Flexoelectric response at defect sites in nematic inversion walls

Electric field experiments have been carried out on +1 and -1 defects formed in alignment inversion walls, in a planarly aligned nematic phenyl benzoate. The results show that the defects are non-singular in the core and exhibit a flexoelectric response to an applied d.c. or low frequency a.c. field. When the c-director flux lines are circular, as in a +1 defect in a wall parallel to the easy axis, flexoelectro-optic switching characterized by an azimuthal angle variation is observed. When the c-director flux is radial, the response is seemingly through polar angle variations involving no rotation of the extinction brushes due to crossed polarizers. This conclusion follows from the field-induced structural distortions observed at a -1 defect having a combination of radial and tangential c-director fields.     

Interaction between a +1 defect in a nematic thin film and the surface wall and flexoelectric response at the defect site

Within the Landau-de Gennes theory, we have investigated the interaction between a +1 defect whose nuclei is ‘circular’ nuclei (i.e. the director flux lines around the defect nuclei are circular) and the surface wall, using the one-dimensional finite-difference iterative method. +1 point defects will evolve into line defects perpendicular to the sample plane due to the existence of the surface wall. Therefore, we consider cylindrically symmetric solutions containing the line defect. The free energy of liquid crystal molecules around the defect nuclei and the surface energy produced by the surface wall are competing with each other. This competition makes polar angle of the director around the defect nuclei change considerably in a certain region, and the scale of this region will decrease with the surface anchoring strength increasing. On application of a DC electric field normal to the sample plane, the defect exhibits a flexoelectric response. We demonstrate that the field-driven structural changes at the defect site involve changes in both azimuthal and polar angles defining the local director.     

Dynamics of nematic point defects in a capillary with tilted boundary conditions

The motion of a single point defect in a cylindrical cavity filled with a nematic liquid crystal is described by solving numerically the simplified equations of nematodynamics. Perfect homeotropic anchoring for the director on the lateral boundary would result in the creation of domains with equal elastic energy, escaped upwards or downwards along the cavity axis and separated by point defects of strength ± 1. Defects do not move as long as they are sufficiently far apart. However, small deviations from homeotropic anchoring remove this degeneracy and the energetically favourable domains start to expand at the expense of the others, thus setting the defects in motion along the tube. We present a new numerical approach, which neglects the backflow, for studying the influence of both the pretilt and the elastic anisotropy (K ₃₃ ≠ K ₁₁) on the motion of a defect. We show how even very small pretilt angles (≈1°) result in speeds observed in experiments. For a moderate elastic anisotropy, the velocity of a +1 defect equals the velocity of a -1 defect, whereas for K ₃₃?K ₁₁ a + 1 defect moves faster than a -1 defect. For small pretilts we confirm a good qualitative agreement with an existing analytical approach, which proves inaccurate for large pretilts.     

Redox and Conformational Equilibria and Dynamics of Cytochrome c at High Electric Fields

Cytochrome c (Cyt‐c) adsorbed in the electrical double layer of the Ag electrode/electrolyte interface has been studied by stationary and time‐resolved surface‐enhanced resonance Raman spectroscopy to analyse the effect of strong electric fields on structure and reaction equilibria and dynamics of the protein. In the potential range between +0.1 and ?0.55 V (versus saturated calomel electrode), the adsorbed Cyt‐c forms a potential‐dependent reversible equilibrium between the native state B1 and a conformational state B2. The redox potentials of the bis‐histidine‐coordinated six‐coordinated low‐spin and five‐coordinated high‐spin substates of B2 were determined to be ?0.425 and ?0.385 V, respectively, whereas the additional six‐coordinated aquo‐histidine‐coordinated high‐spin substate was found to be redox‐inactive. The redox potential for the conformational state B1 was found to be the same as in solution in agreement with the structural identity of the adsorbed B1 and the native Cyt‐c. For all three redox‐active species, the formal heterogeneous electron transfer rate constants are small and of the same order of magnitude (3–13 s^?1), which implies that the rate‐limiting step is largely independent of the redox‐site structure. These findings, as well as the slow and potential‐dependent transitions between the various conformational (sub‐)states, can be rationalized in terms of an electric field‐induced increase of the activation energy for proton‐transfer steps linked to protein structural reorganisation. Further increasing the electric field strength by shifting the electrode potential above +0.1 V leads to irreversible structural changes that are attributed to an unfolding of the polypeptide chain.     

