Pattern formation in diffusion-limited reactions

The conditions for macroscopic segregation ofA andB in a steady-stateA+B 0 reaction are studied in infinite systems. Segregation occurs in one and two dimensions and is marginal ford=3. We note the dependence of these results on the precise experimental conditions assumed in the theory. We also note the difference between these results and our earlier ones for finite systems where the critical dimension isd=2.     

Analogy between the Lorenz strange attractor and a bistable stochastic oscillator

The relation between the aperiodic solution of the Lorenz model and that of a stochastic anharmonic oscillator is explored. The stochastic oscillator is constructed by replacing (t) in the Lorenz model by a stochastic variable(t) of specified statistics. The resulting system is of course not isomorphic to the Lorenz model, but does share with it a number of statistical properties. Thus, within the confines of these measures the two systems are physically very similar.     

Statistical replacement for systems with delta-correlated fluctuations

Nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement. This method is an extension of the previously developed AGREE which was restricted to systems with additive fluctuations. Statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable.     

HPLC isolation and NMR structure elucidation of the most prominent octabromo isomer in technical octabromo diphenyl ether

The major octabromo isomer of technical octabromo diphenyl ether mixture (technical octaBDE) DE-79 was isolated by RP-HPLC. Three serially coupled columns (each 250 mm long) enabled a good separation of the target compound from other congeners using 100% ACN as eluent. Approximately 100 microg of the target compound was isolated with a purity of >90% and investigated by MS for confirmation of the degree of bromination. 1H-NMR and 2-D 1H-13C correlation NMR spectra unequivocally clarified that the octaBDE in question is 2,2',3,3',4,4',6,6'-octabromodiphenyl ether (BDE 197). Based on annual production rates of technical BDE products (1999/2001), approximately 380 tons of BDE 197 were annually produced which, on the long term, may enter the environment. Compared with other individual BDE congeners, BDE 197 has the seventh highest application rate. Reductive debromination of BDE 197 can lead to four hepta-, 15 hexa-, 23 penta-, and 28 tetra-BDE isomers, respectively. This variety includes all known major BDEs of environmental concern (BDE 47, 85, 99, 100, 153, 154, and 183). The identification of BDE 197 in technical octaBDE DE-79 strongly suggests that research on the environmental fate of BDEs should include this key-BDE congener.     

Biosynthesis of cis-Jasmone: a pathway for the inactivation and the disposal of the plant stress hormone jasmonic acid to the gas phase?

Flowers of Jasminum rincospernum convert deuterium-labeled jasmonic acid [²H₅]- 4a and methyl 1,2-didehy-drojasmonate [²H₄]- 8 into labeled cis-jasmone [²H₄]- 1. The labeling pattern of the resulting cis-jasmone ( 1 ) is consistent with a Grob fragmentation of the didehydrojasmonic acid 8a by decarboxylation after protonation of the keto group. The pathway is also operative in leaves of several higher plants, including mono- and dicotyledonous specimens. In Lima beans besides cis-jasmone ( 1 ) an equimolar mixture of trans- and cis-isomers of methyl jasmonate ( 4 ) and epi- 4 , is emitted after treatment with Jasmonic acid ( 4a ). The relative ratio of 1 and 4 /epi- 4 is critically dependent on the concentration of the administered jasmonic acid ( 4a ) and the ambient temperature of the plant. Unlike 4a , the 1,2-didehydrojasmonic acid ( 8a ) is not able to induce volatile biosynthesis. Therefore, the transformation of 4a via 8 a into 1 appears to have a special importance for the irreversible inactivation and disposal of the plant stress hormone jasmonic acid to the gas phase and may serve, besides other modes of inactivation, as a shunt in case of high internal of the stress hormone 4a. The conversion of the biologically active jasmonic acid ( 4a ) into the inactive and volatile cis-jasmone (1) is the first example of a disposal of an inactive metabolite of a phytohormone to the gas phase as an infinite sink.     

Proton magnetic shielding and susceptibility effects in single crystals of ferrocene

The proton NMR in single crystals of ferrocene has been studied by multiple pulse techniques at room temperature. In crystals of natural shape with plane faces the angular dependence of the resonance frequency due to the anisotropy of the shielding and due to the bulk susceptibility was found to be of about equal size, making analysis of the data practically impossible. By using a single crystal sphere the shape dependent part of the susceptibility contribution could be eliminated. In addition, the resolution obtained by the multiple pulse technique is considerably higher for spheres than for non-spherical crystals. As the ferrocene molecules rotate rapidly about their fivefold axes at room temperature, the shielding tensor σ must be axially symmetric. Having this in mind, the data could be analyzed to yield both the shielding tensor with Δσ = σ₆ - σ_⊥ = ?6.5 ± 0.1 ppm, σ_iso = ?4.2 ± 0.5 ppm from a spherical sample of TMS and the anisotropy of the susceptibility Δ _x = 30 × 10^?6 cgs units.     

