Exciplex Formation and Excited State Deactivation of Difluoroborondipyrromethene (Bodipy) Dyads

Two series of geometrically‐related dyads are discussed based on the difluoroborondipyrromethene (Bodipy) unit, and incorporating covalently attached hydroquinone/quinone groups. These units are anchored directly, or via a phenylene spacer, to the Bodipy core at the meso position in one series ( BD‐MHQ , BD‐MQ , BD‐MPHQ , BD‐MPQ ), but for the second series the attachment site is the 2‐position ( BD‐SHQ , BD‐SQ , BD‐SPHQ , BD‐SPQ ). The compounds show various levels of fluorescence depending on the oxidation state of the appended group and the substitution pattern. In non‐polar solvents such as toluene, diethyl ether and dichlorobenzene, the S₁ state deactivation of the Bodipy unit in BD‐SPQ and BD‐MPQ is dominated by ^{1, 3}exciplex formation, which has not been reported for Bodipy derivatives so far. In the latter molecule, the decay of the exciplex is divided between population of the Bodipy triplet state (13 %–21 %) and ground state reformation. This partitioning is not seen for the side‐on substituted derivative, BD‐SPQ , and only ground state reformation is observed following decay of the exciplex. This difference in behavior is explained by the radical‐pair inter‐system‐crossing mechanism, which more effectively operates in BD‐MPQ because of the orthogonality of the donor‐acceptor units. In the more polar solvent CH₃CN all the quinone derivatives show fast formation of the charge‐separated state (k_CS) followed by slower charge recombination (k_CR). The ratio k_CS/k_CR≤80.     

A study into the effect of subtle structural details and disorder on the terahertz spectrum of crystalline benzoic acid

The phonon modes of crystalline benzoic acid have been investigated using terahertz time-domain spectroscopy, rigid molecule atom-atom model potential and plane-wave density functional theory lattice dynamics calculations. The simulation results show good agreement with the measured terahertz spectra and an assignment of the terahertz absorption features of benzoic acid is made with the help of both computational methods. Focussing on the strongest interactions in the crystal, we describe each vibration in terms of distortions of the benzoic acid hydrogen bonded dimers that are present in the crystal structure. The terahertz spectrum is also shown to be highly sensitive to the location of the carboxylic acid hydrogen atoms in the cyclic hydrogen-bonded dimers and we have systematically explored the influence of the observed disorder in the hydrogen atom positions on the lattice dynamics.     

A synchrotron radiation study of the one‐dimensional complex of sodium with (1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d‐ribitol,a member of the 'immucillin' family

The sodium salt of [immucillin‐A–CO₂H]⁻ (Imm‐A), namely catena‐poly[[[triaquadisodium(I)](μ‐aqua)[μ‐(1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d ‐ribitol][triaquadisodium(I)][μ‐(1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d ‐ribitol]] tetrahydrate], {[Na₂(C₁₂H₁₃N₄O₆)₂(H₂O)₇]·4H₂O}_n, (I), forms a polymeric chain via Na⁺—O interactions involving the carboxylate and keto O atoms of two independent Imm‐A molecules. Extensive N,O—H...O hydrogen bonding utilizing all water H atoms, including four waters of crystallization, provides crystal packing. The structural definition of this novel compound was made possible through the use of synchrotron radiation utilizing a minute fragment (volume ∼2.4 × 10⁻⁵ mm⁻³) on a beamline optimized for protein data collection. A summary of intra‐ring conformations for immucillin structures indicates considerable flexibility while retaining similar intra‐ring orientations.     

On the number of distinct prime factors of an odd perfect number

It is not known whether or not there exists an odd perfect number. We describe an algorithmic approach for showing that if there is an odd perfect number then it has t distinct prime factors, and we discuss its application towards showing that t9.     

UV light‐mediated alkylation of inorganic selenium

In the presence of low molecular weight organic acids (formic, acetic, propionic and malonic), inorganic selenium(IV) is converted by UV irradiation to volatile selenium carbonyl, dimethylselenide and diethylselenide, depending on the acid used. Gas chromatography–mass spectrometry analysis of the volatile products shows that, in 0.7 M formic acid solution, approximately 60–70% (v/v) SeH₂ and 30–40% (v/v) SeCO are formed. The presence of nitrate ion appears to increase threefold the formation of SeCO while completely suppressing formation of SeH₂. Copyright © 2003 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.     

Homogenization of the Three-dimensional Hall Effect and Change of Sign of the Hall Coefficient

The notion of a Hall matrix associated with a possibly anisotropic conducting material in the presence of a small magnetic field is introduced. Then, for any material having a microstructure we prove a general homogenization result satisfied by the Hall matrix in the framework of the H-convergence of Murat–Tartar. Extending a result of Bergman, we show that the Hall matrix can be computed from the corrector associated with the homogenization problem when no magnetic field is present. Finally, we give an example of a microstructure for which the Hall matrix is positive isotropic almost everywhere, while the homogenized Hall matrix is negative isotropic.     

Outputs and time lags for linear bioreactors

Linear systems of convection reaction-diffusion equations for bioreactors are shown to have a structure which allows a geometric factorization of steady state problems giving a significant reduction in their dimensionality. Moreover, convection dominated linear systems with quasisymmetric reaction terms may be further simplified by matrix transformations, which uncouple the differential equations. The boundary conditions are also uncoupled when the diagonal diffusivity matrix D governing diffusion in the bioparticle is a scalar multiple of the corresponding matrix H describing the diffusivity characteristic of the fluid boundary layers around the bioparticles. The dominant transient behaviour of the systems may be handled by establishing an analogous system of time independent equations for mean action time variables and higher moments. These equations have the same amenable structure. Outputs, time lags and various mean residence and first passage times, associated with establishing steady outputs from a concentration free initial state, can be expressed in terms of the steady state solutions and mean action time variables.     

The Structural Characterization of Tin- and Titanium-Dopedα-Fe2O3Prepared by Hydrothermal Synthesis

The structural characteristics of tin- and titanium-dopedα-Fe₂O₃prepared by hydrothermal methods have been investigated by Rietveld structure refinement of the X-ray powder diffraction data. The analysis reveals that the dopant ions adopt two distinct sites: in addition to partially substituting at the octahedral Fe sites, they also occupy the interstitial octahedral sites which are vacant in theα-Fe₂O₃structure. The structural model deduced involves clusters of three substituted cations and is rational in that it represents microstructural regions of the rutile structure within a matrix ofα-Fe₂O₃.