Radial Deformation of Carbon Nanotubes in Supersonic Collisions

Jul 7, 2010 - supersonic collisions with a silicon surface. High speed (5 km/s) impact on its sidewall causes an abrupt and partially irreversible def...
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J. Phys. Chem. C 2010, 114, 12565–12572

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Radial Deformation of Carbon Nanotubes in Supersonic Collisions with a Silicon Surface Leton C. Saha,† George C. Schatz,‡ and Joonkyung Jang*,† Department of Nanomaterials Engineering, Pusan National UniVersity, Miryang, 627-706, Republic of Korea, and Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208-3113 ReceiVed: February 24, 2010; ReVised Manuscript ReceiVed: June 16, 2010

Using molecular dynamics simulations, we studied the radial deformation of a carbon nanotube (CNT) in supersonic collisions with a silicon surface. High speed (5 km/s) impact on its sidewall causes an abrupt and partially irreversible deformation of the 0.81 nm diameter CNT. The diameter of the CNT is decreased by more than 50% within 0.3 ps after the onset of the collision. This deformation relaxes on a half picosecond time scale, but vibrational energy in the tube relaxes much more slowly. Upon completion of the relaxation, the CNT shows an irreversible radial compression ranging from 7% to 35% of its original diameter. Also, the CNT penetrates below the surface to a distance of up to 13% of its diameter. In the case of near glancing incidence, the CNT scratches and rolls along the surface. At a speed of 700 m/s, the CNT is either scattered from or bound to the surface without any irreversible deformation. At a speed of 15 km/s, the CNT loses its radial elasticity and is completely fragmented. These results are interpreted by examining the effective temperature of the nanotube that is produced during the collision, and it is found that collisions that produce a local temperature near 2000 °C lead to irreversible damage. This concept is used to interpret recent CNT spraying measurements involving larger multiwalled CNTs. 1. Introduction 1

The mechanical response of carbon nanotubes (CNTs) to an external force has been extensively studied. Examples include, to name but a few, the deformation of CNTs caused by the indentation of an atomic force microscope (AFM) tip,2-6 their buckling under stretching7-9 or compression along their axis,10-13 their distortion when they are embedded in a polymeric film,14,15 and their deformation under torsion16 and axis bending.17-19 The consensus view is that CNTs are extremely stiff and rigid against a load applied along their axis,20 but susceptible to external perturbations along their radial direction. The presence of a neighboring CNT21 or a surface below22 can induce substantial radial deformation in an individual CNT.21,23 A radial deformation of up to 60% of its diameter (for a multiwalled CNT with a diameter of 9 nm) has been reported to be fully reversible.2,4 The radial elasticity of a CNT decreases (and therefore its deformability increases) with increasing diameter3 but does not much depend on chirality.24 Theoretical and experimental studies have shown that a CNT can collapse when its diameter becomes bigger than several nanometers.21,22,24 It has been estimated that the threshold diameter for this collapse of a CNT on a surface is as small as 1 nm for a single-walled CNT on an aluminum surface.21 Other approaches suggest that an isolated CNT cannot collapse without applied hydrostatic pressure and that the threshold for the collapse is about 6.4 nm for single-walled CNTs.24 The present study centers on the radial deformation of CNTs when they undergo supersonic collisions with a surface.25-27 This is relevant to cold spraying experiments25,26 where multiwall CNTs mixed with a metal powder are thrown with velocities ranging from 600 to 1500 m/s, forming a uniform coating on a surface. Restructuring of the nanotubes can occur, * Corresponding author. E-mail: [email protected]. † Pusan National University. ‡ Northwestern University.

