Studies of Size Effects on Carbon Nanotubes' Mechanical Properties by Using Different Potential Functions

Abstract

We use molecular mechanics calculations to study size effects on mechanical properties of carbon nanotubes. Both single-walled nanotubes (SWNTs) and multiwalled nanotubes (MWNTs) are considered. The size-dependent Young's modulus decreases with the increasing tube diameter for a reactive empirical bond order (REBO) potential function. However, we observe a contrary trend if we use other potential functions such as the modified Morse potential function and the universal force field (UFF). Such confliction is only obtained for small tubes within cutoff diameters (3 nm for REBO and 1.5 nm for others). In light of these predictions, Young's moduli of large nanotubes concur with experimental results for all the potential functions. No matter which potential function is used, the Poisson's ratio decreases with the increasing tube diameter. We also study the chirality effects on mechanical properties of SWNTs. We find that the Young's moduli are insensitive to the chirality of nanotubes. The chirality effect on the Poisson's ratio is significant for the UFF but not the REBO or modified Morse potential functions.

Examining the effects of wall numbers on buckling behavior and mechanical properties of multiwalled carbon nanotubes via molecular dynamics simulations

“…For set 2 MWCNTs, Young's modulus as well as buckling strain is more sensitive to the outer diameter than the wall number. Again the dependence of Young's modulus on wall number for the set 2 MWCNTs is also confirmed by other researchers 10,11,18,20 36 using a tight-binding ͑TB͒ method͔.…”

“…For a given inner diameter, the outer diameter of MWCNTs is increased with respect to the wall number. It is concluded by numerous studies 7,11,15,18,20,35 that Young's modulus is inversely dependent on the outer diameter of SWCNT, i.e., a larger outer diameter leads to a lower Young's modulus. For example, Young's modulus of the ͑20,20͒ SWCNT as shown in Table III is 0.9937 TPa, which is smaller than the 1.2853 TPa of the ͑5,5͒ SWCNT with a smaller diameter in Table IV.…”

“…Investigations on MWCNTs normally maintain a constant outer diameter and inner tubes are progressively added to form the MWCNTs 14,17,18 or maintain a constant inner diameter and outer tubes are progressively added to construct the MWCNTs. 6,10,11,[18][19][20] For the sake of brevity, we shall refer to the former category as set 1 MWCNTs and the latter category as set 2 MWCNTs. Garg and Sinnott 14 ran MD simulations using the reactive empirical bond order ͑REBO͒ potential 21 coupled with a long-range Lennar-Jones ͑LJ͒ 22 potential to investigate the indentation of various surfaces by SWCNT and double-walled CNTs ͑DWCNTs͒.…”

Nonlocal elasticity based magnetic field affected vibration response of double single-walled carbon nanotube systems

“…However, classical continuum mechanics is a scale-free theory and cannot account for effects arising from small size. Experimental [5][6][7][8] and atomistic simulations 9,10 have evidenced a significant "size-effect" in mechanical and physical properties when the dimensions of the structures become "small." Size effects are related to atoms and molecules that constitute the materials.…”

The effects of grafted amine groups on the elastic properties of single-walled carbon nanotubes

“…Their basic hexagon units are perpendicular to each other; therefore, the size-dependent Young's modulus should be different. It was reported that the Young's modulus increases with the decreases of the tube radius [36,37]; but opposite trends were also reported [32,33]. …”