Effects of methylaluminoxane immobilization on silica on the performance of zirconocene catalysts in propylene polymerization

Investigation of the characteristics and performance in propylene polymerization of silica‐immobilized methylaluminoxane (MAO), in combination with a moderately and a highly isospecific zirconocene catalyst, has revealed that a simple impregnation of silica with MAO at ambient temperature is insufficient to obtain uniform distribution of MAO throughout the support particle. Homogeneous Al distribution throughout the support, giving increased catalyst activity, was achieved by a more rigorous impregnation of silica with MAO at elevated temperatures. The highest catalyst activities were obtained by precontacting the MAO with the zirconocene to generate the activated species before immobilization on silica. Polymer particle morphology was strongly dependent on the characteristics of the silica used for catalyst immobilization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2734‐2748, 2005     

A further note on the force discrepancy for wing theory in Euler flow

Uniform steady potential flow past a wing aligned at a small angle to the flow direction is considered. The standard approach is to model this by a vortex sheet, approximated by a finite distribution of horseshoe vortices. In the limit as the span of the horseshoe vortices tends to zero, an integral distribution of infinitesimal horseshoe vortices over the vortex sheet is obtained. The contribution to the force on the wing due to the presence of one of the infinitesimal horseshoe vortices in the distribution is focused upon. Most of the algebra in the force calculation is evaluated using Maple software and is given in the appendices. As in the two previous papers by the authors on wing theory in Euler flow [E Chadwick, A slender-wing theory in potential flow, Proc. R. Soc. A461 (2005) 415–432, and E Chadwick and A Hatam, The physical interpretation of the lift discrepancy in Lanchester-Prandtl lifting wing theory for Euler flow, leading to the proposal of an alternative model in Oseen flow, Proc. R. Soc. A463 (2007) 2257–2275], it is shown that the normal force is half that expected. In this further note, in addition it is demonstrated that the axial force is infinite. The implications and reasons for these results are discussed.