but the conditions needed to make this happen are unclear, and the situation is complex due to the presence of coexpanded aluminum/silicon particles in the same system. The current topic also relates to the recent efforts to use molecular beam epitaxy (MBE) to deposit organic molecules on surfaces (so-called organic MBE).28-31 With controlled kinetic energy and orientation of the precursor molecule,29 a highly ordered organic film was able to be grown. Various organic materials (e.g., π-conjugated molecules) were deposited on films, giving an excellent morphology (highly ordered or crystalline). Indeed, organic field-effect transistors have been fabricated by supersonic MBE.31 Given their unique electromechanical and thermal properties, CNTs seem to be a viable candidate for organic or supersonic MBE. Unlike other external forces, a supersonic collision exerts a sudden and drastic (high strain rate) deformation on the CNT, with fracture and necking having been reported for multiwalled CNTs.25,26 However, the molecular mechanism and details of this deformation process are largely unknown. In this context, we recently performed a molecular dynamics (MD) simulation of a CNT colliding with a silicon surface along its symmetry axis.27 This type of collision resulted in the bending of the CNT about its axis. In the present work, we focus on the case where the CNT impacts with its principal axis parallel to a silicon surface and the deformation is directed in the radial direction. Using MD simulations, we present a comprehensive analysis of the CNT deformation and subsequent structural and energy relaxation, and we systematically study the effect of changing speed and angle of the incident CNT. We also illustrate the possible scattering and fragmentation of CNTs at low and high projectile speeds. With these results, we are able to determine what conditions are needed for irreversible CNT restructuring. This provides a mechanistic understanding that can be used to interpret the CNT spraying experiments.

10.1021/jp101686r  2010 American Chemical Society Published on Web 07/07/2010

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Figure 1. Simulation scheme for collision and CNTs deposited on surface after collision. (a) Snapshot of a (6,6) single-walled CNT impacting on a Si (110) surface. The axis of the CNT lies along the Y axis. The CNT has a projectile speed Vp and an incident angle θ measured from the surface normal (the Z axis). The arrow represents the direction of incidence. (b-g) CNTs deposited on the surface using different angles. For a fixed Vp of 5 km/s, θ is varied as 0° (b), 15° (c), 30° (d), 45° (e), 60° (f), and 75° (g). All snapshots are taken at 22 ps after impact. In each panel of (b)-(g), the Si atoms are drawn small, and two different views (along the X and Y axes) of the CNT are shown.

2. Simulation Details A (6,6) single-walled CNT was made to impact on the (110) surface of silicon (Si) with its axis parallel to the surface (along the Y axis, Figure 1a). The CNT is initially separated from the surface by a distance ranging from 1.2 to 1.6 nm. The CNT has a projectile speed Vp and an incident angle θ measured from the surface normal (the Z axis in Figure 1a). The CNT is made of 384 carbon (C) atoms, and is 3.8 nm long and 0.81 nm wide in diameter. We considered a range of velocities, Vp. Our default Vp is 5 km/s, which is hypersonic (above the speed of Mach 5) and several times higher than that used in typical cold spraying experiments (600-1500 m/s).25,26 (The reason for this choice will be apparent later.) We also considered lower Vp’s ranging from 55 to 1100 m/s and an extremely high Vp of 15 km/s. For a given Vp, we varied θ (see Figure 1a) as 0°, 15°, 30°, 45°, 60°, and 75°. The surface is made by taking a slab of a Si crystal with a thickness of 3.83 nm. The Si atoms in the bottom layer of the slab were fixed in the MD simulation. The surface has lateral dimensions of 15.61 nm (the X direction) × 8.97 nm (the Y direction). The total number of Si atoms was 24 360. We used the empirical Tersoff potential32,33 for the self- and cross interactions of the C and Si atoms. This is a short-ranged (for distances below 0.2 nm) reactive potential and has been

