Fourier series of half-range functions by smooth extension

This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L] of the interval [−L, L] in one-dimensional problems and over the sub-domain [0, L_x] × [0, L_y] of the domain [−L_x, L_x] × [−L_y, L_y] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems.     

Nanostructural organization and anion effects in the optical Kerr effect spectra of binary ionic liquid mixtures

This article reports a study of the effect of anions on the optical Kerr effect (OKE) spectra of binary ionic liquid mixtures with one mixture comprising the 3-methyl-1-pentylimidazolium ([C 5mim] (+)) cation and the anions PF 6 (-) and CF 3CO 2 (-) (TFA (-)), and another mixture comprising the [C 5mim] (+) cation and the anions Br (-) and bis(trifluomethanesulfonyl)imide (NTf 2 (-)). The spectra were obtained by the use of optical heterodyne-detected Raman-induced Kerr Effect Spectroscopy at 295 K. The OKE spectra of the mixtures are compared with the calculated mole-fraction weighted sum of the normalized OKE spectra of the neat liquids. The OKE spectra are nearly additive for [C 5mim]Br/[C 5mim][NTf 2] mixtures, but nonadditive for [C 5mim][PF 6]/[C 5mim][TFA] mixtures. In the case of the equimolar [C 5mim][PF 6]/[C 5mim][TFA] mixture, the nonadditivity is such that the experimental OKE spectrum is narrower than the calculated OKE spectrum. The additivity or nonadditivity of OKE spectra for IL mixtures can be explained by assuming ionic liquids are nanostructurally organized into nonpolar regions and ionic networks. The ionic networks in mixtures will be characterized by "random co-networks" for anions that are nearly the same in size (PF 6 (-) and TFA (-)) and by "block co-networks" for anions that differ greatly in size (Br (-) and NTf 2 (-)).     

One-electron reduction of superoxide radical-anions by 3-alkylpolyhydroxyflavones in micelles. Effect of antioxidant alkyl chain length on micellar structure and reactivity

In micellar solutions, one-electron reduction of (*)O 2 (-) radical-anions by 3-alkylpolyhydroxyflavones (FnH) with alkyl chains of n = 1, 4, 6, 10 carbons produces phenoxyl radicals ( (*)Fn) identical to those obtained by one-electron oxidation by (*)Br 2 (-) radical-anions or by repair of tryptophan radicals. In cetyltrimethylammonium bromide (CTAB), F1H localizes in the Stern layer, and alkyl chains of other FnH solubilize in the hydrophobic interior, interacting with cetyl tails. This interaction produces more compact micelles with lower intramicellar fluidity, as suggested by the increase in the pseudo-first-order rate constant of (*)Fn formation ( k 1) from approximately 390 s (-1) for n = 1 to 610 s (-1) for n = 10, leading to an intramicellar bimolecular rate constant of 1 x 10 (5) M (-1) s (-1). Additionally, (*)F1 and (*)F4 decay by intermicellar bimolecular reaction (2 k = 20 and 2 x 10 (5) M (-1) s (-1), respectively) whereas other (*)Fn radicals are stable over seconds due to increased localization with regards to the Stern layer. In contrast, the thick uncharged hydrophilic palisade layer and the compact hydrophobic core of Triton X100 micelles are responsible for a much higher microviscosity resulting in a decrease in k 1 from approximately 15.6 s (-1) for n = 1 to 9.6 s (-1) for n = 10.     

Cyclometallated Pt(II) and Pd(II) complexes with a trithiacrown ligand

We report the synthesis and full characterization for a series of cyclometallated complexes of Pt(II) and Pd(II) incorporating the fluxional trithiacrown ligand 1,4,7-trithiacyclononane ([9]aneS3). Reaction of [M(C insertion mark N)(micro-Cl)]2 (M = Pt(II), Pd(II); C insertion mark N = 2-phenylpyridinate (ppy) or 7,8-benzoquinolinate (bzq)) with [9]aneS3 followed by metathesis with NH4PF6 yields [M(C insertion mark N)([9]aneS3)](PF6). The complexes [M(C insertion mark P)([9]aneS3)](PF6) (M = Pt(II), Pd(II); Cinsertion markP = [CH2C6H4P(o-tolyl)2-C,P]-) were synthesized from their respective [Pt(C insertion mark P)(micro-Cl)]2 or [Pd(C insertion mark P)(micro-O2CCH3)]2 (C insertion mark P) starting materials. All five new complexes have been fully characterized by multinuclear NMR, IR and UV-Vis spectroscopies in addition to elemental analysis, cyclic voltammetry, and single-crystal structural determinations. As expected, the coordinated [9]aneS3 ligand shows fluxional behavior in its NMR spectra, resulting in a single 13C NMR resonance despite the asymmetric coordination environment of the cyclometallating ligand. Electrochemical studies reveal irreversible one-electron metal-centered oxidations for all Pt(II) complexes, but unusual two-electron reversible oxidations for the Pd(II) complexes of ppy and bzq. The X-ray crystal structures of each complex indicate an axial M-S interaction formed by the endodentate conformation of the [9]aneS3 ligand. The structure of [Pd(bzq)([9]aneS3)](PF6) exhibits disorder in the [9]aneS3 conformation indicating a rare exodentate conformation as the major contributor in the solid-state structure. DFT calculations on [Pt([9]aneS3)(ppy)](PF6) and [Pd([9]aneS3)(ppy)](PF6) indicate the HOMO for both complexes is primarily dz2 in character with a significant contribution from the phenyl ring of the ppy ligand and p orbital of the axial sulfur donor. In contrast, the calculated LUMO is primarily ppy pi* in character for [Pt([9]aneS3)(ppy)](PF6), but dx2-y2 in character for [Pd([9]aneS3)(ppy)](PF6).     

