Theoretical treatment of first-order reversible reactions occurring in a chromatographic reactor, on the basis of consecutive reactions

Summary Analytical peak-shape equations were derived for first-order reversible reactions occurring in a chromatographic reactor by treating the reversible reactions as consecutive reactions with alternating products. The results of the analytical peak-shape equations were compared with those from a numerical solution of the partial differential equation system modeling the chromatographic reactor. For small to medium conversions the correspondence was found to be sufficiently close to enable substitution of the numerical solution in fitting procedures for the determination of rate constants. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Spectroscopic and laser properties of Er3+-doped monoclinic BaY2F8 single crystals

The luminescence and absorption properties of Ba(Y_1−x Er _x )₂F₈ (x=0.001, 0.01, 0.05, 0.1, 0.2 and 0.3) and the Er³⁺-ion decay kinetics of luminescent transitions from three initial laser states, the⁴S_3/2,⁴F._9/2 and⁴I_11/2 manifolds, were measured. The crystal-field splitting schemes for allJ-manifolds which are involved in (J →J′)-luminescence transitions and stimulated emission parameters of Er³⁺ -ions in BaY₂F₈ were determined. A comparison of laser powers and efficiencies of BaY₂F₈ and Y₃Al₅O₁₂, Lu₃Al₅O₁₂ and LiYF₄ single crystals doped with Er³⁺-ions shows the similar performance of these materials.

     

Synthesis of 2‐Unsubstituted 1,3‐Selenazoles by Cyclization of Selenoformamide with α‐Bromocarbonyl Compounds

2‐Unsubstituted 1,3‐selenazoles were prepared by cyclization of selenoformamide with α‐bromoacetophenones. Parent 1,3‐selenazole was prepared by cyclization of selenoformamide with α‐bromoacetaldehyde.     

Determination of rate constants in a liquid chromatographic reactor by means of a fitting algorithm

Based on the exponentially modified Gaussian profile, a new equation for the evaluation of product peaks of liquid chromatographic first- order reaction chromatograms is given. It is shown that this equation is able to fit reaction chromatograms corresponding to the linear model of chromatography.     

Hydrogen Peroxide Production of Individual Nanosecond Pulsed Discharges Submerged in Water of Elevated Conductivity

The production of hydrogen peroxide (H₂O₂) is a key parameter for the performance of pulsed discharges submerged in water utilized as advanced oxidation process. So far, any related assessment of the underlying mechanism was conducted for the application of several hundred discharges, which did not allow for a correlation with physical processes. Moreover, the production was rarely investigated depending on water conductivity as one of the most important parameters for the development of submerged discharges. Accordingly, hydrogen peroxide generation was investigated here for individual single discharge events instigated with 100 ns high-voltage pulses in water with three different conductivities and was associated with the discharge development, i. e. spatial expansion and dissipated electrical energy. The approach necessitated the improvement of an electrochemical flow injection analysis based on the reaction of Prussian blue with H₂O₂. Hydrogen peroxide concentrations were quadratically increasing with propagation time and stable for different water conductivities. H₂O₂ production per unit volume of a discharge was constant over time with an estimated rate constant of 3.2 mol ⋅ m⁻¹ s⁻¹, averaged over the crosssectional area of all discharge filaments. However, the individually dissipated energy increased with conductivity, hence, the production efficiency decreased from 6.1 g ⋅ kWh⁻¹ to 1.4 g ⋅ kWh⁻¹, which was explained by increased resistive losses within the bulk liquid.     

[η<Superscript>5</Superscript>-C<Subscript>9</Subscript>H<Subscript>5</Subscript>(1,3-SiMe<Subscript>3</Subscript>)<Subscript>2</Subscript>]HfCl<Subscript>3</Subscript>: A monomeric 12-electron half-sandwich complex

The half-sandwich hafnium complex [gh⁵-C₉H₅(1,3-SiMe₃)₂]HfCl₃ (II) has been synthesized for the first time. The molecular structures of II and its synthetic precursor C₉H₅(1,1,3-SiMe₃)₃ (I) have been determined by X-ray crystallography. Compound II in the crystalline state, is a rare example of a monomeric 12-electron half-sandwich complex.     

Dynamical interface transition in ramified media with diffusion

We consider interaction problems in ramified spaces of a rather general type with a distinguished interface transition in form of a dynamical Kirchhoff condition. These conditions stem from applications and modeling in biology and physics, see for instance [8,21]. In the present paper our principal concern is to derive existence results in the linear and semilinear case and some qualitative principles similar to the classical ones for initial boundary value problems on domains. Moreover, the influence of the dynamical interface condition on the solution is studied in the autonomous reaction-diffusin case.     

Harmonic functions on locally finite networks

Are there nonconstant bounded harmonic functions on an infinite locally finite network under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices? We present sufficient criteria for such a network to be a Liouville space, while we show that a large class of infinite trees admit infinitely many linearly independent bounded harmonic functions. Finally, we show that the standard unit cube grid graphs and some of Kepler’s plane tiling graphs are Liouville spaces.     

The eigenvalues of the Laplacian on locally finite networks

We consider the continuous Laplacian on an infinite locally finite network with equal edge lengths under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices. It is shown that eigenvalues of the Laplacian in a L^∞-setting are closely related to those of the adjacency and transition operator of the network. In this way the point spectrum is determined completely in terms of combinatorial quantities and properties of the underlying graph as in the finite case [2]. Moreover, the occurrence of infinite geometric multiplicity on trees and some periodic graphs is investigated.