Resonance Tongues and Spectral Gaps in Quasi-Periodic Schrödinger Operators with One or More Frequencies. A Numerical Exploration

In this article we investigate numerically the spectrum of some representative examples of discrete one-dimensional Schrödinger operators with quasi-periodic potential in terms of a perturbative constant b and the spectral parameter a. Our examples include the well-known Almost Mathieu model, other trigonometric potentials with a single quasi-periodic frequency and generalisations with two and three frequencies. We computed numerically the rotation number and the Lyapunov exponent to detect open and collapsed gaps, resonance tongues and the measure of the spectrum. We found that the case with one frequency was significantly different from the case of several frequencies because the latter has all gaps collapsed for a sufficiently large value of the perturbative constant and thus the spectrum is a single spectral band with positive Lyapunov exponent. In contrast, in the cases with one frequency considered, gaps are always dense in the spectrum, although some gaps may collapse either for a single value of the perturbative constant or for a range of values. In all cases we found that there is a curve in the (a, b)-plane which separates the regions where the Lyapunov exponent is zero in the spectrum and where it is positive. Along this curve, which is b = 2 in the Almost Mathieu case, the measure of the spectrum is zero.     

Antimicrobial activity of diterpenes from Viguiera arenaria against endodontic bacteria

Six pimarane-type diterpenes isolated from Viguiera arenaria Baker and two semi-synthetic derivatives were evaluated in vitro against a panel of representative microorganisms responsible for dental root canal infections. The microdilution method was used for the determination of the minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) against Porphyromonas gingivalis, Prevotella nigrescens, Prevotella intermedia, Prevotella buccae, Fusobacterium nucleatum, Bacteroides fragilis, Actinomyces naeslundii, Actinomyces viscosus, Peptostreptococcus micros, Enterococcus faecalis and Aggregatibacter actinomycetemcomitans. The compounds ent-pimara-8(14),15-dien-19-oic acid, its sodium salt and ent-8(14),15-pimaradien-3β-ol were the most active, displaying MIC values ranging from 1 to 10 μg mL-1. The results also allow us to conclude that minor structural differences among these diterpenes significantly influence their antimicrobial activity, bringing new perspectives to the discovery of new chemicals for use as a complement to instrumental endodontic procedures.     

Multistage-multiorifice flow fractionation (MS-MOFF): continuous size-based separation of microspheres using multiple series of contraction/expansion microchannels

Previously we introduced a novel hydrodynamic method using a multi-orifice microchannel for size-based particle separation, which is called a multi-orifice flow fractionation (MOFF). The MOFF has several advantages such as continuous, non-intrusive, and minimal power consumption. However, it has a limitation that the recovery yield is relatively low. Although the recovery may be increased by adjusting parameters such as the Reynolds number and central collecting region, poor purity inevitably followed. We newly designed and fabricated a microfluidic channel for multi-stage multi-orifice flow fractionation (MS-MOFF), which is made by combining three multi-orifice segments, and consists of 3 inlets, 3 filters, 3 multi-orifice segments and 5 outlets. The structure and dimensions of the MS-MOFF were determined by the hydrodynamic principles to have constant Reynolds numbers at each multi-orifice segment. Polystyrene microspheres of two different sizes (7 μm and 15 μm) were tested. With this device, we made an attempt to improve recovery and minimize loss of purity by collecting and re-separating non-selected particles of the first separation. The final recovery successfully increased from 73.2% to 88.7% while the final purity slightly decreased from 91.4% to 89.1% (for 15 μm). These values were never achievable with the single-stage MOFF (SS-MOFF) having only one multi-orifice segment in our previous work. The MS-MOFF channel will be useful for clinical applications, such as separation of circulating tumor cells (CTC) or rare cells from human blood samples.     

