Correlation of the molecular structure of discotic nematic liquid crystals with their orientational order and specific features of the nematic-isotropic phase transition

The orientational order parameter S of molecules in high-temperature discotic nematic liquid-crystal phases of triphenylene derivatives is investigated as a function of the length of side flexible molecular chains at different temperatures. It is established that the orientational order parameters S in the range of the transition from the nematic phase to the isotropic liquid phase (the N _D -I transition) are smaller than those predicted from the molecular-statistical theory and computer simulation. It is shown that the N _D -I transition is close to both the isolated Landau point and the tricritical point (regardless of the chemical structure of the molecules and the anisotropy of dispersion intermolecular interactions). Consistent explanations are offered for a number of experimental findings, such as the anomalously small changes in the enthalpy and entropy upon the N _D -I transition (as compared to those revealed upon the N-I transition in calamitic nematic liquid crystals), the anomalously strong response of the isotropic phase of discotic nematic liquid crystals to external fields (thermodynamically conjugate to the order parameter S) and the long relaxation times of this response, and the formation of cybotactic discotic molecular clusters in the isotropic phase in the vicinity of the N _D -I transition.     

Structural features of the polymer-like phase of AC60 fullerides

A new approach is proposed for describing the deformation of the C₆₀ molecule in the polymer-like phase of the fullerides AC₆₀ (A=K, Rb). A discrete basis of orientational states of the molecule is introduced, and orientational ordering is described on the basis of a phenomenological theory. A symmetry analysis of the molecular vibrations in the Fm3m phase is performed. It is shown that small rotations of the C₆₀ can occur at a phase transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 110–115 (25 July 1996)     

Photoproduction of baryons decaying into Nπ and Nη

A combined analysis of photoproduction data on γp↦ πN, ηN was performed including the data on KΛ and KΣ. The data are interpreted in an isobar model with s-channel baryon resonances and π, ρ (ω), K, and K ^* exchange in the t-channel. Three baryon resonances have a substantial coupling to ηN, the well-known N(1535)S ₁₁, N(1720)P ₁₃, and N(2070)D ₁₅. The inclusion of data with open strangeness reveals evidence for further new resonances, N(1840)P ₁₁, N(1875)D ₁₃ and, with weaker evidence, for N(2170)D ₁₃.     

Molecularengineering of discotic nematic liquid crystals

Connecting two columnar phase forming discotic mesogens via a short rigid spacer leads to the formation of a π-conjugated discotic dimer snowing discotic nematic (N _D) phase. Attaching branched-alkyl chains directly to the core in hexaalkynylbenzene resulted in the stabilisation of N_D phase at ambient temperature. Pentalkynylbenzene derivatives possessing a combination of normal- and branched-alkoxy chains display a very broad N_D, phase which is stable well below and above the room temperature.     

Studies on binary mixtures of 4-pentyloxy-4′-cyanobiphenyl with three 4, 4′-di(alkoxy)azoxybenzenes

Eighteen binary mixtures of 4-pentyloxy-4′-cyanobiphenyl (5OCB) and 4, 4′-di(alkoxy)azoxybenzenes (nOAB) with n = 5, 6, and 7 at different concentrations have been studied in detail. Over a wide concentration range, induced SmA phase was observed in all the mixtures except in one. In most of the mixtures, the refractive indices no, ne, and Δn lie between the values of pure components. The optical birefringence of the mixtures is found to decrease non-additively with concentration. The molecular polarizability anisotropy and the orientational order parameter <P₂> of the mixtures were calculated. Nature of variation of polarizability anisotropy with concentration is similar to that of Δn. In allmixtures <P₂> is more in smectic phase than in nematic phase and it also shows non-additive behaviour. Observed <P₂> values of the mixtures were compared with McMillan’s and Maier-Saupe theoretical values and good agreement is found in some mixtures. The transition temperatures obtained by fitting <P₂> data to McMillan’s theory agree with the observed values within a few degrees. Ratio of elastic constants K₃₃ and K₁₁ is determined for mixtures having nematic phase and found to diverge at T_NA transition point.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Macroscopic behavior of non-polar tetrahedratic nematic liquid crystals

