A statistical model of the discotic mesophase

The evaluation of the thermodynamic properties of an ideal discotic mesophase needs the determination of a partition function, that depends upon two basic types of energy storage, translational and rotational. Here, we suppose we can substitute for the complex effective intermolecular potential, different mean potentials acting on each individual molecule. The defining assumptions for a discotic mesophase include the stipulations, first—that each simple disk-like molecule is, during most of the time, confined to a cell, secondly—that each molecule has an external rotation which is more or less hindered by a periodic potential. The cells are stacked in columns and the columns form a regular hexagonal array, each molecule moves in a cell as in an infinite potential well due to the neighbouring molecules. This model has allowed the general formulation of the mesophase-free energy. From this, we obtain the form of the coefficient of isothermal compressibility when the external rotations of the molecules are hindered and the vibrational energy is weak.     

Fast and slow dynamics in a discotic liquid crystal with regions of columnar order and disorder

Aromatic disk-shaped molecules tend to self-organize into a herringbone packing where the disks are inclined at angles ±θ with respect to the axis of the column. In discotic liquid crystals this can introduce defects between stacks of limited length. In a C(3)-symmetric hexa-peri-hexabenzocoronene, solid-state NMR, x-ray scattering, and rheology identifies such a packing with θ=43° and stacks of about seven disks. Disordered regions containing defects fill the space in between the ordered stacks. Biaxial intra- and intercolumnar dynamics differing by eight decades are identified.     

Deuteron NMR study of dynamics and order in the columnar phase of a fluorinated discotic liquid crystal

Measurements have been made of deuteron quadrupolar splitting and spin—lattice relaxation times T _1Q and T _1z in the columnar phase of a ring deuterated 1-fluoro-2,3,6,7,10,11-hexahex-yloxytriphenylene (F-HAT6) as a function of temperature and at two different Larmor frequencies. The disc-like molecules are stacked, with only short range positional order, into columns which are arranged on a 2-dimensional hexagonal lattice. To describe small step reorientations of these molecules, a rotational diffusion model which uses a space-fixed frame to diagonalize the molecular diffusion tensor is adopted. The principal diffusion constants in this so called ‘anisotropic viscosity model’ Dα and Dβ are for rotations of a molecule around and perpendicular to the columnar axis, respectively. A global target analysis of the spectral densities J ₁(ω₀) and J ₂(2ω₀) at seven temperatures and two Larmor frequencies in a single minimization procedure was carried out. It was found that Dα Dβ, which is consistent with the picture that the motion towards or away from the local director (i.e., the columnar axis) tends to disrupt the packing of molecules within the column. Furthermore, the activation energies Eαβ and Eβ_a for these motions were found to be 67.7 kJmol^?1 and 56.3kJmol^?1. That these values are higher in comparison with those for HAT6 is interesting, and believed to be a result of a strong lateral dipole in F-HAT6.     

Chiral spin liquid in a two-dimensional helical XY magnet with two chiral order parameters

The critical properties of an XY helimagnet on a square lattice with two chiral order parameters are studied by Monte Carlo simulations. This model is a modification of the J ₁-J ₂-J ₃ model with J ₂ = 0. The case of different third range order interactions J ₃ are considered, J ₃ ^a ?? J ₃ ^b . A first order transition is found away from the Lifshitz points 4J ₃ ^a = J ₁ and 4 J ₃ ^b = J ₁. It is pointed out that a chiral spin liquid phase possibly exists near the Lifshitz points.     

Liquid-crystalline phase behavior of a colloidal rod-plate mixture

The phase behavior of rod-plate mixtures was investigated using model systems containing unambiguously rod- and plate-shaped colloids. We find that the theoretically disputed biaxial nematic phase is unstable with respect to demixing into an isotropic and two uniaxial nematic phases. The phase behavior at very high densities is exceptionally rich and includes the coexistence of up to four different liquid crystalline phases, which stem from the coupling between the employed particle shapes and polydispersity.     

Spatial disorder in a smectic A mesophase

Starting with the equations of motion for a stiff chain, a projection operator approach is utilized to develop diffusional equations for the dynamics of the end-to-end distance. The diffusion equation resulting has a spatial-dependent diffusion coefficient calculable from equilibrium properties of the chain, and a frequency-dependent part which requires dynamical information. The analysis is applied, in so far as the spatial dependence of D is determined, for three and four bond chains. A critique of this procedure is provided.     

