Estimates of a sum of Dirichlet series

We study the Dirichlet series with an arbitrary abscissa of absolute convergence. The lower and upper estimates for sums of these series are found. The above results allow us to establish some relations between the maximum modulus and the maximal term of Dirichlet series, especially to find conditions that ensure that the maximum modulus and the maximal term have the same many-term asymptotics.     

New molecular topologies by fourfold metathesis reactions within a hydrogen-bonded calix[4]arene dimer

A calix[4]arene tetrapentyl ether in the cone conformation substituted at its wide rim by four m-(omega-octenyloxy)phenyl urea groups forms hydrogen-bonded dimeric capsules in dichloromethane/benzene (95:5). Metathesis reaction with Grubbs' catalyst under high-dilution conditions (1.1 x 10(-4) M) followed by hydrogenation leads to a covalent connection of all the urea groups within a dimer. Three topologically different products may be expected in such a reaction: a bis[2]catenane, a doubly bridged monocatenane and a tetrabridged capsule. All three possible reaction products could be isolated in an overall yield up to 60 % for the separated and purified compounds. Their identification was based on the NMR patterns which reflect the characteristic symmetry properties of the isomeric products especially in the region of the hydrogen-bonded NH protons and were further confirmed by MALDI-TOF mass spectra. Further structural support for the bis[2]catenane comes from a single-crystal X-ray structure, although severe disorder prevents the localization of all atoms in the aliphatic chains connecting the two calix[4]arenes. Kinetic studies for the guest release/exchange (cyclohexane against the solvent [D(6)]benzene) do not show remarkable differences between the starting dimer and the additionally linked dimers, while the mobility of an included tetraethylammonium cation is obviously more restricted.     

Guest exchange in dimeric capsules of a tetraurea calix[4]arene in the solid state

A solid powder of hydrogen bonded dimers of a tetraurea calix[4]arene is able to exchange the encapsulated guest in contact with the vapor of a second guest. The molecules of a guest-free powder obtained from a polar solvent cannot rearrange in the solid phase to form new guest-filled capsules under these conditions.     

Highly efficient glucosylation of flavonoids

Abstract  

A highly efficient procedure for glucosylation of flavonoids by acetobromoglucose is described. Glucosylation is carried out in a two-phase system CHCl₃/H₂O over 96 h using tetrabutylammonium bromide as phase-transfer catalyst. A purification procedure can be performed without column chromatography, and the yields of the glucosylated flavonoids are mostly quantitative. Acetylated glucosides were deprotected with sodium methanolate to afford the desired glucosides of flavonoids.     

Energy transfer in calixarene-based cofacial-positioned perylene bisimide arrays

The synthesis of multichromophoric perylene bisimide-calix[4]arene arrays with up to five perylene units (containing orange, violet, and green perylene bisimide chromophores) and of monochromophoric model compounds was achieved by subsequent imidization of mono-Boc functionalized calix[4]arene linkers with three different types of perylene bisimide dye units. The optical properties of all compounds were studied with UV/vis absorption and steady state and time-resolved fluorescence spectroscopy. Upon excitation of the inner orange dye at 490 nm of array 3, strong fluorescence emission of the outer green perylene bisimide (PBI) chromophore at 744 nm is observed. The fluorescence excitation spectra of compounds 3 and 4 (lambdadet = 850 nm) show all absorption bands of the parent chromophores (e.g., all perylene units contribute to the emission from S1 state of the green PBI). Thus, the fluorescence emission and excitation spectra as well as time-resolved data of fluorescence lifetimes in the absence (tauD = 5.1 ns) and in the presence of an acceptor (tauDA = 0.8 ns) suggest efficient energy transfer processes between the perylene bisimide dye units. For the bichromophoric array 4, the energy transfer rate is calculated to a value of 1.05 x 109 s-1. These results demonstrate highly efficient energy transfer in cofacially assembled dye arrays.     

Synthesis and Structure of Hexa(Diethoxyphosphoryloxy)calix[6]arene

Abstract

Hexapodand 1, which contains six phosphoryl groups at the lower rim of the macrocycle, was synthesized by the reaction of calix[6]arene with diethylchlorophosphate and sodium hydride. The structure is confirmed by X-ray studies: C₆₆H₉₀O₂₄P₆, Pbca, a = 14.867 (4), b = 18.577 (4), c = 26.510(6), D_c = 1.265g/cm³, Z = 4, and R = 0.063 for the 4600 observed reflections. The molecule 1 exists in a centrosymmetrical flattened 1,2,3-alternate conformation, in which diametrically opposed benzene rings are parallel. Four phosphoryl groups are oriented away from the cycle, two other groups are self-included in the macrocycle cavity.     

Yukawa fluid at a hard wall: field theory description

We adopt a field-theoretical approach to study the structure and thermodynamics of a spatially confined fluid interacting with the Yukawa potential. We derive analytic expressions for the pressure, the Helmholtz free energy, the correlation function, the density profile, and the adsorption. Different simple analytic expressions of the density profile are compared with the numerical estimation of the mean field results. Beyond the mean field approximation, we show that fluctuations can contribute significantly to the properties of the system. Notably they lead to a desorption phenomenon regardless of the sign of the interaction. As a consequence, a non-monotonous density profile at the wall and adsorption curves as a function of the density are found for some systems. This behaviour rationalizes the ionic depletion phenomenon responsible for the anomalous behaviour of the electric capacitance as a function of temperature. Particular attention is given to the contact theorem condition.     

Calix[4]arene-functionalized naphthalene and perylene imide dyes

[reaction: see text] Calix[4]arenes bearing one, two, or four 1,8-naphthyl imide groups at the wide rim and bis-calix[4]arenes connected via perylene-bisimide dye spacers have been synthesized. The low-temperature NMR spectrum of the tetranaphthylimide suggests, in agreement with a crystal structure, a C2-symmetrical pinched cone conformation stabilized via face-to-face pi-pi interactions between opposite naphthylimide groups. UV-vis and fluorescence studies have been carried out for the perylene bis-calix[4]arene dyes.     

Self-assembled dimers with supramolecular chirality

The possibilities to form dimeric capsules with supramolecular chirality from tetraurea calix[4]arenes composed of two different phenolic urea units are discussed in general and demonstrated experimentally for various selected examples.