Theory for cholesteric ordering in lyotropic liquid crystals

Summary This paper presents an investigation of the chiral dispersion interaction between macromolecules in the solvent which is considered as a dielectric medium. In particular the results of the molecular statistical theory are reported. The expression for the helical pitch as a function of temperature on the solvent dielectric constant is used to interpret the experimental data. Moreover, the effect of the solvent chirality on the cholesteric ordering in polymer liquid crystals is considered. Finally the cholesteric ordering in the solution of chiral micelles is discussed. Work presented at the First USSR-Italy Bilateral Meeting on Liquid Crystals held in Portonovo, Ancona (Italy), September 30–October 2, 1987.     

Phase diagrams of Ising fluids with Yukawa-Lennard-Jones interactions from an integral equation approach

An integral equation approach is developed to investigate phase coexistence properties of Ising spin fluids with Yukawa ferromagnetic and Lennard-Jones nonmagnetic interactions in the presence of an external field. The calculations are carried out on the basis of the Duh and Henderson closure with a specific Duh-like partitioning of the total potential. The coupled set of the Ornstein-Zernike equation, the closure relation and the external field constraint are solved using an efficient numerical algorithm. The phase diagrams are evaluated in a wide range of varying the external field and the ratio of strengths of Yukawa to Lennard-Jones interactions. Different types of the phase diagram topology as well as various external field dependencies of critical temperatures and densities are identified. The complexity with respect to simple Lennard-Jones fluids is explained by coupling between spatial and spin degrees of freedom in the system. A comparison of the obtained theoretical results with simulation data is made and a good agreement is observed.     

A possible similarity between lyotropic cubic phases and cholesteric blue phases

Summary The common features in structures and properties of lyotropic cubic phases (LCP) and cholesteric blue phases (BP) are discussed. In both systems the cubic phases have nontrivial structures governed by frustrations. The frustration is connected with the double-twist in BPs and with the layer curvatures in LCPs. The structure of BP can be quantitatively described using the minimization of the Landau free energy with tensor order parameter. The order parameter of LCP is unknown till now; however, some minimization procedure can also be used for the solution of the phase problem. It is noted that in both systems the stable amorphous phases are observed (the fog phase or BPIII in BPs andL ₃ phase in lyotropic crystals). The importance of the observation of ?forbidden? reflections for the unequivocal identification of the space groups is emphasized. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Phase transitions in lyotropic nematic gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur. Received 15 February 2002 and Received in final form 14 June 2002     

Phase diagrams of magnetic nanotubes

Analytical expressions for the total magnetic energy of two characteristic internal configurations of nanometric tubes are calculated. A magnetic phase diagram with respect to the aspect ratio of the tubes is obtained which allows a discussion about the possibility of getting ensembles of nanotubes with low coercive fields. A comparison with recently reported coercive fields of three different cobalt nanotube arrays agrees well with the phase diagram derived here.     

Phase diagrams of decomposing nanoalloys

The thermodynamics of nucleation and decomposition in small isolated particles are considered. There exist three possibilities: phase separation, prohibition of decomposition and a metastable state. We investigate the peculiarities of phase diagrams related to depletion of the nanosize parent phase even at the nucleation stage. For small particles the equilibrium diagram becomes split (and shifted and size dependent). Concentration, size and temperature hystereses take place. Size-dependent ‘critical supersaturation’, increasing with decreasing size, has been analysed.     

Phase chirality and stereo-selective swelling of cholesteric elastomers

Cholesteric elastomers possess a macroscopic phase chirality as the director rotates in a helical fashion along an optical axis z and can be described by a chiral order parameter . This parameter can be tuned by changing the helix pitch p and the elastic properties of the network at formation. The cholesterics also possess a local nematic order, changing with temperature or during solvent swelling. In this paper, by measuring the power of optical rotation , we discover how these two parameters vary as functions of temperature or solvent adsorbed by the network. The main result is a finding of pronounced stereo-selectivity of cholesteric elastomers, demonstrating itself in the retention of the correct chirality component of a racemic solvent. It has been possible to quantify the amount of such stereo-separation, and the basic dynamics of the effect.Received: 18 August 2003, Published online: 5 February 2004PACS: 33.55.Ad Optical activity, optical rotation; circular dichroism - 61.30.Vx Polymer liquid crystals - 87.80.Pa Morphometry and stereology     

Phase diagrams and elementary excitations

On the phase boundary separating two crystalline phases, it is shown that d(Tⁿ)/dp/_T=0=constant. The index n depends on the dominant elementary excitations, being 4,$\text{5}\text{2}$ and 2 for phonons, magnons and electronic single-particle excitations respectively.     

