Alkyl-substituted cyclopentadienyl- and phospholyl-zirconium/MAO catalysts for propene and 1-hexene oligomerization

The directed oligomerization of propene and 1-hexene was carried out with a series of Cp′(C₅H₅)ZrCl₂ and Cp₂′ZrCl₂ pre-catalysts (Cp′=C₅HMe₄, C₄Me₄P, C₅Me₅, C₅H₄^tBu, C₅H₃-1,3-^tBu₂, C₅H₂-1,2,4-^tBu₃) together with (C₅H₅)₂ZrCl₂. Oligomers in the molar mass range 300–1500 g/mol for propene and 200–3000 g/mol for 1-hexene were synthesized at 50 °C. The majority of oligomer molecules contain a double-bond end group. Oligomer characterization was carried out by gel permeation chromatography (GPC), ¹H and ¹³C NMR. Vinylidene double bonds (from β-hydrogen elimination) are solely found for the tert-butyl-substituted zirconocenes and for most of the unsymmetrical methyl-substituted Cp′(C₅H₅)ZrCl₂ systems (except Cp′=phospholyl). With (C₄Me₄P)(C₅H₅)ZrCl₂ and with the symmetrical methyl-containing Cp₂′ZrCl₂ pre-catalysts, also vinyl end groups (from β-methyl elimination) are observed in the case of oligopropenes. The vinylidene/vinyl ratio depends on the ligand and the vinyl content increases from C₅HMe₄ (65/35) over C₄Me₄P (61/39) to C₅Me₅ (9/91). The phospholyl zirconocenes and (C₅HMe₄)₂ZrCl₂ also exhibit chain-transfer to aluminum thereby giving saturated oligomers.     

Spectroscopic Studies on the Thermodynamics of the Complexation of Trivalent Curium with Propionate in the Temperature Range from 20 to 90 °C

The thermodynamics of the stepwise complexation reaction of Cm(III) with propionate was studied by time resolved laser fluorescence spectroscopy (TRLFS) and UV/Vis absorption spectroscopy as a function of the ligand concentration, the ionic strength and temperature (20–90 °C). The molar fractions of the 1:1 and 1:2 complexes were quantified by peak deconvolution of the emission spectra at each temperature, yielding the log₁₀ $ K_{n}^{\prime } $ values. Using the specific ion interaction theory (SIT), the thermodynamic stability constants log₁₀ $ K_{n}^{0} (T) $ were determined. The log₁₀ $ K_{n}^{0} (T) $ values show a distinct increase by 0.15 (n = 1) and 1.0 (n = 2) orders of magnitude in the studied temperature range, respectively. The temperature dependency of the log₁₀ $ K_{n}^{0} (T) $ values is well described by the integrated van’t Hoff equation, assuming a constant enthalpy of reaction and $ \Updelta_{\text{r}} C^\circ_{{p,{\text{m}}}} = 0, $ yielding the thermodynamic standard state $ \left( {\Updelta_{\text{r}} H^\circ_{\text{m}} ,\Updelta_{\text{r}} S^\circ_{\text{m}} ,\Updelta_{\text{r}} G^\circ_{\text{m}} } \right) $ values for the formation of the $ {\text{Cm(Prop)}}_{n}^{3 - n} $ , n = (1, 2) species.     

Laser-induced enhancement of tunneling in NHD2

We apply and explore techniques aiming at enhancing the tunneling by laser fields, originally developed for a one-dimensional model, to a complete six-dimensional vibrational model of the inversion motion in NHD(2). The computational study is performed with the multi-configuration time-dependent Hartree method. Assuming an ideal three-dimensional alignment we obtain a driven tunneling time twenty times smaller than the natural one, in rather good agreement with an oversimplified three-state model. In the case of one-dimensional alignment, a linearly polarized field leads to a poor enhancement of the tunneling probability, after averaging over the rotation about the alignment axis, whereas a circularly polarized field improves the rotationally averaged tunneling probability at the end of the pulse.     

A formula for the contribution of a resonance to the canonical partition function

An explicit expression for the Laplace transform of a Lorentzian function is applied to evaluate the contribution to the canonical partition function of ideal-gas molecules stemming from resonances. This formula can be used instead of numerical integration. A discussion of potential errors in replacing this contribution by the conventional formula for the Boltzmann weight is given. When generalised to the complex plane, the known expression is shown to be discontinuous and a new formulation is proposed that removes the discontinuity. As a result, an explicit expression is obtained for the Fourier transform of a Lorentzian function that is truncated at a lower energy bound.     

The absorption spectra of anisole-h8, anisole-d3 and anisole-d8. The assignment of fundamental vibrations in the S0 and the S1 states

The REMPI spectra of anisole-h8, anisole-d3 and anisole-d8 have been measured. The assignment of the fundamental vibrations of anisole in the S(1) state is supported by quantum chemical model calculations, the isotopic shifts, the comparison with the frequencies of corresponding vibrations in other monosubstituted benzenes, especially phenol, and the overtones, combinations and progressions observed in the spectrum of anisole-h8. The frequencies of the 42 fundamental vibrations of anisole in the S(1) state are evaluated and compared with the frequencies of the corresponding vibrations in the electronic ground state. Some assignments given earlier in the literature have been revised.     

Correlation-induced resonances in transport through coupled quantum dots

We investigate the effect of local electron correlations on transport through parallel quantum dots. The linear conductance as a function of gate voltage is strongly affected by the interplay of the interaction U and quantum interference. We find a pair of novel correlation-induced resonances separated by an energy scale that depends exponentially on U. The effect is robust against a small detuning of the dot energy levels and occurs for arbitrary generic tunnel couplings. It should be observable in experiments on the basis of presently existing double-dot setups.     

Atmospheric channel characteristics for quantum communication with continuous polarization variables

We investigate the properties of an atmospheric channel for free space quantum communication with continuous polarization variables. In our prepare-and-measure setup, coherent polarization states are transmitted through an atmospheric quantum channel of 100 m length on the flat roof of our institute’s building. The signal states are measured by homodyne detection with the help of a local oscillator (LO) which propagates in the same spatial mode as the signal, orthogonally polarized to it. Thus the interference of signal and LO is excellent and atmospheric fluctuations are auto-compensated. The LO also acts as a spatial and spectral filter, which allows for unrestrained daylight operation. Important characteristics for our system are atmospheric channel influences that could cause polarization, intensity and position excess noise. Therefore we study these influences in detail. Our results indicate that the channel is suitable for our quantum communication system in most weather conditions.     

Collective dynamics in optomechanical arrays

Optomechanical systems couple light stored inside an optical cavity to the motion of a mechanical mode. Recent experiments have demonstrated setups, such as photonic crystal structures, that in principle allow one to confine several optical and vibrational modes on a single chip. Here we start to investigate the collective nonlinear dynamics in arrays of coupled optomechanical cells. We show that such "optomechanical arrays" can display synchronization, and that they can be described by an effective Kuramoto-type model.