Nature et stabilité des complexes métalliques de cryptands dinucléants en solution II. Polythiamacrotricycles et monocycles apparentés

Nature and Stability of Some Metallic Complexes of Dinucleating Cryptands in Solution II. Polythiamacrotricycles and Related Monocyclic Subunits The stability constants of the Cu²⁺ and Ag⁺ complexes of the cylindrical macrotricycle 1a (1,7,13,19-tetraaza 4,16-dioxa 10,22,27,32-tetrathiatricyclo[17.5.5.5]tetratriacontane) have been determined by pH-metry, as well as those of the Cu²⁺, Co²⁺, Zn²⁺, Cd²⁺, Pb²⁺, and Ag⁺ complexes of the monocyclic subunit 2a (1,7-dimethyl-1,7-diaza 4,10-dithiacyclododecane), in aqueous solutions (NaClO₄) at 25°. In the Cu(II) systems, equilibria were reached slowly, and the results established by pH-metry were confirmed by UV/VIS spectrophotometric studies. The tricycle 1a forms dinuclear cryptates with copper and silver, with overall stability constants log β₂₁₀ (Cu₂- 1a )⁴⁺ = 18.5, log β_21-2 (Cu₂- 1a (OH)₂)²⁺ = 4.8, log β₂₁₀(Ag₂- 1a )²⁺ = 23.0. Ag⁺ also forms a mononuclear (Ag- 1a )⁺ complex, with log β₁₁₀ = 13.1, but no mononuclear species were detected in the Cu- 1a system. The absorption spectra of the bis-Cu(II) complexes of 1a and 2a in aqueous medium, MeOH and propylene carbonate (PC) are given, as well as those, in MeOH and PC, of the bis-copper complexes of the related monocycles 3 and 4 (1,7-diaza-4,10,13-trithiacyclopentadecane and 1.10-diaza 4,7,13,16-tetrathiacyclooctadecane, respectively), and tricycle 5 with two benzyl groups in the lateral chains. The complexing properties of the polyoxa- and polythia macrotricycles (Parts I and II of this series) are compared to those of other bis-chelating ligands, the bicyclic bis-tren and the monocyclic bis-dien.     

Synthesis of a deca-lithium cage containing an [(RN)2As(mu-NR)As(NR)2]4- tetraanion; a homologue of group 15 trianions of the type [E(NR)3]3-

The novel, deca-lithium cage [(mtaNHLi)(As2(Nmta)5)-Li(4).2thf]2 (1) (mtaN = 5-methylthiazolyl, C4H4N2S) contains an imido-bridged tetraanion [(mtaN)2As(mu-Nmta)-As(Nmta)2]4-, which represents a new type of multi-functional imido group 15 ligand framework (homologous with group 15 anions of the type [As(NR)3]3-).     

Measurement of diffusion coefficients of additive molecules in colloidal polymer particles by electron paramagnetic resonance

Nonpolar paramagnetic additives mixed into the aqueous serum of colloidal polymer dispersions are absorbed by the polymer particles with a rate that depends on the diffusion coefficient of the additive in the polymer. The absorption leads to an immobilization of the additive which can be detected in the electron paramagnetic resonance spectrum. By fitting the time dependence of the immobilized fraction to the appropriate diffusion model, it is possible to determine the diffusion coefficient of the additive in the polymer if the polymer particles are approximately uniform in size. This opens up a new way to determine diffusion coefficients in the range between 10^-14 and 10^-17 cm²s^-1, as are expected for low-molecular-weight additives in polymers below their glass-transition temperature.     

Synthesis of a new class of chiral 1,5-diphosphanylferrocene ligands and their use in enantioselective hydrogenation

A new family of ferrocenylphosphane ligands has been prepared. Their flexible synthesis allows many structural modifications. The asymmetric induction of these ligands was examined in the hydrogenation of functionalized C=C, C=O, and C=N bonds. The enantioselectivity of the reaction was strongly dependent on the substituent R at the position alpha to the ferrocene moiety. In many cases, both enantiomeric beta-hydroxyesters of the reduction product can be obtained by simply replacing a dimethylamino group in the ligand with a methyl group.