SUPPLEMENTARY INFORMATION

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1 SUPPLMNTARY INFORMATION Hindered rolling and friction anisotropy in supported carbon nanotubes Marcel Lucas 1, Xiaohua Zhang +, Ismael Palaci 1, Christian Klinke 3, rio Tosatti, 4 * and lisa Riedo 1 * 1 School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA , USA International School for Advanced Studies (SISSA), and CNR-INFM Democritos, Via Beirut 4, Trieste, Italy 3 Institute of Physical Chemistry, University of Hamburg, Grindelallee 117, 0146, Hamburg, Germany 4 International Centre for Theoretical Physics (ICTP), Strada Costiera 11, Trieste, Italy * tosatti@sissa.it * elisa.riedo@physics.gatech.edu nature materials 1

2 1) Friction force calibration The lateral force was calibrated using the wedge method on the Mikromasch TGG01 silicon grating (D. F. Ogletree, R. W. Carpick, and M. Salmeron, Rev. Sci. Instrum. 67, 398 (1996)). A series of topography and friction force images of 1 m x 1 m size were collected at a scanning speed of 4 m/s, for different normal force values. The normal force is nn initially and then decreased step-wise (0.5 nn steps) until the tip is out of contact with the sample. The grating was aligned so that the wedges are perpendicular to the fast scanning direction of the AFM. Also, the grating was placed so that the left half of the images would correspond to the wedge side with a positive slope, and the right half of the images to the side with a negative slope. Topography images indicate that the left side has an inclination of +61, and the right side an inclination of -5. The friction force and the friction loop offset were measured as a function of the normal force (Suppl. Figs. 1 and ). The four sets of data were fitted linearly to determine their slopes: Positive inclination: Friction force slope (W'+): V/nN Loop offset slope ('+): V/nN Negative inclination: Friction force slope (W'-): V/nN Loop offset slope ('-): V/nN Supplementary Figure 1. Friction force as a function of the normal force for the positively (red circles) and the negatively (green triangles) sloped sides of the wedge on the TGG01 grating. nature MATRIALS

3 Supplementary Figure. Average friction loop offset as a function of the normal force for the positively (red circles) and the negatively (green triangles) sloped sides of the wedge on the TGG01 grating. From the four slopes, the friction coefficient on the positively inclined side of the wedge, +, is estimated to be 0.0, and the calibration coefficient is 9.84 nn/v. ) Determination of contact area and shear strength of the interface sample-tip The contact area A (as a function of F + F ) ( N adh ) between the spherical tip and a flat surface (for example HOPG) can be determined using the contact mechanics Hertz theory, modified to add the contribution of the adhesion force (found as the load at which the friction force is zero): A ( ) 3 3 RTIP FN + Fadh ( FN + Fadh ) = π a = π * 4 where R TIP is the tip radius (about 60 nm), and * is the reduced modulus of the silicon tip and the sample (for example HOPG): = ( 1 ν ) ( ν sample ) TIP + 1 * TIP sample Using TIP =0.7, TIP =169 GPa, HOPG =0.8, HOPG =36 GPa, * = 3 GPa. The contact area between the AFM tip and the CNT is calculated using the modified Hertz theory between a sphere and a cylinder (see Palaci et al., Phys. Rev. Lett. 94, (005)). The contact area is expected to be an ellipse of semi-major axis a, and semi-minor axis b: A F + F ) = π ab ( N adh nature materials 3

4 b is given by the following expression: b = 3 3k π 1 ( 1 k ) 1 1 ( F + F ) = ka * R TIP + R NT N adh where R TIP is the AFM tip radius and k is the solution to the following equation: R 1+ R TIP NT = ( 1/ k ) ( 1 k ) K ( 1 k ) K ( 1 k ) ( 1 k ) (k) and K(k) are the complete elliptic integrals of the second kind: K π / ( k ) = ( 1 k sin ) 0 π / ( k ) = ( 1 k sin ) 0 1/ θ dθ 1/ θ dθ The shear strength σ of the different samples is then found by fitting the experimental F F vs. F N curves for the different samples, by using the equation: F F = σ A( FN + Fadh ). The only free fitting parameters are σ and F adh. The values of the Young Moduli for the CNT (about 30 GPa) are taken from Palaci et al., Phys. Rev. Lett. 94, (005). 3) Shear strength and friction of the interface HOPG-Si Tip Supplementary Figure 3. Friction force as a function of the normal force on HOPG. 4 nature MATRIALS

