On the nonsingle-site character of Bis(2-dimethylsilyl-indenyl)zirconium(IV) dichloride/MAO and Bis(2-trimethylsilyl-indenyl)zirconium(IV) dichloride/MAO: polymerization characteristics and mechanistic implications

Ethene polymerization with bis(2-dimethylsilyl-indenyl)zirconium(IV) dichloride (1)/MAO and bis(2-trimethylsilyl-indenyl)zirconium(IV) dichloride (2)/MAO and ethene-co-1-hexene polymerization with 1/MAO are presented. The end group analysis of homopolymers reveals a pronounced dependence of the termination rate on temperature changes. In combination with the high molecular weights obtained, these results are in accord with theoretical predictions. Gel permeation chromatography, Fourier transform infrared, and 13C NMR analyses of copolymerization products from 1/MAO as a function of comonomer concentration at two different temperature series denote its tendency to form inhomogeneous polymer blends. Thermal analysis and fractionation results of one such blend indicate an inhomogeneity in the enchainment process and the existence of multiple active sites of differing geometry. These indications are further supported by AMBER force field and density functional theory studies of the catalyst precursors and the active site of 1/MAO. For this system, delta-agostic interactions for the stabilization of the zirconium cation are favored over beta-agostic interactions, which, in contrast to the situation in studies on bis-Cp systems, is a sparsely populated species. The gap in activation enthalphies for beta-hydride transfer and elimination is marginalized for these bulky zirconocenes, and conceptually new mechanisms for the isomerization of the vinyl end groups are discussed. Further, unexpected activation of the silicon-hydrogen bond within the ligand framework is observed with an activation enthalpy as low as 14 kcal/mol.     

Interpretation of capillary pressure curves using invasion percolation theory

Invasion percolation was studied on three-dimensional regular lattices of various node numbers. A new model has been developed to obtain the pore-size distribution from capillary pressure measurements. The new model is superior to the conventional percolation model, since it takes into account the physical trapping of the wetting phase. The irreducible wetting phase saturation includes the film of the wall of the pores, the dead-end pore volume, and the main contribution by pores isolated from the outlet of the medium by the nonwetting phase. This has been related to the node number and the sample 3dimensions. Over 100 capillary pressure curves of consolidated media have been collected. Good agreement was obtained between this data set out and our invasion percolation predictions using node numbers of 6–13, as reported by Mishra and Sharma. The pore-throat size distribution function estimated by our new model is broader than from the conventional percolation and the capillary tube models.Nomenclature c constant - D pore throat diameter [m] - D _max maximum pore diameter [m] - f(D) correlation function of pore throat size and pore body size - L a parameter representing the dimension of a sample - n node number - p pressure [N/m²] - S _n the nonwetting phase saturation - x random number ranging from 0 to 1.0 - X ^a X _t ^a /X/ _t - X _e ^a X _t ^a –X _t ⁱ - X ⁱ X _t ⁱ /X _t ^a - X _nw fraction of pore volume occupied by the injected phase - X _t fraction of pores larger thanD - X _t ^a total accessibility of pores larger thanD - X _t ⁱ total isolation of pores larger thanD - contact angle - interfacial tension [N/m] - (D) pore throat size distribution     

High-pressure vapor–liquid equilibria of systems containing ethylene glycol,water and methane: Experimental measurements and modeling

This work presents new experimental phase equilibrium measurements of the binary MEG–methane and the ternary MEG–water–methane system at low temperatures and high pressures which are of interest to applications related to natural gas processing. Emphasis is given to MEG and water solubility measurements in the gas phase. The CPA and SRK EoS, the latter using either conventional or EoS/G^E mixing rules are used to predict the solubility of the heavy components in the gas phase. It is concluded that CPA and SRK using the Huron–Vidal mixing rule perform equally satisfactory, while CPA requires fewer interaction parameters.     

Possible effects on the polyethene chain structure of trimethylaluminum coordination to zirconocene catalysts

Ethene was polymerized with the catalytic systems L₂ZrCl₂/MAO/TMA (where L = Cp, Me₅Cp, or Me₄Cp; Cp = η⁵‐cyclopentadienyl; MAO = methylaluminoxane; and TMA = trimethylaluminum) at 60 °C, 2 bar, and Al_TMA/Zr ratios of 0–2700. The polymerization activity was reduced with the addition of TMA for L = Cp but was almost unaffected for the methyl‐substituted catalysts. Increasing the TMA concentration resulted in a lower molecular weight of the polymer, with the largest effect for L = Me₅Cp. A gel permeation chromatography analysis of the polymers revealed a high molecular weight shoulder and a nearly bimodal distribution for L = Me₅Cp at high TMA concentrations. A possible explanation of such a shoulder in terms of long‐chain branching was ruled out by dynamic viscosity measurements. The origin of this effect more likely stemmed from competition between chain transfer to aluminum and β‐hydrogen transfer reactions at two different sites, one TMA‐sensitive and one TMA‐insensitive. Polymerizations at various pressures and temperatures substantiated this assumption. A clue to the underlying mechanism came from investigations of chain transfer to TMA studied with density functional calculations. Complexation of Me₃Al to Zr was much stronger for L = Cp than for L = Me₅Cp. However, the overall chain‐transfer barrier was much higher for L = Cp. These results agreed both with the reduced activity for L = Cp and with the strongly reduced molecular weight for L = Me₅Cp observed with the addition of TMA. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3566–3577, 2001     

