A new configurational transition in inhomogeneous nematics

Abstract

At the wall in a hybrid cell with strong anchoring, the nematic director is parallel to one wall and perpendicular to the other. Usually, the free energy is minimized by a configuration where the director orientation changes continuously with position across the cell. The boundary conditions can also be satisfied, however, by a biaxial configuration without such rotation. Under certain conditions, such as under increased curvature strains, a transition can take place between these configurations. The transition typically occurs when the wavelength of the deformation becomes comparable to the coherence length of the material. The hybrid cell considered is a simple illustrative example; in real systems, such a transition may be expected in highly strained thermotropics, or in strained lyotropics which are easily made biaxial.     

A new configurational transition in inhomogeneous nematics

At the wall in a hybrid cell with strong anchoring, the nematic director is parallel to one wall and perpendicular to the other. Usually, the free energy is minimized by a configuration where the director orientation changes continuously with position across the cell. The boundary conditions can also be satisfied, however, by a biaxial configuration without such rotation. Under certain conditions, such as under increased curvature strains, a transition can take place between these configurations. The transition typically occurs when the wavelength of the deformation becomes comparable to the coherence length of the material. The hybrid cell considered is a simple illustrative example; in real systems, such a transition may be expected in highly strained thermotropics, or in strained lyotropics which are easily made biaxial.     

Invited Lecture. Defects in small-molecule and polymeric nematics

Abstract

After a reminder of the essential topological characters of defects in phases with nematic symmetries, a review is given of the observations of textures and defects in polymeric liquid crystals. Emphasis is placed on (a) the diversity of these observations according to the type and character of the polymer, and (b) the differences with small-molecule liquid crystals. However, the topological characters are common. The differences have to be explained in terms of molecular configurations. In this respect, we develop some physical consequences of the scarcity of chain ends, in particular a possible segregation and ordering process that relaxes strong splay deformations and that occurs in the cores of disclinations with a wedge character. After having discussed models of isolated disclinations, we investigate the possibility of the thermodynamical stability of sets of disclinations. We show that this problem has some analogies with the classical Flory-Huggins theory of the stability of polymers in solution, the disclinations playing here the role of the polymeric chains. Finally we indicate the existence of other features specific to polymeric nematics, apart from the question of chain ends, such as the correlations between chains and the related phenomena of frustration.     

Controllable alignment of nematics by nanostructured polymeric layers

A method for a continuous control of the pretilt angle of the easy axis in the range 0–90° degrees and of the anchoring strength by using nanostructured polymers as alignment layers is described. The nanostructured polymers are blends of two different side-chain polymers each of them promoting planar and homeotropic alignment, respectively. A model to interpret the alignment of a nematic liquid crystal induced by such polymer layers is proposed. We show that in this case the anisotropic part of the surface tension can be approximated by a simple extension of the Rapini–Papoular expression. The predicted trend of the pretilt of the easy axis versus the concentration of the side-chain polymer promoting the planar alignment, for instance, is in good agreement with the experimental data. We also show that the effective anchoring strength of the system depends on the concentration of the side-chain polymer promoting planar alignment, and exhibits a minimum for a well-defined value of this quantity. The results obtained in this work seems to be of importance for liquid crystal displays technology since the control of the pretilt and the anchoring strength strongly affect the performance of liquid crystal displays.     

The Ericksen number and Deborah number cascades in sheared polymeric nematics

Samples of liquid crystalline poly(γ-benzyl-glutamate) solutions are sheared between glass surfaces with gaps, d = 10-500 μ, and shearing velocities, V = 0·05-10 000 μs^-1 so that the Ericksen number E ≡ Vdγ₁/K is varied over a large range, E ≈ 1-10⁷. Here γ₁ is the rotational viscosity and K₁ is the Frank splay constant, with γ₁/K₁ estimated to be approximately 1 s μ^-2 for our samples. We observe by polarizing microscopy a sequence of transitions with increasing Ericksen number analogous to that observed in small molecule tumbling nematics: namely rotation of the director out of the shearing plane and into the vorticity direction at Vd ≈ 25 μ² s^-1, and formation of roll cells at Vd ≈ 50 μ² s^-1. The roll cells become finer with increased Vd in accord with predictions of linear stability theory using the Leslie-Ericksen equations, and at Vd ≳ 500 μ² s^-1, the cells become very irregular, producing director turbulence. The turbulence becomes finer in scale as Vd increases, reaching sub-micron, and possibly molecular scales when Vd ≧ 10⁵ μ² s^-1. At the highest velocities, transitions in orientation and texture are controlled by the Deborah number De≡λV/d, where λ is the molecular relaxation time, and uniform texture-free samples are obtained when De ≳ 5.     