Free-standing films of twist grain boundary TGBA and UTGBC* liquid crystals studied by fluorescence confocal polarizing microscopy

The director structures, meniscus profile, and defects in free-standing films of the twist grain boundary TGB_A and UTGB_C* liquid crystals were studied. The films were characterized by a combination of polarizing microscopy and fluorescence confocal polarizing microscopy. Five principal regions of meniscus were distinguished. When film thickness in the meniscus is much smaller then the TGB pitch, there is no difference between the free-standing films of TGB and ordinary smectic A liquid crystals. When the film thickness is larger than the TGB pitch, filamentary texture is observed. The 3D director pattern of the filaments are similar to the ground state director fields of TGB_A and UTGB_C* liquid crystals. In the intermediate thickness region of the meniscus, when the film thickness and TGB pitch are commensurate, a unique radial pattern is observed. Based on the fluorescence confocal polarizing microscopy studies of the director field, we propose a model for the 3D director structure in this part of the meniscus.     

Preparation and Characterization of Mg‐Zr Mixed Oxide Aerogels and Their Application as Aldol Condensation Catalysts

A series of Mg‐Zr mixed oxides with different nominal Mg/ (Mg+Zr) atomic ratios, namely 0, 0.1, 0.2, 0.4, 0.85, and 1, is prepared by alcogel methodology and fundamental insights into the phases obtained and resulting active sites are studied. Characterization is performed by X‐ray diffraction, transmission electron microscopy, X‐ray photoelectron spectroscopy, N₂ adsorption–desorption isotherms, and thermal and chemical analysis. Cubic Mg_xZr_1?xO_2?x solid solution, which results from the dissolution of Mg²⁺ cations within the cubic ZrO₂ structure, is the main phase detected for the solids with theoretical Mg/ (Mg+Zr) atomic ratio ≤0.4. In contrast, the cubic periclase (c‐MgO) phase derived from hydroxynitrates or hydroxy precursors predominates in the solid with Mg/(Mg+Zr)=0.85. c‐MgO is also incipiently detected in samples with Mg/(Mg+Zr)=0.2 and 0.4, but in these solids the c‐MgO phase mostly arises from the segregation of Mg atoms out of the alcogel‐derived c‐Mg_xZr_1?xO_2?x phase during the calcination process, and therefore the species c‐MgO and c‐Mg_xZr_1?xO_2?x are in close contact. Regarding the intrinsic activity in furfural–acetone aldol condensation in the aqueous phase, these Mg? O? Zr sites located at the interface between c‐Mg_xZr_1?xO_2?x and segregated c‐MgO display a much larger intrinsic activity than the other noninterface sites that are present in these catalysts: Mg? O? Mg sites on c‐MgO and Mg? O? Zr sites on c‐Mg_xZr_1?xO_2?x. The very active Mg? O? Zr sites rapidly deactivate in the furfural–acetone condensation due to the leaching of active phases, deposition of heavy hydrocarbonaceous compounds, and hydration of the c‐MgO phase. Nonetheless, these Mg‐Zr materials with very high specific surface areas would be suitable solid catalysts for other relevant reactions catalyzed by strong basic sites in nonaqueous environments.     

Orientational fluctuations in a nematic liquid crystal as seen by neutron scattering

Abstract

Real time neutron scattering is used in the study of the slow orientational fluctuations of the director in a nematic sample. A statistical analysis of the observed time series gives the Hurst exponent H and β exponent of the frequency power spectrum that satisfy the scaling relationship β = 2H + 1. In the nematic phase, but not in the solid and in the isotropic liquid phases, the exponent values are those expected for a self-organized critical state. When a magnetic field, of the order of the Freedericksz field is applied, the nematic sample is observed to display persistent oscillations of the director. We confront this observation with theoretical predictions.     

