Modelling interactions between a PBB and fullerenes

Fullerenes have many uses including in medical and electronic nanodevices. High pressure liquid chromatography (HPLC) columns are generally used to extract a certain structure of fullerne from a mixture of them. In this paper, we investigate the interactions between various types of fullerenes and a station phase in HPLC known as pentabromobenzyl (PBB). The Lennard-Jones potential and a continuum approach are employed to determine the van der Waals energy of these interactions within the HPLC columns. The equilibrium configurations for any given distance between a fullerene and the centre of a PBB are obtained. Results of this study may assist the design of a chromatography column for fullerene separation.     

Wave-like deformations for oscillating carbon nanotubes

Carbon nanostructures such as nanotubes and fullerenes, represent future materials because of their remarkable mechanical, electrical and thermal properties. Double-walled carbon nanotubes are widely studied as possible gigahertz oscillators, where the inner tube oscillates within the outer tube. These oscillators are believed to generate frequencies in the gigahertz range and typically of the order of 1–74 GHz. They are also known to generate wave-like formations on the outer surface. In this paper, we study such induced deformations on the surface of the outer tube, as generated by the moving inner tube. Following previous authors we assume that double-walled carbon nanotubes can be modelled as transversely isotropic linearly elastic materials. Using a previously derived approximate force distribution for the resultant van der Waals forces arising from the interatomic interactions, we solve a dynamic linearly elastic problem, and show that the resulting solution exhibits wave-like behaviour.     

Toroidal molecules formed from three distinct carbon nanotubes

In order to design nanotori for nanomechanical systems, perhaps involving oscillating components, precise physical parameters for the nanotori are necessary. Toroidal shaped molecules of carbon have been investigated previously by the present authors as constructed by connecting elbow sections formed from joining armchair and zigzag nanotubes through a pentagonal–heptagonal pair defect. In this paper, we extend this design by constructing the elbow structures from three distinct carbon nanotubes. Since for a toroidal molecule, there is a constraint on the bend angles in the elbow sections to add up to 360°, particular elbow types which can accommodate this requirement are (5,0)–(4,4)–(7,0) and (3,3)–(6,0)–(4,4). We adopt a least squares approach for the bond length to minimise the variation from the ideal carbon–carbon bond length, which is taken to be σ = 1.42 Å. Moreover, formulae for the mean generating radius of the nanotori and the mean radius of the nanotubes are obtained from certain integral expressions. This purely geometrical approach can be formally directly related to certain numerical energy minimisation methods used by a number of authors.     

Enantiodivergent Synthesis of Benzoquinolizidinones from L-Glutamic Acid

Benzoquinolizidinone systems were synthesized in both enantiomeric forms from L-glutamic acid. The key chiral arylethylglutarimide intermediate was synthesized from dibenzylamino-glutamate and homoveratrylamine. Aldol reaction of the glutarimide afforded a mixture of syn and anti-aldol adducts. Subsequent regioselective hydride reduction of the glutarimide carbonyl followed by N-acyliminium ion cyclization afforded a product with opposite absolute configurations at C3 and C11b. Cope elimination of the dibenzylamino group then converted the two diastereomers into enantiomers.     

Novel <Emphasis Type="Italic">β</Emphasis>-<Emphasis Type="Italic">N</Emphasis>-acetylglucosaminidases from <Emphasis Type="Italic">Vibrio harveyi 650</Emphasis>: Cloning,expression, enzymatic properties,and subsite identification

Background  

Since chitin is a highly abundant natural biopolymer, many attempts have been made to convert this insoluble polysaccharide into commercially valuable products using chitinases and β-N-acetylglucosaminidases (GlcNAcases). We have previously reported the structure and function of chitinase A from Vibrio harveyi 650. This study t reports the identification of two GlcNAcases from the same organism and their detailed functional characterization.     

