Produktintegration mit nicht-äquidistanten Stützstellen

Summary For the numerical evaluation of , 0<<1 andx smooth, product integration rules are applied. It is known that high-order rules, e.g. Gauss-Legendre quadrature, become normal-order rules in this case. In this paper it is shown that the high order is preserved by a nonequidistant spacing. Furthermore, the leading error terms of this product integration method and numerical examples are given.

     

Electrical and thermal conductivity of CePd3, YPd3, GdPd3 and some dilute alloys of CePd3 with Y and Gd

Resistivity and thermal conductivity of the intermediate valence compound CePd₃ between 1.3 and 300 K are compared with those of the nonmagnetic and magnetic reference compounds YPd₃ and GdPd₃ and of alloys of the type Ce₁–xRE _x Pd₃ with RE=Y, Gd and 0.01<x<0.5. The analysis reveals the existence of a maximum metallic resistivity of 300 cm for CePd₃. The intrinsic resistivity of CePd₃ rises proportional toT ² up to 100 K, with a coefficientB about 10⁷ times larger than e.g. in copper. We interpret this with indirect electron-electron scattering mediated through valence transitions.     

Mono-, di-, and trimetallic complexes of the nonalternating polycondensed pi-perimeter decacyclene, C36H18: synthesis, structure, and spectroelectrochemistry of

Reaction of the half-sandwich complexes [(eta5-Me4RC5)M(eta2:O-acac)] (M = Co, Ni; R = Me or Et) with di- and trianions of the polycondensed pi-hydrocarbon decacyclene results in formation of the first Co and Ni triple-decker complexes of this hydrocarbon. For the title compound NMR spectra as well as a crystal structure analysis reveal an antarafacial coordination of two (eta5-Me4EtC5)Co fragments at the central six-membered ring and one of the neighboring five-membered rings of decacyclene. The bridging pi-perimeter decacyclene displays a bowl-shaped topology. In the case of Ni, coordination of two (eta5-Me5C5)Ni fragments at the central six-membered ring of decacyclene is observed, based on the results of 1H and 13C NMR studies. This coordination mode is without precedent for nickel organometallic compounds reported so far. The cobalt complex shows a rich spectroelectrochemistry. Results of cyclic voltammetry and coupled ESR experiments reveal a strong interaction of both metal centers in the mixed-valent monocation of [(eta5-Me4EtC5)Co2(mu-eta5:eta4-C36H18)]. This categorizes the title compound into Robin Day class III.     

A DSC-Study of Donor/Acceptor Side-Chain Polymers with Flourinated Taper-Shaped Tails

It is shown that insertion in methacrylic polymers of bulky electron donor/acceptor side-groups with taper-shaped flourinated tails promotes a self-organization of the respective side-chain polymers due to the space demands of the bulky D/A side-groups, leading to a columnar hexagonal mesophase. The presence of an Lc-phase is evidenced by DSC and identified by X-ray analysis. The orientation in the respective copolymers and polymer blends is additionally improved by the CT-interaction between the D/A side-groups. An increased packing effect due to this CT-orientation effect is evidenced in DSC by an increase of the respective transition temperatures. CT-interaction is responsible as well for a preferential polymerization of monomeric D/A-complexes leading to copolymers of alternating structures and for a zip-like arrangement along the main chain of the A/D-complexes between the interacting side-groups in polymer blends. Formation of mesophases is even observed in CT-interacting blends between the Lc-D/A side-chain polymethacrylates and the respective amorphous D/A side-chain polysiloxanes.This revised version was published online in November 2005 with corrections to the Cover Date.     

Collision induced fragmentation of mass-selected (CO2) n + clusters

The collisional velocity dependence of the cross sections for fragmentation of mass-selected (CO₂) _n ⁺ (n+2...7) clusters in collisions with Ar atoms is presented. Interesting structure can be observed in the cross sections which indicate that the collision occurs between the Ar atom and one CO₂ molecule within the cluster. The results may be explained by assuming that the collision leads to either vibrational excitation of a loosely bound CO₂ monomer which then leaves the cluster or excitation of the entire cluster to a dissociative state.     

Binding N2, N2H2, N2H4, and NH3 to transition-metal sulfur sites: modeling potential intermediates of biological N2 fixation