Periodic deformations induced by a magnetic field in planar twisted nematic layers

Magnetic field-induced spatially periodic deformations of planar nematic layers twisted by an angle Φ were investigated numerically. Chiral nematics with pitches compatible with the twist angle and non-chiral nematics twisted by Φ ? π/2 were considered. Two different modes of deformation, taking the form of stripes, were found: the so called Mode X, with periodicity parallel to the mid-plane director in the undisturbed structure, and Mode Y with periodicity perpendicular to the mid-plane director. The static director distributions were calculated for various magnetic field strengths, twist angles and elastic parameters. The influence of surface tilt was also investigated. Mode X appeared for sufficiently large Φ and was possible in nematics with typical elastic properties. Mode Y appeared provided that the k ₂₂/k ₁₁ elastic constant ratio and the twist angle Φ were sufficiently small. Both modes arose from the undistorted state when the magnetic field exceeded a threshold value. The spatial period of the patterns increased with field strength. At high field, regions with almost homogeneous deformation arose in the two halves of each stripe. Their width and, simultaneously, the spatial period diverged to infinity at some critical field. This divergence corresponds to the transition to a homogeneously deformed state. Diagrams were constructed showing the ranges of parameters favouring the periodic distortions.     

Crystalline morphology of a thermotropic aromatic polyester crystallized from nematic melt

The crystalline morphology of a thermotropic aromatic polyester crystallized from a nematic melt was investigtated by means of polarized optical microscopy (POM) and scanning electron microscopy (SEM). Due to POM measurements it was found that spherulites of two different types are formed within the two different temperature regions. When T_c was exceeding 170°C, spherulites of type‐1 showing a negative birefringence grew with a radial fibrillar morphology and exhibited a clear Maltese‐cross pattern. The radius growth rate of type‐1 spherulites was about 2.2 μm/min at 185°C. When T_c was smaller than 160°C, spherulites of type‐2 were formed and exhibited a radially outward growing structure but no evident Maltese‐cross pattern. These spherulites could be seen by the naked eyes due to their size reaching several millimeters. SEM observations revealed that the spherulites of type‐1 exhibited a ripple‐like homocentric morphology with periodical compact fibrils having a diameter of about 150 nm perpendicular to the radial direction. In contrast, the spherulites of type‐2 exhibited, as apparent from performed SEM images, radially growing crystallites of about 500 nm in size with no periodicity in the radial direction.     

Solution of the mixed Dirichlet–Neumann problem for molecular orientation in liquid crystals

The orientation of the nematic director field under the action of an external time‐dependent field is theoretically investigated as a mixed Dirichlet–Neumann boundary‐value problem. This mathematical problem represents the situation in which a nematic liquid crystal sample is limited by two inhomogeneous flat surfaces, separated by a distance d, on which the anchoring is weak. By considering the one‐constant approximation and a parabolic approximation for the surface energy, the initial conditions and boundary‐value problem for the profile of the tilt angle can be analytically solved even in the case in which the surfaces are not identical, which represents the more general situation. The results are valid for small deviations from the homeotropic orientation and for θ?Θ?1, where θ is the actual tilt angle and Θ characterizes the easy direction imposed by the surface, and can be relevant to investigation of the molecular orientation in a nematic cell submitted to a small external voltage.     

Correction for instrument time constant and baseline in determination of reaction kinetics

Rates of reactions can be expressed as dn/dt = kf(n), where n is moles of reaction, k is a rate constant, and f(n) is a function of the properties of the sample. Instrumental measurement of rates requires c(dn/dt) = ckf(n), where c is the proportionality constant between the measured variable and the rate of reaction. When the product of instrument time constant, τ, and k is ? 1, the reaction is much slower than the time response of the instrument and measured rates are unaffected by instrument response. When τ k < 1, = 1, or >1, the reaction rate and instrument response rate are sufficiently comparable that measured rates are significantly affected by instrument response and correction for instrument response must be done to obtain accurate reaction kinetics. This paper describes a method for simultaneous determination of τ, k, c, and instrument baseline by fitting equations describing the combined instrument response and rate law to rates observed as a function of time. When τ cannot be neglected, correction for instrument response has previously been done by truncating early data or by use of the Tian equation. Both methods can lead to significant errors that increase as τk increases. Inclusion of instrument baseline as a fitting parameter significantly reduced variability in k and c compared with use of measured instrument baselines. The method was tested with data on the heat rate from acid‐catalyzed hydrolysis of sucrose collected with three types of calorimeters. In addition, to demonstrate the generality of this method of data analysis, equations including τ, k, c, and instrument baseline are derived for the relation between the reaction rate and the observed rate for first order, second order (first in each reactant), nth order in one reactant, autocatalytic, Michaelis–Menten kinetics, and the Ng equation. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 43: 53–61, 2011     

