Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.     

Spatially resolved dynamic eigenmode spectrum of Co rings

The spatially resolved eigenmode spectrum of micrometer-sized Co ring elements has been determined by means of combined vector network analyzer ferromagnetic resonance and time resolved magneto-optic Kerr effect measurements. Up to 5 resonant eigenmodes were observed in the frequency range from 45 MHz to 20 GHz as a function of an external magnetic bias field. A well-defined mode structure was found for the two equilibrium states (vortex and onion) which correspond to distinctive spatial modes. The effect of dynamic inter-ring coupling on the modes in the remanent states was evinced. The experimental results are found to be in good agreement with those of micromagnetic simulations. Our results demonstrate that, in analogy to the well-defined static equilibrium magnetic states of ring elements, the eigenmode spectra of this high symmetry geometry consist of a well-defined and simple mode structure.     

Phenacenes from Diels-Alder trapping of photogenerated o-xylylenols: phenanthrenes and benzo[e]pyrene bisimide

[structure: see text] The synthesis of phenanthrene and benzo[e]pyrene bisimides, 1 and 2, was accomplished via the Diels-Alder trapping of sterically congested o-xylylenols photochemically generated from 3,6-dibenzoyl-o-xylene and 1,4-dibenzoyl-9,10-dihydroanthracene, respectively. Absorption and emission from 2 are red-shifted from 1 and unsubstituted benzo[e]pyrene. The fluorescence quantum yield for 2 is an order of magnitude lower than that of 1 and comparable to that of the parent benzo[e]pyrene.     

Synchronization of eukaryotic cells by periodic forcing

We study a cell population described by a minimal mathematical model of the eukaryotic cell cycle subject to periodic forcing that simultaneously perturbs the dynamics of the cell cycle engine and cell growth, and we show that the population can be synchronized in a mode-locked regime. By simplifying the model to two variables, for the phase of cell cycle progression and the mass of the cell, we calculate the Lyapunov exponents to obtain the parameter window for synchronization. We also discuss the effects of intrinsic mitotic fluctuations, asymmetric division, and weak mutual coupling on the pace of synchronization.     

‘It takes me longer,but I understand better’ – student feedback on structured derivations

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of understanding. Our findings indicate that the main drawbacks experienced by the students are related to time and length. Nevertheless, the overall feedback on the approach was found to be positive, thus encouraging further use of structured derivations in mathematics education.     

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.     

Key steps and intermediates in the catalytic mechanism for the reduction of peroxides by the antioxidant ebselen

Hydrogen peroxide and lipid hydroperoxides are formed during aerobic metabolism and contribute to oxidative stress, a major factor in many diseases and degenerative conditions. Although the selenoenzyme glutathione peroxidase (GPx) affords antioxidant protection in vivo by catalytically reducing harmful peroxides with glutathione, certain conditions benefit from the administration of small-molecule GPx mimetics for additional protection. To date, ebselen has been the most widely studied such compound, but its catalytic mechanism is complex and highly variable with conditions. Progress in elucidating the mechanistic details of its antioxidant activity is described in this review.     

Analytical selenoamino acid studies by chromatography with interfaced atomic mass spectrometry and atomic emission spectral detection

Consumption of selenium enriched plants or yeast-based nutritional supplements has been reported to provide anticarcinogenic benefits which are selenium compound dependent. Separation and identification of these selenium compounds is critical to understand the activity. Plants and yeast convert inorganic selenium in the soil or growth media into organoselenium compounds, probably following a route similar to the sulfur assimilatory pathway. Non-volatile selenium compounds produced include selenoamino acids, some of which have shown anticarcinogenic activity. Volatile compounds produced by chemical reaction of involatile precursors have also been found. An ion pair chromatographic method with ICP-MS detection for the separation of selenoamino acid standards potentially present in real samples is given. The method allows separation of selenoamino acids including such analytes as the cis-trans isomers of Se-1-propenyl-dl-selenocysteine. The method also provides the capability of determining the presence of selenoxides and possibly selenones, and tracking of other functionalities and reactions by selective derivatization. Alternatively, selenoamino acids are treated with ethylchloroformate to produce stable volatile derivatives which are amenable to GC separation with element specific atomic emission detection (GC-AED). Results of total selenium determination and speciation of selenium enriched yeast-based nutritional supplements, selenium enriched allium vegetables and bioremediation samples are presented.     

1,3-Dipolar cycloadditions of acetylenic sulfones in solution and on solid supports

Several representative acetylenic sulfones were immobilized on a polymer support derived from Merrifield resin by means of ester linkers that were used to couple free carboxylic acid groups on the solid support with benzylic hydroxyl functions on the arylsulfonyl moieties of the acetylenes. Several examples of reversed ester linkers, using Merrifield resin directly, were also successfully prepared. The 1,3-dipolar cycloadditions of the solid-supported acetylenic sulfones were investigated with a series of 1,3-dipoles, including benzyl azide, ethyl diazoacetate, diazomethane, as well as representative nitrile oxides, nitrile imines, nitrile ylides, nitrones, azomethine imines, azomethine ylides, munchnones, and sydnones. In general, analogous cycloadditions were also performed with acetylenic sulfones in solution phase for comparison. The cycloadditions typically afforded good to excellent yields of the desired products in both solution and solid phase, although the latter reactions sometimes required more vigorous conditions. Except in the case of benzyl azide and diazo compounds, where mixtures of regioisomers were obtained, the other 1,3-dipoles reacted with high regioselectivity and afforded essentially unique regioisomers. Cleavage of the products from the resin was smoothly effected by alkaline hydrolysis, while several attempts at reductive desulfonylation with sodium amalgam or samarium diiodide-HMPA resulted in N-O or C-O scission, in addition to cleavage from the polymer. The method provides access to a number of important classes of heterocycles, including variously substituted and functionalized triazoles, pyrazoles, 1,2-oxazoles, pyrroles, as well as their dihydro and bicyclic analogues. The success of the cycloadditions on polymer supports paves the way to future investigations of sequential transformations leading to libraries of useful heterocycles.     

Tandem conjugate additions and 3-aza-Cope rearrangements of tertiary allyl amines and cyclic alpha-vinylamines with acetylenic sulfones. Applications to simple and iterative ring expansions leading to medium and large-ring nitrogen heterocycles

Tertiary acyclic allyl amines and tertiary cyclic alpha-vinyl amines undergo conjugate additions to acetylenic sulfones to produce zwitterion intermediates, followed by 3-aza-Cope rearrangements. In the case of cyclic alpha-vinyl amines, the process results in ring-expansion, providing a novel route to 9- to 17-membered cyclic amines. The Hammett plot for the reaction of 8b with 2a- 2f shows rho = +1.19, which is consistent with formation of the proposed zwitterion in the rate-determining step, where electron-withdrawing substituents on the arylsulfonyl moiety stabilize the negative charge and enhance the rate of the reaction. Alternative pathways were observed in methanol in the case of 11, where a methoxy substituent promotes a dissociative mechanism of the corresponding zwitterion via a stabilized allyl cation, whereas the zwitterion derived from amine 12 undergoes ring-opening by direct attack of methanol upon the strained aziridinium moiety instead of by rearrangement. An iterative process was developed, where the product of one ring-expansion is converted into a new cyclic alpha-vinyl amine, followed by a repetition of the conjugate addition and [3,3] rearrangement. This protocol was illustrated by its application to the synthesis of motuporamine A and B.