Hexatic ordering in freely suspended liquid crystal films

In this paper, we report results from synchrotron X-ray scattering studies of thefluid/hexactic/solid phases and phase transitions in both very thick and very thin, freely suspended films of tilted hexatic liquid crystals. Contrary to the thick film case, the higher Fourier coefficients describing the bond orientational order are suppressed in very thin films. This suppression is consistent with a two-dimensional bond orientational order parameter, ₆, rather than the three-dimensional bond orientational order parameter found in very thick films. For a film containing twently-three (23) smectic layers we find that ₆ is two-dimensional whereas the positional order in the crystallineS _J phase is three-dimensional. We present an analysis of the thick film data in terms of the three-dimensionalXY-model and a new mean field theory model which incorporates explicitly the quasi two-dimensional nature of bulk smectic phases.     

Optical activity measurements in the smectic blue phases

Optical activity measurements have been performed on the smectic blue phases ( BP _Sm), which are a new kind of chiral liquid crystal. BP _Sm exhibit both three-dimensional orientational order, like the classical blue phases, and smectic positional order. Thus, they can be viewed as the three-dimensional counterpart of the twist grain boundary phases. A comparison with the optical activity of the classical blue phases is carried out, and an estimation of the BP _Sm lattice parameter is reported for the first time. Received 25 May 2001     

The structure of strongly dipolar hard sphere fluids with extended dipoles by Monte Carlo simulations

We have investigated the structural change of dipolar hard sphere fluid while we change the dipole from an idealised point dipole (pDHS fluid) to a physically more realistic extended dipole (eDHS fluid) by increasing the distance d of the two point charges ±q while keeping the dipole moment μ = qd fixed. We discuss our results on the basis of the first- and second-rank orientational order parameters, angular distribution functions, chain-length distributions, and snapshots. At a low density, we have found chain formation with longer chains as the distance d is increased. At a high density, we have found phase transition from an orientationally ordered ferroelectric nematic phase (at low d) into an isotropic liquid containing chains (at large d).     

Insights on some chiral smectic phases

Combining layered positional order as smectic order and chirality can generate complex architectures since twist parallel to the layers is not allowed. This paper will review some new experimental results on different phases resulting from the competition between smectic positional order and twist orientational order. It concerns the TGB_A and the NL^*, that is the liquid line phase as well as the SmQ phase. Chiral effects in the isotropic phase will also be discussed.     

Scaling properties of dynamic response in orientational glasses

The freezing transition in dipolar and quadrupolar glasses is characterized by the presence of local random electric and strain fields generated by substitutional disorder. The dynamic response in the ergodic phase above the freezing temperature T_F is studied in terms of Langevin dynamics applied to the recently formulated symmetry-adapted random-bond-random-field (SARBRF) model of orientational glasses. Following the theory of spin glasses it is assumed that for T≥T_F the response can be written in a dynamic scaling form by introducing a scaling exponent v and a frequency scaling variable. The value of v(T) is explicitly evaluated for the quadrupolar (100) SARBRF model, and its relation to the experimentally observed effective exponent u_eFF(T) in dipolar and quadrupolar glasses is discussed.     

Molecular dynamics study of a classical two-dimensional electron system: positional and orientational orders

Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation functions, we have found an indication that the solid phase has a quasi-long-range (power-law correlated) positional order and a long-range orientational order. This implies that the long-range 1/r system shares the absence of the true long-range crystalline order at finite temperatures with short-range ones to which Mermin's theorem applies. We also discuss the existence of the “hexatic” phase predicted by the Kosterlitz–Thouless–Halperin–Nelson–Young theory.     

Determination of Orientational Anisotropy in Glassy Solids by 2D Dipolar Spectra With Sample Flipping

A method is proposed for the quantitative measurement of orientational anisotropy in glassy solids based on 2D dipolar NMR spectra with sample flipping (dipolar DECODER experiment). Purely dipolar spectra are obtained by chemical shift refocusing by a multiple pulse sequence. The experiment is applied to an investigation of a doubly¹³C-labeled sample of bisphenol-A polycarbonate deformed in a channel-die apparatus. The orientational distribution function is determined by an expansion of the distribution in terms of spherical harmonics up to degree four.     