Polymer Capsules as a Theranostic Tool for a Universal In Vitro Screening Assay—The Case of Lysosomal Storage Diseases

Lysosomal storage disorders are rare genetic diseases characterized by a lysosomal enzyme deficiency. The defect leads to an accumulation of normally degraded substrates within the lysosomes. The accumulation of polymeric capsules inside the lysosomes is exploited to create a universal in vitro theranostic tool for lysosomal storage disorders. The diagnostic ability of this tool based on pH‐sensitive fluorophores is demonstrated by monitoring the lysosomal pH in Krabbe‐disease cell models upon accumulation of the substrate psychosine. Krabbe‐affected cells maintain their normal pH, while the lysosomes of their healthy counterparts undergo alkalinization, which can be correlated to toxicity. The potential of this tool for therapy based on enzymes inside the capsules is evaluated within the context of enzyme replacement therapy. Enzymatic degradation of the capsules inside the lysosome leads to release of the encapsulated active enzyme and the prevention of adverse effects of accumulated psychosine upon capsule‐based delivery of the functional enzyme is confirmed. In Fabry‐affected cells the intracellular enzymatic activity of the drug Replagal released from capsules shows the same kinetics as the free enzyme, which constitutes the current therapy, although the activity is smaller. Encapsulating Replagal nevertheless represents an alternative to receptor‐mediated endocytosis, overcoming limitations such as low or absent receptor expression.     

Determination of metal ions extracted by DTPA in a soil treated with effluent using an Hg-electroplated-Pt microelectrode

Determinations of Cu, Fe, Mn and Zn were performed in an oxisol soil treated with effluent originated from a biodigester septic cesspool. The extracts were obtained from a DTPA/TEA (pH 7.3) solution and analysed by electroanalytical methodologies using square wave anodic stripping voltammetry (SWASV) for the analysis of Cu, Mn and Zn and square wave voltammetry (SWV) for Fe analysis, both of them with a thin mercury film microelectrode (ME-Hg). DTPA (diethylenetriaminepentaacetic acid) complexes with Cu, Mn and Fe show electroactivity in the potentials range close to the ones for the free ions in solution, but the Zn complex did not show any electroactivity at the potential range analysed. SWASV/ME-Hg and SWV/ME-Hg results were in good agreement (r² = 0.996) with the flame atomic absorption spectroscopy (FAAS) analyses, demonstrating that electroanalytical methodologies can be used for micronutrient determinations in soil extracts without serious interferences of the matrix components. Some characteristics of the complex formed between DTPA-metals are explored by EPR experiments.     

A supramolecular copper(II) compound with double bridging water ligands: synthesis, crystal structure, spectroscopy, thermal analysis, and magnetism

A complex of composition {[{Cu(NDC)(OH₂)(tn)(μ-OH₂)}₂]·2H₂O}_∞ (1) and a mononuclear complex salt [Cu(OH₂)₂(tn)₂](NDC)·3H₂O (2), where NDC = 2,6-naphthalenedicarboxylate dianion and tn = 1,3-diaminopropane, were simultaneously crystallized from an aqueous solution of the copper(II) naphthalenedicarboxylate—1,3-diaminopropane—methanol system. The crystal and molecular structures of both complexes were determined by single-crystal X-ray diffraction. Compound (1) consists of a supramolecular coordination complex in which the monomeric unit is assembled from a homodinuclear Cu(II) bridged by two water ligands. The Cu(II) centers exhibit distorted octahedral coordination; the equatorial plane is provided by one chelating tn ligand, one NDC^2? ligand, one μ-H₂O while the axial positions are occupied by H₂O and μ-H₂O. Strong intra- and/or intermolecular hydrogen bonds, also involving the crystallization water molecules, together with π–π stacking interactions, are involved in building up the supramolecule. The solid structure of compound (2) includes three water molecules of crystallization, the counter ion NDC^2?, and a Cu(II) cationic complex in which the metal is six-coordinated in an axially elongated octahedron defined by two chelating tn ligands in the equatorial plane and two water ligands in the axial positions. Thermal analyses of (1) show two significant weight losses corresponding to water molecules (lattice and coordinated), followed by the decomposition of the network.     

