Spatial extent of the singlet and triplet excitons in luminescent angular-shaped transition-metal diynes and polyynes comprising non-pi-conjugated group 16 main group elements

A novel approach based on conjugation interruption has been developed and is presented for a series of luminescent and thermally stable chalcogen-bridged platinum(II) polyyne polymers trans-[{-Pt(PBu3)2C[triple bond]C(C6H4)E(C6H4)C[triple bond]C-}n] (E = O, S, SO, SO2). Particular attention was focused on the photophysical properties of these Group 10 polymetallaynes and comparison was made to their binuclear model complexes trans-[Pt(Ph)(PEt3)2C[triple bond]C(C6H4)E(C6H4)C[triple bond]CPt(Ph)(PEt3)2] and their closest Group 11 gold(I) and Group 12 mercury(II) neighbours, [MC[triple bond]C(C6H4)E(C6H4)C[triple bond]CM] (M = Au(PPh3), HgMe; E = O, S, SO, SO2). The regiochemical structures of these angular-shaped molecules were studied by NMR spectroscopy and single-crystal X-ray structural analyses. Upon photoexcitation, each one has an intense purple-blue fluorescence emission near 400 nm in dilute fluid solutions at room temperature. Harvesting of the organic triplet emissions harnessed through the strong heavy-atom effects of Group 10-12 transition metals was studied in detail. These metal-containing aryleneethynylenes spaced by chalcogen units were found to have large optical gaps and high-energy triplet states. The influence of metal- and chalcogen-based conjugation interrupters on the intersystem crossing rate and on the spatial extent of the lowest singlet and triplet excitons was fully elucidated. We discuss and compare the phosphorescence spectra of these transition-metal diynes and polyynes in terms of the nature of the metal centre, conjugated chain length and Group 16 spacer unit. Our work here indicates that high-energy triplet states in these materials intrinsically give rise to very efficient phosphorescence with fast radiative decays and one could readily observe room-temperature phosphorescence for the platinum polyynes.     

Analysis of cyanobacterial toxins by physicochemical and biochemical methods

Cyanobacteria (blue-green algae) produce a wide range of low molecular weight metabolites that include potent neurotoxins, hepatotoxins, and cytotoxins. The accumulation of such toxins in freshwaters, and in brackish and marine waters presents hazards to human and animal health by a range of exposure routes. A review is presented of developments in the detection and analysis of cyanobacterial toxins, other than bioassays, including application of physicochemical, immunoassays, and enzyme-based methods. Analytical requirements are considered with reference to recently derived guideline levels for the protection of health and to the availability, or otherwise, of purified, quantitative cyanobacterial toxin standards.     

Neutral Calabi-Yau Structures on Kodaira Manifolds

We construct neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds. Our structures are symmetric with respect to the central tori.Partially supported by The European Contract HPRN-CT-2000-00101, MURST and GNSAGA (Indam) of ItalyPartially supported by The European Contract HPRN-CT-2000-00101Partially supported by NSF     

Cluster mode-coupling approach to weak gelation in attractive colloids

Mode-coupling theory (MCT) predicts the arrest of colloids in terms of their volume fraction, and the range and depth of the interparticle attraction. We discuss how the effective values of these parameters evolve under cluster aggregation. We argue that weak gelation in colloids can be idealized as a two-stage ergodicity breaking: first at short scales (approximated by the bare MCT) and then at larger scales (governed by MCT applied to clusters). The competition between the arrest and phase separation is considered in relation to recent experiments. We predict a long-lived "semiergodic" phase of mobile clusters, showing logarithmic relaxation close to the gel line.     

Does gravity cause load-bearing bridges in colloidal and granular systems?

We study structures which can bear loads, "bridges", in particulate packings. To investigate the relationship between bridges and gravity, we experimentally determine bridge statistics in colloidal packings. We vary the effective magnitude and direction of gravity, volume fraction, and interactions, and find that the bridge size distributions depend only on the mean number of neighbors. We identify a universal distribution, in agreement with simulation results for granulars, suggesting that applied loads merely exploit preexisting bridges, which are inherent in dense packings.     

On the Dirichlet's box principle

In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in Hong Kong.     

Elastic properties of spherically anisotropic piezoelectric composites

Effective elastic properties of spherically anisotropic piezoelectric composites, whose spherically anisotropic piezo-electric inclusions are embedded in an infinite non-piezoelectric matrix, are theoretically investigated. Analytical solutions for the elastic displacements and the electric potentials under a uniform external strain are derived exactly. Taking into account of the coupling effects of elasticity, permittivity and piezoelectricity, the formula is derived for estimating the effective elastic properties based on the average field theory in the dilute limit. An elastic response mechanism is revealed, in which the effective elastic properties increase as inclusion piezoelectric properties increase and inclusion dielectric properties decrease. Moreover, a piezoelectric response mechanism, of which the effective piezoelectric response vanishes due to the symmetry of spherically anisotropic composite, is also disclosed.     

Anomalous scaling behaviour of cobalt cluster size distributions on graphite,epitaxial graphene and carbon-rich (6√3 × 6√3)R30°

The influence of the underlying interface on adsorption of cobalt (Co) is investigated by comparing the nucleation and growth of Co at room temperature on three carbon (C) surfaces, i.e. highly oriented pyrolytic graphite (HOPG), epitaxial graphene/SiC(0001) (hereafter abbreviated as EG) and precursor of EG i.e. C-rich (6√3 × 6√3)R30°/SiC(0001) (hereafter abbreviated as 6√3). On all three surfaces, Co adopts Volmer–Weber growth mode via formation of three-dimensional dome-shaped nanoclusters. Co clusters formed on 6√3 surface are smaller but denser than Co/HOPG or Co/EG. Scaling analysis reveals a critical nucleus size, i* = 1 (atom) and the smallest stable cluster (i* + 1) would be a dimer. Co/HOPG and Co/EG have the same order of magnitude for their cluster densities and sizes. Scaling analyses however show that the i* for Co/EG (i* = 3) is larger than Co/HOPG (i* = 0) and in this respect the smallest stable cluster would be tetramer and monomer respectively. This difference is attributed to the influence of an interface situated between graphene and SiC bulk. It appears that EG is more inert than HOPG towards the adsorption of Co and may act as a better substrate to host Co clusters.