We discuss the symmetry properties and the macroscopic behavior of a nematic liquid crystal phase with D_2d symmetry. Such a phase is a prime candidate for nematic phases made from banana-shaped molecules where the usual quadrupolar order coexists with octupolar (tetrahedratic) order. The resulting nematic phase is nonpolar. While this phase could resemble the classic D _∞h nematic in the polarizing microscope, it has many static as well as reversible and irreversible properties unknown to nonpolar nematics without octupolar order. In particular, there is a linear gradient term in the free energy that selects parity leading to ambidextrously helical ground states when the molecules are achiral. In addition, there are static and irreversible coupling terms of a type only met otherwise in macroscopically chiral liquid crystals, e.g. the ambidextrous analogues of Lehmann-type effects known from cholesteric liquid crystals. We also discuss the role of hydrodynamic rotations about the nematic director. For example, we show how strong external fields could alter the D_2d symmetry, and describe the non-hydrodynamic aspects of the dynamics, if the two order structures, the nematic and the tetrahedratic one, rotate relative to each other. Finally, we discuss certain nonlinear aspects of the dynamics related to the non-commutativity of three-dimensional finite rotations as well as other structural nonlinear hydrodynamic effects.     

Orientational diffusivities measured by Rayleigh scattering in a lyotropic calamitic nematic () liquid crystal phase: the backflow problem revisited

Using a light-beating technique we have measured the damping time of thermal fluctuations of the nematic director for the so called cylindrical or calamitic nematic (N_C) phase of the lyotropic system K-laurate/decanol/. By varying the scattering angle in suitable geometries, we have been able to estimate the orientational diffusivities associated to the three pure deformations of splay, twist and bend. A former measurement made in the disk-like N_D phase of the same system yielded a large deviation between the splay and twist diffusivities. The effect was then attributed to induced flows, or backflow, which could be responsible for the reduction of the splay viscosity. In fact, this is the analogous effect, for disks, to the one recognized since long time ago arriving for rod-like molecules in a classical nematic, though in this case it is associated with bend deformations. The analogy comes about thanks to the interchange of the role played by disks and cylinders for, respectively, splay and bend fluctuations.The measurements reported here provide a new test on the applicability of the backflow model to a nematic system composed of micelles, that is, aggregates made of amphiphilic (surfactant) molecules, in its cylindrical-like variant, i.e. the N_C phase. In addition, the comparative study made here with the previous results existing in the literature for the N_D phase, allows us to conjecture on structural issues concerning lyotropic nematics. Received: 29 April 1998 / Revised: 19 August 1998 / Accepted: 31 August 1998     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

Thermodynamic parameters of diffuse phase transitions in Ag2Te

A differential thermal analysis in vacuum and studies of the coefficients of electrical conductivity and thermal conductivity, and of the thermal emf are made in Ag₂Te in the neighborhood of the structural phase transition. It is shown that these data can be used to calculate the switching factor L(T), determine the region in which the phases coexist within the transition, and calculate the thermodynamic parameters. Prior to and after the main phase transition, additional displacement transitions are observed. It is found that the phase transition takes place roughly according to the scheme α _{385 K}→α′_{405 K}→β′_{420 K}→β _{440 K}. The specific heat C _p, changes in entropy ΔS and transition enthalpy ΔH, as well as the minimum phase fluctuation volume V, and the heat Q of the phase transition are determined. It is shown that excesses of Te and Ag have almost no effect on the transition temperatures T ₀, but have a substantial effect on the thermodynamic parameters. Fiz. Tverd. Tela (St. Petersburg) 40, 1693–1697 (September 1998)     

Spectral investigations of surface ordering in ultrathin molecular films

Surface molecular ordering in ultrathin molecular films is investigated. The optical transmission spectra of molecular films ranging in thickness from 2 to 13 smectic layers (6.7–43 nm) in the region of the electronic absorption bands in the smectic A phase of cyanobiphenyl CB9 are measured. The thickness and temperature dependences of the permittivity are determined. It is found that the orientational ordering of the molecules depends on the film thickness. The penetration depth of the surface molecular orientational order does not exceed two smectic layers (<7 nm). Zh. éksp. Teor. Fiz. 115, 1833–1842 (May 1999)     