Scaling properties of the Miesowicz coefficients

In this work a set of experimental data points is used to study some scaling properties of Miesowicz coefficients. Using the fact that all the compounds studied present two critical points—the crystal–nematic and the nematic–isotropic phase transitions—a common temperature scale was defined. With the use of this unique temperature scale two relevant aspects that distinguish the viscosity of these materials can be simultaneously extracted and studied: (1) the molecular shape anisotropy and (2) the different strengths of molecular interaction of the different compounds. Through the study of the scaling properties associated with these properties, the existence of a common law connecting the Miesowicz coefficients with the associated decay time is proposed.     

Use of two different coating temperatures for a cold fiber headspace solid‐phase microextraction system to determine the volatile profile of Brazilian medicinal herbs

In this study, the experimental extraction conditions on applying headspace solid‐phase microextraction and cold fiber headspace solid‐phase microextraction (CF‐HS‐SPME) procedures to samples of six medicinal herbs commonly found in southern Brazil were optimized. The optimized conditions for headspace solid‐phase microextraction were found to be an extraction temperature of 60°C and extraction time of 40 min. For CF‐HS‐SPME, the corresponding values were 60°C and 15 min. In the case of the coating temperature for the CF‐HS‐SPME system, two approaches were investigated: (i) Temperature of 5°C applied during the whole extraction procedure; and (ii) the use of two fiber temperatures in the same extraction procedure with the aim of extracting the volatile and semivolatile compounds, the ideal condition being 60°C for the first 7.5 min and 5°C for the final 7.5 min. The three extraction procedures were compared. The CF‐HS‐SPME procedure had good performance only for the more volatile compounds whereas the strategy using two coating temperatures in the same procedure showed good performance for all compounds studied. It was also possible to determine the profile for the volatile fraction of each herb studied applying this technique followed by GC‐MS.     

Determination of 48 pesticides and their main metabolites in water samples by employing sonication and liquid chromatography-tandem mass spectrometry

In this work, a rapid and sensitive analytical multiresidue method has been developed for the simultaneous determination of 48 pesticides and 19 metabolites in waters (tap, leaching and sewage), using liquid chromatography-tandem mass spectrometry (LC-MS/MS) with triple quadrupole in selected reaction monitoring (SRM) mode. The procedure involves initial single phase extraction of samples with acetonitrile by sonication, followed by liquid-liquid partition aided by “salting out” process using NaCl. Matrix influence on recoveries was evaluated for the three waters. More than 50% of the compound presented very low signal suppression. The method presents good linearity over the range assayed 10-500 μg L⁻¹ and the most frequent detection limits was 0.05 ng mL⁻¹. The average recovery by the LC-MS/MS method obtained for these compounds varied from 74.6 to 111.2% with a relative standard deviation between 2.5 and 8.9%. The proposed method was used to determine pesticides levels in leaching water samples from 5 lysimeters from an experimental greenhouse located in Murcia.     

Ultrathin zirconium disulfide nanodiscs

We present a colloidal route for the synthesis of ultrathin ZrS(2) (UT-ZrS(2)) nanodiscs that are ~1.6 nm thick and consist of approximately two unit cells of S-Zr-S. The lateral size of the discs can be tuned to 20, 35, or 60 nm while their thickness is kept constant. Under the appropriate conditions, these individual discs can self-assemble into face-to-face-stacked structures containing multiple discs. Because the S-Zr-S layers within individual discs are held together by weak van der Waals interactions, each UT-ZrS(2) disc provides spaces that can serve as host sites for intercalation. When we tested UT-ZrS(2) discs as anodic materials for Li(+) intercalation, they showed excellent nanoscale size effects, enhancing the discharge capacity by 230% and greatly improving the stability in comparison with bulk ZrS(2). The nanoscale size effect was especially prominent for their performance in fast charging/discharging cycles, where an 88% average recovery of reversible capacity was observed for UT-ZrS(2) discs with a lateral diameter of 20 nm. The nanoscale thickness and lateral size of UT-ZrS(2) discs are critical for fast and reliable intercalation cycling because those dimensions both increase the surface area and provide open edges that enhance the diffusion kinetics for guest molecules.