Structure preserving integrators for non-linear structural dynamics

A well known and major drawback of standard time integration schemes in the field of non-linear elastodynamics is their unstable behavior in the case of stiff material behaviour. Even second order accurate implicit time integration schemes are unable to resolve the problem under consideration effectively. To remedy this drawback, structure preserving integrators have been developed. Therefore, the goal of this paper is to compare recently developed integrators. In particular, an energy and momentum conserving scheme, based on a publication by Betsch & Steinmann [1], as well as a symplectic variational integrator, proposed by Lew et al. [4] and Wendlandt & Marsden [3], based on a mid-point evaluation of the discrete Lagrangian, are presented. Two representative numerical examples will outline the characteristics of the different approaches. In particular, a stiff non-linear spring pendulum and a finite element model of non-linear structural dynamics are considered. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of two diverse classes of poly(amino-alkoxide) chelates and their mononuclear and polynuclear lanthanide(III) complexes

Factors that influence aggregation of lanthanide(III) (Ln(III)) ions to form polynuclear complexes were studied utilizing 1-aziridineethanol as a versatile source of macrocyclic and acyclic chelates. The facile ring-opening cyclo-oligomerization of 1-aziridineethanol leads to the formation of a series of polyaza cyclic oligomers (series A). In the presence of ethylenediamine, a competing N-alkylation reaction occurs to produce a new class of acyclic ligands (series B). The cyclo-oligomerization of four 1-aziridineethanol units is the most favorable process, leading to the formation of the 12-membered cyclen-type macrocycle, H(4)L(1) (1,4,7,10-tetrakis(2-hydroxyethyl)-1,4,7,10-tetraaza-cyclododecane). Ring-opening cyclo-oligomerization of 1-aziridineethanol in the presence of Ln(III) ions produces self-assembled mononuclear, tetranuclear, and pentanuclear compounds of H(4)L(1). In the presence of ethylenediamine, oligomerization of 1-aziridineethanol results in a dinuclear complex of an acyclic poly(amino-alkoxide) H(2)L(2). The coordinative unsaturation of (i) the alkoxy sites of [H(x)L(1)](x)(-)(4) (where x < 4) and (ii) Ln(III) ions in coordination numbers less than nine are critical factors in the formation of the polynuclear Ln(III) complexes. The identities of mononuclear, dinuclear, tetranuclear, and pentanuclear complexes herein discussed were established by X-ray crystallography.     

Chromium determination in pharmaceutical grade barium sulfate by solid sampling electrothermal atomic absorption spectrometry with Zeeman-effect background correction

A procedure for chromium (Cr) determination in pharmaceutical grade barium sulfate by direct solid sampling electrothermal atomic absorption spectrometry (DSS-ET AAS) with Zeeman-effect background correction was developed. Operational conditions for the proposed procedure and the use of citric acid, ammonium phosphate, palladium and magnesium nitrate as chemical modifiers were evaluated. Pyrolysis and atomization temperatures were set at 1500 and 2400 °C, respectively and the use of matrix modifiers did not improve these conditions. Graphite platform presented high degradation rate, but minima changes were observed in the sensitivity or signal profile. Samples (0.3-1 mg) were weighted and introduced into the furnace using a manual solid sampling system. The linear concentration range of the calibration curve was from 100 to 1800 pg (R² > 0.995). The characteristic mass was 7.7 pg and the limit of detection was 2.4 pg. Chromium concentration in commercial samples ranged from 0.45 to 1.06 μg g⁻¹ and these results were confirmed by standard addition method. The mean reproducibility was 12% (n = 20 in a 3-day period) and repeatability was less than 9%. Results obtained using inductively coupled plasma optical emission spectrometry and conventional electrothermal atomic absorption spectrometry after extraction with HNO₃ were around 20% lower than those obtained by the proposed procedure. It was assumed that the low results were due to incomplete extraction even using hard conditions related to temperature and pressure. The proposed procedure by DSS-ET AAS provided some advantages related to recommended pharmacopoeias methodology, as lower risks of contamination and analyte losses, higher specificity, accuracy and sensitivity, no toxic or unstable reagents are required, and calibration with aqueous standards was feasible.     

Control over the Redox Cooperative Mechanism of Radical Carbene Transfer Reactions for the Efficient Active-Metal-Template Synthesis of [2]Rotaxanes

A 5,15-bis(1,1′-biphenyl)porphyrin-based molecular clip covalently connected to a ditopic aliphatic ester loop moiety yields a semi-rigid macrocycle with a well-defined cavity. The resulting macrocycle fits the structural requirements for the preparation of porphyrinates capable of promoting formation of C−C bonds. To demonstrate the usefulness of porphyrin-based macrocycles, an active-metal-template synthesis of rotaxanes through a redox non-innocent carbene transfer reaction is described. Coordination of Co^II ions into the porphyrin subunit followed by addition of appropriate monodentate nitrogen-based additives to function as axial ligands enables the radical carbene transfer reactions to styrene derivatives to occur exclusively through the cavity of the macrocycle to afford cyclopropane-linked rotaxanes in excellent 95 % yield. Investigation of the product distribution afforded from the rotaxane assembly reaction reveals how the redox cooperative action between the carbene species and the Co^II ions can be manipulated to gain control over the radical-type mechanism to favor the productive rotaxane forming process.     