Saha et al. successfully applied to various problems involving C, Si, and Ge atoms.32-35 The strength of an interatomic bond depends on the coordination number (or bond order) as determined by its local environment. For example, the presence of a third atom weakens the two-body interatomic potential. Mathematical forms and values of parameters for Tersoff potential can be found in refs 32 and 33. In addition to the Tersoff potential, there is a longer-ranged van der Waals (vdW) potential between atoms i and j. Following Mao et al.,36 we take the vdW interaction to be a Lennard-Jones ′ but to be zero for rij < rs′. rm ′ and rs′ are (LJ) potential for rij > rm cutoffs depending on the atomic species i and j, and are listed ′ , the vdW interaction is a in ref 36. For rij’s between rs′ and rm cubic polynomial of rij. The coefficients of the polynomial are ′ and determined by using the continuity conditions at rij ) rm rs′.37 We checked the importance of the vdW interaction in several ways. The root-mean-squared displacement (rmsd) and Tv for Vp ) 700 m/s and θ ) 0°, for example, remained virtually unchanged when including the vdW interaction (see Figure S1 in the Supporting Information). Only at a very low speed of Vp ) 55 m/s does the vdW interaction cause the CNT to stick to the surface, while it bounces without the vdW interaction. On the basis of these observations, the vdW interaction is excluded in the present MD simulation. We used periodic boundary conditions38 to simulate a horizontally infinite surface. The simulation box length along the Z axis was 50 nm, so that the periodicity in the Z-direction is virtually removed. The CNT and surface were separately equilibrated at temperatures near 300 K by running constant temperature (NVT) MD simulations. Three different initial conditions for the collision were selected out of the equilibrations. The initial motion of the nanotube is defined by incrementing the speed of each atom in the nanotube by an amount Vp in the direction perpendicular to its axis and with the velocity vector forming an angle θ relative to the surface normal (see Figure 1a). We used a constant energy (NVE) MD method38 for simulation of the collision. The MD trajectory was propagated using the velocity Verlet algorithm38 with a time step of 0.2 or 0.4 fs. An impact is defined as an event in which the CNT approaches the surface such that the nearest carbon atom is within 0.178 nm from the surface (0.178 nm is the C-Si distance in a silicon carbide nanotube39). The MD simulations typically were run for 22 ps after impact. The MD methods detailed above were implemented using the DLPOLY package.40 We calculated the vibrational temperature of the CNT, Tv, as follows. At each time step of the simulation, we calculated the center of mass (CM) position and velocity of the CNT, b Rcm and b Vcm, respectively. The internal position and velocity of the Vi (i ) 1, ..., 384), were obtained by subtracting ith C atom, b ri and b b Vcm from the position and velocity of each C atom, Rcm and b Vi’s to calculate the internal respectively. We used these b ri’s and b Vi2 (m ) mass of C atom), the kinetic energy, Kint ) (m/2)∑i b angular momentum, b L, and the moment of inertia, I. By L) · b L, evaluating the rotational kinetic energy Krot ) (1/2)(I-1b we obtained the vibrational kinetic energy Kvib as Kvib ) Kint Krot. We converted Kvib to Tv by using the equipartition theorem Tv ) 2Kvib/((3N - 6)kB), where kB and N are the Boltzmann constant and the number of C atoms, respectively. We quantified the time-dependent deformation of the CNT by calculating the rmsd from its initial structure before collision. To do so, the displacement of each C atom from its initial value was calculated. The average value of the square of the displacement was taken by summing over all of the C atoms. The rmsd is defined as the square root of that average. Note

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the rmsd is a quantity averaged over (not summed over) each C atom. Because this rmsd depends on the translation and orientation of the CNT, we chose the minimum of the rmsd values obtained for various translations and orientations. The minimum was calculated using the method of Kabsh41 implemented in the Visual Molecular Dynamics package.42 3. Results A snapshot of a CNT impacting on the Si surface is shown in Figure 1a. After impact with Vp ) 5 km/s, as shown in Figure 1a, the sidewall of the CNT binds to the Si surface. Figure 1b-g shows the CNTs deposited after collision with Vp ) 5 km/s for angles of 0° (b), 15° (c), 30° (d), 45° (e), 60° (f), and 75° (g). All of the snapshots are taken at 22 ps after impact. In each of the panels b-g, we present two different views (along the X and Y axes) to clarify the structure of the CNT. The Si atoms are drawn small for clarity. Each CNT is noticeably deformed near its open ends. One (for θ ) 0°) or both (for angles of 30° and 45°) of the open ends are closed due to deformation. Overall, the deformation of CNT occurs primarily along its radial direction: the diameter of the original CNT is compressed vertically (Z direction) and expanded horizontally (X direction). As a result, the radial cross section of CNT is approximately oval with its bottom flattened (see Figure 1b and c). The CNT penetrates below the surface and displaces some of the Si atoms from their original positions. Depending on θ, the collision of the CNT shows different behavior. A CNT with a small θ (45°) has most of its speed directed in the horizontal (X) direction. The CNT lands smoothly in the vertical direction and does not penetrate deep below the surface. The CNT in this case scratches, rather than penetrates, the surface, and rolls over along the surface until it finally stops. The distance moved away from the position of impact was 1.6 nm for θ ) 60°and 4.4 nm for θ ) 75°. The rolling of the CNT strips several Si atoms from the surface. These Si atoms that are stripped by the CNT are either attached to the CNT or ejected into vacuum. The initial impact in this case creates a carbon-silicon bond. The subsequent rolling of CNT on the surface pulls the silicon atom out of its place on the surface. This rolling also exerts a torque on the nascent carbon-silicon bond. This torque sometimes is large enough to break the nascent C-Si bond and eject an isolated Si atom into the vacuum. For θ ) 75°, a single C atom at the open end of the CNT is separated from its rolling body and captured by the surface. We measured the penetration depth of the CNT below the surface. Figure 2a plots the depth measured from the top layer of the surface. All of the data in Figure 2 are averages over three different MD simulation trajectories. The error bars represent standard deviations of these quantities. As expected, the depth decreases as θ increases. The depth reaches 0.1 nm at low θ and decreases to 0.035 nm as θ increases to 75°. The largest depth in Figure 2a corresponds to 13% of the original diameter of the CNT (0.81 nm). These depths are smaller than those of the CNTs colliding along their axes (which ranged from 0.2 to 1.1 nm).27 We quantified the radial deformation of the CNT at the completion of the collision by calculating the vertical height (Figure 2b) and horizontal width (Figure 2c) of its radial cross section along the XZ plane. To calculate the height, we divided the CNT into 40 segments according to the Y coordinates of the C atoms. Within each segment, we calculated the difference

