The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Molecular orientation in poly(vinyl chloride) studied by Raman spectroscopy and birefringence measurements

The ratios of the intensities of Raman scattering in the C? CI stretching region for eight combinations of sample orientation and directions of polarization of incident and scattered light have been measured for 15 samples of poly(vinyl chloride) (PVC) containing 0, 5, 10, 15 or 20 pph dioctyl sebacate (DOS) plasticizer which had been drawn uniaxially at 22, 70, 75, 80, or 90°C to draw ratios in the range 1–4.5. The birefringences of the samples were also measured. The Raman data were analyzed to give 〈P₂(cosθ)〉_cryst and 〈P₄(cosθ)〉_cryst, the values of the second- and fourth-order Legendre polynomials in cosθ averaged over the distribution of orientations of the crystallites, where θ is the angle between the c axis of a typical crystallite and the draw direction. Comparison of 〈P₂(cosθ)〉_cryst with the birefrigence showed that the crystallites are more highly oriented than the noncrystalline material in samples containing the higher amounts of plasticizer drawn at the higher temperatures. A value of 13.0 × 10^?3 was deduced for the birefringence of fully oriented PVC. The values of 〈P₄(cosθ)〉_cryst for a given 〈P₂(cosθ)〉_cryst were found to be higher than predicted by calculations based on two simple models, the pseudoaffine rigid-rod rotation model and the affine rubber elasticity model.     

Computer modelling of the director configuration in a supertwist nematic liquid crystal cell

Abstract

The director distribution in a supertwist nematic cell, containing La-Roche liquid crystal mixture 3010, has been studied extensively using Berreman's computer simulation approach. It is seen that the director distribution in the cell depends critically on the total twist angle θ_t, the surface tilt angle θ_o and the ratio of the cell thickness to the pitch d/p. The values of θ_o and φ_t have been optimized to yield a small bistability (ΔV = 0.06 V) and a relatively large change in the midplane tilt angle (Δθ_m = 51°) in an unstrained cell with ?_t = (d/p) × 360°. The optimum values of θ_o and Ø_t were found to be 15° and 240°, respectively. The effect of varying d/p on the director distribution has also been studied in great detail in supertwist cells with θ_o = 30° and Ø_t = 270°. Some interesting features in understrained and overstrained cells have been observed.     

Quantum mechanics and quasiclassical study of the H/D+FO → OH/OD+F,HF/DF+O reactions: Chemical stereodynamics

The time‐dependent quantum wave packet and the quasi‐classical trajectory (QCT) calculations for the title reactions are carried out using three recent‐developed accurate potential energy surfaces of the 1¹A′, 1³A′, and 1³A″ states. The two commonly used polarization‐dependent differential cross sections, dσ₀₀/dω_t, dσ₂₀/dω_t, with ω_t being the polar coordinates of the product velocity ω′, and the three angular distributions, P(θ_r), P(Φ_r), and P(θ_r,Φ_r), with θ_r, Φ_r being the polar angles of the product angular momentum, are generated in the center‐of‐mass frame using the QCT method to gain insight into the alignment and the orientation of the product molecules. Influences of the potential energy surface, the collision energy, and the isotope mass on the stereodynamics are shown and discussed. Validity of the QCT calculation has been examined and proved in the comparison with the quantum wave packet calculation. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Multiple collisions in molecular beam scattering experiments

Due to the forward peaked differential cross section for elastic atom—atom scattering the effect of multiple collisions has to be considered in the analysis of crossed beam measurements of the total cross section and especially of the small angle differential cross section at large values of the beam attenuation. At angles θ ≈ θ₀, with θ₀ the quantum mechanical scaling angle of the elastic differential cross section, the correction for the latter case amounts to 20% at beam attenuations I/I₀ = exp(?1). Firstly, a careful analysis of the probabilities for single and multiple scattering is given, resulting in an expression for the measured beam signals which is correct for all values of the beam attenuation. The probability for multiple scattering is then calculated for an inverse power potential V(r) = ?C_sr^?s, with s = 4 through s = 7, which include both the case of ion—atom scattering (s = 4) and atom—atom scattering (s = 6). The results are given as effective differential cross sections σ_n(θ) for n-fold scattering. They are described by a single, simple analytical function with four free parameters that have been determined for n = 2, 3 and 4 by a least squares method. The σ_n(θ) are normalised to the total cross section Q.     

