Uniaxial Phase Research Articles

Uniaxial-biaxial phase transition in lyotropic nematic solutions: Local biaxiality in the uniaxial phase.

It has been recently shown that the system potassium laurate-- decanol--water presents three nematic phases, two uniaxial and one biaxial. We are currently investigating the structure of these phases by scattering methods. The study reported here describes the first experiment, neutron scattering with contrast variation, which demonstrates that the aggregates in one uniaxial phase in the vicinity of the transition to the biaxial phase are statistically biaxial. This observation provides a new insight into the uniaxial-biaxial phase transition.

Order and micellar density fluctuations in the biaxial, uniaxial (Nc and ND), and isotropic phases of a lyotropic nematic liquid crystal studied by light beating spectroscopy

We have performed Rayleigh scattering measurements to study thermally excited fluctuations in a lyotropic nematic liquid crystal system exhibiting uniaxial and biaxial nematic phases. The biaxial nematic order parameter has been defined by de Gennes as a symmetric, traceless, 2nd rank tensor. The dynamics of the order parameter fluctuations predicts 5 normal modes: 2 are associated to the fluctuations in the (uniaxial and biaxial) magnitudes of the order (scalar modes); 3 are associated to the small rigid rotations of the order parameter ellipsoid, around its principal axes (orientational modes). Using a Landau-Khalatnikov formalism we have estimated the temperature dependence of the relaxation rates for these 5 modes, valid for the uniaxial and biaxial phases. We present relaxation rate data obtained from polarized and depolarized Rayleigh scattering in the biaxial, uniaxial N C , uniaxial N D (N C -negative birefringence; N D -positive birefringence), and isotropic phases of the K-laurate, decanol, D 2 O, lyotropic nematic system. We have identified the 5 expected modes arising from the order parameter fluctuations. In particular, we present the experimental demonstration of the new orientational mode associated to the rotations of the biaxial «director», and the observation, in ordered phases, of the magnitude fluctuations of the uniaxial and bia Par mesures de diffusion Rayleigh en lumiere diffusee polarisee et dipolarisee, etude de la dynamique des fluctuations thermiques dans les phases nematiques uniaxe et biaxe d'un cristal liquide lyotrope (systeme laurate de K+decanol-1+D 2 O). Identification des 5 modes prevus par la theorie de Landau-Khalatnikov, associes aux fluctuations du parametre d'ordre. Demonstration d'un nouveau mode orientationnel, associe aux rotations du directeur biaxe, de fluctuations associees au module du parametre d'ordre uniaxe et biaxe dans les phases ordonnees et d'un nouveau mode scalaire en diffusion polarisee

Motion in surface layers of N2 on graphite

A molecular-dynamics simulation of nitrogen adsorbed on graphite has been used to study the phonons and librons in a molecular adsorbate. Simulations of the commensurate-ordered (16 K), uniaxial (14 K) and commensurate-disordered (40 K) phases of the adsorbed solid are analysed. In addition results on a commensurate simulation in the vicinity of the orientational phase transition (25 K) are also reported. We find significant dispersion of the translational phonons in two orthogonal directions. There is clear evidence of coupling between librational and translational phonons which is responsible for the structure in the librational density of states. The simulation shows the longitudinal phonons inducing rotational disorder in the low-temperature phase and the transverse phonons inducing rotational ordering in the high-temperature phase. These couplings are not strong enough to produce an incommensurate wave of static distortion in the overlayer.

The polymorphic phases of the hexaalkanoyloxytriphenylene liquid crystals, as studied by deuterium NMR spectroscopy

Deuterium NMR spectra are reported for several specifically deuterated hexaalkanoyloxytriphenylenes in their corresponding liquid crystalline phases. The higher homologs of this series are polymorphic and exhibit a variety of discotic mesophases, including both biaxial (D0 and D1) and uniaxial (D2) columnar phases. The ordering characteristics of these phases are studied using the quadrupolar splittings of the aromatic and aliphatic deuterons. The results show that during the transition from the biaxial D1 to the axial D2 phase the major susceptibility tensor switch orientation, apparently due to strong tilting of the molecules with respect to the columnar axis in the biaxial phase. Characteristic features which appear in the spectra of these phases are interpreted in terms of intercolumnar jumps of mesogen molecules.

