Influence of Process Parameters on the Reaction Kinetics of the Chromium‐Catalyzed Trimerization of Ethylene

In this paper we report the results of an extensive experimental kinetic study carried out on the novel ethylene trimerization catalyst system, comprising the chromium source [CrCl₃(thf)₃] (thf=tetrahydrofuran), a Ph₂P‐N(iPr)‐P(Ph)‐N(iPr)H (PNPNH) ligand (Ph=phenyl, iPr=isopropyl), and triethylaluminum (AlEt₃) as activator. It could be shown that the initial activity shows a first‐order dependency on the ethylene concentration. Also, a first‐order dependency was found for the catalyst concentration. The initial activity follows a typical Arrhenius behavior with an experimentally determined activation energy of 52.6 kJ mol^?1. At elevated temperatures (ca. 80 °C), a significant deactivation was observed, which can be tentatively traced back to a ligand rearrangement in the presence of AlEt₃. After a fast initial phase, a pronounced ‘kink’ in the ethylene‐uptake curve is observed, followed by a slow, almost linear, further increase of the total ethylene consumption. The catalyst composition, in particular the ligand/chromium and the cocatalyst/chromium molar ratio, has a strong impact on the catalytic performance of the trimerization of ethylene.     

"Compression-only" behavior: a second-order nonlinear response of ultrasound contrast agent microbubbles

Oscillating phospholipid-coated ultrasound contrast agent microbubbles display a so-called "compression-only" behavior, where it is observed that the bubbles compress efficiently while their expansion is suppressed. Here, a theoretical understanding of the source of this nonlinear behavior is provided through a weakly nonlinear analysis of the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the radial dynamics of the bubble can be considered as a superposition of a linear response at the fundamental driving frequency and a second-order nonlinear low-frequency response that describes the negative offset of the mean bubble radius. The analytical solution deduced from the weakly nonlinear analysis shows that the compression-only behavior results from a rapid change of the shell elasticity with bubble radius. In addition, the radial dynamics of single phospholipid-coated microbubbles was recorded as a function of both the amplitude and the frequency of the driving pressure pulse. The comparison between the experimental data and the theory shows that the magnitude of compression-only behavior is mainly determined by the initial phospholipids concentration on the bubble surface, which slightly varies from bubble to bubble.     

Knudsen gas provides nanobubble stability

We provide a model for the remarkable stability of surface nanobubbles to bulk dissolution. The key to the solution is that the gas in a nanobubble is of Knudsen type. This leads to the generation of a bulk liquid flow which effectively forces the diffusive gas to remain local. Our model predicts the presence of a vertical water jet immediately above a nanobubble, with an estimated speed of ～3.3 m/s, in good agreement with our experimental atomic force microscopy measurement of ～2.7 m/s. In addition, our model also predicts an upper bound for the size of nanobubbles, which is consistent with the available experimental data.     

Tailoring of high-Q-factor surface plasmon modes on silver microtubes

We investigate the excitation of surface plasmon polaritons on silver tubes with finite-difference time-domain simulations. These surface plasmon polaritons exhibit azimuthal whispering gallery modes with quality factors in the hundreds. We show that the high quality factors arise from the coupling of the surface plasmon modes to photonic modes inside the tube. We examine the influence of a gain material on the quality factors and find that for material data of rhodamine 6G, the quality factors are enhanced significantly up to values of 3000.     

Solid-state photodimerization of 4-aryl-1,4-dihydropyridines studied by C CPMAS NMR spectroscopy

¹³C CPMAS NMR spectroscopy has been applied to monitor the solid-state reaction of two different photodimerizing 4-phenyl-1,4-dihydropyridines yielding a cage dimer in one case and an anti-dimer in the other case. The spectra of the reacting monomers exhibit a magnetical inequivalence of chemically equivalent CO and C2/4 carbon atoms caused by a rotation of the pseudoaxially oriented 4-phenyl substituent out off the plane through N1, C3, C8 which could be determined by X-ray crystal structure analyses of the centrosymmetrically arranged monomers. The ¹³C CPMAS NMR monitoring of the cage dimer formation proves that the reaction takes place in two steps via a syn-dimer for which a non-symmetrical structure was derived from the spectrum. The non-symmetrical structure was confirmed by X-ray crystal structure analysis of one structurally related derivative. A centrosymmetric structure for both the finally formed cage dimer and the anti-dimer of the other monitored photoreaction was proved by their spectra with one set of signals for each half of the dimers, respectively. Thus, conformational properties of the molecules as well as the symmetry of the products can be directly derived from the ¹³C CPMAS NMR spectra.     

Phenomenological studies on structure and elemental composition of nanosecond and femtosecond laser-generated aerosols with implications on laser ablation inductively coupled plasma mass spectrometry

In laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS), the properties of laser-generated aerosols, such as size and composition, are crucial for matrix-independent quantification. In this study, the aerosol particle morphology and elemental composition generated by two state-of-the-art laser systems (ArF excimer nanosecond-UV laser and Ti:sapphire femtosecond-IR laser) were investigated by electron microscopic techniques. Electrostatic sampling of the aerosols directly onto transmission electron microscopy (TEM) grids allowed us to study the morphology and elemental composition of the aerosols using TEM and TEM–EDX (energy dispersive X-ray spectroscopy) analyses, respectively. The results of the electron microscopic studies were finally compared to the LA-ICPMS signals of the main matrix components. The investigations were carried out for non-conducting materials (glass and zircon), metallic samples (steel and brass) and semiconductors (sulfides). The studies confirm that ns-LA-generated aerosols dominantly consist of nanoparticle agglomerates while conducting samples additionally contain larger spherical particles (diameter typically 50 to 500 nm). In contrast to ns-laser ablation, fs-LA-generated aerosols consist of a mixture of spherical particles and nanoparticle agglomerates for all investigated samples. Surprisingly, the differences in elemental composition between nanoparticle agglomerates and spherical particles produced with fs-LA were much more pronounced than in the case of ns-LA, especially for zircon (Si/Zr fractionation) and brass (Cu/Zn fractionation). These observations indicate different ablation and particle formation mechanisms for ns- and fs-LA. The particle growth mechanism for ns-LA is most likely a gas-to-particle conversion followed by agglomeration and additional hydrodynamic sputtering for conducting samples. On the other hand, phase explosion is assumed to be responsible for the mixture of large spherical particles and nanoparticle agglomerates as found for fs-LA-generated aerosols. Based on these mechanisms, the overall temporal elemental fractionation effects in ns-LA-ICPMS seem to occur mainly during the ablation. This effect was not observed for fs-LA-ICPMS despite the element separation into different particle fractions, which, on the other hand, could induce severe ICP-induced fractionation.     

Asymptotische LÖsungen Der Translationsgleichung

For the solutions of the translation equation special asymptotic developments are considered. It is shown that the coefficients of such developments can be determined by linear recursion formulas or by Lie-series. Examples illustrate these results.