Computer Simulation of the Kinetics of Complicated Gas Phase Reactions

Modern digital methods and powerful computers make it possible to simulate the time behavior of chemical reactions. These calculations can be performed on systems containing an almost unlimited number of elementary reactions. Generally, however, the reaction models used should contain only those elementary reactions which describe the bulk of the conversion. Such a reaction model may be obtained by reduction of the complete set of elementary reactions. Another possibility is analysis of the chemical system starting from conditions ensuring a simple chemistry, which is generally the case at low temperatures and low conversions. The reaction model may then be extended into the range of the reaction variables (temperature, time) of interest. Mathematical simulations may be helpful during the development of the reaction model, and sometimes even decisive. These methods were applied to the pyrolysis of ethylbenzene and n-hexane, and to CO oxidation. They yield information on the reaction paths, the importance of particular elementary reactions, and reaction stability. Furthermore, quantitative data can be obtained concerning the influence of single elementary reactions on the product distribution. The sensitivity matrix shows, e.g., whether the determination of kinetic parameters of an elementary reaction from kinetic data of the overall reaction is possible in principle, and how high the accuracy of the rate constants should be for simulation of the reaction. Both results are important for modeling chemical reactions.     

Determination of halogen species of humic substances using HPLC/ICP-MS coupling

A mass spectrometric method for the determination of chlorine, bromine and iodine species of humic substances (HS) has been developed by coupling a HPLC system with ICP-MS. Using size exclusion chromatography, the method was applied to the characterization of natural water samples (ground water, seepage water from soil, brown water) and a sewage water sample. Quantification of iodine/HS species was carried out by the on-line isotope dilution technique, which was not possible for bromine and chlorine species because of mass spectroscopic interferences by using a quadrupole ICP-MS. Characteristic fingerprints of the halogen/HS species, correlated with the corresponding UV chromatogram, were obtained dependent on the different origin of HS. Biological influences were indicated when following changes of the iodine/HS species composition by aging. The formation of iodine/HS species from inorganic iodide was investigated by labelling experiments with an ¹²⁹I^– spike solution, resulting in the finding that specific HS fractions are preferably iodinated.     

Electron energy loss spectroscopy of liquid glycerol

The inelastic scattering of low energy electrons from liquid glycerol has been studied. For the first time, electron energy loss spectra of liquids are sufficiently well resolved to permit the identification of vibrations corresponding to individual bonds, namely the C–H and O–H stretching vibrations in glycerol. The angular distribution of the specular peak is very broad, indicating the absence of long-range order at the surface of the liquid. The measurement of the loss signals as a function of the primary electron energy suggests a hybrid mechanism of excitation. The excitation mechanism for the O–H vibration has a stronger impact character as compared to the C–H vibration. A negative ion resonance of glycerol is found at a primary energy of 8 eV. The signal intensities measured as a function of the specular angle of the electron beam appear to be influenced by the angular dependence of the dipole and impact scattering cross-section and a possible preferred orientation of the C–H and O–H groups at the surface of the liquid.     

Heterogeneous polymer systems. IV. Mechanism of rubber particle formation in rubber-modified vinyl polymers

A mechanism for the formation of rubber particles in the polymerization of solutions of rubber in vinyl monomers is presented. A polymeric oil-in-oil emulsion is formed in the first phase of the polymerization. This polymeric oil-in-oil emulsion is transtormed into a solid dispersion of rubber in vinyl polymer in the second phase of the polymerization. A phase inversion takes place in the emulsion in the first phase of the polymerization. Rubber solution droplets are formed at the phase inversion point. These droplets harden as the polymerization proceeds and are gradually transformed into the solid, crosslinked rubber particles of the final polymer.     

Synthesis of enantiomerically enriched atrolactic acid and other α-hydroxy acids

The α-anions of 2-substituted 1,3-dioxolan-4-ones derived from chiral mandelic and lactic acid ($\text{2a}$, $\text{2b}$; $\text{3a}$; $\text{10a}$, $\text{10b}$) were alkylated with high stereoselectivity. The products formed were hydrolysed to α-hydroxy acids with 65–85% e.e. ((S)(+)-$\text{5}$,$\text{7}$,$\text{9}$, (R)(–)-$\text{13}$).     

Carboxylate and alkyl carbonate coordination at the hydrophobic binding site of redox-active dicobalt amine thiophenolate complexes

A series of new dicobalt complexes of the permethylated macrocyclic hexaamine dithiophenolate ligand H(2)L(Me) have been prepared and investigated in the context of ligand binding and oxidation state changes. The octadentate ligand is an effective dinucleating ligand that supports the formation of bioctahedral complexes with a central N(3)Co(mu-SR)(2)(mu-X)CoN(3) core structure, leaving a free bridging position X for the coordination of the substrates. The acetato- and cinnamato-bridged complexes [(L(Me))Co(II)(2)(mu-O(2)CMe)](+) (2) and [(L(Me))Co(II)(2)(mu-O(2)CCH=CHPh)](+) (5) were prepared by reaction of the mu-Cl complex [(L(Me))Co(II)(2)(mu-Cl)](+) (1) with the corresponding sodium carboxylates in methanol. The electrochemical properties of these and of the methyl carbonate complex [(L(Me))Co(II)(2)(mu-O(2)COMe)](+) (8) were also investigated. All complexes undergo two stepwise oxidations at ca. E(1)(1/2) = +0.22 and at E(2)(1/2) = ca. +0.60 V vs SCE, affording the mixed-valent complexes [(L(Me))Co(II)Co(III)(mu-O(2)CR)](2+) (3, 6, 9) and the fully oxidized Co(III)Co(III) forms [(L(Me))Co(III)(2)(mu-O(2)CR)](3+) (4, 7, 10), respectively. Compounds 3, 6, 9 and 4, 7, 10 refer to acetato-, cinnamato-, and methylcarbonato species, respectively. The Co(II)Co(III) compounds were prepared by comproportionation of the respective Co(II)(2) and Co(III)(2) compounds. The Co(III)Co(III) species were prepared by bromine oxidation of the Co(II)Co(II) forms. The crystal structures of complexes 2.BPh(4).MeCN, 3.(I(3))(2), 5.BPh(4).2MeCN, 6.(ClO(4))(2).EtOH, 7.(ClO(4))(3).MeCN.(H(2)O)(3), and 9.(ClO(4))(2).(MeOH)(2).H(2)O were determined by single-crystal X-ray crystallography at 210 K. The oxidations occur without gross structural changes of the parent complexes. The Co(II)Co(III) complexes are composed of high-spin Co(II) (d(7)) and low-spin Co(III) (d(6)) ions. The Co(III)Co(III) complexes are diamagnetic. The oxidation reactions affect the binding mode of the substrates. In the Co(II)(2) and Co(II)Co(III) forms the carboxylates bridge the two Co(2+) ions in a symmetric mu-1,3 fashion with uniform C-O bond distances, whereas asymmetric bridging modes, with one short C=O and one long C-O distance, are adopted in the fully oxidized species. This is consistent with the observed shifts in vibrational frequencies for nu(as)(C-O) and nu(s)(C-O) across the series.     

Global uniqueness for an inverse boundary problem arising in elasticity

Summary We prove that we can determine the Lamé parameters of an elastic, isotropic, inhomogeneous medium in dimensionsn3, by making measurements of the displacements and corresponding stresses at the boundary of the medium.Oblatum 14-VI-1993 & 22-XII-1993Partially supported by NSF Grant DMS-9100178 and ONR grant N 0014-93-1-0295