On the Determination of Elastic Properties of Single-Walled Boron Nitride Nanotubes by Numerical Simulation

Abstract

The elastic properties of chiral and non-chiral single-walled boron nitride nanotubes in a wide range of their chiral indices and diameters were studied. With this aim, a three-dimensional finite element model was used to assess their rigidities and, subsequently, elastic moduli and Poisson’s ratio. An extensive study was performed to understand the impact of the input parameters on the results obtained by numerical simulation. For comparison, the elastic properties of single-walled boron nitride nanotubes are shown together with those obtained for single-walled carbon nanotubes.

Elastic Properties of Single-Walled Phosphide Nanotubes: Numerical Simulation Study

“…Similar to what was found in the authors’ previous work for the SWBNNTs [ 39 ], the straight lines in Figure 9 a–f can be expressed as follows: where , and are the fitting parameters. The values of these parameters, obtained from the graphs in Figure 9 a–f for single-walled phosphide NTs, are shown in Table 6 .…”

“…As for the cases of the single-walled carbon nanotubes (SWCNTs) [ 40 , 41 ] and single-walled boron nitride nanotubes (SWBNNTs) [ 39 ], and for the phosphide NTs under study, the values of the tensile rigidity, EA, can be represented by a linear function of nanotube diameter, (see Figure 9 a,b), and the values of bending, EI, and torsional, GJ, rigidities can be represented by a linear function of (see Figure 9 c–f).…”

“…As previously deduced for SWCNTs [ 40 , 41 ] and SWBNNTs [ 39 ], the Young’s and shear moduli of NTs structures can be calculated using the following expressions, respectively: where EA, EI and GJ are the tensile, bending and torsional rigidities, respectively, and is the nanotube wall thickness. The EA, EI and GJ rigidities can be calculated from the results of the FE analysis by Equations (30)–(32), respectively, or evaluated analytically using Equations (33)–(35), respectively.…”

“…Since the phosphide NTs have a potential application in the NT-based devices and hybrid nanostructures, where they can be combined with carbon or other non-carbon NTs, the surface Young’s and shear moduli of the SWBPNTs, SWAlPNTs, SWGaPNTs and SWInPNTs were compared with respective surface elastic moduli of the SWCNTs and SWBNNTs in Table 9 . and of carbon and boron-nitride NTs were calculated from the results of the authors’ previous work [ 39 ], using the expressions and , respectively, and taking into account that the value of the nanotube wall thickness = 0.34 nm, for both classes of NTs.…”

“…The chiral indices of NTs were chosen in order to obtain structures with comparable diameters. The length of the NTs was chosen to be about 30 times greater than the NT diameter to ensure that the mechanical response of nanotubes is independent of the NT length [ 39 ].…”