Figure 2. Surface penetration and radial deformation of the CNT. (a) The penetration depth of the CNT vs θ. (b) Vertical height in the radial cross section (parallel to the XZ plane) of the CNT vs θ. (c) Horizontal width in the radial cross section of the CNT vs θ. All data were obtained by averaging over three MD trajectories, and the error bars represent the standard deviations. The lines are drawn as a visual guide.

in the maximal and minimal Z coordinates. This difference is averaged over the segments to give the height. We further averaged this height over the three different MD simulations and plotted the results in Figure 2b. The height is always smaller than the original diameter of the CNT. The height increases as θ increases from 0° and levels off at θ ) 60°. The shrinkage in height ranges from 7% to 35% of its original diameter. A 35% compression in diameter is slightly below the experimentally measured 40% deformability for indentation for a multiwalled CNT (with a diameter of 6.3 nm).4 Figure 2c shows the horizontal width of the CNT for various angles. As in the height calculation, the CNT is divided into 40 segments along the Y direction. The difference between the maximal and minimal X coordinates of each segment is averaged to give the width. This width is further averaged over three different MD simulations. At low angles, the horizontal width is about 0.94 nm, which is 16% wider than the diameter of an isolated CNT. As θ increases, the width decreases, but is always larger (at least by 3%) than the original diameter. The degree of expansion in width (3-16% of the original diameter) is smaller than the 7-35% decrease in height. One might wonder why the width for 60° is slightly larger than that for 75°. It should be noted that, for incidence angles of 60° and 75°, the CNT rolls over along the surface after it initially impacts on the surface. Both the width in Figure 2c and the height in Figure 2b are measured after the CNT finishes its rolling and completely stops on the surface. Therefore, for CNTs rolling over along the surface, the width in Figure 2c (and the height in Figure 2b) should not be interpreted by referring to the velocity of CNT at impact. Instead, the width and height are determined by the interaction of a rolling CNT with the surface. In the case of 60°, the surface strongly drags the rolling CNT, and some of silicon atoms are attached to the CNT wall like glue. This dragging force acts laterally (parallel to the surface) and decreases the width of the vertically compressed diameter of CNT due to its interaction with the underlying surface. Therefore, the width is lower for 60° than for 75°. However, the widths for 60° and 75° are quite similar, considering the sizes of error bars in Figure 2c. Likewise, the heights for incidence angles of 60° and 75° in Figure 2b are similar too. In Figure 3, we compare the collision dynamics resulting from the two limiting angles, 0° (solid lines) and 75° (dotted lines).

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Figure 3. Dynamics of collision for two limiting incident angles θ of 0° and 75°. The solid (dotted) lines represent the case of θ ) 0° (θ ) 75°). The impact occurs at time zero. (a) The penetration depth vs time. (b) The nearest distance between the C and Si atoms dmin vs time. (c) The Z component of the CM velocity of the CNT Vcm,z vs time.

