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.     

Carleson measures for weighted holomorphic Besov spaces

We obtain characterizations of positive Borel measures μ on B ⁿ so that some weighted holomorphic Besov spaces B _s ^p (ω,B ⁿ ) are embedded in L ^p (d μ).     

Rational Tuning of the Reactivity of Three-Membered Heterocycle Ring Openings via SN2 Reactions

The development of small-molecule covalent inhibitors and probes continuously pushes the rapidly evolving field of chemical biology forward. A key element in these molecular tool compounds is the “electrophilic trap” that allows a covalent linkage with the target enzyme. The reactivity of this entity needs to be well balanced to effectively trap the desired enzyme, while not being attacked by off-target nucleophiles. Here we investigate the intrinsic reactivity of substrates containing a class of widely used electrophilic traps, the three-membered heterocycles with a nitrogen (aziridine), phosphorus (phosphirane), oxygen (epoxide) or sulfur atom (thiirane) as heteroatom. Using quantum chemical approaches, we studied the conformational flexibility and nucleophilic ring opening of a series of model substrates, in which these electrophilic traps are mounted on a cyclohexene scaffold (C₆H₁₀Y with Y=NH, PH, O, S). It was revealed that the activation energy of the ring opening does not necessarily follow the trend that is expected from C−Y leaving-group bond strength, but steeply decreases from Y=NH, to PH, to O, to S. We illustrate that the HOMO_Nu–LUMO_Substrate interaction is an all-important factor for the observed reactivity. In addition, we show that the activation energy of aziridines and phosphiranes can be tuned far below that of the corresponding epoxides and thiiranes by the addition of proper electron-withdrawing ring substituents. Our results provide mechanistic insights to rationally tune the reactivity of this class of popular electrophilic traps and can guide the experimental design of covalent inhibitors and probes for enzymatic activity.     

Scaffolds for Sustained Release of Ambroxol Hydrochloride,a Pharmacological Chaperone That Increases the Activity of Misfolded β‐Glucocerebrosidase

Ambroxol is a pharmacological chaperone (PC) for Gaucher disease that increases lysosomal activity of misfolded β‐glucocerebrosidase (GCase) while displaying a safe toxicological profile. In this work, different poly(ε‐caprolactone) (PCL)‐based systems are developed to regulate the sustained release of small polar drugs in physiological environments. For this purpose, ambroxol is selected as test case since the encapsulation and release of PCs using polymeric scaffolds have not been explored yet. More specifically, ambroxol is successfully loaded in electrospun PCL microfibers, which are subsequently coated with additional PCL layers using dip‐coating or spin‐coating. The time needed to achieve 80% release of loaded ambroxol increases from ≈15 min for uncoated fibrous scaffolds to 3 days and 1 week for dip‐coated and spin‐coated systems, respectively. Furthermore, it is proven that the released drug maintains its bioactivity, protecting GCase against induced thermal denaturation.     

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.     

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.     

A neutral zwitterionic molecular solid

We report on the acid ethylenedithiotetrathiafulvaleneamidoglycine (EDT-TTF-CO-NH-CH(2)-CO(2)H; 1; EDT-TTF=ethylenedithiotetrathiafulvalene) and the 1:1 adduct [(EDT-TTF)(·+)-CO-NH-CH(2)-(CO(2))(-)][(EDT-TTF)-CO-NH-CH(2)-(CO(2)H)]·CH(3)OH (2), a new type of hydrogen-bonded, 1:1 acid/zwitterion hybrid embrace of redox peptidics into a two-dimensional architecture, an example of a system deliberately fashioned so that oxidation of π-conjugated cores toward the radical-cation form would interfere with the activity of the appended ionizable residues in the presence of a templating base during crystal growth. First-principles calculations demonstrate that, notwithstanding preconceived ideas, a metallic state is more stable than the hole-localized alternatives for a neat 1:1 neutral acid/zwitterion hybrid. The inhomogeneous Coulomb field associated with proton-shared, interstacks O-H···O hydrogen bonds between the ionizable residues distributed on both sides of the two-dimensional π-conjugated framework leads, however, to a weak hole localization responsible for the activated but high conductivity of 1 S cm(-1). This situation is reminiscent of the role of the environment on electron transfer in tetraheme cytochrome c, in which the protonation state of a heme propionate becomes paramount, or ion-gated transport phenomena in biology. These observations open rather intriguing opportunities for the construction of electronic systems at the interface of chemistry and biology.     

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.     

Quantification of arecoline (areca nut alkaloid) in neonatal biological matrices by high-performance liquid chromatography/electrospray quadrupole mass spectrometry

A high-performance liquid chromatography (HPLC) method with mass spectrometric detection is described for determination of arecoline in newborn meconium, urine and cord serum, using pilocarpine as internal standard. The analytes were extracted from neonatal biological matrices with chloroform/isopropanol (95:5, v/v) at alkaline pH. Extracts were analyzed by HPLC coupled to an electrospray (ESI) interface and a quadrupole mass spectrometer. Chromatography was performed on a C(8) reversed-phase column using 10 mM ammonium acetate (pH 4.3)/acetonitrile (90:10, v/v) as mobile phase. The mass spectrometer was operated in selected ion monitoring mode. The method was validated over the concentration range 0.005-1.00 micro g/g meconium, 0.004-1.00 micro g/mL cord serum and 0.001-1.00 micro /mL urine. Mean recoveries ranged between 86.5 and 90.7% for arecoline in the different biological matrices, with precision always better than 10%. The quantification limits of arecoline were 0.005 micro g/g meconium, 0.004 micro g/mL cord serum, and 0.001 micro g/mL urine. The method was applied to the analysis of neonatal biological matrices to assess eventual fetal exposition to arecoline. Two newborns from Asian mothers who declared areca nut consumption presented arecoline in meconium with concentrations in the range 0.006-0.008 micro g/g; also the urine from one neonate tested positive for the drug.