Modeling the join curve between two co-axial carbon nanotubes

Making use of an applied mathematical model, we employ a calculus of variations technique to join two co-axial nanotubes. Due to the axial symmetry of the tubes, the three-dimensional problem can be reduced to a problem in two dimensions. The curvature squared for the join region is minimized for a prescribed join length and given tube radii. In this model, a certain non-dimensional parameter B arises, which approximately has the same numerical value when compared with the standard method for the joining between any two carbon nanotubes of different radii. This value occurs in consequence of adopting an angle of inclination of 9.594°, which occurs in the conventional method for joining two carbon nanotubes of different radii and which is necessary to accommodate a single pentagon. The simple calculus of variations model described here provides a general framework to connect nanotubes or other nanostructures.     

Encapsulation behaviours of nanoparticles entering two-section carbon nanotubes

Carbon nanotubes are special nanostructures due to their unique mechanical and electronic properties. One of the proposed applications is a container for drug delivery. In this paper, we consider two-section carbon nanotubes for their uses as nanocapsules to encapsulate a single atom and a C $_{60}$ fullerene. The Lennard-Jones function and the continuous approach are employed to determine the molecular interactions. Moreover, the explicit forms of their interaction energies are determined. The suction energies are utilised to determine the encapsulated conditions of both nanoparticles, where they depend on the radii of the particle and the nanocapsule. This theoretical study can be thought of as the first step to design the nanocapsule for the drug delivery devices.     

Proximal point algorithm for nonlinear multivalued type mappings in Hadamard spaces

In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Δ‐convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.     

Force distribution for double-walled carbon nanotubes and gigahertz oscillators

Advances in nanotechnology have led to the creation of many nano-scale devices and carbon nanotubes are representative materials to construct these devices. Double-walled carbon nanotubes with the inner tube oscillating can be used as gigahertz oscillators and form the basis of possible nano-electronic devices that might be instrumental in the micro-computer industry which are predominantly based on electron transport phenomena. There are many experiments and molecular dynamical simulations which show that a wave is generated on the outer cylinder as a result of the oscillation of the inner carbon nanotube and that the frequency of this wave is also in the gigahertz range. As a preliminary to analyze and model such devices, it is necessary to estimate accurately the resultant force distribution due to the inter-atomic interactions. Here we determine some new analytical expressions for the van der Waals force using the Lennard–Jones potential for general lengths of the inner and outer tubes. These expressions are utilized together with Newton’s second law to determine the motion of an oscillating inner tube, assuming that any frictional effects may be neglected. An idealized and much simplified representation of the Lennard–Jones force is used to determine a simple formula for the oscillation frequency resulting from an initial extrusion of the inner tube. This simple formula is entirely consistent with the existing known behavior of the frequency and predicts a maximum oscillation frequency occurring when the extrusion length is (L ₂ – L ₁)/2 where L ₁ and L ₂ are the respective half-lengths of the inner and outer tubes (L ₁ < L ₂).     

Modelling of carbon dioxide: methane separation using titanium dioxide nanotubes

The separation of carbon dioxide (CO₂) and methane (CH₄) mixture is of considerable interest in order to purify natural gas, and one suggestion is that titanium dioxide (TiO₂) nanotubes might be exploited to separate a gaseous mixture of methane and carbon dioxide. In this study, we employ both Coulomb’s law and the Lennard–Jones potential to determine the total energy of adsorption CO₂ and CH₄ into a TiO₂ nanotube. The CH₄ is a nonpolar molecule, and therefore the Coulombic interaction may be neglected. The total energy of the systems is evaluated utilizing the continuous approximation, which assumes that the two gas molecules are spheres of certain radii, while the tube is modelled as a cylinder. Further, both electrostatic and van der Waals potentials are determined and expressed in the exact analytical formulae. The numerical results predict that a single molecule of CO₂ or CH₄ can be encapsulated into the tube. On assuming both gases may form clusters with the same proportion of atom species, a cluster of CO₂ will not be adsorbed into the tube when its radius exceeds 3.32?. On the other hand, a cluster of CH₄ can be encapsulated into an appropriate radius of TiO₂ nanotube. These results indicate that TiO₂ nanotubes may be useful in the purification of CH₄.