Formfactors in the half-filled Hubbard model

We consider dynamical spin-spin correlation functions in the one dimensional repulsive half-filled Hubbard model. We propose an exact expression for the two spinon formfactor of spin operators. We use this to derive the two spinon contribution to the dynamical structure factor.Comment: 5 pages of revtex, 3 figure

Preparation of ethylene/1-hexene copolymers from ethylene using a fully silica-supported tandem catalyst system

A silica-supported tandem catalyst system, capable of producing ethylene/1-hexene copolymers from ethylene being the single monomer, has been investigated. As tandem couple a phenoxyimine titanium catalyst for ethylene trimerization was combined with a metallocene catalyst for α-olefin polymerization. Two different approaches were pursued to combine the two catalysts as silica-supported tandem partners. The co-immobilization of the catalysts on the same support particles led to low polymerization activities and yielded products with low comonomer content due to interference of the two catalysts on the support. Immobilization of the two catalysts on separate supports prevented this interaction and led to high polymerization activities while the comonomer content of the product was controlled by the employed catalyst ratio. The copolymers obtained via the latter method were thoroughly analyzed with respect to their chemical composition distribution (CCD) by DSC-SSA, Crystaf, and HT-HPLC. The obtained data indicate a broad and in some cases bimodal CCD, which was explained by the synergy of composition drift during the polymerization and increasing diffusion limitation within the expanding polymer particle

Effect of aluminum alkyls on a homogeneous and silica-supported phenoxy-imine titanium catalyst for ethylene trimerization

A phenoxy-imine titanium catalyst (FI-catalyst) for selective ethylene trimerization was immobilized on methyl aluminoxane (MAO) pretreated silica and its activity and selectivity was compared with that of the corresponding homogeneous catalyst system. The homogeneous and heterogeneous ethylene oligomerization was conducted in the presence of different aluminum alkyls, commonly used as scavengers during olefin polymerization to remove residual oxygen and moisture from the reaction medium. Both the homogeneous and heterogeneous catalysts were strongly affected by the presence of scavenger in the reaction medium. Upon activation with R3Al/MAO (R= Et, nOct, iBu), the homogeneous catalyst switches selectivity from ethylene trimerization to polymerization. NMR spectroscopic investigations indicate that this change of selectivity can be attributed to ligand exchange between the precatalyst and the aluminum alkyl and reduction of the titanium species. The thereby formed ligand-free and/or reduced titanium alkyls act as polymerization catalysts and are responsible for the increasing polymer formation. Using the heterogeneous catalyst, the scavenger employed during ethylene trimerization was found to be of crucial influence regarding the activity of the catalyst and the occurrence of reactor fouling. Employing aluminum alkyls like iBu3Al and nOct3Al resulted in catalyst leaching and homogeneous polymer formation. The latter was prevented using Me3Al or Et3Al as scavengers; however, in general the supported catalyst was poisoned by aluminum alkyls, resulting in a low overall activity. It was found to be beneficial for the heterogeneous trimerization system to employ silica-supported scavengers. By physical separation of the catalyst and the scavenger this poisoning effect was effectively prevented, resulting in a highly active heterogeneous catalyst