In the quest for low-molecular-weight metal sulfur complexes that bind nitrogenase-relevant small molecules and can serve as model complexes for nitrogenase, compounds with the [Ru(PiPr(3))('N(2)Me(2)S(2)')] fragment were found ('N(2)Me(2)S(2)'(2-)=1,2-ethanediamine-N,N'-dimethyl-N,N'-bis(2-benzenethiolate)(2-)). This fragment enabled the synthesis of a first series of chiral metal sulfur complexes, [Ru(L)(PiPr(3))('N(2)Me(2)S(2)')] with L=N(2), N(2)H(2), N(2)H(4), and NH(3), that meet the biological constraint of forming under mild conditions. The reaction of [Ru(NCCH(3))(PiPr(3))('N(2)Me(2)S(2)')] (1) with NH(3) gave the ammonia complex [Ru(NH(3))(PiPr(3))('N(2)Me(2)S(2)')] (4), which readily exchanged NH(3) for N(2) to yield the mononuclear dinitrogen complex [Ru(N(2))(PiPr(3))('N(2)Me(2)S(2)')] (2) in almost quantitative yield. Complex 2, obtained by this new efficient synthesis, was the starting material for the synthesis of dinuclear (R,R)- and (S,S)-[micro-N(2)[Ru(PiPr(3))('N(2)Me(2)S(2)')](2)] ((R,R)-/(S,S)-3). (Both 2 and 3 have been reported previously.) The as-yet inexplicable behavior of complex 3 to form also the R,S isomer in solution has been revealed by DFT calculations and (2)D NMR spectroscopy studies. The reaction of 1 or 2 with anhydrous hydrazine yielded the hydrazine complex [Ru(N(2)H(4))(PiPr(3))('N(2)Me(2)S(2)')] (6), which is a highly reactive intermediate. Disproportionation of 6 resulted in the formation of mononuclear diazene complexes, the ammonia complex 4, and finally the dinuclear diazene complex [micro-N(2)H(2)[Ru(PiPr(3))('N(2)Me(2)S(2)')](2)] (5). Dinuclear complex 5 could also be obtained directly in an independent synthesis from 1 and N(2)H(2), which was generated in situ by acidolysis of K(2)N(2)(CO(2))(2). Treatment of 6 with CH(2)Cl(2), however, formed a chloromethylated diazene species [[Ru(PiPr(3))('N(2)Me(2)S(2)')]-micro-N(2)H(2)[Ru(Cl)('N(2)Me(2)S(2)CH(2)Cl')]] (9) ('N(2)Me(2)S(2)CH(2)Cl'(2-) =1,2-ethanediamine-N,N'-dimethyl-N-(2-benzenethiolate)(1-)-N'-(2-benzenechloromethylthioether)(1-)]. The molecular structures of 4, 5, and 9 were determined by X-ray crystal structure analysis, and the labile N(2)H(4) complex 6 was characterized by NMR spectroscopy.     

The reduction of methylene blue by sulfide ion in the absence and presence of oxygen: Simulation of the methylene blue-O2?HS?-CSTR oscillations

A mechanism is discussed which reproduces in simulations the oscillations during the methylene-blue catalyzed reduction of O₂ by HS^– in a continuous-flow, strirred tank reactor (CSTR). It contains 14 reactions and is based on experiments and simulations of simpler reactions including the reduction of MB⁺ by HS^– in the absence and presence of O₂ and the reactions of H₂O₂ and O₂ with HS^–. All experiments on component reactions as well as the CSTR oscillations can be simulated by the same set of reactions and rate constants. The major dynamic feature of the mechanism is the competition for MB^. by the oxidizing agents O₂ and H₂O₂ and the reducing agents HS^– and HS^.. The species MB^. is the radical intermediate between the colored (MB⁺) and colorless (MBH) forms of methylene blue.     

111In(111Cd) quadrupole interaction in the chalcogenide spinel CdCr2Se4

The¹¹¹Cd quadrupole coupling in the spinel CdCr₂Se₄ is investigated by TDPAC after different sample treatments. The experiments are consistent with Se vacancies causing the non-cubic probe environments and with the assumption that the majority of the¹¹¹In atoms are positioned at A-sites.     

Flow sorption calorimetry, a powerful tool to investigate the acid-base character of organic polymer surfaces

Flow sorption calorimetry (FSC) can be a useful tool to estimate the Lewis acid-base behaviour of the surface of organic polymers with less than 1 m²/g surface area. Polyethylene powders grafted with different amounts of acrylic acid have been chosen as samples. The surface of the powders was investigated by means of X-ray photoelectron spectroscopy (XPS) at first and than brought into contact with the strong electron donor triethylamine in a special FSC measuring system. The heat of the displacement isotherm together with the surface excess isotherm of triethylamine adsorbed onto the powders was determined. The results obtained with FSC and XPS were well correlated and gave a comprehensive picture of the acidic surface character of modified polyethylene. Received: 19 September 1996 / Revised: 22 January 1997 / Accepted: 26 January 1997     

The solubility of an hydroxyaluminosilicate

Hydroxyaluminosilicates (HAS) are critical secondary mineral phases in the biogeochemical cycle of aluminium. They are formed from the reaction of silicic acid (Si(OH)₄) with an aluminium hydroxide template and act as a geochemical control of the biological availability of Al. There are two main forms of HAS which we have called HAS_A and HAS_B and which of these will predominate will depend upon the Si(OH)₄ to Al ratio in any one environment. In all but the most heavily weathered environments or those undergoing a progressive acidification Si(OH)₄ will be present in significant excess to Al and HAS_B will be the dominant secondary mineral phase. We have tried to determine the solubility of HAS_B(s) so that its contribution to Al solubility control might be compared with other secondary minerals such as Al(OH)_3(gibbsite). In preliminary experiments, the dissolution of HAS_B(s) was found to be non-congruent with almost no Al being released during 18 months ageing. We then demonstrated that HAS_B(s) was significantly less soluble than Al(OH)_3(s) prepared under identical experimental conditions. We have used this information to describe a solubility expression for HAS_B(s) at a predefined quasi-equibrium and to calculate a solubility constant.

K^*Al₂Si₂O₅(OH)₄=[Al₂O⁴⁺][SiO₂]²[OH^-]⁴