Plotted are the time variations of the penetration depth (a), the minimal distance between the C and Si atoms dmin (b), and the Z component of the CM velocity of the CNT Vcm,z (c). We shifted the times so that the impact occurs at zero. In the case of θ ) 0° (solid line, Figure 3a), the CNT penetrates as deep as 0.42 nm at 0.36 ps (a negative depth corresponds to penetration below the surface). As the time increases from 0.36 ps, the CNT bounces up a little, and the depth approaches a smaller negative value (-0.25 nm roughly). The fluctuation in the depth represents the vertical vibration of the CNT while it is attached to the surface. The CNT for θ ) 75° temporarily penetrates up to a depth of 0.13 nm, but the average depth of penetration is insignificant. The depth fluctuates in time as for θ ) 0°. Figure 3b shows that dmin approaches 0.175 nm with the fluctuation in time, regardless of θ. Because this distance is close to that of a covalently bonded C-Si pair, the CNT is considered to be chemisorbed. dmin temporarily becomes as small as 0.15 nm for θ ) 0°, and its fluctuation after impact is more pronounced for θ ) 75°. Vcm,z in Figure 3c oscillates with time for both θ ) 0° and 75°, again due to the vertical vibration of the CNT bound to the surface. The amplitude of oscillation of the CNT is bigger for θ ) 0° because its Z velocity is larger. A supersonic collision with Vp ) 5 km/s induces a sudden and drastic deformation of the CNT. Within 0.3 ps after impact, the cylindrical CNT flattens out due to the compression of its diameter by more than one-half. At this moment of maximal deformation, the changes in the height and width of the CNT are greater than those obtained at long times (those in Figure 2b and c). Figure 4 plots the changes in the height and width for the diameter of the CNT at its maximal deformation. These changes are expressed as percentages relative to the original diameter and plotted versus θ. The compression in height (Figure 4a) is close to 56%, except for θ ) 75°. Because 56% corresponds to an absolute height of 0.35 nm, the diameter of the CNT in this case is flattened like a ribbon (the distance of two graphene layers is typically 0.34 nm43). This 56% deformation is close to the experimental upper limit of reversible deformation (60%) for a multiwalled CNT (with a diameter of 9.3 nm).2 The change in the height of the CNT drastically decreases to 36% for θ ) 75° because of its reduced vertical compression. The increase in the width of the radial cross section

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Figure 4. Changes in height and width for the radial cross section of the CNT at its maximum deformation. (a) Shrinkage in height, expressed as a percentage relative to the original diameter of the CNT, is plotted vs the incident angle θ. (b) Increase in width relative to the original diameter is plotted as a percentage vs θ. All symbols represent averages over three MD trajectories, and the error bars represent the standard deviations. The lines are drawn as a visual guide.

(Figure 4b) varies from 18% to 24% (again, this change in width is smaller than in the height) and does not show any clear dependence on θ. The near independence of the width on the incidence angle in Figure 4b can be explained as follows. For low incidence angles, a large vertical (along the surface normal) compression at impact leads to an increase in the width. As the incidence angle increases, the vertical compression of CNT diminishes, but the lateral component of the impact velocity grows, increasing the lateral distortion in the radial cross section of CNT. As a result, the width at the maximal deformation turns out to be independent of the incidence angle. It is to be noted that the CNT recovers from the temporary collapse (56% decrease in height) as time goes by. The height and width approach the values in Figure 2 at long times. This recovery is consistent with the previous theoretical prediction that only cylindrical configurations are stable for single-walled CNTs with diameters less than 2.42 nm.24 We now investigate how the CNT relaxes its deformation and the excited energy after impact. Figure 5a and b shows the time-dependent rmsd and Tv, respectively, for θ ) 45°. Both the rmsd and the Tv rapidly rise after impact (time zero) from their initial values of 0.031 nm and 342 K, respectively. The times required for the rmsd and Tv to reach their maxima (0.212 nm and 2100 K, respectively) are 0.26 and 0.25 ps, respectively. In Figure 5a, we also show the CNT structures at impact (0 ps), at its maximal deformation (0.26 ps), and at 22 ps after impact. The initially cylindrical CNT flattens out at its maximal deformation. At 22 ps, the CNT recovers its cylindrical shape, but vertical compression (and horizontal expansion) of its diameter and the flattening of its bottom are apparent. After excitation to their maximal values, the rmsd and Tv relax by decreasing and leveling off to lower values (0.136 nm for the rmsd and 530 K for Tvib). The rmsd and Tv at 22 ps are larger than those before excitation, due to the incomplete relaxation. Fluctuations with time are visible for both the rmsd and the Tv. The relaxation could be approximated as an exponential decay with time t. Specifically, we fitted the rmsd to as exp(-t/τs) + bs and Tv to av exp(-t/τv) + bv. τs and τv are the structural and vibrational temperature relaxation times, respectively. The fits (solid lines in Figure 5a and b) closely follow the MD results

