Methane in carbon nanotube: molecular dynamics simulation

The behaviour of methane molecules inside carbon nanotubes at room temperature is studied using classical molecular dynamics simulations. A methane molecule is represented either by a shapeless super-atom or by a rigid set of five interaction centres localized on atoms. Different loadings of methane molecules ranging from the dense gas density to the liquid density, and the influence of flexibility of the CNT on structural and dynamic properties of confined molecules are considered. The simulation results show the decreases of the diffusion coefficient of methane molecules with density. At higher densities diffusion coefficient values are almost independent of molecular shape, but at low densities one observes faster motion of the super-atom molecule than that for the tetrahedral model of the molecule. For loadings of methane considered here the nanotube flexibility, introduced by the reactive empirical bond order (REBO) potential for interactions between carbon atoms of nanotube, does not have an effect on diffusivity of methane molecules, and its impact on the molecular structure is weak. It is found that methane molecules in the vicinity of the nanotube wall show tripod orientation with respect to the nanotube surface.     

Beardon's Diophantine Equations and Non-Free Mobius Groups

Let µ be a real number. The Möbius group G_µis the matrix group generated by It is known that G_µ is free if |µ| 2 (see [1])or if µ is transcendental (see [3, 8]). Moreover, thereis a set of irrational algebraic numbers µ which is densein (–2, 2) and for which G_µ is non-free [2, p. 528].We may assume that µ > 0, and in this paper we considerrational µ in (0, 2). The following problem is difficult. Let G^nf denote the set of all rational numbers µ in (0,2) for which G_µ is non-free. In 1969 Lyndon and Ullman[8] proved that G^nf contains the elements of the forms p/(p²+ 1) and 1/(p + 1), where p = 1, 2, ..., and that if µ₀ G^nf, then µ₀/p G^nf for p = 1, 2, .... In 1993 Beardon[2] studied problem (P) by means of the words of the form A^rB^s A^t and A^r B^s A^t B^u A^v, and he obtained a sufficient conditionfor solvability of (P), included implicitly in [2, pp. 530–531],by means of the following Diophantine equations: 1991 Mathematics SubjectClassification 20E05, 20H20, 11D09.     

Chirality of toroidal molecular graphs

Symmetry properties of a class of toroidal molecular graphs, arising as covers of certain bipartite cubic Cayley graphs of dihedral groups, are studied. Although these symmetries make all vertices and all edges indistinguishable, they imply intrinsic chirality.     

Stereoselective synthesis of cobalt(III) anionic complexes with chiral pyruvylaminoacid oximes and metal–ligand interactions in aqueous solution

A series of cobalt(III) anionic complexes with hydroxyimino analogs of dipeptides – oximes of pyruvylglycine, pyruvyl-l-alanine, pyruvyl-l-methionine and pyruvyl-l-phenylalanine (H₂pamaco, amac = amino acid) of composition Cat₃[Co(H₋₁pamaco)₂] · nH₂O (Cat – a monovalent metal cation) has been synthesized and investigated by UV–Vis, CD and ¹H NMR spectroscopy. It was established that for the two latter ligands, non-racemic mixtures of two diastereomeric complexes were formed as a result of synthesis. In comparison with the complex containing pyruvyl-l-alanine, in which the relative content of R (C₂) and S (C₂) isomers is approximately equal, the presence of bulky substituents in the molecules of Met- and Phe-containing ligands results in a significant discrimination in formation of the S (C₂) isomer. This conclusion was drawn upon analysis of the CD and NMR spectral data as well as from molecular modeling. The relative content of the diastereomers was evaluated on the basis of NMR data. The protonation constants of the ligands have been determined in aqueous solution by glass electrode potentiometry, whereas their interactions with Co(II) were studied both under argon and oxygen atmosphere.     

Density of O-atoms in an Afterglow Reactor During Treatment of Wool

Density of neutral oxygen atoms in the ground state has been measured during treatment of wool fabric samples. Samples were placed in an afterglow reactor with a volume of about 5 l, which was pumped with a two stage rotary pump with the nominal pumping speed of 28 m³/h. The source of the oxygen atoms was a microwave discharge operating in the surfatron mode at 2.45 GHz and adjustable output power up to 300 W. The density of O-atoms in the afterglow chamber was measured with a fiber-optics catalytic probe. For the empty reactor, the O density depended on discharge parameters and was between 0.8 and 2.8 × 10²¹ m⁻³ at 40 and 50 Pa respectively. During the treatment of wool, the O density depended largely on the exposure time. For untreated samples, the O density was below the detection limit of the probe, while prolonged treatment allowed for recovering the O density. The recovery always occurred after having submitted wool samples to the dose of the order of 10²³ atoms/m². The results were explained by oxidation of the thin lipid layer on the surface of the wool fibres.     

Cardinal invariants concerning bounded families of extendable and almost continuous functions

In this paper we introduce and examine a cardinal invariant closely connected to the addition of bounded functions from to . It is analogous to the invariant defined earlier for arbitrary functions by T. Natkaniec. In particular, it is proved that each bounded function can be written as the sum of two bounded almost continuous functions, and an example is given that there is a bounded function which cannot be expressed as the sum of two bounded extendable functions.

     

Determination of melatonin and its precursors and metabolites using capillary electrophoresis with UV and fluorometric detection

A micellar electrokinetic chromatography method has been developed for simultaneous determination of melatonin and its precursors and metabolites. A 20 mM borate buffer pH 9.5 with 50 mM SDS served as the electrolyte. Tryptophan, 5-methoxyindoleacetic acid, 6-hydroxymelatonin, melatonin, serotonin, and 5-methoxytryptamine were baseline separated in less than 13 min. The limits of detection for UV detection and fluorometric detection based on native fluorescence of analytes were at the sub-ppm level. The proposed method with UV detection was applied to melatonin content control in pharmaceutical tablets with a precision expressed as RSD (n = 7) = 1.6%. For biological samples extraction with chloroform and ethyl acetate was examined. With ethyl acetate and chloroform recoveries of 87.2% and 82.1% melatonin, respectively, were obtained from plasma samples. The recovery of melatonin from spiked urine samples was 80.0% for ethyl acetate and 82.5% for chloroform. Fluorometric detection provides about two-fold improvement over UV in the detection of melatonin and minor improvements for three other analytes, but is much poorer than UV for tryptophan and 6-hydroxymelatonin in applied conditions.