Narrow Results

A nanotube is a nanometer–scale tube-like structure, it is a kind of nanoparticle, and may be large enough to serve as a pipe through which other nanoparticles can be channeled, or, depending on the material, may be used as an electrical conductor or an electrical insulator. For computing the structural information of nanotubes, the graph entropies have become the information theoretic quantities. The graph entropy measure has attracted the research community due to its potential application in discrete mathematics, biology, and chemistry. In this paper, our contribution is to explore graph entropies for structures of some nanotubes based on novel information function, which is the number of different degree vertices along with the number of edges between various degree vertices. More precisely, we computed entropies of some classes of nanotubes such as titania nanotube TNT${}_3[m,n]$, TNT${}_6[m,n]$ and carbon nanotubes HAC${}_5{C}_6{C}_7[m,n]$ by making a relation of degree-based topological indices with the help of information function.

This paper starts with the preparation of anatase titania nanotube (TN) in large quantities by hydrothermal routes with different calcination temperatures, and then delves into a thorough investigation for the characterization of fine structures or formation mechanism of TN. Experimentally, anatase TiO₂ nanoparticle was used as a precursor for TN synthesis. The results showed that the length and diameter of TN range are 50–100 nm and 10–15 nm, respectively. The XRD patterns and BET isotherms indicated that TN owns anatase-typed structures with a surface area of 292m²/g. By extended X-ray absorption fine structure (EXAFS) spectra, the valency and framework of TN are Ti(IV) with octahedral structures. The EXAFS data also revealed that TN has a first shell of Ti–O bonding with bond distances of 1.95 Å and coordination numbers were 2. The results revealed that the TiO₂ anatase nanoparticles can be solved into layer under strong alkaline. The layer of TN further curling itself to reduce the energetics was postulated and found. For calcination temperature larger than 400°C, the microstructure of TN might transform from nanotube into nanoparticles accompanying with the sharp increase for the nanoparticle crystalline phase. With the understanding of pore structure variation on the basic dye (Basic Green 5 (BG5)), the adsorption ability, mechanisms, and kinetics of (Basic Green 5 (BG5)) dye onto TN were examined as well.