Synthesis of ultra‐low‐molecular‐weight polyethylene wax using a bulky Ti(IV) aryloxide–alkyl aluminum catalytic system

Complexes of titanium(IV) with bulky phenolic ligands such as 2‐tert‐butyl‐4 methylphenol, 2, 4‐di‐tert‐butyl phenol and 3,5‐di‐tert‐butyl phenol were prepared and characterized. These catalyst precursors, formulated as [Ti(OPh*)_n(OPrⁱ)_4?n] (OPh* = substituted phenol), were found to be active in polymerization of ethylene at higher temperatures in combination with ethylaluminum sesquichloride (Et₃Al₂Cl₃) as co‐catalyst. It was observed that the reaction temperature and ethylene pressure had a pronounced effect on polymerization and the molecular weight of polyethylene obtained. In addition, this catalytic system predominantly produced linear, crystalline ultra‐low‐molecular‐weight polyethylenes narrow dispersities. The polyethylene waxes obtained with this catalytic system exhibit unique properties that have potential applications in surface coating and adhesive formulations. Copyright © 2007 John Wiley & Sons, Ltd.     

The height of ideals and regular sequences

Summary We prove that given a Noetherian ringR and a finitely generatedR-inoduleM, there exists a finite set of prime idealsΛ inR such that the depth of an arbitrary idealI onM is determined by the height ofI modulo each of the primes inΛ. As an application we answer a question raised by the second author and V. Srinivas concerning m-adic approximations of regular sequences in a local ring. This article was processed by the author using the Springer-Verlag T_EX P Jourlg macro package 1991.     

Synthesis and catalytic activity of binuclear Mn(III,III)–BINOL complexes for epoxidation of olefins

The novel binuclear complexes [Mn₂^{(III, III)}(BINOL)₃L₂]2H₂O, where, L = 2, 2′‐bipyridine (Bpy) or 1,10‐phenanthroline (Phen) and BINOL = 1, 1′‐bi‐2‐naphthol were synthesized and characterized by elemental analyses, magnetic susceptibility and various spectral methods. The catalytic activity of these complexes was studied for the epoxidation reaction of unfunctionalized olefins like styrene, 1‐hexene, 1‐octene and 1‐decene. The products thus obtained were analyzed by GC. The epoxidation reactions were carried out, in the presence of catalyst with different oxidants, to study the effect of the nature of the oxidant on the reactions. The different oxidants used were the peroxide oxygen donor (e.g. TBHP and H₂O₂), mono oxygen donor (e.g. PhIO) and dioxygen donor (e.g. molecular O₂). TBHP was found to be the best oxidant for the epoxidation reaction. To study the effect of the solvent on the epoxidation, the reactions were carried out in different media, such as a polar media (e.g. with CH₃OH as solvent), non‐polar media (e.g. with CH₂Cl₂ and C₆H₆ as solvents) and coordinating solvent (e.g. CH₃CN). The maximum epoxide formation was observed in CH₂Cl₂ medium. The epoxidation reactions with optically active BINOL catalysts under optimum established conditions were carried out to examine the enantioselectivity of the catalysts. The complexes were, however, found not to be enantioselective. Copyright © 2006 John Wiley & Sons, Ltd.     

X-ray reflectivity study on gold films during sputter deposition

We performed in-situ X-ray reflectivity measurements of gold films during sputter deposition on polished silicon substrates. The measurements were performed at several substrate temperatures and under two argon pressures. The gold surfaces were also examined by scanning tunneling microscopy after deposition to obtain their real-space topographic images. These images were used to complement the X-ray reflectivity measurements in determining the effect of argon pressure on the gold surface and its height-height difference functions. An approximation for height-height difference functions was employed to analyze the X-ray reflectivity data. The measured interface width during growth followed a simple power law, consistent with recent theoretical results of dynamic scaling behavior. The scaling exponents, however, do not agree well with predictions based on some models in 2 + 1 dimensions.     

The electrical conductivity of silica sols

Proceedings - Mathematical Sciences - In the case of silica sols prepared by peptizing silica gel with ammonia, ammonium silicate is the stabilizing electrolyte. When the sols are allowed to age,...     

Intensity fluctuations in thermal light with orthogonally polarised multiple-peak spectrum

The moment generating function of the integrated light intensity of thermal radiation having multiple peak spectrum is obtained. Cases of two-peak and three-peak spectra where different peaks are in orthogonal states of polarisation are considered. The moment generating function is shown to be the product of two simpler generating functions.     

Multimodal nonlinear optical polarizing microscopy of long-range molecular order in liquid crystals

We demonstrate orientation-sensitive multimodal nonlinear optical polarizing microscopy capable of probing orientational, polar, and biaxial features of mesomorphic ordering in soft matter. This technique achieves simultaneous imaging in broadband coherent anti-Stokes Raman scattering, multiphoton excitation fluorescence, and multiharmonic generation polarizing microscopy modes and is based on the use of a single femtosecond laser and a photonic crystal fiber as sources of the probing light. We show the viability of this technique for mapping of three-dimensional patterns of molecular orientations and show that images obtained in different microscopy modes are consistent with each other.     

Multiobjective analog/RF circuit sizing using an improved brain storm optimization algorithm

This paper presents a multiobjective analog/RF circuit sizing tool using an improved brain storm optimization (IMBSO) algorithm with the purpose of analyzing the tradeoffs between competing performance specifications of analog/RF circuit block. A number of improvements are incorporated into IMBSO algorithm at different steps. At first, the clustering step of IMBSO algorithm is augmented with k-means\(++\) seeding technique to select the initial cluster centroids while clustering using k-means clustering technique. As a second improvement, the proposed IMBSO algorithm makes use of random probabilistic decision-making of river formation dynamics scheme to select optimal cluster centroids during population generation step. As a third improvement, an adaptive mutation operator is incorporated inside the IMBSO algorithm to generate new population. Finally, two separate constraint handling techniques are employed to handle both boundary and functional constraints during analog/RF circuit optimization. The performance of the proposed IMBSO algorithm is demonstrated in finding optimal Pareto fronts among different performance specifications of a two-stage operational amplifier circuit, a folded cascode amplifier circuit and a low noise amplifier circuit.