5 The friction force was measured by AFM in air on Highly Ordered Pyrolytic Graphite (HOPG) as a function of the normal load (Suppl. Fig. 3). A linear fit of the data yields a friction coefficient μ ~ , in agreement with previous experiments performed on HOPG in air (see Udo D. Schwarz et al. Phys. Rev. B (1997)). The adhesion force (defined as the load at which the friction force is zero) is difficult to determine from our data, a rough estimate gives F adh ~ From a different type of experiment, where the AFM tip is loaded on HOPG and then retracted, the adhesion force can be measured as the pull-out force. These data give F adh ~ From our F F vs. F N curves and by using F adh ~ , we calculated the shear strength between a freshly cleaved HOPG surface and our silicon AFM tip, following the method described above. The results give σ ~ 3 60 MPa. It is important to note that this value could be smaller in the case the estimated contact area was larger, for example in case a small flake of graphene was attached to the AFM tip. 4) Characterization of the used carbon nanotubes and Sample preparation Supplementary Figure 4. In (a) a transmission electron micrograph of the used carbon nanotubes is shown; (b) and (c) are higher magnification images of the nanotubes. In (d) a statistic demonstrates the diameter distribution and the ratio of inner to outer diameter. We used commercially available multiwall carbon nanotubes (Baytubes) purchased from Bayer in Germany. They are synthesized in a fluidized bed catalytic chemical vapor deposition process. Transmission electron microscopy reveals a good crystallinity of the nanotubes with sporadic defects. The distribution of the outer and inner diameter is relatively broad. Nevertheless the ratio between the outer and inner diameter is quite defined with a mean value of.83 and a standard deviation of For our studies, we suspended the multiwall nanotubes in DC (1,-dichloroethane) by sonication in an ultrasound bath for about 1 hour. The density is chosen in a way that the solution appears slightly greyish after sonication. Right after the sonication we took a droplet of the solution and put it on the surface (~ 1 nature materials 5

6 cm ) of an untreated silicon wafer. We leave the droplet there for about 30 sec and than we blow it away with a nitrogen pistol. In this way, the CNT are adsorbed on the Si substrate and can be used for the AFM experiments. Preliminary experimental data on home made CVD CNT of higher structural quality show a friction anisotropy similar that one reported in this work. 5) xperimental rrors and Method Discussion xample of error analysis to determine the error on the shear strength: (R = 5.5 nm) Transverse CNT F = σ Area + (see paragraph of this supplementary material) F ( FN Fadh) The linear fit below gives: Shear Strength (σ ) =.0884e+09 ± 9.43e+07 8x10-9 Friction (N) Area (m ) 4 5x10-18 Supplementary Figure 5. Similarly, all the other friction measurements give rise to errors of about ± 0.1 GPa in the determination of the shear strength. However, this error could be larger due to supplementary errors in the measurements of the friction force (estimated to be about ± 0.4 nn), and the tip radius. Friction Measurement on the CNT: After imaging friction and topography of the desired section of the CNT and the surrounding silicon substrate (for example Fig. 1c in our manuscript), we zoom in on an area at the top of the tube where the topography and the friction look flat by using the SPIP software. For example, for a CNT of radius of 7 nm we zoomed in on an area of 0 nm x 100 nm in the center of the tube. By considering the convolution of the AFM tip (radius 60 nm) with a CNT of 7 nm, a width of w convoluted = ± 10 nm at the top of the imaged tube corresponds roughly to a width w real = ± 1 nm on top of the real nanotube: w R + R w tip CNT real = convoluted R. We then take the average friction value inside this area. The FWHM of CNT the corresponding histogram of the data inside this area is usually around 1 nn. Comparing different averaged friction values in different parallel sections of the same CNT gives an error of about 0.4 nn or less. 6 nature MATRIALS

7 Supplementary Figure 6. Uncalibrated friction force average (LFT), and 1 friction force single profiles (RIGHT) inside the white dashed area of Fig. 1c in the manuscript. 6) Simulation Movies Supplementary Movie frames of the transverse sliding on the chiral tube, collected with time interval of 7.5 ps. The sliding distance is 0.84 nm over which the friction force is calculated. The normal force is.5 nn. Supplementary Movie. 15 frames of the longitudinal sliding on the chiral tube, with sliding distance of 0.96 nm. Supplementary Movie frames of the longitudinal sliding on the nonchiral tube, with sliding distance of 0.96 nm. Suppl. Movies 1 and show the transverse and longitudinal sliding on the chiral tube, and Suppl. Movie 3 shows the longitudinal sliding on the nonchiral tube. Friction force does not show clear dependence on the sliding distance (we have used 0.84 nm, 0.96 nm, and 1.08 nm) and the off-axis position of the tip. In the transverse case (Suppl. Movie 1), the rightwards overall rolling is hindered by the frozen C-Au bonds (not shown, but labeled in Fig.4). The left-right tube oscillation shows in detail the softness of deformation, which becomes stronger at larger simulation sliding speed, e.g., from 1 m/sec to m/sec. This softness will play a role at much lower sliding speed, as our experiments show, when the atomic stick-slip is expected to replace smooth sliding, and smooth rubbing will correspondingly be replaced by slips and kicks on the nanotube. In the simulated longitudinal sliding the leftwards rolling is hindered (see Suppl. Movie ), and the oscillation is small but still finite due to the outer tube chirality, differently from the nonchiral tube where no transverse oscillation is observed (see Suppl. Movie 3). nature materials 7

8 7) Friction Calculation In MD Simulations Supplementary Figure 7. Typical lateral force-displacement curves for two transverse sliding loops, used for extracting the simulated frictional dissipation. Normal forces are.6 nn (top graph), and 1.4 nn (bottom graph), and the sliding distance is 0.96 nm. We calculated the friction force by dividing the total dissipated energy, i.e., the enclosed area of one sliding loop, by the corresponding sliding distance. Top: Although globally above the red curve, the blue curve is S-shaped, indicating the effect of the strong oscillation that can be observed in Suppl. Movie 1. Bottom: As the normal force is decreased the dissipated energy becomes smaller, showing the load dependence of friction. The sharp oscillations reflect the kick exerted by sharp tip speed reversals at the left and right ends of the sweeps. 8 nature MATRIALS