Synthesis of Some New Fluorene Esters with Mesomorphic Behavior

Abstract A number of 2-fluorenyl 4′-alkylbenzoates and 4′-alkoxybenzoates have been synthesized to study the effects of the central ester linkage on their mesomorphic behavior. These compounds typically show nematic (N) and the uniaxial smectic phases. Many isomeric fluorene esters with reversed ester linkage were also prepared, but no major differences were observed. The presence of a lateral substituent in the phenyl ring decreases the nematic-isotropic (N-I) temperature by about 28°C. Replacement of phenylene by trans-cyclohexylene has the unusual effect of increasing the N-I transition temperature by about 21°C. The presence of a nitro group at position (7) of the fluorene ring increases N-I temperature by about 66°C and stabilizes the SA.

Mössbauer spectroscopy study of the randomly mixed two-dimensional antiferromagnet with competing spin anisotropies K2CoxFe1-xF4.

We have studied the randomly mixed two-dimensional antiferromagnet ${\mathrm{K}}_{2}$${\mathrm{Co}}_{\mathrm{x}}$${\mathrm{Fe}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{F}}_{4}$ (x=0.27, 0.55, and 0.70) with M\"ossbauer absorption. In the latter two compounds a phase transition to a uniaxial antiferromagnetic phase with the Fe moments aligned along the Co easy axis (c axis) is observed, and ${T}_{N}$=90\ifmmode\pm\else\textpm\fi{}1 and 97\ifmmode\pm\else\textpm\fi{}1 K, respectively. In the x=0.27 compound below ${T}_{N}$=64\ifmmode\pm\else\textpm\fi{}1 K, the Fe moments acquire a static component along the c axis. Below ${T}_{L}$=27\ifmmode\pm\else\textpm\fi{}2 K the transverse components also become ordered, at least on the M\"ossbauer time scale, confirming previous neutron-diffraction experiments. A comparison with the results of this technique further shows the Co and Fe spins to differ in orientation by up to 30\ifmmode^\circ\else\textdegree\fi{}, depending on the local surroundings. The M\"ossbauer spectra at 4.2 K reveal a widening of the distribution of the hyperfine parameters when x approaches the multicritical value. In the case of x=0.27, the widening increases sharply towards ${T}_{L}$, and reflects substantial fluctuations of the transverse components persisting over an unusually large critical regime above ${T}_{L}$.

Electro-Optical Effects of a Small-Pitch Blue-Phase System

Abstract A system which shows a relatively large blue-phase range is investigated. Owing to the small value of the cholesteric pitch the blue-phase shows no Bragg-reflections in visible light. Nevertheless, electric-field induced birefringence shows quite large values. The response times are a few tens of microseconds below 10°C. Crude estimates of the effects lead to values reasonably close to the experimental ones. Zero voltage birefringence effects are encountered, field induced and slowly decaying at higher temperatures and surface induced at lower temperatures where a uniaxial phase appears to be stable.

Reorientation of N2adsorbed on graphite in various computer simulated phases

The reorientational motion of nitrogen molecules adsorbed on graphite was investigated in simulations of four phases. In the low temperature orientationally ordered commensurate and uniaxial phases the amplitude of reorientation is small. The out-of-plane motion is nearly harmonic. The in-plane motion is somewhat more complex, but we show that it can be related to the relevant angular velocity autocorrelation function via a cumulant expansion. The complexity is due to interactions between nitrogen molecules which do not affect the out-of-plane motion. In the simulations of the orientationally disordered phases the amplitudes of reorientation are larger and the simple cumulant approximation is no longer valid. The out-of-plane motion, while still harmonic, is more strongly damped, and the in-plane motion shows features similar to those seen in liquids. There is surprisingly little qualitative difference between the reorientational motion observed in the commensurate and uniaxially compressed phases at corr...

Computer simulation studies of anisotropic systems

A model nematogenic mixture of rod-like and plate-like particles has been studied using Monte Carlo computer simulation. The mixture is found to separate into two uniaxial phases and does not form a biaxial nematic as previously proposed.

Magnetostatic properties of K2Co x Fe1−x F4, a system with competing anisotropies

The magnetostatic properties of K2CoxFe1−xF4 have been investigated by susceptibility and Mossbauer measurements at different concentrations and temperatures. Three magnetically ordered phases are found: a planar phase, an OAF phase, and an uniaxial phase. The experimental results are compared to a molecular-field calculation. At certain concentrations and temperatures it is not possible to obtain a good least squares fit of the Mossbauer spectra, which is tentatively assigned to relaxation effects due to fast spin fluctuations at the OAF phase transition.