Static periodic distortion above bend Freedericksz transition in nematics

The linearized mathematical model developed by Allender, Hornreich and Johnson [1987, Phys. Rev. Lett., 59, 2654], for explaining the appearance of the magnetic field induced stripe phase (SP) above the bend Freedericksz threshold in a nematic close to the smectic transition, is generalized to the case of uniform tilt θ₁ of the nematic director n₀ away from the homeotropic with the field H acting normal to n₀. Calculations of SP threshold and domain wave vector Q are presented for different elastic ratios and tilts θ₁, by exact computation of the ground state homogeneous deformation (HD) under the rigid anchoring hypothesis. Approximate estimates based on energetics, explicitly taking into account the modal symmetry of perturbations, agree well with the results of exact calculations based on the solution of torque equations. For homeotropic alignment (θ₁ = 0) calculations predict that the SP domain width should decrease when the sample is heated away from the smectic transition point; at a given temperature when H is rotated through a small angle with respect to the sample planes the domains should grow wider. These points can be verified experimentally. It is also shown that for sufficiently high initial tilt θ₁ away from the homeotropic director alignment, SP may be quenched. Materials, such as nematic polymers, which exhibit static periodic domains (PD) in splay geometry (of the kind discovered by Lonberg and Meyer, 1985, Phys. Rev. Lett., 55, 718) may also show SP for director tilts θ₁ close to the homeotropic. It appears possible to make tentative predictions regarding the effects of weak anchoring and oblique magnetic fields on the SP threshold and domain wave vector.     

Electrically induced anchoring transition in nematics with small or zero dielectric anisotropy

The orientational transitions induced by electrically controlled ionic modification of surface anchoring in liquid crystal cells based on the nematics with small or zero dielectric anisotropy Δε are considered. The type of director reorientation is shown to be independent of the sign of dielectric anisotropy and can be the same for the nematics with both negative and positive Δε. Besides, the orientational transition and corresponding switchable optical states do not depend on the Δε value and can be effectively realised even for the nematics with zero dielectric anisotropy.     

Freedericksz transition in polymeric hexatic liquid crystals

The threshold voltage for the Freedericksz transition of a polymer hexatic liquid crystal depends on the film thickness. This behaviour is attributed to the coupling of the director and the bonds defined by the hexatic order. We fit the results of a simple elastic continuum model to threshold data. The fit is suitable for the estimation of several material constants.     

Free surface-induced bilayer smectic A phase in polar liquid crystals

Abstract

Here the influence of the free surface on both a thick (semi-infinite) layer and a thin freely suspended film of a polar liquid crystal is investigated. It is shown that within the temperature range of the monolayer smectic A phase (S_A1 ) the interaction between polar molecules and the free surface of the liquid crystal gives rise to a bilayer smectic A, a structure with long range antiferroelectric order (S_A2 ) in the surface region of the semi-infinite layer. The dependence of the bilayer smectic order parameter on the strength of the interaction between the constituent molecules and the free surface as well as temperature and the distance to the free surface are determined. Sufficiently far from the S_A1 -S_A2 transition the latter dependence has an exponential character and the depth of the S_A2 phase penetration into bulk liquid crystal is equal to the longitudinal correlation length for the bilayer smectic A structure fluctuations in the S_A1 phase. However, near the S_A1 -S_A2 transition the bilayer smectic order parameter decays non-exponentially and more rapidly with increasing distance to the free surface. In addition, it is found that the bilayer S_A2 phase can form several smectic layers at the free surface of a semi-infinite polar liquid crystal layer with the S_A1 phase. Finally, it is shown that in a freely suspended film the free surface-induced S_A2 phase can completely occupy the volume of the sample. Hence in a freely suspended polar liquid crystal film the S_A1 -S_A2 transition occurs with decreasing film thickness.     

Free surface-induced bilayer smectic A phase in polar liquid crystals

Here the influence of the free surface on both a thick (semi-infinite) layer and a thin freely suspended film of a polar liquid crystal is investigated. It is shown that within the temperature range of the monolayer smectic A phase (S_A1) the interaction between polar molecules and the free surface of the liquid crystal gives rise to a bilayer smectic A, a structure with long range antiferroelectric order (S_A2) in the surface region of the semi-infinite layer. The dependence of the bilayer smectic order parameter on the strength of the interaction between the constituent molecules and the free surface as well as temperature and the distance to the free surface are determined. Sufficiently far from the S_A1-S_A2 transition the latter dependence has an exponential character and the depth of the S_A2 phase penetration into bulk liquid crystal is equal to the longitudinal correlation length for the bilayer smectic A structure fluctuations in the S_A1 phase. However, near the S_A1-S_A2 transition the bilayer smectic order parameter decays non-exponentially and more rapidly with increasing distance to the free surface. In addition, it is found that the bilayer S_A2 phase can form several smectic layers at the free surface of a semi-infinite polar liquid crystal layer with the S_A1 phase. Finally, it is shown that in a freely suspended film the free surface-induced S_A2 phase can completely occupy the volume of the sample. Hence in a freely suspended polar liquid crystal film the S_A1-S_A2 transition occurs with decreasing film thickness.     

