A relaxed model and its homogenization for nematic liquid crystals in composite materials

We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen–Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non‐linear. We employ two‐scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd.     

Mathematical problems of liquid crystal flows

This article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions, phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius–Duhem inequality.     

Kinetic theories and mesoscopic models for solutions of nonhomogeneous liquid crystal polymers

We present a systematic derivation of hydrodynamic theories for nonhomogeneous nematic liquid crystal polymers (LCPs) by approximating the molecules as rigid ellipsoids, which can be either uniaxial molecules (spheroids) or biaxial ones. The short range interaction is assumed to be dominated by the excluded volume effect. Additional molecular properties with ellipsoidal molecules, e.g., a dipole–dipole interaction in extended nematics and chiral molecular structure in cholesterics, are accounted for through additional intermolecular potentials. Long-range molecular interaction is implemented through an averaged mean-field potential characterized by interaction functions. The extra elastic stress tensor is calculated using an extended virtual work principle consistent with conservation of angular momentum on the material volume, whereas the extra viscous stress is obtained by Batchelor’s volume averaging method. In the isothermal case, the theories are shown to satisfy the second law of thermodynamics, i.e., they admit positive production of entropy or energy dissipation. In the case of cholesterics, the kinetic theory reduces to the Leslie–Ericksen theory in the limit of weak translational diffusion, weak long range interaction, and weak flow.     

High mobility of dithiophene-tetrathiafulvalene single-crystal organic field effect transistors

Single-crystal field effect transistors of the organic semiconductor dithiophene-tetrathiafulvalene (DT-TTF) were prepared by drop casting. Long, thin crystals connected two microfabricated gold electrodes, and a silicon substrate was used as a back gate. The highest hole mobility observed was 1.4 cm2/Vs, which is the highest reported for an organic semiconductor not based on pentacene. A high ON/OFF ratio of at least 7 x 105 was obtained for this device.     

Linked crystallites in the conducting topmost layer of polymer bilayer films controlled by temperature: from micro- to nanocrystallites.

Temperature has great impact on the structure and size of the linked crystallites of the conducting topmost layer formed at the surface of a polycarbonate film via the reaction BEDT-TTF+IBr [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]. We show that fine temperature control permits formation of a semiconducting topmost layer of alpha'-(BEDT-TTF)(2)(I(x)Br(1-x))(3) crystallites with either micro- or nanometre size, a result that opens a route to miniaturized conducting plastic materials.     

Radical para-benzoic acid derivatives: transmission of ferromagnetic interactions through hydrogen bonds at long distances

Investigation of the transmission of magnetic interactions through hydrogen bonds has been carried out for two different benzoic acid derivatives which bear either a tert-butyl nitroxide (NOA) or a poly(chloro)triphenylmethyl (PTMA) radical moiety. In the solid state, both radical acids formed dimer aggregates by the complementary association of two carboxylic groups though hydrogen bonding. This association ensured that atoms with most spin density are separated from one another by more than 15 A. Thus, no competing through-space magnetic exchange interactions are expected in these dimers and, hence, they provide good models to investigate whether noncovalent hydrogen bonds play a role in the long-range transmission of magnetic interactions. The nature of the magnetic exchange interaction and their strengths within similar dimer aggregates in solution was assessed by electron spin resonance (ESR) spectroscopy. In the case of radical NOA, low-temperature ESR experiments showed a weak ferromagnetic interaction between the two radicals in the dimer aggregates (which have the same geometry as in the solid state). In contrast, the corresponding solution ESR study performed with radical PTMA did not lead to any conclusive results, as aggregates were formed by noncovalent interactions other than hydrogen bonds. However, the bulkiness of the poly(chloro)triphenylmethyl radical prevented interdimer contacts in the solid state between regions of high spin density. Hence, solid-state measurements of the alpha phase of PTMA radical provided evidence of the intradimer interaction to confirm the transmission of a weak ferromagnetic interaction through the carboxylic acid bridges, as found for the NOA radical. Moreover, crystallization of the PTMA radical in presence of ethanol to form the beta phase of PTMA radical prevented the dimer formation; this resulted in the suppression of this interaction and provides further evidence of the magnetic exchange mechanism through noncovalent hydrogen bonds at long distances.     