Dielectric properties of a mixture of dipolar hard spheres

A theory for the dielectric constant, ε, of a fluid mixture of dipolar hard spheres is formulated by generalizing the methods developed by Ramshaw and Wertheim for the pure fluid case. The resulting expression for ε depends on the pair distribution functions, g _αβ(r ₁, θ₁, r ₂, θ₂) for a dipolar mixture. Due to the unavailability of exact representations for these dipolar pair distribution functions, the results of the mean spherical approximation are employed in the formalism developed. Numerical results are given for ε as calculated from the pair distribution functions for a spherical volume of macroscopic dimensions. The compositional dependence of the ε obtained in this way for a specific mixture is compared with the corresponding properties of the well established theories of Clausius-Mossotti-Debye and Onsager. In addition, the relative importance of the dipole moment and size of the hard sphere parameters in determining ε for a dipolar mixture (the correlative behaviour of which is described by the mean spherical approximation) is evaluated. It is found that the differences in hard core diameters can be largely ignored, in that ε for an ‘effective’ single component fluid can be given to within 2–5 per cent relative error (at worst) of the mean spherical approximation's result. Such an ‘effective pure fluid’ is described as having the same polarization content as the actual mixture being considered. Thereby, the properties of the effective fluid are determined by the quantity y = 4πβ(m ₁ ² ρ₁ + m ₂ ² ρ₂)/9 where m_i and ρ _i are the dipole moment and number density of component i in the binary mixture, with β = (kT)^-1.     

Freezing and melting of binary mixtures confined in a nanopore

This paper reports on a Grand Canonical Monte Carlo study of the freezing and melting of Lennard–Jones Ar/Kr mixtures confined in a slit pore composed of two strongly attractive structureless walls. For all molar compositions and temperatures, the pore, which has a width of 1.44?nm, accommodates two contact layers and one inner layer. Different wall/fluid interactions are considered, corresponding to pore walls that have a larger affinity for either Ar or Kr. The solid/liquid phase diagram of the confined mixture is determined and results compared with data for the bulk mixture. The structure of the confined mixture is studied using 2D order parameters and both positional g(r) and bond orientational G₆(r) pair correlation functions. It is found that in the confined solid phase, both the contact and inner layers have a hexagonal crystal structure. It is shown that the freezing temperature of the Ar/Kr confined mixture is higher than the bulk freezing point for all molar compositions. Also, it is found that the freezing temperature becomes larger as the ratio α of the wall/fluid to the fluid/fluid interactions increases, in agreement with previous simulation studies on pure substances confined in nanopores. In the case of pore walls having a stronger affinity for Kr atoms (ε _Ar/W<ε _Kr/W), it is observed that both the contact and inner layers of the confined mixture undergo, at the same temperature, a transition from the liquid phase to the crystal phase. The freezing of Ar/Kr mixtures confined between the walls having a stronger affinity for Ar (ε _Ar/W?>?ε _Kr/W) is more complex: for Kr molar concentration lower than 0.35, we observe the presence of an intermediate state between all layers being 2D hexagonal crystals and all the layers being liquid. This intermediate state consists of a crystalline contact layer and a liquid-like inner layer. It is also shown that the qualitative variations of the increase of freezing temperature with the molar composition depend on the affinity of the pore wall for the different components. These results confirm that, in addition to the parameter α the ratio of the wall/fluid interactions for the two species, η=?_Ar/W/?_Kr/W, is a key variable in determining the freezing and melting behaviour of the confined mixture.     

Magic Angle-Oriented Sample Spinning (MAOSS): A New Approach toward Biomembrane Studies

