Effect of different types of pseudopotentials on study of electronic dispersion for graphene and a (5,5) SWCNT

We study the electronic dispersion for a graphene sheet and also a (5,5) single wall carbon nanotube (SWCNT) by using the PWscf code from the ‘Quantum Espresso’ package. Two different types of pseudopotentials, ‘norm conserving’ and ‘ultra soft’, have been employed and the results are more or less similar up to the Fermi level. By energy relaxation, it was found that, if the inter-layer distance of graphite expands up to 4.5 times its in-layer (hexagonal) lattice constant, then each layer can be considered as an individual graphene sheet and, in a bundle of (5,5) SWCNTs, the optimum separation between the tubes’ centers is about 19 a.u. and, if it expands to 22 a.u., then a single wall tube consideration can be made. The calculated band structure and density of states (DOS) for the (5,5) SWCNT show that in the vicinity of the Fermi level there is no energy gap (so that it is metallic) and there is a general agreement between them and zone-folding studies or other ab initio methods in the literature. The effects of curvature on the band shifts and DOS have been considered, and they magnify the departure from Mintmire and White’s universal prediction. PACS  71.20.Tx; 71.15.Mb; 73.61.Wp     

Local asymptotic laws for the Brownian convex hull

Summary We prove a general theorem for the precise rate at which the convex hull of Brownian motion gets created. The latter result relates large deviation theory to P. Lévy's geometric proof of Strassen's law of the iterated logarithm. This also answers a question of S. Evans. Moreover, we give a partial solution to a question of J. Hammersley and P. Lévy regarding the slowness of the growth of the hull process. Several examples, some classical and some new, are given to illustrate the theorems. Finally, we present applications to the convex hull of random walks ind dimensions.     

Rapid green synthesis of gold nanoparticles using Rosa hybrida petal extract at room temperature

This study reports a green method for the synthesis of gold nanoparticles using the aqueous extract of rose petals. The effects of gold salt concentration, extract concentration and extract quantity were investigated on nanoparticles synthesis. Gold nanoparticles were characterized with different techniques such as UV-vis spectroscopy, FT-IR spectroscopy, X-ray diffraction, energy dispersive X-ray spectroscopy, dynamic light scattering and transmission electron microscopy. Transmission electron microscopy experiments showed that these nanoparticles are formed with various shapes. FT-IR spectroscopy revealed that gold nanoparticles were functionalized with biomolecules that have primary amine group (-NH2), carbonyl group, -OH groups and other stabilizing functional groups. X-ray diffraction pattern showed high purity and face centered cubic structure of gold nanoparticles. Dynamic light scattering technique was used for particle size measurement, and it was found to be about 10nm. The rate of the reaction was high and it was completed within 5 min.     

Density functional study of super cell N-doped (10,0) zigzag single-walled carbon nanotubes as CO sensor

N-doped SWCNT with different concentration of doped nitrogen atoms were investigated through density functional theory (DFT) calculations for detecting CO molecule. The CO molecule was adsorbed to different sites of the modified nanotubes and their geometric structures and electronic properties were investigated after full optimization. A significant change can be observed in adsorption energies and electronic properties of N-doped SWCNT after CO adsorption. By increasing the number of nitrogen atoms in each unit cell, these properties change more obviously. So these modified nanotubes can be used as CO sensors.