Efficient synthesis of an aldehyde‐capped polythiophene containing fluorinated electron‐withdrawing groups

To incorporate an acceptor type polythiophene segment onto a supramolecular block copolymer for potential light harvesting applications, effective synthetic routes for the end‐functionalized and acceptor‐substituted polythiophenes are critical. The Ullmann coupling reaction can be utilized to obtain electron‐deficient polythiophenes and to attach terminal thiophene units that carry functional groups. In this article, the reactions involving a 2,5‐dibromothiophene monomer containing an electron‐withdrawing fluorinated ester and 5‐bromo‐2‐thiophenecarboxaldehyde (the end‐capper) were studied in detail. It was found that the Ullmann coupling reaction of the dibromide is very fast (completed in a few minutes) and the terminal bromine group does not survive long under the reaction condition. These findings lead to the development of an effective procedure for aldehyde end‐capping of electron‐deficient polythiophenes. Polymers with molecular weights around 4000 Da are routinely obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 41–47, 2007     

Photooxidation of aqueous trichloroethylene using a buoyant photocatalyst with reaction progress monitored via micro-headspace GC/MS

Although photooxidation has previously been shown to be successful in removing organic contaminants from water, methods combining the rapid photooxidation of the desired contaminant with easy catalyst manipulation and removal are few and far between. In the absence of an easy means of catalyst removal, the photooxidation process becomes more costly and time consuming, and photocatalysis cannot be employed as an in situ method for the remediation of aqueous organic contaminants. In this study, the photocatalyst was added to an aqueous trichloroethylene (TCE) solution in the form of TiO₂-coated buoyant microspheres. The solution, placed in a flow-cell photoreactor along with the buoyant catalyst, was irradiated with a UV-filtered Xenon light source. Limited sample sizes necessitated the development of a low-cost headspace GC/MS analysis method, utilizing a standard direct-injection autosampler. This analytical technique aptly monitored reaction progress and indicated that aqueous TCE concentration decreases by nearly 90% in the first hour of irradiation. Subsequent solvent extraction GC/MS analysis indicated that the TCE is initially sorbed by the photocatalyst spheres, but as irradiation continued, TCE is removed from the catalyst spheres surfaces. During the course of irradiation, the expected TCE mineralization product hydrochloric acid appeared, as indicated by a decrease in pH and ion chromatography analysis. The microsphere-born catalyst was easily removed from the treated solution by filtration. Thus, it is possible that a method for effective, low-cost in situ photooxidation of aqueous organic contaminants will be realized in the near future.     

Analytical formulas for the velocity field induced by an infinitely thin vortex ring

Three different analytical solutions are presented for a potential vortex ring using three different streamfunctions. Verification studies confirm that all three approaches are valid. It is found that the solution obtained using the Biot–Savart law is the most efficient method due to its simplicity. It is shown that all analytical results are accurate to within machine accuracy and sample calculations are included. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of blockwise shrinkage wavelet estimates via lower bounds for no-signal setting

A blockwise shrinkage is a popular procedure of adaptation that has allowed the statisticians to establish an impressive bouquet of asymptotic mathematical results and develop softwares for solving practical problems. Traditionally risks of the estimates are studied via upper bounds that imply sufficient conditions for a blockwise shrinkage procedure to be minimax. This article suggests to analyze the estimates via exact (non-asymptotic) lower bounds established for a no-signal setting. The approach complements the familiar minimax, Bayesian and numerical analysis, it allows to find necessary conditions for a procedure to attain desired rates, and it sheds a new light on popular choices of blocks and thresholds recommended in the literature. Mathematical results are complemented by a numerical study. Supported in part by NSF Grants DMS-9971051 and DMS-0243606.