Collocation by singular splines

Splines determined by the kernel of the differential operator are known to be useful to solve the singular boundary value problems of the form . One of the most successful methods is the collocation method based on special Chebyshev splines. We investigate the construction of the associated B-splines based on knot-insertion algorithms for their evaluation, and their application in collocation at generalized Gaussian points. Specially, we show how to obtain these points as eigenvalues of a symmetric tridiagonal matrix of order k. This research was supported by Grant 037-1193086-2771, by the Ministry of science, education and sports of the Republic of Croatia.     

Rheological behavior of self-assembling PEG-beta-cyclodextrin/PEG-cholesterol hydrogels

The rheological properties of a recently developed self-assembling hydrogel system composed of beta-cyclodextrin (betaCD)- and cholesterol-derivatized 8-arm star-shaped poly(ethylene glycol) (PEG8) were investigated. To understand and predict the gel rheological properties, data fitting with the Maxwell model as well as comparing the system's concentration-dependent behavior with Cates' model for reversibly breaking chains were performed. To investigate the influence of the polymer architecture, networks were also prepared by replacing the cholesterol-derivatized 8-arm star-shaped PEG by linear bifunctional PEG-cholesterol or by using 4-arm instead of 8-arm polymers. Rheological analysis showed that the 8-arm polymer-based mixtures yielded tight viscoelastic networks, but their storage and loss moduli significantly deviated from those predicted by the Maxwell model. The scaling of the plateau moduli, relaxation times, and zero-shear viscosities with concentration for gels composed of 8-arm cholesterol- and betaCD-derivatized PEG followed a power law with exponents higher than predicted by Cates' model. On the other hand, hydrogels in which linear bifunctional PEG-cholesterol was used instead of 8-arm star-shaped PEG-cholesterol or which were based on 4-arm polymers showed a substantially better fit with the Maxwell model and reduced differences between empirical and Cates' theoretical scaling exponents. Rheological analysis also showed that the hydrogels were thermoreversible. At low temperatures, the gels showed viscoelastic behavior due to slow overall relaxation of the polymer chains. At higher temperatures, however, a reduced number of betaCD/cholesterol complexes and concomitant faster chain relaxation processes eventually led to liquid-like behavior. The relationship between temperature and the relaxation time was used to determine an activation energy of 46 kJ/mol for breaking and reptation of the polymers.     

Glycine enolates: the effect of formation of iminium ions to simple ketones on alpha-amino carbon acidity and a comparison with pyridoxal iminium ions

Equilibrium constants in D2O were determined by 1H NMR analyses for formation of imines/iminium ions from addition of glycine methyl ester to acetone and from addition of glycine to phenylglyoxylate. First-order rate constants, also determined by 1H NMR, are reported for deuterium exchange between solvent D2O and the alpha-amino carbon of glycine methyl ester and glycine in the presence of increasing concentrations of ketone and Br?nsted bases. These rate and equilibrium data were used to calculate second-order rate constants for deprotonation by DO- and by Br?nsted bases of the alpha-imino carbon of the ketone adducts. Formation of the iminium ion between acetone and glycine methyl ester and between phenylglyoxylate and glycine is estimated to cause 7 unit and 15 unit decreases, respectively, in the pKa's of 21 and 29 for deprotonation of the parent carbon acids. The effect of formation of iminium ions to phenylglyoxylate and to 5'-deoxypyridoxal (DPL) [Toth, K.; Richard, J. P. J. Am. Chem. Soc. 2007, 129, 3013-3021] on the carbon acidity of glycine is similar. However, DPL is a much better catalyst than phenylglyoxylate of deprotonation of glycine, because of the exceptionally large thermodynamic driving force for conversion of the amino acid and DPL to the reactive iminium ion.     

A Computational and Experimental Approach Linking Disorder,High‐Pressure Behavior,and Mechanical Properties in UiO Frameworks

Whilst many metal–organic frameworks possess the chemical stability needed to be used as functional materials, they often lack the physical strength required for industrial applications. Herein, we have investigated the mechanical properties of two UiO‐topology Zr‐MOFs, the planar UiO‐67 ([Zr₆O₄(OH)₄(bpdc)₆], bpdc: 4,4′‐biphenyl dicarboxylate) and UiO‐abdc ([Zr₆O₄(OH)₄(abdc)₆], abdc: 4,4′‐azobenzene dicarboxylate) by single‐crystal nanoindentation, high‐pressure X‐ray diffraction, density functional theory calculations, and first‐principles molecular dynamics. On increasing pressure, both UiO‐67 and UiO‐abdc were found to be incompressible when filled with methanol molecules within a diamond anvil cell. Stabilization in both cases is attributed to dynamical linker disorder. The diazo‐linker of UiO‐abdc possesses local site disorder, which, in conjunction with its longer nature, also decreases the capacity of the framework to compress and stabilizes it against direct compression, compared to UiO‐67, characterized by a large elastic modulus. The use of non‐linear linkers in the synthesis of UiO‐MOFs therefore creates MOFs that have more rigid mechanical properties over a larger pressure range.     