Non‐monotonic temperature dependence of the alignment of a nematic mixture on a ferroelectric substrate

Polarization optic techniques have been applied to study specific features of the anisotropic interaction between a dye‐doped eutectic mixture of nematic liquid crystals p‐methoxybenzylidene‐p‐n‐butylaniline and p‐ethoxybenzylidene‐p‐n‐butylaniline and a polar surface of a ferroelectric triglycine sulphate crystal over the temperature range including the substrate Curie point T _c. It has been found that the temperature‐induced structural changes in the nematic layer in the vicinity of T _c are related to the changes in the orientational part of the tensor order parameter Q_ik . The temperature dependence of the director angle θ¯, averaged over the nematic layer, has been obtained from the effective dichroism values of solute absorption. The experimental data were interpreted using the model, in which the anisotropic part of the surface energy has two terms with orthogonal easy axes.     

Molecular and Supramolecular Deformations and Disclinations in a Liquid Crystalline Copolyether Thin Films under an Electrostatic Field

An alignment study of a liquid crystalline copolyether TPP‐7/11(5/5) thin films has been carried out in a 10 kV·cm^–1 electrostatic field parallel to the thin film surface normal. This copolyether possesses a negative dielectric anisotropy. The chain molecules are homogeneously aligned in the electric field and they form two‐dimensionally ordered lamellae in a tilted columnar phase when the samples were cooled to room temperature. It is observed that the chain molecules are splayed to form bent lamellae and the chain direction is perpendicular to the tangential direction of the lamellar surfaces. These lamellae thus become replicas of the chain orientation. Due to the flexoelectric effect and density fluctuation on the thin film free surface, disclinations having topological strength s = 1, c = π/4 and defect walls form. These s = 1 disclinations possesses both left‐ and right‐handednesses. Discussion of the defect formations have been attempted.     

Re‐formation Reaction of Cyclic Nitroxide‐Based Alkoxyamines: Steric and Polar/Stabilization Effects

In nitroxide‐mediated radical polymerization, the polymerization times decrease with the increasing re‐formation rate constant of the C? ON bond (→ alkoxyamine) between the growing polymer chain and the nitroxide radical. The factors influencing the re‐formation rate constant are of considerable interest, but up to now, the polar/stabilization effects have not been addressed thoroughly. The combination of new data with previously reported data now showed that the re‐formation rate constant k_c increases with the increasing polar character of the substituents attached to the nitroxide moiety. The polar/stabilization effects are weaker for the re‐formation than for the homolysis of the C? ON bond, and may be mainly attributed to the relocation of the odd electron onto the O‐atom of the N? O moiety, i.e., the stabilization of the nitroxide moiety. Hence, it is possible to predict the values of k_c by combining both the polar/stabilization (σ_I) and steric effects (E ), i.e., log(k_c/M ^?1 s^?1) = 9.86 + 0.57 ? σ_I + 0.40 ? E_s.     

(1R,2S)‐2‐[N‐Methyl‐N‐(4‐toluene­sulfonyl)amino]‐1‐phenylpropan‐1‐ol

In the title compound, C₁₇H₂₁NO₃S, the S atom is in a distorted tetrahedral geometry and the N atom exhibits sp² character. The antiperiplanar conformation is observed for the N and hydroxyl‐O atoms and the torsion angle around the N—C linkage is ?136.3 (2)°. The mol­ecules are linked by O—H?O intermolecular hydrogen bonds to form an infinite one‐dimensional chains along the c axis.     