Nitrogen rotational excitation by collisions with argon-observations and comprison with theory

Measurements of the distribution of rotational states in a nitrogen molecular beam before and after deflection by collision with rare gas atoms are interpreted in terms of the intermolecular potential. A potential of the form V(R, θ) = 4?(1 + b₂P₂(cosθ)| R^*12 ? 4θ [1 + α₂P₂(cosθ)]/R^*6 is used with semiclassical theory using the sudden approximation to fit the observations. As α₂ is known, as well as ? and the size parameter, σ, the objective is to find b₂. However, the calculated state distributions are found to systematically vary from those measured, irrespective of the value of b₂. This result is tentatively explained as due to the inadequacies of the 12-6 potential.     

Molecular shape,shape of the geometrically active atomic states,and hybridization

In a recent publication [C. A. Nicolaides and Y. Komninos, Int. J. Quant. Chem. 67 , 321 (1998)], we proposed that in certain classes of molecules the fundamental reason for the formation of covalent polyatomic molecules in their normal shape is to be found in the existence of a geometrically active atomic state (GAAS) of the central atom, whose shape, together with its maximum spin‐and‐space coupling to the ligands, predetermines the normal molecular shape (NMS). The shape of any atomic state was defined as that which is deduced from the maxima of the probability distribution ϱ(cos θ₁₂) of the angle formed by the position vectors of two electrons of an N‐electron atom. Because the shape of the GAAS determines the NMS and because the NMS allows the construction of corresponding hybrid orbitals, we examined and discovered the connection between the GAAS shape and Pauling's function for the strength of two equivalent orthogonal orbitals at angle θ₁₂ with one another. It is shown that the computed ϱ(cos θ₁₂) of the GAAS can be cast in a form which allows the deduction of the composition of the hybrid orbitals of maximum spin states with configurations sp³, sp³d⁵, sp³d⁵f⁷, slⁿ, s²lⁿ and the demonstration of the central atom's tendency to form bonds in directions which coincide with the nodal cones of the hybrid bond orbitals. These results not only reinforce the validity of the theory as to the fundamental “mechanism” for the formation in the normal shape of coordination compounds and covalently bonded polyatomic molecules, but also provide the justification for the relevance and importance of the hybridization model. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 25–34, 1999     

The use of single exponential orbitals in one-center molecular orbital calculations

Single-exponential Slater type orbitals of the form ψ₁ = (1 + L₁(r, θ) + L₂(r, θ) +…?+ L_n(r, θ)) exp (? αr) are examined for their potential use as one-center molecular orbitals. These are then to be used as molecular fragments in a LCMO study. The system examined is HeH^{+ +} with calculated energies and dipole moments being compared to the exact values. These functions behave best in the region of chemical interest (the bonding region) and thus demonstrate a possible usefulness in LCMO calculations and in the field of one-electron diatomics.     

Evaluation of the orientation coefficient for the c axis in poly(ethylene terephthalate) fibers

The literature methods for the determination of the mean of the crystallite orientation distribution for the c axis, that is of the orientation coefficient f_c, for poly(ethylene terephthalate) (PET), based on the azimuthal scan of the (1 05) reflection, are reviewed. These methods appear unsuitable for samples presenting the “tilted orientation”; that is, the molecular chain axis inclined by some degrees with respect to the fiber axis, as frequently occurs for PET fibers. A new method for the determination of f_c for PET, also based on the azimuthal scan of the (1 05) reflection (which can be applied also to samples with “tilted orientation”), is proposed. This method implies as a first step the determination of the tilt angle, for which the complete fiber pattern is required. A possible simplifying assumption, which allows use of the sole azimuthal (1 05) profile and makes the method also applicable to poorly oriented samples (for which the determination of the tilt angle is not easy), is also discussed. © 1995 John Wiley & Sons, Inc.     

The influences of surface polarization on NLC cells

The influence of the surface polarization, P_s , on a nematic liquid crystal (NLC) cell is investigated analytically. Flexoelectric polarization is considered, but selective ion absorption is ignored. The differential equations are derived for tilt angle, θ, of director n and the corresponding boundary conditions based on Gibbs free energy, and their solutions discussed. Equations for the reduced threshold voltage, u_th , and the reduced saturation voltage, u_sat , are deduced and the relationships between u_th , u_sat and reduced strength of surface polarization, p, derived.     