Electromembrane extraction of gonadotropin‐releasing hormone agonists from plasma and wastewater samples

In the present study, for the first time electromembrane extraction followed by high performance liquid chromatography coupled with ultraviolet detection was optimized and validated for quantification of four gonadotropin‐releasing hormone agonist anticancer peptides (alarelin, leuprolide, buserelin and triptorelin) in biological and aqueous samples. The parameters influencing electromigration were investigated and optimized. The membrane consists 95% of 1‐octanol and 5% di‐(2‐ethylhexyl)‐phosphate immobilized in the pores of a hollow fiber. A 20 V electrical field was applied to make the analytes migrate from sample solution with pH 7.0, through the supported liquid membrane into an acidic acceptor solution with pH 1.0 which was located inside the lumen of hollow fiber. Extraction recoveries in the range of 49 and 71% within 15 min extraction time were obtained in different biological matrices which resulted in preconcentration factors in the range of 82–118 and satisfactory repeatability (7.1 < RSD% < 19.8). The method offers good linearity (2.0–1000 ng/mL) with estimation of regression coefficient higher than 0.998. The procedure allows very low detection and quantitation limits of 0.2 and 0.6 ng/mL, respectively. Finally, it was applied to determination and quantification of peptides in human plasma and wastewater samples and satisfactory results were yielded.     

Homogeneous tritylation of cellulose in 1-butyl-3-methylimidazolium chloride

1-Alkyl-3-methylimidazolium-based ionic liquids, having chloride as a counter ion, were studied for cellulose solubility; and the influence of different alkyl chain lengths was also investigated. The alkyl chain length was incrementally varied from ethyl to decyl to determine structure-dissolution properties; a distinct odd-even effect was observed for short chain lengths. In addition, the tritylation of cellulose was performed in 1-butyl-3-methylimidazolium chloride using pyridine as base. The influences of reaction time and the ratio of trityl chloride per cellulose monomer unit on the degree of substitution were investigated in detail by elemental analysis and 1H NMR spectroscopy. A DS of around 1 was obtained after 3 h reaction time using a six fold excess of trityl chloride.     

Removal of pharmaceutical residues in a pilot wastewater treatment plant

Concern is growing over the contamination of the environment with pharmaceutical residues, among which non-steroidal anti-inflammatory drugs (NSAIDs) are one of the most abundant groups. Their widespread appearance in the aquatic environment is because of their high consumption and their incomplete removal during wastewater treatment. Because effective operation of wastewater-treatment plants is important for minimising the release of xenobiotic compounds, for example pharmaceutical products, into the aquatic environment, our study focuses on removal of commonly used NSAIDs (ibuprofen, naproxen, ketoprofen, diclofenac) and clofibric acid in a specially designed small-scale pilot wastewater treatment plant (PWWTP). This study shows that, except for diclofenac, steady-rate removal of NSAIDs over a two-year monitoring period has been achieved. Elimination of the compounds in the PWWTP was ≥87% for ibuprofen, naproxen and ketoprofen but only 49–59% for diclofenac. We also studied clofibric acid. Results after one month of operation revealed 30% elimination with no sign of adaptation by the biomass. Also described are degradation products of diclofenac, which we were able to identify because of the similarity of their mass spectra with those in the NIST library and by comparing the retention times of different compounds. Although the structures of these compounds were confirmed with a high probability (99%), we still need to compare the fragmentation of authentic compounds with degradation products formed under our experimental conditions. Degradation products of ibuprofen, naproxen, ketoprofen, and clofibric acid were found but these must be identified by use of high-resolution mass spectrometry and analysis of authentic compounds.     

Isomer-specific fuel destruction pathways in rich flames of methyl acetate and ethyl formate and consequences for the combustion chemistry of esters

The influences of fuel-specific destruction pathways on flame chemistry are determined for two isomeric ester fuels, methyl acetate, CH3(CO)OCH3, and ethyl formate, H(CO)OC2H5, used as model representatives for biodiesel compounds, and their potential for forming air pollutants is addressed. Measurements are presented of major and intermediate species mole fractions in premixed, laminar flat flames using molecular-beam sampling and isomer-selective VUV-photoionization mass spectrometry. The observed intermediate species concentrations depend crucially on decomposition of the different radicals formed initially from the fuels. The methyl acetate structure leads to preferential formation of formaldehyde, while the ethyl formate isomer favors the production of acetaldehyde. Ethyl formate also yields higher concentrations of the C2 species (C2H2 and C2H4) and C4 species (C4H2 and C4H4). Benzene concentrations, while larger for ethyl formate, are at least an order of magnitude smaller for both flames than seen for simple hydrocarbon fuels (ethylene, ethane, propene, and propane).     

Theoretical study of the double Renner effect for A2Pi MgNC/MgCN: higher excited rovibrational states

The authors report here the implementation of a newly developed, highly efficient matrix diagonalization routine in the DR program [T. E. Odaka et al., J. Mol. Struct. 795, 14 (2006)]. The DR program solves the rovibronic Schrodinger equation for a triatomic molecule with a double Renner effect, i.e., with two accessible linear arrangements of the nuclei at which the electronic energy is doubly degenerate. With the new routines, the authors can extend the DR calculations of rovibronic energies for A 2Pi MgNC/MgCN by considering a much larger set of rovibronic states, in particular, states at higher J values, than the authors were able to access previously.