Pyrolysis mass spectrometry for distinguishing potential hoax materials from bioterror agents

Pyrolysis mass spectrometry (PyMS) was investigated as a rapid tool to distinguish potential bioterror hoax materials from samples containing pathogenic bacteria. A pyrolysis time-of-flight (TOF) mass spectrometer equipped with an alternative ionization technique, metastable atom bombardment (MAB), was used to produce sample spectra. These spectra were analyzed by principal component and discriminant analysis for pattern recognition. Materials investigated were two strains of Vibrio parahaemolyticus, one of which produced the tdh toxin, two Salmonella enterica serotypes, a biological mosquito control product containing spores of Bacillus thuringiensis, and several white to off-white powders (which could be used as hoax materials), such as flour, corn starch, methyl cellulose, and xanthan gum. PyMS distinguished bacterial samples from hoax materials. Furthermore, pattern analysis differentiated Vibrios from Salmonellae, Salmonella enterica Anatum from S. enterica Heidelberg, and the two V. parahaemolyticus strains from each other. The B. thuringiensis mixture was distinguished from other bacteria and powders, suggesting that PyMS with pattern recognition may differentiate samples containing pathogens, including Bacillus spp., from nonbiological agents and that it can be a rapid method for detection of bacteria. MS data acquisition took only 7 min for each sample.     

Ion-selective electrodes for basic drugs

Coated-wire ion-selective electrodes based on dinonylnaphthalene sulfonic acid (DNNS) are prepared for methadone, methylamphetamine, cocaine and protriptyline in protonated form. In each set, nearly-Nernstian responses are obtained while detection limits range from 10^-5.5M for cocaine and methylamphetamine electrodes, to 10^-6.0M for methadone, and 10^-6.5 M for protriptyline electrodes. Selectivity is found to decrease in the order methadone, protriptyline, cocaine and methylamphetamine; these results are consistent with systematic selectivity studies reported earlier for electrodes in this family.     

Polyborane reactions in ionic liquids: new efficient routes to functionalized decaborane and o-carborane clusters

In contrast to reactions that have been observed in traditional organic solvents, decaborane olefin-hydroboration and alkyne-insertion reactions have been found to proceed in ionic liquid solvents without the need of a catalyst. These reactions now provide important new, high-yield synthetic pathways to functionalized decaborane and o-carborane clusters.     

Synthesis of cyclopropyl-iron σ complexes by decarbonylation of acyl complexes

Contrary to earlier reports [1,2] cyclopropyliron σ complexes can be conveniently prepared in fair to excellent yields by photodecarbonylation of the corresponding acyl complexes.     

Oligoether-strapped calix[4]pyrrole: an ion-pair receptor displaying cation-dependent chloride anion transport

A ditopic ion-pair receptor (1), which has tunable cation- and anion-binding sites, has been synthesized and characterized. Spectroscopic analyses provide support for the conclusion that receptor 1 binds fluoride and chloride anions strongly and forms stable 1:1 complexes ([1·F](-) and [1·Cl](-)) with appropriately chosen salts of these anions in acetonitrile. When the anion complexes of 1 were treated with alkali metal ions (Li(+), Na(+), K(+), Cs(+), as their perchlorate salts), ion-dependent interactions were observed that were found to depend on both the choice of added cation and the initially complexed anion. In the case of [1·F](-), no appreciable interaction with the K(+) ion was seen. On the other hand, when this complex was treated with Li(+) or Na(+) ions, decomplexation of the bound fluoride anion was observed. In contrast to what was seen with Li(+), Na(+), K(+), treating [1·F](-) with Cs(+) ions gave rise to a stable, host-separated ion-pair complex, [F·1·Cs], which contains the Cs(+) ion bound in the cup-like portion of the calix[4]pyrrole. Different complexation behavior was seen in the case of the chloride complex, [1·Cl](-). Here, no appreciable interaction was observed with Na(+) or K(+). In contrast, treating with Li(+) produces a tight ion-pair complex, [1·Li·Cl], in which the cation is bound to the crown moiety. In analogy to what was seen for [1·F](-), treatment of [1·Cl](-) with Cs(+) ions gives rise to a host-separated ion-pair complex, [Cl·1·Cs], in which the cation is bound to the cup of the calix[4]pyrrole. As inferred from liposomal model membrane transport studies, system 1 can act as an effective carrier for several chloride anion salts of Group 1 cations, operating through both symport (chloride+cation co-transport) and antiport (nitrate-for-chloride exchange) mechanisms. This transport behavior stands in contrast to what is seen for simple octamethylcalix[4]pyrrole, which acts as an effective carrier for cesium chloride but does not operates through a nitrate-for-chloride anion exchange mechanism.