Small-angle light scattering from hedrites,ovoids, and spiral ovoids. I. Theoretical considerations

Taking into consideration results of our microscopy studies and data given in the literature on the structure of hedrites, ovoids, and spiral ovoids, we have developed optical models for these morphological entities. These models are applied to calculations of small-angle scattered light intensity distributions for these structural elements. Analytic formulae computed for the V_v and H_v scattering patterns contain terms dependent only on azimuthal angle μ and vertical angle θ. For hedrites and ovoids, equations are derived relating the characteristic points of scattered light intensity patterns to structural parameters. The corresponding diagrams of light intensity distributions are given.     

Invited Lecture. Order-parameter theories of phase diagrams for antiferroelectric smectic-A phases

Using exact relations between Landau and molecular approaches, the symmetryinduced topologies of phase diagrams are studied for antiferroelectric smectic-A phases. In particular, the tricritical points are found for a large class of orderparameter theories of nematic-smectic A (-A₁, -A_d) and -A₂ (NA) phase transitions. These include generalizations to antiferroelectric smectic-A phases of McMillan and Meyer-Lubensky mean-field theories and the Ramakrishnan-Youssouff(RY) density-functional approach. The use of these different approaches allows study of influence of various couplings between nematic (orientational) and smectic (translational) degrees of freedom and polarization field, P₁ (cos θ), on various NA and AA phase transitions. From the results, it is of interest that the coupling between orientational degrees of freedom (P₄(cos θ) and density waves can destabilize the smectic-A phase at low temperatures-pointing to the existence of a nematic-smectic-A-reentrant-nematic phase transition. A possible relation of this result to A_d, C₂, C_d and [ctilde] phases is discussed. Some relations between Fourier components of correlation functions and order parameters at tricritical points are derived from the RY density-functional theory. Despite some limitations, the theory presented here seems to provide the simplest approach to study topologies of phase diagrams in molecular theories.     

Self-motion response and incoherent scattering function in classical liquids

Abstract

The self-motion response function and incoherent scattering function S_s(k, ω) for simple classical liquids is studied using an exact representation presented in a previous paper. The latter can be termed a generalized mean field representation to distinguish it from the generalized hydrodynamic representation introduced elsewhere. It is shown that the present formalism offers a natural and convenient way of relating the experimentally determined S_s(k, ω) to some basic quantities involving only the interaction. Using a small part of the recent experimental data on incoherent neutron scattering in liquid argon, we are able to calculate S_s(k, ω) and other quantities of interest and to compare with the rest of the data     

The calculation of 2J(HH) couplings in benzyl groups

The results of FPT/INDO theory together with the observed ²J(HH) coupling in benzyl groups (Ph · CH₂X) leads to a simple equation ²J(HH) = A+B cos θ+C cos 2θ where θ is the C.C.C.X dihedral angle, and X = C,H. The extension to other X substituents can be obtained from additivity rules.     

Effects of memory on the coherent scattering function for the rouse–zimm model of dilute polymer solutions

We study the effect of the memory function on the coherent scattering function of a dilute polymer solution, taking into account hydrodynamic interactions among the polymer segments. The line shape, given by a sum of two exponentials, is very accurate numerically for ka ? 3 (with a the length of a polymer segment) and for times such that ω₀(k)t ? 1.5 [with ω₀(k) the initial slope]. However, this approximation to the scattering function is not nearly so accurate at the smaller values of ka encountered in light scattering experiments. The amplitudes and relaxation times associated with the two exponentials are found to be markedly dependent on the strength of the hydrodynamic interactions.     

Studies of the effect of orientation on the elastic constants of stretched and hydrostatically extruded polychlorotriflouroethylene: A reorientational model in semicrystalline polymers

A reorientational model of polymer solids is given. The solid is described as a collection of small, orientable units. The elastic constants of the oriented polymer are given as a combination of the elastic constants of the orientable units and of the orientation parameters 〈P₂(cosθ)〉 and 〈P₄(cosθ)〉. The elastic constants of stretched and hydrostatically extruded samples of polychlorotriflouroethylene are obtained with Brillouin light scattering. These are fitted to the model and the orientation parameters are calculated. The elastic constants from the extruded samples are fit well by the model but the fit to the stretched film is less satisfactory. Hydrostatic extrusion in polymers is thus assumed to be a reorientation process in the amorphous phase, but the stretching process is not completely reorientational.