Thermal diffusivity measurements in a lyotropic discotic nematic phase

The present work is focused on thermal diffusivity (D)$(D)$ measurements, via Z  -scan experiment, in a discotic nematic phase of the lyotropic mixture comprised of potassium laurate, decanol and D₂O${\text{D}}_2\text{O}$. In this experiment, the nematic sample is translated through the focal region of a focused Gaussian laser beam. The experimental data are analyzed according to the thermal lens model and the ratio between the thermal diffusivities parallel (D_∥)$(D_{\parallel })$ and perpendicular (D_⊥)$(D_{\perp })$ to the director of the nematic sample has been found to be smaller than one. The results are compared to others obtained with different liquid crystals and explained by using a simple model where this ratio is correlated to the shape anisotropy of the micelles.     

Interplay of exchange and electromagnetic effects in the coexistence of superconductivity and helical spin order

A correct Ginzburg-Landau free-energy functional for exchange (EX) and electromagnetic (EM) effects in a magnetic superconductor is derived. We study the second-order transition from the superconducting phase to the superconducting phase with helical spin order. The temperature T_M of the onset of the helical ordering and the wave vector of the helix Q are calculated for some cases.     

Experimental investigations of a new TGBC mesophase

We report on optical and structural X-ray studies on a smectic C twist grain boundary phase (TGB) of a pure liquid crystalline material. It is shown that this TGB phase, which exists over a large range of temperature, is definitely different from previously reported and predicted TGB phases. The two main experimental features are: (i) the observation in planar geometry of an optical texture exhibiting a square grid pattern, and (ii) the detection of a broad Bragg ring in reciprocal space instead of one (TGB) or two (TGB) sharp rings. We suggest a few possible tracks that can be explored to understand the complex structure of this new phase. Received 25 January 1999     

Orientation of discotic and ferroelectric liquid crystals in a macroporous silicon matrix

Macroporous silicon with deep regular channels 3–4.5 μm in diameter was infiltrated with discotic and ferroelectric liquid crystals (LCs) at the temperature of the isotropic phase, and then, the system was slowly cooled to room temperature, with the liquid crystalline mesophase formed. The orientation of the LC molecules in the porous matrix was studied by FTIR spectroscopy. The alignment of LCs was ascertained by comparing the behavior of various vibrational bands of a liquid crystal introduced into the porous matrix with that for LC inside the bulk cells of planar and homeotropic alignment. The molecules of the discotic LC show a planar orientation of their column’s axis with respect to the surface of the macroporous silicon wafer; i.e., they are perpendicular to the channel axis. The long molecular axis of the ferroelectric LC is aligned with the pore walls, having homeotropic orientation with respect to the wafer surface. In a macroporous silicon matrix, both kinds of LCs show unexpected enhancement of the low-frequency vibrational bands. From Fizika Tverdogo Tela, Vol. 44, No. 6, 2002, pp. 1145–1150. Original English Text Copyright ? 2002 by Perova, Astrova, Tsvetkov, Tkachenko, Vij, Kumar. This article was submitted by the authors in English.     

Depletion-driven four-phase coexistences in discotic systems

ABSTRACT

Free volume theory (FVT) is a versatile and tractable framework to predict the phase behaviour of mixtures of platelets and non-adsorbing polymer chains in a common solvent. Within FVT, three principal reference phases for the hard platelets are considered: isotropic (I), nematic (N) and columnar (C). We derive analytical expressions that enable us to systematically trace the different types of phase coexistences revealed upon adding depletants and confirm the predictive power of FVT by testing the calculated diagrams against phase stability scenarios from computer simulation. A wide range of multi-phase equilibria is revealed, involving two-phase isostructural transitions of all phase symmetries (INC) considered as well as the possible three-phase coexistences. Moreover, we identify the system parameters, relative disk shapes and colloid–polymer size ratios, at which four-phase equilibria are expected. These involve a remarkable coexistence of all three-phase states commonly encountered in discotics including isostructural coexistences I₁–I₂–N–C, I–N₁–N₂–C and I–N–C₁–C₂.     

Surface tension energy in discotic hexagonal and tetragonal phases

Discotic thread resonance under oscillating electric field excitation is described. The experimental results allow the measurement of the surface tension energy in discotic hexagonal or tetragonal phase. We discuss the obtained values of the constant surface energy and deduce a characterisation of the discotic phase.     

Liquid-crystalline ordering in the solution of semiflexible macromolecules

The solution of semiflexible polymer macromolecules with steric repulsion between the parts of the polymer chains is considered. The conditions for formation of the liquid-crystalline phase in this solution are determined by means of the Onsager method.