Trochoidal Solutions to the Incompressible Two-Dimensional Euler Equations

Within the Lagrangian framework we present an approach yielding some explicit solutions to the incompressible two-dimensional Euler equations, generalizing the celebrated Gerstner flow. The solutions so obtained, for which explicit formulas of each particle trajectory are provided, represent either flows in domains with a rigid boundary or free-surface flows for a fluid of infinite depth. For some of these solutions the trajectories are epitrochoids or hypotrochoids. Possibilities for obtaining further flows of this type are indicated.     

An Incremental System To Predict the Effect of Different London Dispersion Donors in All-meta-Substituted Azobenzenes

Predictive models based on incremental systems exist for many chemical phenomena, thus allowing easy estimates. Despite their low magnitude in isolated systems London dispersion interactions are ubiquitous in manifold situations ranging from solvation to catalysis or in biological systems. Based on our azobenzene system, we systematically determined the London dispersion donor strength of the alkyl substituents Me, Et, iPr up to tBu. Based on this data, we were able to implement an incremental system for London dispersion for the azobenzene scheme. We propose an equation that allows the prediction of the effect of change of substituents on London dispersion interactions in azobenzenes, which has to be validated in similar molecular arrangements in the future.     

A faux hawk fullerene with PCBM-like properties

Reaction of C₆₀, C₆F₅CF₂I, and SnH(n-Bu)₃ produced, among other unidentified fullerene derivatives, the two new compounds 1,9-C₆₀(CF₂C₆F₅)H (1) and 1,9-C₆₀(cyclo-CF₂(2-C₆F₄)) (2). The highest isolated yield of 1 was 35% based on C₆₀. Depending on the reaction conditions, the relative amounts of 1 and 2 generated in situ were as high as 85% and 71%, respectively, based on HPLC peak integration and summing over all fullerene species present other than unreacted C₆₀. Compound 1 is thermally stable in 1,2-dichlorobenzene (oDCB) at 160 °C but was rapidly converted to 2 upon addition of Sn₂(n-Bu)₆ at this temperature. In contrast, complete conversion of 1 to 2 occurred within minutes, or hours, at 25 °C in 90/10 (v/v) PhCN/C₆D₆ by addition of stoichiometric, or sub-stoichiometric, amounts of proton sponge (PS) or cobaltocene (CoCp₂). DFT calculations indicate that when 1 is deprotonated, the anion C₆₀(CF₂C₆F₅)^– can undergo facile intramolecular S_NAr annulation to form 2 with concomitant loss of F^–. To our knowledge this is the first observation of a fullerene-cage carbanion acting as an S_NAr nucleophile towards an aromatic C–F bond. The gas-phase electron affinity (EA) of 2 was determined to be 2.805(10) eV by low-temperature PES, higher by 0.12(1) eV than the EA of C₆₀ and higher by 0.18(1) eV than the EA of phenyl-C₆₁-butyric acid methyl ester (PCBM). In contrast, the relative E _1/2(0/–) values of 2 and C₆₀, –0.01(1) and 0.00(1) V, respectively, are virtually the same (on this scale, and under the same conditions, the E _1/2(0/–) of PCBM is –0.09 V). Time-resolved microwave conductivity charge-carrier yield × mobility values for organic photovoltaic active-layer-type blends of 2 and poly-3-hexylthiophene (P3HT) were comparable to those for equimolar blends of PCBM and P3HT. The structure of solvent-free crystals of 2 was determined by single-crystal X-ray diffraction. The number of nearest-neighbor fullerene–fullerene interactions with centroid···centroid (⊙···⊙) distances of ≤10.34 Å is significantly greater, and the average ⊙···⊙ distance is shorter, for 2 (10 nearest neighbors; ave. ⊙···⊙ distance = 10.09 Å) than for solvent-free crystals of PCBM (7 nearest neighbors; ave. ⊙···⊙ distance = 10.17 Å). Finally, the thermal stability of 2 was found to be far greater than that of PCBM.     

Synthesis, characterization, and theoretical study of stable isomers of C70(CF3)n (n = 2, 4, 6, 8, 10)

Reaction of C70 with ten equivalents of silver(I) trifluoroacetate at 320-340 degrees C followed by fractional sublimation at 420-540 degrees C and HPLC processing led to the isolation of a single abundant isomer of C70(CF3)n for n = 2, 4, 6, and 10, and two abundant isomers of C70(CF3)8. These six compounds were characterized by using matrix-assisted laser desorption ionization (MALDI) mass spectrometry, 2D-COSY and/or 1D 19F NMR spectroscopy, and quantum-chemical calculations at the density functional theory (DFT) level. Some were also characterized by Raman spectroscopy. The addition patterns for the isolated compounds were unambiguously found to be C1-7,24-C70(CF3)2, C1-7,24,44,47-C70(CF3)4, C2-1,4,11,19,31,41-C70(CF3)6, Cs-1,4,11,19,31,41,51,64-C70(CF3)8, C2-1,4,11,19,31,41,51,60-C70(CF3)8, and C1-1,4,10,19,25,41,49,60,66,69-C70(CF3)10 (IUPAC numbering). Except for the last compound, which is identical to the recently reported, crystallographically characterized C70(CF3)10 derivative prepared by a different synthetic route, these compounds have not previously been shown to have the indicated addition patterns. The largest relative yield under an optimized set of reaction conditions was for the Cs isomer of C70(CF3)8 (ca. 30 mol % of the sublimed mixture of products based on HPLC integration). The results demonstrate that thermally stable C70(CF3)n isomers tend to have their CF3 groups arranged on isolated para-C6(CF3)2 hexagons and/or on a ribbon of edge-sharing meta- and/or para-C6(CF3)2 hexagons. For Cs- and C2-C70(CF3)8 and for C2-C70(CF3)6, the ribbons straddle the C70 equatorial belt; for C1-C70(CF3)4, the para-meta-para ribbon includes three polar hexagons; for C1-7,24-C70(CF3)2, the para-C6(CF3)2 hexagon includes one of the carbon atoms on a C70 polar pentagon. The 10.3-16.2 Hz 7JF,F NMR coupling constants for the end-of-ribbon CF3 groups, which are always para to their nearest-neighbor CF3 group, are consistent with through-space Fermi-contact interactions between the fluorine atoms of proximate, rapidly rotating CF3 groups.     

