate and cholesteryl laurate). Significant sudden variations of the potential difference across the samples were detected at solid crystal → isotropic, isotropic → mesophase phase transitions of these liquid crystals. The variations are due to the formation of thermodielectric electrets by spontaneous polarization. The phase transitions are identified and their temperatures are in agreement with the literature.     

Induced birefringence in the isotropic phase of cholesteric liquid crystals

The birefringence induced by an acoustic field in the isotropic phase of the cholesteryl myristate cholesteric liquid crystal has been measured. The measurements were performed at sound frequencies of 3.2 and 9.8 MHz in a wide temperature range. Based on the results of the measurements of the induced birefringence, the relaxation time of the orientation of the liquid crystal molecules is estimated.     

Ferroelectricity in mixtures of mesogenic and nonmesogenic compounds

It is shown that by adding potassium nitrate (1 % by weight) to compensated cholesteric mixtures (cholesteryl chloride-cholesteryl myristate 63.63:36.37% by weight and cholesteryl laurate-cholesteryl chloride 35.65% by weight) or to smectic sitosteryl undecilenate, the mixtures exhibit ferroelectric behaviour. Values of P_s = 10-⁹ - 10-⁸ C/cm² were obtained in the high-temperature range. In compensated cholesteric mixtures, the spontaneous polarisation reached a minimum at a temperature corresponding to the cholesteric-nematic transition. The results are explained by assuming coupling between the dipoles of the antiferroelectric KNO₃ and the dipoles of the mesogenic compound.     

Phase transition in cholesteryl oleate and cholesteryl linoleate

A differential scanning calorimeter study of cholesteryl oleate (CO) and cholesteryl linoleate (CL) reveals a new solid — solid transition in CO at 265 K with enthalpy difference 1.8 cal/g. Glass transitions (T_g CO=226 K, CL=215 K) and crystal nucleation temperatures are reported.     

Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal field is studied within the mean-field theory. The phase diagrams and magnetization curves are obtained by diagonalizing the Hamiltonian H_i of the Ising system numerically, and the first order-order phase transitions, the first order-disorder phase transitions, and the second-order phase transitions are discussed in details. Reentrant phenomenaoccur when the value of the transverse field is not zero and the reentrantdiagram is given.     

Logarithmic divergence of the shear viscosity in the isotropic phase of two cholesterics

The transition from the isotropic liquid to the cholesteric blue phase in cholesteryl oleyl carbonate and cholesteryl oleyl carbonate and cholesteryl oleate is accompanied by an anomaly in the shear viscosity which follows a pseudocritical logarithmic divergence as a function of temperature.     

Re-entrant phase transitions of the Blume-Emery-Griffiths model

We have investigated the spin-1 Ising model on the simple cubic lattice with bilinear, biquadratic interaction and anisotropic energy (BEG model). We have been specially interested in the case of antiferro biquadratic interaction, because the interaction will cause the competition with bilinear interaction and anisotropy. A two-sublattice ordering, so called the staggered quadrupole (SQ) phase, occurs as long as biquadratic interaction is negative large enough. We have obtained a full phase diagram in the whole interaction parameter space (for the positive bilinear interaction) by the Bethe approximation, and found several kinds of phase transitions, such as successive, re-entrant and double re-entrant transitions. These transitions are also confirmed by Monte Carlo simulations on simple cubic lattices.     

Grain Boundary Phase Transitions and their Influence on Properties of Polycrystals

Grain boundary (GB) phase transitions can change drastically the properties of polycrystals. The GB wetting phase transition can occur in the two-phase area of the bulk phase diagram where the liquid (L) and solid (S) phases are in equlibrium. Above the temperature of the GB wetting phase transition a GB cannot exist in equlibrium contact with the liquid phase. The experimental data on GB wetting phase transitions in numerous systems are analysed. The GB wetting tie-line can continue in the one-phase area of the bulk phase diagram as a GB solidus line. This line represents the GB premelting or prewetting phase transitions. The GB properties change drastically when GB solidus line is crossed by a change in the temperature or concentration. The experimental data on GB segregation, energy, mobility and diffusivity obtained in various systems both in polycrystals and bicrystals are analysed. In case if two solid phases are in equilibrium, the GB “solid state wetting” can occur. In this case the layer of the solid phase 2 has to substitute GBs in the solid phase 1. Such GB phase transition occurs if the energy of two interphase boundaries is lower than the GB energy in the phase 1.     

Ising model with a new class of four-spin interactions

The Ising model on a Union-Jack lattice, described by a Hamiltonian with second-neighbor pair-pair, four-spin, infinite-range interactions is considered. The model is solved exactly and the results are compared with MFA predictions. Within the exact treatment two new classes of phase transitions are obtained. The first one includes transitions from a disordered to a metastable, ordered and then to a stable and ordered phase with decreasing temperature. The metastable phase does not appear if the temperature is increased. The second one contains transitions between ordered and partialy ordered, partialy frustrated phases.     