Thermal reactions of leadhillite Pb4SO4(CO3)2(OH)2

AbstractReactions undergone by leadhillite from the type locality on heating to 1000°C have been followed by DTA, TG, DSC, evolved gas analysis, continuous-heating XRD and IR, and hot-stage microscopy. Intermediate decomposition products were identified by X-ray powder photography. At 80°C, biaxial leadhillite inverts to a uniaxial phase with properties similar to those of susannite, a naturally occurring polymorph of leadhillite, but this higher-temperature modification only partially reverts to the original structure on cooling (up to 24 hours at room temperature is required for complete reversion). Between 250 and 600°C the mineral undergoes two decomposition reactions: PbO.PbCO3 and PbO.PbSO4 form during the first reaction (PbCO3 may form in the initial stages) and 4PbO.PbSO4 during the second. α-2PbO.PbSO4 appears at 650°C due to solid-state reaction between the other lead oxysulphate products. Melting occurs above 850°C. The reaction products are discussed in relation to the phase diagrams for the systems PbO-CO2 and PbO-PbSO4.

Biaxial order in liquid crystals and their mixtures: A Potts-Ising model

A lattice model for binary mixtures of prolate and oblate molecules is studied, by a mapping onto a 13-state Potts-Ising model, followed by an approximate renormalization-group analysis. Four different types of phase diagram are obtained, exhibiting prolate uniaxial, biaxial, and oblate uniaxial phases. Local disorder has the nonordering property of an effective vacancy and is thus included into our mapping. Such effective vacancies can cause first-order phase transitions. Thus the biaxial phase can disorder either directly through a ridge of first-order transitions, or via an intermediate uniaxial phase which vanishes at a multicritical point. In the biaxial region, the system is shown to be related to the six-state clock model, so that the latter point may be replaced by a segment of algebraic (Kosterlitz-Thouless) order in films. Similar considerations are applied to one-component systems of biaxially shaped molecules.

Nearest-neighbor Ising model with a uniaxial incommensurate phase and a Lifshitz point

The anisotropic triangular nearest-neighbor Ising model, with antiferromagnetic interactions, is studied. The phase diagram, as a function of temperature and field, has a complex structure. Two commensurate ordered phases are found. The transition to one is Ising-type. The second is reached from the disordered phase in one of two ways: either via an intermediate uniaxial incommensurate phase---which is reached at high temperatures by a Kosterlitz-Thouless transition and at low temperatures undergoes an incommensurate-commensurate transition---or by a single continuous transition. The latter transition is in the same universality class as the chiral three-state Potts model, with thermal exponent within 4% of that of the three-state Potts model. These two transition regimes are found to be separated by a Lifshitz point. The phase diagram and critical behavior were determined by analytical (symmetry analysis and free-fermion approximation) as well as numerical (phenomenological renormalization-group and Monte Carlo) methods.

Light transmission at the uniaxial-biaxial lyotropic nematics phase transitions

Results are reported on light transmission versus the temperature near the phase transitions between lyotropic nematics. Strong pretransitional effects are observed when the phase transitions occur between biaxial nematic and uniaxial phases. The light is strongly depolarized both at the calamitic-biaxial and at biaxial-discotic phase transitions. The results are qualitatively explained.

Field-Induced Order in Nematic Liquid Crystals

Abstract The effect of an external magnetic field on the orientational order of a nematic liquid crystal has been examined using both Landau-de Gennes and Maier-Saupe theories. In the Maier-Saupe approach a rotationally invariant form of the pseudo-potential is introduced, which in the absence of an external field leads to three degenerate isomorphic solutions for the order parameter, corresponding to alignment along three principal axes; a similar result is obtainable from the Landau-de Gennes theory. Application of a magnetic field lifts the degeneracy of these solutions, and for materials having a positive diamagnetic susceptibility anisotropy, the uniaxial solution with alignment along the field direction is always energetically favorable. For materials with a negative susceptibility anisotropy, a biaxial solution minimizes the free energy at low temperatures, but on increasing the temperature there is a transition from a biaxial phase to an uniaxial phase. The field dependence of the transition tempe...

Structure and orientational ordering of nitrogen molecules physisorbed on graphite

The structure and orientational ordering of nitrogen molecules physisorbed on graphite have been studied by low-energy diffraction (LEED). A two-sublattice in-plane herringbone structure with glide lines along two perpendicular directions is inferred from LEED patterns at T < 30 K from the monolayer where the molecular centers have the commensurate ( 3 × 3 ) 30° structure. The orientational order-disorder transition of this commensurate phase was examined by superlattice spot intensity and angular profile measurements for 20 < T < 38 K. A rapid drop in superlattice intensity is observed near 27 K. The persistence of some intensity to 38 K. is suggestive of residual short-range orientational ordering and perhaps finite size or heterogeneity effects. For increasing coverage at T = 15 K, there is first a transition to a previously unobserved uniaxial incommensurate phase and then a transition to an apparently triangular incommensurate phase. The orientational superlattice spots are clearly present in the uniaxial phase, but are much weaker in the triangular incommensurate phase. At 31 < T < 35 K, an apparently triangular incommensurate phase with no detectable orientational superlattice spots is observed. The lattice constant versus equilibrium vapor pressure curve has been determined in the latter case assuming a continuous transition. The lattice constants of the incommensurate phases are used to place limits on the extent of possible phase-coexistence regions between the commensurate, uniaxial incommensurate, and triangular incommensurate phases. The LEED patterns from the bilayer at T = 15 K indicate a double-period superlattice structure of the triangular incommensurate phase which does not have the glide line symmetries of the commensurate monolayer. Some effects of heterogeneity on these phase transitions are discussed. A phase diagram for 10 < T < 40 K is proposed.