Phase diagrams of multilayer adsorbed methane

We propose multilayer phase diagrams based on recent observations of methane adsorbed on graphite and gold (111). Methane wets graphite at all temperatures observed, but it fully wets gold only above the bulk triple point. Possible reasons for this difference in behavior are discussed. The methane-graphite phase diagram also includes layer by layer condensation with critical points leading to a predicted bulk roughening temperature, and an extension of the bulk melting curve into the multilayer film region where it closes at a triple point with a compressed incommensurate first layer solid phase. Experimental evidence for these features is presented and discussed.     

Phase diagrams for hard disc mixtures

Phase diagrams for binary hard disc mixtures are predicted for diameter ratios between 0.15 and 1, using a new equation of state for the liquid based on recent calculations of the fifth virial coefficient, and a cell model for the solid. At diameter ratios close to 1, a substitutional solid solution is formed, and both azeotropic and eutectic phase behaviour are predicted. At smaller diameter ratios, a square sodium chloride lattice and a trigonal AB₂ lattice are observed.     

Phase diagrams of laser-processed nanoparticles of brass

Nanoparticles of brass are prepared by ablation of a brass target in ethanol using radiation of a copper-vapor laser at various laser fluences. The nanoparticles are characterized by TEM and optical spectroscopy. The multipulse laser irradiation leads to formation both the nanoparticles in liquid and well-ordered micro-structures on a surface of a target. It is revealed that both the morphology and absorption spectra of brass nanoparticles depend on presence of the micro-structures. Nanoparticles with the various phase diagrams are formed from a flat brass surface and from the same surface with micro-structures. The results are compared with a model of phase diagrams, in which size and composition effects are taken into account.     

Phase diagrams of a laser with absorber

Thermodynamic phase diagrams permit a comprehensive and compact account of steady states and limit cycle behavior of a laser with absorber.     

Phase diagrams of a transverse Ising nanowire

Phase diagrams of a cylindrical nanowire described by the transverse Ising model are investigated by the use of two theoretical frameworks, namely the mean field theory and the effective field theory with correlations. The phase diagram of the system is strongly affected by the surface situations. Some characteristic phenomena are found in the phase diagram, depending on the ratio of the physical parameters in the surface shell and the core.     

Phase diagrams for semilinear photorefractive coherent oscillator

The sequence of optical phase transitions is considered for a photorefractive coherent oscillator with a conventional mirror and a four-wave mixing phase conjugate mirror. Analogous to phase transitions in solids, the phase diagrams are constructed and defined qualitatively as different states of a whole system (light-induced scattering below the threshold of oscillation, single-frequency oscillation, two-frequency oscillation, and multimode mirrorless oscillation). The attempt of experimental mapping of a phase diagram is presented for a coherent oscillator with Co-doped BaTiO₃. PACS 42.65.Hw; 05.45.-a; 42.65.Pc; 42.65.Sf.     

Phase behaviour of lyotropic liquid crystals in external fields and confinement

This mini-review discusses the influence of external fields on the phase behaviour of lyotropic colloidal liquid crystals. The liquid crystal phases reviewed, formed in suspensions of highly anisotropic particles ranging from rod- to board- to plate-like particles, include nematic, smectic and columnar phases. The external fields considered are the earth gravitational field and electric and magnetic fields. For electric and magnetic fields single particle alignment, collective reorientation behaviour of ordered phases and field-induced liquid crystal phase transitions are discussed. Additionally, liquid crystal phase behaviour in various confining geometries, e.g. slit-pore, circular and spherical confinement will be reviewed.     

Phase diagrams of diluted mixed spin XY model

Phase diagrams of diluted mixed spin XY magnetic systems on 3D cubic lattice are investigated by the use of the variational principle and the replica method. The results are given with the consideration of the different nearest-neighbour interactions between randomly occupied magnetic sites.Dilution and competition are found to be responsible of the spin glass phase. The range of dilution in which this phase may appear depends on the spin number, the sign and strength of magnetic interactions.The experimental phase diagrams of the particular 3D hexagonal Fe_pMn_1−pTiO₃ and the planar system K₂Cu_pMn_1−pF₄ are well represented by the obtained results.     

Phase diagrams of lattice systems with residual entropy

We introduce an equivalence relation on the family of ground states and generalize the Peierls and Pirogov-Sinai theory of phase transitions to systems with residual entropy. The idea consists in the replacement of the periodic ground states by equivalence classes together with an entropy factor. We apply these results to discuss the phase diagrams of diluted spin-1/2 systems.On leave of absence from the Central Research Institute for Physics, Budapest, Hungary.