Measurement of radial deformation of single-wall carbon nanotubes induced by intertube van der Waals forces

A cylindrical single-wall carbon nanotube (SWCNT) deforms in a nanotube bundle by van der Waals forces. The deformation is hard to measure, but is required in order to understand the properties of bundles. Here, we show that such deformations can be measured from changes in electron diffraction intensities. We demonstrate this for a bundle of two SWCNTs ($d=2.05$ and $1.56\mathrm{nm}$). Deformation model predicted by atomistic simulations is scaled to fit the experiment. We show that the best fit gives flattening values of 0.7 and $0.35\mathrm{\AA }$ at the middle of the binding surface for the two SWCNTs.

Figure 1

(Color online) (a) Experimental DP recorded from a bundle of two single-wall carbon nanotubes. There are two sets of layer lines from two tubes as indexed at left (B) and right (A). (b) The profile of equatorial line $E$ and the profile obtained by curve fitting using the following parameters: the diameters of the two tubes and the separation distance $d$. The $R$ is in $1∕\mathrm{\AA }$.

Figure 2

(Color online) Deformation of the (19,11) and (17,5) bundle predicted by atomistic simulations and from the best fit model with experiment. (Top) the cross sections of the deformed tubes. (Middle) the radial deformation measured in the percentage of the original radius $\left({\rho }_o\right)$ plotted as a function of angle $\theta$ (in deg) for the (19,11) tube and (bottom) for the (17,5) tube.

Figure 3

(Color online) The effects of tube deformation on the layer line intensity for the (19,11) tube and layer lines of (10), (01), and $\left(1\overline{1}\right)$. The solid lines are calculated with the deformation shown in Fig. 2. The dashed lines are the same layer lines calculated with the cylindrical (19,11) tube (nondeformed). The large changes in layer line intensities can be used for experimental determination of tube deformation. The $R$ is in $1∕\mathrm{\AA }$.

Figure 4

(Color online) A comparison between experiment and different tube models: nondeformed (circular), deformed tubes as predicted by atomistic simulations (Fig. 2, labeled as 1.0), deformed tubes with the radial deformation scaled by a factor of 0.75. The crosses are experimental data. The $R$ is in $1∕\mathrm{\AA }$.