The blocking probability of spider-web networks

We determine the limiting behavior of the blocking probability for spider-web networks, a class of crossbar switching networks proposed by Ikeno. We use a probabilistic model proposed by the author, in which the busy links always form disjoint routes through the network. We show that if the occupancy probability is below the threshold 2 - √2 = 0.5857…, then the blocking probability tends to zero, whereas above this threshold it tends to one. This provides a theoretical explanation for results observed empirically in simulations by Bassalygo, Neiman, and Vvedenskaya.     

Ionic liquids as reagents and solvents in conjunction with microwave heating: rapid synthesis of alkyl halides from alcohols and nitriles from aryl halides

We show that using ionic liquids as reagents in conjunction with microwave heating it is possible to prepare primary alkyl halides from the corresponding alcohols rapidly. Using ionic liquids as solvents in conjunction with microwave heating it is possible to prepare aryl nitriles from the corresponding aryl bromides or iodides. The scope and limitations of using microwave-promotion as a tool in these reactions is discussed.     

Fabrication of material-independent morphology gradients for high-throughput applications

Gradient surfaces allow rapid, high-throughput investigations and systematic studies in many disparate fields, including biology, tribology and adhesion. We describe a novel method for the fabrication of material-independent morphology gradients, involving a two-step process of particle erosion followed by a chemical polishing procedure that preferentially removes features with a small radius of curvature as a function of time. Gradients are fabricated on aluminium surfaces, but they may be readily transferred to other materials via a replication technique, which allows for the production of identical roughness gradient samples with any chosen surface chemistry. The gradients have been characterized by means of scanning electron microscopy and optical profilometry. Standard roughness parameters (Ra, Rq, Rz, Sm and Sk) were calculated from optical profilometry data. The roughness has also been assessed over different wavelength windows by means of a fast Fourier transformation approach.     

Characterisation of the photocatalyst Pilkington Activ™: a reference film photocatalyst?

Pilkington Glass Activ™ represents a possible suitable successor to P25 TiO₂, especially as a benchmark photocatalyst film for comparing other photocatalyst or PSH self-cleaning films. Activ™ is a glass product with a clear, colourless, effectively invisible, photocatalytic coating of titania that also exhibits PSH. Although not as active as a film of P25 TiO₂, Activ™ vastly superior mechanical stability, very reproducible activity and widespread commercial availability makes it highly attractive as a reference photocatalytic film. The photocatalytic and photo-induced superhydrophilitic (PSH) properties of Activ™ are studied in some detail and the results reported. Thus, the kinetics of stearic acid destruction (a 10⁴ electron process) are zero order over the stearic acid range 4–129 monolayers and exhibit formal quantum efficiencies (FQE) of 0.7×10⁻⁵ and 10.2×10⁻⁵ molecules per photon when irradiated with light of 365±20 and 254 nm, respectively; the latter appears also to be the quantum yield for Activ™ at 254 nm. The kinetics of stearic acid destruction exhibit Langmuir–Hinshelwood-like saturation type kinetics as a function of oxygen partial pressure, with no destruction occurring in the absence of oxygen and the rate of destruction appearing the same in air and oxygen atmospheres. Further kinetic work revealed a Langmuir adsorption type constant for oxygen of 0.45±0.16 kPa⁻¹ and an activation energy of 19±1 kJ mol⁻¹. A study of the PSH properties of Activ™ reveals a high water contact angle (67°) before ultra-bandgap irradiation reduced to 0° after prolonged irradiation. The kinetics of PSH are similar to those reported by others for sol–gel films using a low level of UV light. The kinetics of contact angle recovery in the dark appear monophasic and different to the biphasic kinetics reported recently by others for sol–gel films [J. Phys. Chem. B 107 (2003) 1028]. Overall, Activ™ appears a very suitable reference material for semiconductor film photocatalysis.     

Winding Clusters in Percolation on the Torus and the Möbius Strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Möbius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Möbius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.