The application of magic angle sample spinning (MAS) NMR to uniformly aligned biomembrane samples is demonstrated as a new general approach toward structural studies of membrane proteins, peptides, and lipids. The spectral linewidth from a multilamellar lipid dispersion is dominated, in the case of protons, by the dipolar coupling. For low-γ or dilute spins, however, the chemical shift anisotropy dominates the spectral linewidth, which is reduced by the two-dimensional order in a uniformly aligned lipid membrane. The remaining line broadening, which is due to orientational defects (“mosaic spread”) can be easily removed at low spinning speeds. This orientational order in the sample also allows the anisotropic intermolecular motions of membrane components (such as rotational diffusion, τ_c= 10⁻¹⁰s) for averaging dipolar interactions to be utilized, e.g., by placing the membrane normal parallel to the rotor axis. The dramatic resolution improvement for protons which are achieved in a lipid sample at only 220 Hz spinning speed in a 9.4 T field is slightly better than any data published to date using ultra-high fields (up to 17.6 T) and high-speed spinning (14 kHz). Additionally, the analysis of spinning sidebands provides valuable orientational information. We present the first¹H,³¹P, and¹³C MAS spectra of uniformly aligned dimyristoylphosphatidylcholine (DMPC) bilayers. Also,¹H resolution enhancement for the aromatic region of the M13 coat protein reconstituted into DMPC bilayers is presented. This new method combines the high resolution usually achieved by MAS with the advantages of orientational constraints obtained by working with macroscopically oriented samples. We describe the general potential and possible perspectives of this technique.     

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     

Orientational order and distribution function in nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene

The refractive indices (n _e,?n _o) and density have been measured as a function of temperature in the liquid-crystalline and liquid phases of nematic 1-(4-trans hexylcyclohexyl)-4-[(2-4-isothiocyanato phenyl)ethyl] benzene. The molecular polarizability and orientational order parameter have been computed using the Neugebauer anisotropic local field model. The distribution function f(β), and hence the higher order parameter ?P ₄?, and nematic pair-potential have been computed at different temperatures in the nematic phase.     

Orientational order parameter studies in two symmetric dimeric liquid crystals – an optical study

The optical technique developed by [W. Kuczynski, B. Zywucki, and J. Malecki, Determination of orientational order parameter in various liquid-crystalline phases, Mol. Cryst. Liq. Cryst. 381 (2002), pp. 1–19; B.J. Zywucki and W. Kuczynski, IEEE transactions on optical phenomena – The orientational order in nematic liquid crystals from birefringence measurements, Dielectr. Electr. Insul. 8 (2001), pp. 512–515] is fabricated and used to determine the orientational order parameter in two dimeric liquid crystalline compounds nematic and SmA phases of α,ω-bis(4-alkylanilinebenzylidene-4′-oxy)alkane (m.OnO.m) homologous series. The compounds studied are 5.O8O.5 and 5.O10O.5 which exhibit nematic and SmA, and nematic phases, respectively. The orientational order parameter in both the phases of nematic and SmA phases of the compound one and the nematic phase of the compound two are obtained using the principle of Newton's rings which gives directly the birefringence, δn of the liquid crystal dimer. The merits of the technique used are presented over the conventional techniques for the determination of orientational order parameter. The results for the two compounds are compared with those values estimated from n _e, n _o and density using the two internal field models due to Vuks and Neugebauer applicable to nematic phase.     

Information Entropy Dynamics in Spin-1 Dipolar Bose-Einstein Condensates

Information entropy is an important topic due to its relevance to cold atom system. Motivated by the recent work in a scalar dipolar Bose-Einstein condensates (BECs), we extend this issue to the dynamics of information entropy in spin-1 dipolar BECs. Our results show that the periodicity of S_r, S_k and S is broken in the presence of magnetic dipole-dipole interactions (MDDIs). With the increase of dipole strength, the total entropy S and momentum component S_k increase, wile S_r decreases. This is completely opposite with scalar dipolar BECs. In particular, the order parameter δ decay quickly with stronger dipolar interaction, showing that the increase of dipole strength makes the system become more and more disordered.

     

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions C_l (t) = <P(cos δθ(t))> were calculated for l = 1 through 4 ; P_l is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.     

Orientational disordering in crystals—II: A model for the evaluation of thermodynamic properties of orientational disordering in crystals

A statistical mechanical model for the evaluation of thermodynamic properties of orientational transitions in crystals developed by Aston is generalised by taking into account the existence of more than two allowed molecular orientations (nγ 2) in the rotator crystal phase explicitly. An orientational transition work function is derived in order to generate full thermodynamic functions leading to a formal expression for the configurational energy change in terms of transition enthalpy change and an entropy integral. The value of n for camphor predicted by this equation compares very well with the one computed from another independent method and that reported by previous workers. A general scheme, based on both spectroscopic and thermodynamic data, by which n and phase eigenstates may be computed including the case where configurational and thermal properties are strongly coupled is presented. An analytical expression is obtained for the relative potential energy barrier ν_eff in a single-lattice model which parallels that defined for a double sub-lattice model of positional disorder by Pople and Karasz and their followers. It is shown that the value of ν_eff for a given value of n is not uniquely defined for all substances which may not have common values of other thermodynamic parameters.     