An error assessment of single-crystal 2πdata from four-circle diffractometry

The criteria developed in the error analysis of 2θ powder data for cubic and uniaxial phases [Frevel (1978). J. Appl. Cryst. 11, 184–189] are extended to biaxial single-crystal data. A methodology is described for applying the focusing matrix method to exhaustive sets of 2θ data for pinacoid and prism reflections measured on a four-circle diffractometer. A spheroidal crystal of hyperpure Si is used to calibrate a Syntex P{\bar 1} automated diffractometer and to establish an effective wavelength for graphite-monochromated Mo Kβ 1 β 3 radiation. A high-quality single-crystal of cis-[bis(7,9-dimethylhypoxanthine) (ethylenediamine)platinum(II)] hexafluorophosphate, [Pt(C2H8N2)(C 7H8N4O)2].(PF6)2, serves as a test case for comparing the normal least-squared analysis with the focusing matrix method. It is concluded that an absolute accuracy greater than one part in 2000 for cell constants of biaxial crystals is difficult to achieve from automated four-circle diffractometer data (2θ ≤ 40°) for non-spheroidal crystals with linear dimensions ca 0.2 mm.

The Saupe ordering matrices for solutes in uniaxial liquid crystals

A theory is described for U(θ2), the potential of mean torque of rigid solutes at infinite dilution in a uniaxial liquid crystal phase. The general form of U(θ2), is an infinite expansion of modified spherical harmonics CLn (θ2), and truncation at the second rank terms produces a practical form for U(θ2) which is used to calculate Sxx-Syy and Szz , the principal elements of the Saupe ordering matrix of a biaxial solute. The theory predicts that the dependence of Sxx-Syy on Szz for a particular solute-solvent mixture is determined entirely by λ, a parameter describing the departure from cylindrical symmetry of the potential of mean torque, and which is independent of temperature. Furthermore, if U(θ2) is determined entirely by dispersion forces then λ is predicted to be independent of the solvent and to depend entirely on the anisotropy of the electric polarizability tensor of the solute. These predictions are tested by determining the values of Sxx-Syy and Szz by analysing proton N.M.R. spectra of a solut...

Observation of a uniaxial incommensurate phase for orientationally ordered nitrogen molecules physisorbed on graphite and proposal of a phase diagram

Observation of a uniaxial incommensurate phase for orientationally ordered nitrogen molecules physisorbed on graphite and proposal of a phase diagram

A theory of orientational ordering in uniaxial liquid crystals composed of molecules with alkyl chains

The constituent molecules of thermotropic liquid crystals invariably contain an aromatic core to which is attached one and often two n -alkyl chains. Nuclear magnetic resonance investigations have revealed that the chain does not exist entirely in an all- trans configuration and that the orientational order of the methylene groups varies markedly along the chain. In this paper we develop a theory to explain these variations for a uniaxial phase at a given temperature and pressure. Our theory contains two distinct parts: one is a model for the conformational distribution of the alkyl chains while the other is for the potential of mean torque experienced by a conformer and which is responsible for its alignment with respect to the director. We use the rotameric state model developed by Flory to describe the conformations adopted by the alkyl chain. The potential of mean torque presents a more difficult problem and we assume that it may be represented by a sum of contributions from each rigid group in the molecule. The order parameters for the methylene and methyl groups in the alkyl chains of the 4- n -pentyl and 4- n -octyl-4'-cyanobiphenyls predicted by the theory are found to be in good accord with those obtained experimentally. We have also used the theory to predict the conformational distributions for both the isotropic and nematic phases of these mesogens; the calculated distributions are contrasted with those assumed by other models. In addition we have obtained the ordering matrices for the various conformers adopted by the two 4- n -alkyl-4'-cyanobiphenyls. The results of these calculations do not support the notion that the orientational order of such molecules can be described by a single, cylindrically symmetric ordering matrix.