Adsorption equilibria of binary gas mixtures on graphitized carbon black

Adsorption equilibria for binary gas mixtures (methane-carbon dioxide, methane-ethane, and carbon dioxide-ethane) on the graphitized carbon black STH-2 were measured by the open flow method at 293.2 K. The experimental pressure range was (0 to 1.6) MPa. The extended Langmuir (EL) model and the ideal adsorption solution theory (IAST) have been adopted to predict the equilibria of binary gas mixtures. The results indicate that gas mixtures adsorbed on the homogeneous surface of STH-2 exhibit the nonideal behavior, which is mainly induced by adsorbate-adsorbate interactions. The real adsorption solution theory (RAST) has been used to analyze the property of the adsorbed mixtures. The activity coefficients have been correlated with the Wilson equation. The investigation demonstrates that the nonideality of adsorbed phase is completely dissimilar with the bulk liquid phase. The adsorption of the heavier component would benefit the adsorption of the lighter component.     

Measurements of the thermal, dielectric, piezoelectric, pyroelectric and elastic properties of porous PZT samples

The introduction of porosity into ferroelectric ceramics has been of great interest in recent years. In particular, studies of porous lead-zirconate-titanate ceramic (PZT) have been made. In the research reported, samples of Ferroperm Pz27 with porosities of 20, 25 and 30% were studied. Very complete measurements were made of all of the physical properties relevant for ferroelectric applications including thermal conductivity and diffusivity, heat capacity, dielectric, pyroelectric, piezoelectric and elastic properties. Scanning electron micrographs indicated a change from 3-0 to 3-3 connectivity with increasing porosity. Although most of the physical properties are degraded by the presence of porosity, both piezoelectric and pyroelectric figures-of-merit are improved because of the markedly reduced relative permittivity. Porous ferroelectric ceramics are very promising materials for a number of applications.     

Laser cooling with a single laser beam and a planar diffractor

A planar triplet of diffraction gratings is used to transform a single laser beam into a four-beam tetrahedral magneto-optical trap. This "flat" pyramid diffractor geometry is ideal for future microfabrication. We demonstrate the technique by trapping and subsequently sub-Doppler cooling (87)Rb atoms to 30 μK.     

On a homogeneous algorithm for the monotone complementarity problem

Received May 15, 1995 / Revised version received May 20, 1998 Published online October 21, 1998     

A Reduction Theorem for Capacity of Positive Maps

We prove a reduction theorem for capacity of positive unital maps of finite dimensional C*−algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.     

Upscaling of Two-Phase Immiscible Flows in Communicating Stratified Reservoirs

A semi-analytical method for upscaling two-phase immiscible flows in heterogeneous porous media is described. This method is developed for stratified reservoirs with perfect communication between layers (the case of vertical equilibrium), in a viscous dominant regime, where the effects of capillary forces and gravity may be neglected. The method is discussed on the example of its basic application: waterflooding in petroleum reservoirs. We apply asymptotic analysis to a system of two-dimensional (2D) mass conservation equations for incompressible fluids. For high anisotropy ratios, the pressure gradient in vertical direction may be set zero, which is the only assumption of our derivation. In this way, the 2D Buckley–Leverett problem may be reduced to a one-dimensional problem for a system of quasi-linear hyperbolic equations, of a number equal to the number of layers in the reservoir. They are solved numerically, based on an upstream finite difference algorithm. Self-similarity of the solution makes it possible to compute pseudofractional flow functions depending on the average saturation. The computer partial differential equation solver COMSOL is used for comparison of the complete 2D solutions with averaged 1D simulations. Cases of both discrete and continuous (log-normal) permeability distribution are studied. Generally, saturation profiles of the 1D model are only slightly different from the 2D simulation results. Recovery curves and fractional flow curves fit well. Calculations show that at a favorable mobility ratio (displaced to displacing phase) crossflow increases the recovery, while at an unfavorable mobility ratio, the effect is the opposite. Compared with the classical Hearn method, our method is more general and more precise, since it does not assume universal relative permeabilities and piston-like displacement, and it presumes non-zero exchange between layers. The method generalizes also the study of Yortsos (Transp Porous Media 18:107–129, 1995), taking into account in a more consistent way the interactions between the layers.