Excitation of phase transitions in dipole lattices

Phase transitions in hexagonal lattices with three and four rows of dipoles arising as a result of the reorientation of different sets of dipoles by the external field have been studied. The conditions of the implementation of two types of symmetric phase transitions and the asymmetric transitions, when the configurations of the system to the left and to the right of the excitation region are different, have been established. Merging of two regions of the phase transitions has been considered. Unidirectional phase transitions, in which either the left or the right phase transition front propagates from the excitation region along the lattice, have been obtained in a lattice with four rows of dipoles. The variations of the total dipole moment of the system and the energy of the dipole-dipole interaction during the phase transitions have been given.     

First-principles calculations of structure and high pressure phase transition in gallium nitride

The phase transitions of semiconductor GaN from the Wurtzite (WZ) structure and the zinc-blende (ZB) structure to the rocksalt (RS) structure are investigated by using the first-principles plane-wave pseudopotential density functional method combined with the ultrasoft pseudopotential scheme in the generalized gradient approximation (GGA) correction. It is found that the phase transitions from the WZ structure and the ZB structure to the RS structure occur at pressures of 46.1 GPa and 45.2 GPa, respectively. The lattice parameters, bulk moduli and their pressure derivatives of these structures of GaN are also calculated. Our results are consistent with available experimental and other theoretical results. The dependence of the normalized formula-unit volume $V/V_{0 }$ on pressure $P$ is also successfully obtained.     

Reorientation phase transition in temperature in a two- and three-dimensional ferromagnet with the account of magnetoelastic coupling

In the paper, we have investigated reorientation phase transitions in a two-dimensional ferromagnet. It is shown that the account of magnetoelastic coupling results in the appearance of an angular phase, and the phase transitions are of the first order. The temperature interval of the angular phase existence is determined mainly by elastic and magnetoelastic parameters of the system. For a three-dimensional system the observable effect disappears. The obtained results are consistent with experimental data.     

Phase studies and thermal stability of binary systems of cholesteric liquid crystals

The binary mixture of cholesteryl oleyl carbonate (COC) and cholesteryl nonanoate (CN) with different ratios has been characterized by differential scanning calorimetry (DSC) to determine the phase diagrams. Their normal shelf-life and accelerated stability studies were also examined. A novel microscopic Fourier-transform infrared (FT-IR) spectrometer equipped with DSC was also used to measure simultaneously the chemical structural variation and the thermal response of these liquid crystals. The results indicate that the binary mixture might transform from smectic to cholesteric and then to isotropic liquid (CN composition <50%); from solid to cholesteric and then to isotropic liquid (CN composition >50%). Therefore, the 50% CN composition might play a critical role in the phase transition of the binary COC-CN mixture. The microscopic FT-IR/DSCsystem could also confirm the phase transition, but could measure the phase trasition temperature of liquid crystals more easily and sharply than the DSC method. The long-term accelerated thermal stability of the COC-CN mixture seemed to be more constant when stored at 4 °C than in any other temperature conditions.     

Ground-State Phase Diagram of Transverse Spin-2 Ising Model with Longitudinal Crystal-Field

The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/z J-longitudinal crystal D/zJ field plane. We find that there are the first order-order phase transitions in a very smallrange of D/zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions.     

Identification of a TGBA liquid crystal phase via its defects

We have shown that cholesteryl nonanoate, a thermotropic compound which is well known to exhibit pretransitional effects at the smectic A (SmA) cholesteric (N*) transition (W.L. McMillan, Phys. Rev. A 4, 1238 (1971); 6, 936 (1972)), has in fact a TGBA phase in between. Our arguments rely on the observation of new TGBA defects, either in Robinson spherulites cooled from the N* phase or in free-standing films. The same new defects can be obtained in a well-documented TGBA phase of a tolane compound. We analyze qualitatively the TGBA defects in both geometries, in particular their relation to the disclination radius of the N* Robinson spherulites. Received 12 February 2001     

Interrelation of antiferrodistortive and ferroelectric phase transitions in Sr1−xAxTiO3 (A=Ba, Pb)

A dielectric and ultrasonic velocity study of antiferrodistortive and ferroelectric phase transitions in Sr_1−xA_xTiO₃ (A=Ba, Pb) is reported. It is shown that both phase transitions co-exist at x<0.03 but at the higher concentration the ferroelectric phase transition entirely suppresses the antiferrodistortive phase transition. The experimentally obtained phase diagrams are discussed in the framework of the Landau phenomenological theory.