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.     

Experimental designs and response surface modeling applied for the optimization of metal-cyanide complexes analysis by capillary electrophoresis

The development of capillary zone electrophoresis (CZE) methods for the determination of metal cyanide complexes in real samples showed some problems, such as the low detection signal of Au (CN)2- and the low resolution between Ni(II) and Fe(II) cyanides in gold processing solutions, and the lack of separation of Pt(CN)4(2-) and Pd(CN)4(2-) in the leachates from automobile catalytic converters. To optimize some analytical parameters, the present study thus focused on the application of experimental designs and multiregression models. The following factors were examined by a two-level factorial design: applied voltage, injection time, detection wavelength, buffer ion, ionic strength and buffer modifiers. For optimization of the CZE method, subsequent response-surface experiments with the important factors were made with the two kinds of leaching solutions. Optimal analytical conditions were obtained in each case, giving good detection signals and resolution for the components of the studied leachates.     

High-performance liquid chromatography of amino acids, peptides and proteins CXXV. Molecular dynamics simulation of n-butyl chains chemically bonded to silica-based reversed-phase high-performance liquid chromatography sorbents

The molecular dynamics method has been applied to investigate the conformations of n-butyl ligands immobilised onto an amorphous silica surface analogous to those utilised with silica-based RP-HPLC sorbents. Three systems were constructed which corresponded to ligand densities of 1.64, 2.67 and 3.69 μmol/m². A number of parameters related to the structure of the sorbent materials were derived in order to characterise the molecular properties of each system. These parameters included the hydrocarbon layer thickness, the frequency of gauche conformations, the distance distribution for carbon atoms and the diffusion coefficients of individual atoms in the n-butyl ligands. From these properties, the positions of chains with respect to the surface as well as their mobility were estimated. It was found that at higher densities, the n-butyl chains are predominantly perpendicular to the surface while at low density they are highly tilted or lying almost parallel to the surface. The degree of ligand flexibility decreased with increasing surface density. Mobility of individual carbon atoms as well as chain disorder increased with distance from the surface for all ligand densities. The simulated properties of n-butyl chains immobilised to a silica surface correlated well with results obtained by Fourier transform IR and ¹³C-cross polarisation magic angle spinning NMR experimental methods and statistical predictions of the behaviour of immobilised chains.     

Cycloaddition reactions of alkoxy alkynyl Fischer carbene complexes with o-quinodimethanes (oQDMs)

[reaction: see text] The reaction of o-quinodimethanes (oQDMs) with alkoxy alkynyl Fischer carbene complexes is highly dependent on the carbene complex. Thus, for arylalkynyl carbene complexes, the initial [4 + 2]-cycloadduct evolves opening a new entry to the benzo[b]fluorene skeleton, which is present in many natural products. However, for alkenylalkynyl carbene complexes, the reaction takes place through the double bond, instead of the triple bond, in an unprecedented fashion, leading to new functionalized alkynyl carbene complexes.     

Production,purification, and characterization of a low-molecular-mass xylanase from Aspergillus sp. and its application in baking

An extracellular xylanase produced by a Mexican Aspergillus strain was purified and characterized. Aspergillus sp. FP-470 was able to grow and produce extracellular xylanases on birchwood xylan, oat spelt xylan, wheat straw, and corncob, with higher production observed on corncob. The strain also produced enzymes with cellulase, amylase, and pectinase activities on this substrate. A 22-kDa endoxylanase was purified 30-fold. Optimum temperature and pH were 60 degrees C and 5.5, respectively, and isoelectric point was 9.0. The enzyme has good stability from pH 5.0 to 10.0, retaining >80% of its original activity within this range. Half-lives of 150 min at 50 degrees C and 6.5 min at 60 degrees C were found. K(m) and activation energy values were 3.8 mg/mL and 26 kJ/mol, respectively, using birchwood xylan as substrate. The enzyme showed a higher affinity for 4-O-methyl-D-glucuronoxylan with a K(m) of 1.9 mg/mL. The enzyme displayed no activity toward other polysaccharides, including cellulose. Baking trials were conducted using the crude filtrate and purified enzyme. Addition of both preparations improved bread volume. However, addition of purified endoxylanase caused a 30% increase in volume over the crude extract.     

Culture conditions dictate protease and tannase production in submerged and solid-state cultures of Aspergillus niger Aa-20

Undesirable protease production by Aspergillus niger Aa-20 in submerged culture and solid-state culture was evaluated using different concentrations of tannic acid as sole carbon source in a model system designed for tannase production. Protease production was found to be dependent on the culture system used (submerged culture or solid-state culture) and on the initial tannic acid concentration. Expression of protease activity in submerged culture was higher (up to 10 times) than activity obtained in solid-state culture, using identical culture medium composition. In submerged culture, the lowest final protease activity (0.13 IU) was obtained with the highest tannic acid concentration, while in solid-state culture protease activity was not affected by changes in initial substrate concentration. Absence of detectable proteolytic activity in solid-state culture is related to high production of tannase enzyme. Hence, the use of solid-state culture for fungal enzyme production may allow for higher and more stable enzyme titers present in culture extracts.     

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.