Application of capillary electrophoresis with different sample stacking strategies for the determination of a group of nonsteroidal anti-inflammatory drugs in the low microg x L(-1) concentration range

Several on-column sample preconcentration modes--large-volume sample stacking using the EOF pump (LVSEP), LVSEP with anion-selective exhaustive injection (LVSEP-ASEI) and field-amplified sample injection with sample matrix removal using the electroosmotic flow (EOF) pump (FAEP)--were used to analyze some nonsteroidal anti-inflammatory drugs (NSAIDs) by capillary electrophoresis, and then compared. Methanol was the background electrolyte solvent to suppress the EOF. The effect of the type and length of the solvent plug, and the sample injection time were investigated in FAEP to determine the conditions that provided the best response. LVSEP, LVSEP-ASEI, and FAEP improved the sensitivity of the peak area by 100-, 1200-, and 1800-fold, respectively. The methodology developed, in combination with solid-phase extraction (SPE), was applied to the analysis of water samples.     

The law of the solution to a nonlinear hyperbolicSPDE

Let { _s,t ,(s,t ₊ ² } be a white noise on ₊ ² . We consider the hyperbolic stochastic partial differential equation {ie863-3} The purpose of this paper is to study the law of the solution to this equation. We analyze the existence and smoothness of the density using the tools of Malliavin Calculus. Finally we prove a large deviation principle on the space of continuous functions, for the family of probabilities obtained by perturbation of the noise in the equation.This work has been partially supported by the grant of the DGICYT No. PB 930052 and the EU Science project CT 910459.     

Interdependence of redox state,hydrogen bonding,anion recognition and charge partition in crystals of (EDT-TTF-CONHMe)6 [Re6Se8(CN)6] (CH3CN)2(CH2Cl2)2

Neutral pi-conjugated molecules and their radical cations co-exist in [(EDT-TTF-CONHMe+*)4(EDT-TTF-CONHMe0)2] [Re6Se8(CN)6]4- (CH3CN)2(CH2Cl2)2 whose crystal structure reveals that, upon one-electron oxidation, an activation of the N-H and C-H hydrogen bond donor ability is coupled to a deactivation of the hydrogen bond acceptor character of the carbonyl oxygen atom: this is expressed in the supramolecular hydrogen bond pattern and, ultimately, into charge localisation and partition in the solid state.     

Solvent extraction and spectrophotometric determination of titanium (IV) with 3-phenyl-3-methyl-2-mercaptopropenoic acid by use of the synergistic effect of pyridine

Summary The distribution equilibria of 3-phenyl-3-methyl-2-mercaptopropenoic acid (PhMMP), pyridine and the titanium (IV)-PhMMP complex in the presence of pyridine have been studied in the chloroform-water system. An extraction-photometric method for the determination of micro amounts of titanium has been developed. The synergistic effect of pyridine, and the influence of pH, the reagent concentration and the presence of electrolytes and masking agents on the equilibrium have been determined. From slope analysis of the distribution curves, the composition of the extracted species has been found to be Ti(OH)₂(HR)₂·py. The complex is extracted quantitatively. Beer's law is obeyed over the range 0.09–4.30g/ml titanium (IV) and the molar absorptivity is 1.30×10⁴1·mole^–1·cm^–1 at 447 nm. The method has been applied to the determination of titanium in ceramics.

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Über die Extraktion und spektrophotometrische Bestimmung von Titan(IV) mit 3-Phenyl-3-methyl-2-mercaptopropensäure mit Hilfe der synergistischen Wirkung des Pyridins

Zusammmenfassung Das Verteilungsgleichgewicht von 3-Phenyl-3-methyl-2-mercaptopropensäure (PhMMP), Pyridin und Titan-PhMMP-Komplex in Gegenwart von Pyridin wurde in einem Wasser-Chloroform-System untersucht. Eine extraktionsphotometrische Methode für die Bestimmung von Mikromengen Titan(IV) wurde ausgearbeitet. Die synergistische Wirkung des Pyridins sowie der Einfluß des pH, des Reagens und der Gegenwart von Elektrolyten und maskierenden Reagenzien in der wäßrigen Phase auf das Gleichgewicht wurden bestimmt. Aus der Richtung der Verteilungskurven wurde für den extrahierten Komplex die Zusammensetzung Ti(OH)₂(HR)₂·py ermittelt. Der Komplex wird quantitativ extrahiert. Das Beersche Gesetz ist von 0,09–4,30g·ml^–1 Ti(IV) erfüllt, der molare Absorptionskoeffizient ist 1,13·10⁴1·mol^–1·cm^–1; die Sandell-Empfindlichkeit beträgt 3,7ng·cm^–2 bei 447 nm. Diese Methode wurde für die Bestimmung von Titan in keramischem Material verwendet.