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Ethene polymerization in toluene has been studied in the temperature range -7 to +97°C and pressure range 0.28 to 9 bar, using two different L 2ZrCl2/methylaluminoxane (MAO) catalyst systems. With bis(cyclopentadienyl)zirconium dichloride (Cp2ZrCl2, L ) Cp), the average activity over 1 h increases with temperature between 10 and 97°C. With bis(pentamethylcyclopentadienyl)zirconium dichloride (Cp*2ZrCl2, L ) Cp*), a maximum average activity over 1 h is observed at 45°C. If propagation and deactivation effects are separated through kinetic modeling, the activity corresponding to chain propagation is found to increase in the whole temperature range for both catalysts. The molecular weight is higher with L ) Cp* than with L ) Cp below 80°C. Above 80°C, the opposite is observed. With L ) Cp*, the molecular weight increases with increasing ethene pressure up to about 2 bar, where it levels off. With L ) Cp, the molecular weight is independent of pressure between 0.28 and 9 bar. The ratio between vinyl and trans-vinylene unsaturation is approximately 6:1 with L ) Cp and 1:1 with L ) Cp*, both slightly increasing with increasing ethene pressure. As the temperature is increased, the relative vinyl content decreases with L ) Cp and increases with L ) Cp*. On the basis of density-functional calculations, we present a reaction scheme consistent with most of the experimental results. This reaction scheme, in which different agostic interactions play a crucial role, assumes a Cossee-like mechanism for chain propagation, chain termination via hydrogen transfer to a coordinated monomer (for both catalysts) or to the metal (for L ) Cp*), and chain isomerization via partial hydrogen transfer to the metal, relative rotation of the olefin and the hydride, and reinsertion of the coordinated olefin. The calculated activation energy for propagation is 25-35 kJ/mol for L ) Cp*, in fair agreement with the experimental value of 17 kJ/mol. For L ) Cp, we calculate an activation energy of 10-20 kJ/mol, whereas the experimentally derived value is 61 kJ/mol. The poor agreement for L ) Cp may indicate that the polymerization is influenced by the surrounding solvent and MAO. The calculated difference in activation energy between chain propagation and termination is larger for L ) Cp* than for L ) Cp, in qualitative agreement with the stronger temperature dependence of the molecular weight observed with L ) Cp*. Chain isomerization is found to be easier, relative to termination, with L ) Cp* than with L ) Cp. This may account for the large amount of trans-vinylene unsaturation observed when Cp* 2ZrCl2 is used as catalyst.

Binary mixtures of Cp2ZrMe2, Cp2ZrCl2, dimethylaluminum chloride, trimethylaluminum, and methylaluminoxane (MAO), as well as Cp2ZrMe2 with boron-based activators, have been studied by in situ IR spectroscopy (Cp = cyclopentadienyl, Me = methyl). The position of a strong band near 800 cm(-1), corresponding to the out-of-plane vibration of the Cp hydrogen atoms, is sensitive to the bonding environment around Zr and can be used to monitor reactions and the formation of new products in these mixtures. Harmonic frequencies determined by density functional theory correlate well with experimental values and have been used to assist in the interpretation of the data. The frequency of the Cp out-of-plane vibration, ranging from 797 to 832 cm(-1) in our experiments, is found to increase with increasing electron density on the Cp ring and decreasing Zr-Cp distance. In the mixture of MAO and Cp2ZrMe2, a stable complex is rapidly formed at low Al/Zr ratios. A mechanism that may explain the need for a large MAO excess is proposed for the activation of metallocenes with MAO. The proposed mechanism involves the formation of dimers or oligomers of MAO cages that tend to dissipate the charge of the anion. This destabilization of the Cp2ZrMe2-MAO complex facilitates the formation of the catalytically active cation.

We consider resonant tunneling through a double barrier when the electrons interact with longitudinal-optical phonons in the double-barrier well. We use a tight-binding model for the electron Hamiltonian, with a linear coupling to the phonon modes. Phonon-mediated scattering amplitudes for the double-barrier structure are efficiently obtained by a recursive Green-function technique. This technique allows us to go beyond the unrealistic assumption of Lorentzian line shapes, used in previous treatments. Our results are in qualitative agreement with earlier calculations, but quantitatively the phonon peaks are enhanced typically by 50%.

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