Nanomechanics of Carbon Nanotubes

Abstract

We discuss the mechanical properties of carbon nanotubes, in particular the pressure-dependence of the Raman modes and the collapse pressure, and their relation to the corresponding mechanical properties of graphite and graphene. The frequencies of the Raman G-mode and radial breathing mode (RBM), as well as the pressure dependence of the RBM can be largelyexplained in the existing framework of C-C stretching modes and envirionmental effects induced by the pressure medium. The pressure dependence of the G-mode is still missing such an explanation. The collapse pressure can be understood in terms of the continuum theory for thin-walled tubes.

Buckling of ZnS-filled single-walled carbon nanotubes – The influence of aspect ratio

“…Lastly, for an aspect ratio of 20, both empty and filled (13,0) SWCNT showed first an elastic response reaching small yield strains, followed by an almost constant residual force.The collapse under compressive force of an empty and filled (26,0) SWCNT is illustrated inFigure Four different stages are highlighted, namely, I) the initial, relaxed configuration, II) the system just before it buckles, III) immediately after the structural collapse and IV) the final, fully compressed configuration obtained at 10% strain. A similar buckling behaviour was recently reported from Monte Carlo simulations also for applied hydrostatic pressure[35]. The higher deformability of the empty SWCNT seen inFigure 2provides a clear visual clue of how the yield strength is increased with the inclusion of the ZnS.…”

From mesoscale to nanoscale mechanics in single-wall carbon nanotubes

“…Our experimental and theoretical results for the collapse pressures are collected and compared in Figure 4. We also compare them with the MD and G-band Raman data reported in the literature et al [8] and the DFTB results previously reported for bundled nanotubes without PTM [5] (these are given and for the MC model [29] as well as for DFTB calculations [5]. In the polygon model, the R −3 dependence was observed for all n g -gons, but with a correction term in n g so that the normalised collapse pressure could be written as P N C ≃ 24D(1−β 2 g /n 2 g ) with β g ≃ 5.3 (here β g stands for "geometric β").…”

“…In the simulations, armchair and zig-zag nanotubes with diameters up to 5.7 nm were hydrostatically loaded. Some of the collapse pressures were previously reported [29].…”

“…The onset of collapse corresponds then to a bifurcation, and its completion to a value of the smallest diameter close to the graphite interlayer distance. This is done in Figure 3 for MC and DFTB as well as for two simple models, the elastic ring model [2,25] and the polygonal model [29]. The latter is derived from the continuum elastic ring model by moving all the distributed compliance to n discrete points.…”

Pressure dependence of the interlayer and intralayer E2g Raman-active modes of hexagonal BN up to the wurtzite phase transition

“…The GGA approach used in these calculations provides an improved description of the strong intralayer valence bonds in relation to previous studies based on the local density approximation [37,[42][43][44], and yields frequency values that are in excellent agreement with the experimental results. In the case of graphite, it has been argued that the sublinear pressure dependence of the E high 2g frequency is largely due to the reduced in-plane force on the sp 2 bonds resulting from the large c-axis compression under pressure, which introduces sublinearity in the pressure dependence of the biaxial inplane force [45]. Since the c-axis linear compresibility of h-BN (β 0 = 37.7 GPa, β = 6.3) is comparable to that of graphite (β 0 = 35.7 GPa, β = 10.8), the same effect is expected in h-BN.…”