External field in Landau theory of the weakly-first-order phase transition. Effect of uniaxial pressure on the orientational ordering in solid C70

The effect of the external conjugate field on a weakly discontinuous first-order phase transition is analyzed within Landau theory. The third-degree term in the Ginzburg-Landau expansion is shown to preserve the phase transition for some external fields, in contrast with the second-order case. The free-energy expansion is shown to correspond to a second-order phase transition under the influence of an “effective” external field that depends on both the temperature and the real field. The case of the orientational phase transition in solid C₇₀ is considered, and the transition thermoelastic phenomena caused by the coupling of order parameter with elastic strain are analyzed. It is shown that the uniaxial mechanical pressure along the direction of the 3-fold axis appears to be an external conjugate field for orientational ordering in crystalline C₇₀. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 594–599 (25 April 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Effect of local molecular ordering on the temperature behavior of the relaxation time of order-parameter fluctuations in the isotropic phase of PAA nematic liquid crystal

The behavior of the relaxation time of order-parameter fluctuations in the isotropic phase of PAA nematic liquid crystal was investigated on the basis of the spectra of depolarized (inelastic) light scattering in a wide temperature range including the immediate vicinity to the temperature of the nematic phase transition. The experimental data were analyzed within the Landau—de Gennes theory. The temperature limits of applicability of the Landau—de Gennes theory to the isotropic-phase dynamic properties are obtained. The minimum correlation length is determined, at which the effect of local ordering on the dynamics of slow orientational motion of isotropic-phase molecules is dominant.     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

Phase transitions in a solution of rodlike macromolecules of two different sizes

Phase equilibria for a solution of long rigid rods of diameters D_i and lengths L_i (i = 1,2) are studied analytically using Gaussian trial functions. The conditions on the molecular size parameters for a nematic—nematic phase transition to be possible are determined, and found to be satisfied everywhere except in a closed domain in the diameter ratio—length ratio plane. Information on the relative ordering of the two components is also provided.     

Structure and elastic properties of a nematic liquid crystal: A theoretical treatment and molecular dynamics simulation

The Frank elasticity constants which describe splay (K ₁), twist (K ₂), and bend (K ₃) distortion modes are investigated for 4-n-pentyl-4'-cyanobiphenyl (5CB) in the nematic liquid crystal. The calculations rest on statistical-mechanical approaches where the absolute values of K _i (i=1,2,3) are dependent on the direct correlation function (DCF) of the corresponding nematic state. The DCF was determined using the pair correlation function by solving the Ornstein-Zernike equation. The pair correlation function, in turn, was obtained from molecular dynamics (MD) trajectory. Three different approaches for calculations of the elasticity constants were employed based on different level of approximation about the orientational order and molecular correlations. The best agreement with experimental values of elasticity constants was obtained in a model where the full orientational distribution function was used. In addition we have investigated the approximation about spherical distribution of the intermolecular vectors in the nematic phase, often used in derivation of various mean-field theories and employed here for the construction of the DCF. We found that this assumption is not strictly valid, in particular a strong deviation from the isotropic distribution is observed for short intermolecular distances. Received 22 March 2000 and Received in final form 9 June 2000     

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.     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Characteristic features of the magnetic ordering of Dy3+ ions in a monoclinic RbDy(WO4)2 single crystal

The investigation of the specific heat of a RbDy(WO₄)₂ single crystal at temperatures 0.2–2.5 K and in magnetic fields up to 2 T are reported. The temperature dependence of the specific heat near T _N=0.818 K is compared with the predictions for different models. The 2D Ising model describes satisfactorily C(T) below T _N, while for T>T _N none of the theoretical models agree with the behavior of C(T) of RbDy(WO₄)₂. The H-T phase diagram for H∥c is complicated and possesses a triple point, where regions of existence of three magnetic phases converge. The magnetic ordering is analyzed from the standpoint of the Jahn-Teller nature of the structural phase transitions occurring in RbDy(WO₄)₂ at higher temperatures. It is shown that the form of the phase diagram depends on the direction of the vector H, for the general case of an arbitrary direction of H, two phase transitions can occur with increasing field. Fiz. Tverd. Tela (St. Petersburg) 41, 491–496 (March 1999)