Second order elasticity in nematics: A new anchoring source

By considering, in the expression of the nematic free energy density, an additional term in the square of the director second derivatives, an unexpected anchoring source results, due only to surface and bulk elastic constants. As an example, the case of a planar homogeneous and of a homeotropic nematic cell, equally anchored on both walls, is discussed. In both situations the new anchoring source has a destabilizing effect.     

Channel confined active nematics

Active nematics is a popular model fluid for active matter. The popularity comes from the fact that several biological systems involving cells and cytoskeletal elements closely match active nematic fluid. Moreover, the theory of active nematics is amenable for analytical and computational developments. This review discusses different flow states and flow transitions exhibited by channel confined active nematics. The discussions based on experimental and theoretical investigations reveal the role of inherent hydrodynamic instabilities, the unique fluid properties, and the bounding geometry in dictating the behavior of active nematic fluids in channel confinements. The discussions also highlight the current and outstanding research questions in the field.     

Hydroxyapatite surface-induced peptide folding

Herein, we describe the design and surface-binding characterization of a de novo designed peptide, JAK1, which undergoes surface-induced folding at the hydroxyapatite (HA)-solution interface. JAK1 is designed to be unstructured in buffered saline solution, yet undergo HA-induced folding that is largely governed by the periodic positioning of gamma-carboxyglutamic acid (Gla) residues within the primary sequence of the peptide. Circular dichroism (CD) spectroscopy and analytical ultracentrifugation indicate that the peptide remains unfolded and monomeric in solution under normal physiological conditions; however, CD spectroscopy indicates that in the presence of hydroxyapatite, the peptide avidly binds to the mineral surface adopting a helical structure. Adsorption isotherms indicate nearly quantitative surface coverage and Kd = 310 nM for the peptide-surface binding event. X-ray photoelectron spectroscopy (XPS) coupled with the adsorption isotherm data suggests that JAK1 binds to HA, forming a self-limiting monolayer. This study demonstrates the feasibility of using HA surfaces to trigger the intramolecular folding of designed peptides and represents the initial stages of defining the design rules that allow HA-induced peptide folding.     

A new selective and high affinity polymeric complexing agent for transition metal ions

Summary The synthesis and characteristics of a new chelating glycinohydroxamate-containing polymer resin is described. The functionality of the polymer is 1.76 mmolg^–1. The hydrogen capacity, water regain and adsorption capacities for iron(III), cadmium(II), cobalt(II), copper(II), nickel(II) and zinc(II) were measured at various pH values; uptake of the metal ions increased with pH and was quantitative above pH 3 for most of the metal ions. All cations studied showed high exchange rates towards the resin. The half saturation times for iron(III), cadmium(II), copper(II) and zinc(II) were all less than 1 min. The coordination behaviour of the resin was studied with the help of e.p.r., i.r., u.v. and potentiometry. The pK _a of the resin is 10.70 and the log value of the stability constants for iron(III), copper(II), lead(II), zinc(II), cobalt(II), manganese(II), cadmium(II) and nickel(II) were measured as 21.81, 19.50, 19.20, 18.59, 18.51, 18.46, 18.37 and 18.36, respectively, at 25 ° C and I = 0.2M KCl.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Dynamics of the Frederiks transition in nematics consisting of disc-like molecules Thermal dependence of a bend viscosity coefficient

We report measurements of the dynamics of the magnetic Frederiks transition in nematics consisting of disc-like molecules. In this paper the results are presented for three 2, 3, 6, 7, 10, 11-hexakis(p-alkoxybenzoyloxy)triphenylenes, which exhibit a normal nematic phase, and for three 2, 3, 7, 8, 12, 13-hexa(alkanoyloxy)truxenes, which exhibit an inverted nematic phase. We find that the thermal dependence of a bend viscosity coefficient (γ*₁) can be accurately described by the expression, γ*₁ ∼ S² exp (E_a/kT). The absolute value of γ*₁ is found to be higher (by a factor of 10-100) than is commonly encountered in nematics consisting of rod-like molecules.     

Viscoelastic coefficients of glass-forming nematics

In this paper, we report measurements of the viscoelastic properties of nematic liquid crystals which exhibit a glass transition in the nematic phase. We have studied the Freedericksz transition in planar cells with a magneto-optical method. K₁ was determined from the critical field, and the rotational viscosity, γ₁, from the response time for the director orientation by the external field. We found a temperature dependence of γ₁ of the Vogel type, with absolute values ranging over several orders of magnitude, and K₁ values similar to those of conventional thermotropic low molar mass nematics.     

Surface energy of biaxial nematics

In this paper, a form of surface energy for biaxial nematics is derived. The methods follow those for deriving Landau elastic energy Frank elastic energy for bulk nematics. The surface energy can also be derived in rotation matrix expansion. The result shows that in the first order approximation, there are four independent coefficients in the surface energy. When each of the three orthogonal directors of biaxial nematics coincides with its corresponding easy axis, the surface energy is linearly proportional to the order parameters. An application of this surface energy is discussed and possible experimental measurements of three linear combinations of the four coefficients are explored.