Co-crystallization of octahedral and icosahedral fluoroanions in K3(AsF6)(B12F12) and Cs3(AsF6)(B12F12). Rare examples of salts containing fluoroanions with different shapes and charges

Crystals grown from anhydrous HF solutions of CsAsF₆ and Cs₂B₁₂F₁₂ or KAsF₆ and Cs₂B₁₂F₁₂ are shown by Raman spectroscopy and single-crystal X-ray diffraction to be the ternary salts K₃(AsF₆)(B₁₂F₁₂) or Cs₃(AsF₆)(B₁₂F₁₂). Both compounds exhibit a modified version of the anti-perovskite structure. They are rare examples of crystals that simultaneously contain octahedral and icosahedral molecular species and are also rare examples of salts containing fluoroanions with different shapes and charges. The crystallographic results show that both compounds are densely packed.     

Synthesis and characterization of ammonioundecafluoro-closo-dodecaborates(1-). New superweak anions

The ammonioborane monoanion H(3)NB(12)H(11)(-) was per-B-fluorinated with elemental fluorine in liquid hydrogen fluoride to yield the first member of a new class of weakly coordinating anions, H(3)NB(12)F(11)(-) (isolated as [N(n-Bu)(4)](2)[H(2)NB(12)F(11)] in 41% yield). The pK(a) of the H(3)NB(12)F(11)(-) anion is 9.6. Several salts of the tri-N-alkylated anions Me(3)NB(12)F(11)(-) and Dd(3)NB(12)F(11)(-) (Dd = n-C(12)H(25)) were also prepared. The structure of [CPh(3)][Me(3)NB(12)F(11)] was determined by single-crystal X-ray diffraction: monoclinic, space group P2(1)/c, a = 18.053(3) A, b = 33.139(5) A, c = 9.600(2) A, beta = 91.459(4) degrees, V = 5742(2) A(3), Z = 8, T = 173(2) K, R(1) = 0.045. It revealed that the only direct interactions between the undecafluoroammonioborate monoanions and the trityl cations in the two independent ion pairs were long and weak BF...CPh(3) interactions of 2.992(6) and 2.942(6) A. Salts of the new anions were chemically, electrochemically, and thermally stable. The conductivity of Li(Me(3)NB(12)F(11)) in dimethoxyethane was comparable to that of LiPF(6) but less than half the value of Li(1-Me-CB(11)F(11)).     

Enhancing electron transfer at a cytochrome c-immobilized microelectrode and macroelectrode

The redox reaction of cytochrome c immobilized on the bare surfaces of microelectrodes and macroscopic electrodes (macroelectrodes) composed of different planes of highly oriented pyrolytic graphite has been investigated using cyclic voltammetry. The protein-immobilized microelectrodes were fabricated using a simple masking method. For both macroelectrodes and microelectrodes, the redox reaction of immobilized cytochrome c needs to be activated by increasing the electrochemical potential maximum of cyclic voltammetry to a high positive value. The redox currents of this protein-electrode system can be enhanced using two approaches. The oxidation and reduction currents of cytochrome c adsorbed on microelectrodes that are composed of the edge plane show an anomalous enhancement compared to those for macroelectrodes composed of the basal plane. The difference in the surface chemical properties of the two kinds of electrodes results in the current anomaly. The oxidation current of the macroelectrode can be selectively enhanced by decreasing the potential minimum.     

Simultaneous determination of lidocaine and its metabolites in plasma and myocardium

No validated method exists for measuring lidocaine and its metabolites in myocardial tissue. We modified a previously described high-performance liquid chromatographic assay and applied it to plasma and to homogenized myocardial samples obtained from dogs that had received lidocaine by a double-infusion technique. Recovery of lidocaine, monoethylglycylxylidide and glycylxylidide after homogenization and extraction is reported. Assay variability, sensitivity and linearity over a wide range of sample sizes are also described. The results obtained with high-performance liquid chromatographic analysis are compared to quantitation of 14C-labeled lidocaine plus metabolites measured by an oxidation-scintillation technique. Myocardium to plasma partition coefficients for lidocaine, monoethylglycylxylidide and glycylxylidide were 2.16, 4.27, and 2.91, respectively.