Coupling of orientational and translational modes in solid C60 and C70

The orientational phase transitions in solid C₆₀ and C₇₀ are accompanied by quite different anomalies in the crystalline strains. In solid C₆₀ the phase transition Fm3m→Pa3 is primarily an orientational effect (antiferro-rotational), which is driven by the condensation of orientational modes belonging to X₅ ⁺ irreducible representation (irreps) of Fm3m. These modes are the primary order parameters (oops) and their number is equal to the number of irreps of T_2g and T_1g symmetry within the manifolds under consideration. Taking into account irreps up to the manifold 1=12, we have studied the rotation-rotation-translation (RRT) coupling between the oops and the lattice displacements. We have investigated the resulting lattice contraction and the change of the elastic constant c₁₁ at the phase transition. In solid C₇₀ (fcc-phase) we investigate the bilinear coupling of orientational fluctuations of T_2g symmetry to transverse acoustic lattice displacements. This coupling is the driving mechanism for the ferroelastic phase transition Fm3m → R3m. Finally we investigate the transition from the rhombohedral phase to a low temperature monoclinic phase. This transition in antiferro-rotational.     

Effect of short and long range forces on the structure of water. II. Orientational ordering and the dielectric constant

The effects of short and long range interactions on the structure of water, both spatial and orientational, has been studied in detail by computing the full pair correlation function, site-site correlation functions, 2-dimensional site-site correlation functions in the (r _OO, r _OH) and (r _OO, r _HH) planes, dipole-dipole correlation function, radial Kirkwood g factor, and the dielectric constant. Two model potentials, the T1P4P and ST2, and their short range versions have been considered at ambient and elevated temperatures and under supercritical conditions. The Ewald summation under different conditions has been used to investigate also their effect on results. An analysis of the results shows that although all site-site correlation functions for the short and long range systems are similar, the orientational ordering in systems of different range may be considerably different, this evidence being provided mainly by the dipole-dipole correlation function and the radial Kirkwood factor. The orientational ordering is only short range in long range systems, whereas in short range systems the hydrogen bonding gives rise to a damped long range regular pattern of alignment. Nonetheless, the resulting dielectric constants for the short and long range systems coincide within the combined error bars. All findings are more pronounced at low temperatures but otherwise they are only marginally temperature and density dependent.     

Local-field anisotropy of a light wave in quasi-two-dimensional soft-matter objects

Experimental values of the Lorentz tensor components L _j for uniaxial quasi-two dimensional “soft matter” objects on substrates (bilayer lipid membranes, multilayer Langmuir films, smectics A, hexatic smectics B, submicron films of discotics Col _hd , micron anisotropic films of liquid-crystal comblike polymers and macromolecular polymers, submicron films of conjugated conductive polymers), freely suspended submicron films of smectics A, and uniaxially stretched micron films of conjugated conductive polymers have been determined using dispersion of refractive indices in the visible range. The dependences of the components L _j on the type of orientation (axial, planar) of uniaxial molecules (structural units of the film) with respect to the optical axis of the film, the film thickness, the substrate type, the chemical structure of molecules, and their long-range orientational order are established. It is revealed that the smectic A-hexatic B phase transition and two-dimensional crystallization of the smectic layer lead to changes in the components L _j due to the change in the orientational ordering of molecules as a result of the relation between the orientational and hexatic order parameters. All the above objects are characterized by isotropization of the Lorentz tensor L and the local-field tensor f with a simultaneous decrease in the birefringence of the sample and in the anisotropy of the molecular polarizability due to the change in the electronic structure of molecules. The correction for the anisotropy of the local-field tensor f to the orientational order parameter or the anisotropy of the molecular polarizability increases. The existing model approaches to calculating the components L _j for the objects under consideration are compared with the experimental data.