Diameter-Dependent Bending Modulus of Individual Multiwall Boron Nitride Nanotubes

Abstract

The mechanical properties of individual multiwall boron nitride nanotubes (MWBNNTs) synthesized by a growth-vapor-trapping chemical vapor deposition method are investigated by a three-point bending technique via atomic force microscopy. Multiple locations on suspended tubes are probed in order to determine the boundary conditions of the supported tube ends. The bending moduli (EB) calculated for 20 tubes with diameters ranging from 18 to 58 nm confirm the exceptional mechanical properties of MWBNNTs, with an average EB of 760 ± 30 GPa. For the first time, the bending moduli of MWBNNTs are observed to increase with decreasing diameter, ranging from 100 ± 20 GPa to as high as 1800 ± 300 GPa. This diameter dependence is evaluated by Timoshenko beam theory. The Young's modulus and shear modulus were determined to be 1800 ± 300 and 7 ± 1 GPa, respectively, for a trimmed data set of 16 tubes. The low shear modulus of MWBNNTs is the reason for the detected diameter-dependent bending modulus and is likely due to the presence of interwall shearing between the crystalline and faceted helical nanotube structures of MWBNNTs.

Hyperelasticity of three-dimensional carbon nanotube sponge controlled by the stiffness of covalent junctions

“…Our proposed model also predicts that the apparent modulus is dependent on the diameter squared and the elastic modulus of the CNT junction. It has been proved that the elastic modulus of CNTs has a strongly nonlinear, diameter-dependent characteristic [34,35]. Here, by assuming the CNTs and CNT junctions share a similar correlation between diameter and elastic modulus (see the Supplemental information for details) [35], the diameter-dependent apparent modulus of N-MWCNT sponges is predicted and drawn in Fig.…”

The Buckling Behavior of Boron Nitride Nanotubes under Bending: An Atomistic Study

“…Potential applications of BN-NTs need a comprehension of the mechanical properties and performance of BN-NTs under various loading conditions. BN-NTs under compression [13][14][15], tension [16,17], torsion [16,[18][19][20] and bending with 2 fixed or simple supports [21,22] have been investigated. So far, theoretical studies of the buckling behavior under bending of BN-NTs seem still unexplored.…”

Size-dependent bending modulus of nanotubes induced by the imperfect boundary conditions

“…However, in contrast to the result of the tensile test17 a unique size-dependent bending modulus was reported in most existing TPB tests of CNTs and BNNTs9101112131415. To explain the size-dependent elastic modulus of nanotubes observed in the TPB tests, a transverse shear theory was proposed by Salvetat et al 11.…”

“…To characterize the mechanical properties of nanotubes a variety of experimental approaches have been proposed78, among which the three-point bending (TPB) test conducted with the atomic force microscope (AFM) is widely used910111213141516. In such AFM-based TPB test nanotubes are deposited onto a stiff substrate with a topographical pattern, such as polished porous aluminium oxide membranes or silica gratings patterned with trenches (see Fig.…”

“…To explain the size-dependent elastic modulus of nanotubes observed in the TPB tests, a transverse shear theory was proposed by Salvetat et al 11. initially in 1999 and then widely adopted by many other researchers12131415. By tacitly assuming that the size-dependence phenomenon originates from the transverse shear effect, the “curve fitting technique” was used to explain the size-dependence of the bending modulus.…”