The PI index is a graph invariant defined as the summation of the sums of edges of neu and nev over all the edges of connected graph G, where neu is the number of edges of G lying closer to u than to v and nev is the number of edges of G lying closer to v than to u. The index is very simple to calculate and has disseminating power similar to that of the Wiener and the Szeged indices. The compre...

We consider theoretically an armchair carbon nanotube (CNT) in the presence of an electric field and in contact with an s-wave superconductor. We show that the proximity effect opens up superconducting gaps in the CNT of different strengths for the exterior and interior branches of the two Dirac points. For strong proximity induced superconductivity the interior gap can be of the p-wave type, w...

The behavior and electronic structure of the carbon boron nitride nanotubes that interact with iron atom were studied using Lennard–Jones potential hybrid discrete-continuum approach. iron-filled explored by means classical applied mathematics in order to develop an understanding underlying mechanisms encapsulation metal atoms inside nanotubes. Herein, we examined suction energy then equilibriu...

Black phosphorus (BP), a new two-dimensional material, has been the focus of scientists' attention. BP nanotubes have potential in the field of optoelectronics due to their low-dimensional effects. In this work, the bending strain energy, electronic structure, and optical properties of BP nanotubes were investigated by using the first-principles method based on density functional theory. The re...

We have performed density functional theory (DFT) calculations to investigate the properties of defect in arepresentative armchair model of silicon nanotubes (SiNTs). To this aim, the structures of pristine and defective(5,5) SiNTs have been optimized and the properties such as bond lengths, total energies, binding energies,.formation energies, gap energies, and dipole moments have been evaluat...

In this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT) - reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. Molecular structural mechanics (MSM)/finite ...

This work addresses the problem of modification mechanical parameters carbon nanotubes as a result Congo red and Evans blue adsorption, functionalization surfaces by carboxyl groups generation surface defects. The studies were also focused on quantum chemical analysis effects adsorption properties nanotubes. We found that is rather physisorbed than chemisorbed it does not significantly affect e...