Evaluation of oxygen pressurized microwave-assisted digestion of botanical materials using diluted nitric acid

The feasibility of diluted nitric acid solutions for microwave-assisted decomposition of botanical samples in closed vessels was evaluated. Oxygen pressurized atmosphere was used to improve the digestion efficiency and Al, Ca, K, Fe, Mg and Na were determined in digests by inductively coupled plasma optical emission spectrometry (ICP OES). Efficiency of digestion was evaluated taking into account the residual carbon content (RCC) and residual acidity in digests. Samples were digested using nitric acid solutions (2, 3, 7, and 14 mol L⁻¹ HNO₃) and the effect of gas phase composition inside the reaction vessels by purging the vessel with Ar (inert atmosphere, 1 bar), air (20% of oxygen, 1 bar) and pure O₂ (100% of oxygen, 1 bar) was evaluated. The influence of oxygen pressure was studied using pressures of 5, 10, 15 and 20 bar. It was demonstrated that a diluted nitric acid solution as low as 3 mol L⁻¹ was suitable for an efficient digestion of sample masses up to 500 mg of botanical samples using 5 bar of oxygen pressure. The residual acidities in final digests were lower than 45% in relation to the initial amount of acid used for digestion (equivalent to 1.3 mol L⁻¹ HNO₃). The accuracy of the proposed procedure was evaluated using certified reference materials of olive leaves, apple leaves, peach leaves and pine needles. Using the optimized conditions for sample digestion, the results obtained were in agreement with certified values. The limit of quantification was improved up to a factor of 14.5 times for the analytes evaluated. In addition, the proposed procedure was in agreement with the recommendations of the green chemistry once it was possible to obtain relatively high digestion efficiency (RCC < 5%) using only diluted HNO₃, which is important to minimize the generation of laboratory residues.     

Desorption electrospray ionization mass spectrometry (DESI-MS) applied to the speciation of arsenic compounds from fern leaves

The different chemical forms of arsenic compounds, including inorganic and organic species, present distinct environmental impacts and toxicities. Desorption electrospray ionization mass spectrometry (DESI-MS) is an excellent technique for in situ analysis, as it operates under atmospheric pressure and room temperature and is conducted with no/minimal sample pretreatment. Aimed at expanding its scope, DESI-MS is applied herein for the quick and reliable detection of inorganic (arsenate—As(V): AsO₄ ^3? and arsenite—As(III): AsO₂ ^?) and organic (dimethylarsinic acid—DMA: (CH₃)₂AsO(OH) and disodium methyl arsonate hexahydrate: CH₃AsO₃·2Na·6H₂O) arsenic compounds in fern leaves. Operational conditions of DESI-MS were optimized with DMA standard deposited on paper surfaces to improve ionization efficiency and detection limits. Mass spectra data for all arsenic species were acquired in both the positive and negative ion modes. The positive ion mode was shown to be useful in detecting both the organic and inorganic arsenic compounds. The negative ion mode was shown only to be useful in detecting As(V) species. Moreover, MS/MS spectra were recorded to confirm the identity of each arsenic compound by the characteristic fragmentation profiles. Optimized conditions of DESI-MS were applied to the analysis of fern leaves. LC-ICP-MS was employed to confirm the results obtained by DESI-MS and to quantify the arsenic species in fern leaves. The results confirmed the applicability of DESI-MS in detecting arsenic compounds in complex matrices.     

General boundary conditions for the wave equation around non-homogenous scatterers

To solve the wave equation inside a region that contains an inhomogenous dielectric material of arbitrary shape under the influence of an incoming wave, we establish a generalized boundary condition. The solutions inside a finite region resulting form a given incoming wave from the outside, are determined by a linear relation between the normal gradient and the function values on the boundary. This boundary condition is non-local and we show how it can be used in conjunction with the variational principle applied to an open system.     

Digestion of biological materials using the microwave-assisted sample combustion technique

In this study a procedure for sample digestion based on sample combustion assisted by microwave radiation is proposed. Combustion is started by microwave radiation in the presence of oxygen under pressure using ammonium nitrate as aid for ignition. The system was adapted in a microwave oven with quartz closed vessels. A quartz piece is used simultaneously as a sample holder and as protection to the cap of quartz vessel from the flame generated in the combustion process. Sample was pressed into a pellet and placed on a disc paper in the holder and 50 μl of 50% m/v ammonium nitrate solution was added. The influence of the absorption solution (diluted and concentrated nitric acid or water) on the recoveries for Cu and Zn was evaluated. About 3 s of microwave irradiation was necessary to start the combustion. The combustion process was evaluated in relation to the influence of sample mass on the ignition time, combustion time and maximum operation pressure. Bovine liver, milk powder and oyster tissue certified reference materials were used to evaluate the accuracy of the procedure for determination of copper and zinc. Good agreement for zinc (96% to 103%) was obtained from bovine liver certified reference material when microwave combustion and microwave combustion followed by reflux were used to sample decomposition, even if water was used for absorption of analyte. For copper, the combustion followed by reflux of 5 min allows an agreement from 96% to 100%. Similar results were obtained for oyster tissue samples. However, for milk powder good agreement close to 100% was obtained only if 4 mol l^− 1 HNO₃ was used with a reflux step. Results from the proposed procedure were also compared to those from conventionally used procedures for biological samples decomposition, such as wet digestion in open vessels and microwave-assisted digestion in closed vessels. The advantages of this procedure include the complete sample decomposition in less time than other procedures and the acid consumption was always lower than 2%. Another advantage is the low residual carbon content, less of 1.4% without reflux and less than 0.3% with the reflux step and the possibility of use of diluted acid as absorbing solution. Moreover, the new holder allows an effective protection of the vessel cap to burnt high masses.