Chiral Supramolecular Switches Based on (R)‐Binaphthalene–Bipyridinium Guests and Cucurbituril Hosts

We designed and synthesized the three molecular tweezers 1 a – c ⁴⁺ containing an electron acceptor 4,4′‐bipyridinium (BPY²⁺) unit in each of the two arms and an (R)‐2,2′‐dioxy‐1,1′‐binaphthyl (BIN) unit that plays the role of chiral centre and the hinge of the structure. Each BPY²⁺ unit is connected to the BIN hinge by an alkyl chain formed by two‐ ( 1 a ⁴⁺), four‐ ( 1 b ⁴⁺), or six‐CH₂ ( 1 c ⁴⁺) groups. The behavior of 1 a – c ⁴⁺ upon chemical or photochemical reduction in the absence and in the presence of cucurbit[8]uril (CB[8]) or cucurbit[7]uril (CB[7]) as macrocyclic hosts for the bipyridinium units has been studied in aqueous solution. A detailed analysis of the UV/Vis absorption and circular dichroism (CD) spectra shows that the helicity of the BIN unit can be reversibly modulated by reduction of the BPY²⁺ units, or by association with cucurbiturils. Upon reduction of 1 a – c ⁴⁺ compounds, the formed BPY^{+ .} units undergo intramolecular dimerization with a concomitant change in the BIN dihedral angle, which depends on the length of the alkyl spacers. The alkyl linkers also play an important role in association to cucurbiturils. Compound 1 a ⁴⁺, because of its short carbon chain, associates to the bulky CB[8] in a 1:1 ratio, whereas in the case of the smaller host compound CB[7] a 1:2 complex is obtained. Compounds 1 b ⁴⁺ and 1 c ⁴⁺, which have longer linkers, associate to two cucurbiturils regardless of their sizes. In all cases, association with CB[8] causes an increase of the BIN dihedral angle, whereas the formation of CB[7] complexes causes an angle decrease. Reduction of the CB[8] complexes results in an enhancement of the BPY^{+ .} dimerization with respect to free 1 a – c ⁴⁺ and causes a noticeable decrease of the BIN dihedral angle, because the BPY^{+ .} units of the two arms have to enter into the same macrocycle. The dimer formation in the CB[8] complexes characterized by a 1:2 ratio implies the release of one macrocycle showing that the binding stoichiometry of these host–guest complexes can be switched from 1:2 to 1:1 by changing the redox state of the guest. When the reduction is performed on the CB[7] complexes, dimer formation is totally inhibited, as expected because the CB[7] cavity cannot host two BPY^{+ .} units.     

Energetics of Stretching of Conformational Defects in Extended Poly(methylene) Chains

The deformation energetics of highly extended poly(methylene) segments with conformational defects of the kink and jog types, is investigated by molecular mechanics calculations. The deformation potential displays abrupt discontinuities as a result of sudden gauche‐to‐trans conformational transitions accompanied by a release of the elastic energy stored in all valence parameters. By stretching, the chain defects are sequentially annihilated, with the weakest elements interconverting first. Due to sudden drops in force the calculated force–length curves F(R) display a sawtooth‐like profile. The force jumps define a maximum load F_c that defect chains can bear prior to conformational “yielding”. The F_c in the range about 0.7–1.1 nN is found in highly extended multikink chains. The results suggest that the sawtooth‐like profile can be a common feature of mechanochemistry of bridging polymers with the restricted number of available conformations. A similar pattern of F(R) curves were previously observed at stretching and sequential unfolding of compact structural domains in biomacromolecules. Further, the calculations predict a distinct reduction of the longitudinal Young's modulus E with increasing concentration of kinks in molecules.     

Long‐range orientation correlations and molecular alignment in sheared thermotropic copolyester. In situ light and X‐ray scattering

Orientation correlations induced by shear flow and their relaxation were investigated using in situ small‐angle light scattering (SALS) in the thermotropic random copolyester of 60 mol% hydroxybenzoic acid (B) and 40 mol% ethylene terephthalate (ET). B‐ET displays a nematic polydomain texture, the SALS and wide‐angle X‐ray scattering (WAXS) patterns are amorphous and isotropic. Shear flow produced optical defect multiplication with the consequent reduction of the micro–domains size. However, SALS detected long‐range spatial correlations within the optically chaotic texture, the SALS patterns showed bimodal orientation of defects. After cessation of shear the orientation correlation rapidly relaxed back to a polydomain and the SALS pattern became again isotropic. Above a threshold shear rate of about the SALS pattern showed unimodal orientation arising from line defects oriented nearly orthogonal to the velocity axis. Strikingly, the texture relaxation now showed the well known “banded texture”. The threshold shear rate coincided with a significant increase in the degree of molecular alignment as determined from in situ X‐ray scattering. This technique also showed that shear flow always oriented the molecular chains along the flow direction regardless of the shear rate. Copyright © 2007 John Wiley & Sons, Ltd.     

Core–shell functionalized MWCNT/poly(m‐aminophenol) nanocomposite with large dielectric permittivity and low dielectric loss

Core–shell carboxyl‐functionalized multiwall carbon nanotube (c‐MWCNT)/poly(m‐aminophenol) (PmAP) nanocomposite were prepared through in‐situ polymerization of m‐aminophenol (m‐AP) in the presence of MWCNTs, and explicated as a dielectric material for electronic applications. The formation of thin PmAP layer on individual c‐MWCNT with excellent molecular level interactions at interfaces was confirmed by morphological and spectroscopic analyses. Here we conducted a comparative study of the dielectric performances of PmAP based nanocomposite films with pristine MWCNTs and c‐MWCNTs as fillers. Compared to PmAP/MWCNT nanocomposites, the PmAP/c‐MWCNT nanocomposites exhibited higher dielectric permittivity and lower dielectric loss. The well dispersed c‐MWCNTs in PmAP/c‐MWCNT nanocomposite produce huge interfacial area together with numerous active polarized centers (crystallographic defects), which in turn intensified the Maxwell‐Wagner‐Sillars (MWS) effect based on excellent molecular level interactions and thus, produce large dielectric permittivity (8810 at 1 kHz). The percolation threshold of PmAP/c‐MWCNT nanocomposites is found lower than that of the PmAP/MWCNT nanocomposites, which could be attributed to homogeneous distribution of c‐MWCNTs and strong c‐MWCNT//PmAP interfacial interactions in the nanocomposites. Copyright © 2016 John Wiley & Sons, Ltd.     

The equilibrium melting points of random ethylene‐octene copolymers: A test of the Flory and Sanchez–Eby theories

Ethylene/l‐octene copolymers produced with metallocene catalysts are believed to have a homogeneous comonomer content with respect to molecular weight. Two series of copolymers of different molecular weights with a 1‐octene content ranging from 0 to 39 branches per 1000 carbon atoms were studied. The influence of branch content on structure and melting behavior as well as on isothermal and nonisothermal bulk crystallization was studied. In this article, the equilibrium melting temperatures of ethylene/l‐octene random copolymers is the focus. The principal techniques used were thermal analysis and small‐angle X‐ray scattering. The use of Hoffman–Weeks plots to obtain the equilibrium melting temperatures of ethylene/l‐octene random copolymers resulted in nonsensical high values of the equilibrium melting point or showed behavior parallel to the T_m = T_c line, resulting in no intercept and, hence, an infinite equilibrium melting point. The equilibrium melting temperatures of linear polyethylenes and homogeneous ethylene/l‐octene random copolymers were determined as a function of molecular weight and branch content via Thompson–Gibbs plots involving lamellar thickness data obtained from small‐angle X‐ray scattering. This systematic study made possible the evaluation of two equilibrium melting temperature depression equations for olefin‐type random copolymers, the Flory equation and the Sanchez–Eby equation, as a function of defect content and molecular weight. The range over which the two equations could be applied depended on the defect content after correction for the effect of molecular weight on the equilibrium melting temperature. The equilibrium melting temperature, T(n, p_B), of the ethylene/l‐octene random copolymers was a function of the molecular weight and defect content for low defect contents (p_B ≤ 1.0%). T(n, p_B) was a weak function of molecular weight and a strong function of the defect content at a high defect content (p_B ≥ 1.0%). The Flory copolymer equation could predict T(n, p_B) at p_B ≤ 1.0% when corrections for the effect of molecular weight were made. The Sanchez–Eby uniform inclusion model could predict T(n, p_B) at a high defect content (1.6% ≤ p_B ≤ 2.0%). We conclude that some defects were included in the crystalline phase and that the excess free energies (18–37 kJ/mol) estimated in this study were within the theoretical range. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 154–170, 2000