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Figure 5. Relaxation in deformation and excited vibrational temperature of CNT. In the case of θ ) 45°, the rmsd (a) and vibrational temperature Tv (b) are plotted vs time as dotted lines. The solid lines are exponential fits to the relaxation data (data after the maxima of rmsd and Tv, see text). Time zero represents the time of impact.

Figure 6. Relaxation parameters of CNT for collisions with Vp ) 5 km/s. (a) The structural relaxation time τs vs the incident angle θ. (b) The long-time asymptotic rmsd bs vs θ. (c) The relaxation time of the vibrational temperature τv vs θ. All data points were calculated by averaging over three MD trajectories, and the error bars represent standard deviations. The lines are a guide for the eyes.

(dotted lines). The fits give τs ) 0.174 ps and τv ) 5.25 ps, showing that the temperature relaxation is 30 times slower than the structural relaxation. The long-time asymptotic value of the rmsd, bs (0.135 nm in this case), quantifies the permanent deformation of the CNT from its initial shape. A bs value larger than the rmsd of an isolated CNT (0.03 nm on average) indicates that there is a permanent deformation of the CNT. However, a bs only slightly larger than 0.03 nm (e.g., 0.04 or 0.05 nm) does not give any noticeable deformation from the original cylindrical shape of an isolated CNT. Therefore, a plastic deformation is defined as a bs value above 0.06 nm (see below for the justification of this choice). In the case of Vp ) 5 km/s, bs is always larger than 0.06 nm. As we saw in Figures 1 and 2, the deformation mostly involves the decrease in height and the widening of the radial cross section of CNT. The C atoms on the wall of a deformed CNT retain their 3-fold coordination with their nearest neighbor C atoms, although chemical bonds to Si atoms occur for some of the C atoms in contact with the surface. No defects or holes are found on the wall. Irreversible deformation of the surface area near the CNT occurs as well (in the case of Vp ) 5 km/s and θ ) 0°, the rmsd of surface approaches 0.15 nm per Si atom). The Si surface is typically heated to a temperature more than 500 K at long times (22 ps) for Vp ) 5 km/s. We inspected the relaxation parameters for various angles. By varying θ from 0° to 75°, we calculated τs, bs, and τv for the collisions with Vp ) 5km/s. Plotted in Figure 6 are τs, bs, and τv averaged over three different MD trajectories (the error bars are the standard deviations). τs (Figure 6a) is nearly constant (varying from 0.11 to 0.24 ps) for angles less than or equal to 45°. It increases to 0.57 and 2.22 ps for angles of 60° and 75°, respectively. Note that the τs’s for low angles (e45°) are below 0.3 ps. The relaxation of the deformed structure in this case is very fast (as fast as the excitation), because it involves the breathing motion of its diameter. The relatively slow relaxation (a large τs) for θ ) 60° and 75° arises from the rolling of the CNT on the surface. As compared to the fast vibration of the CNT, its rolling is significantly slower. Except for 75°, the τs’s are smaller than those of the CNTs colliding along their axes (which ranged from 0.28 to 0.84 ps27). Figure 6b shows that bs is always larger than the rmsd of an isolated CNT (0.03 nm). bs is nearly constant (roughly 0.11 nm) for θ e 45° and

decreases to 0.07 nm as θ increases to 60° and 75°. This trend of bs with increasing θ can be explained by the fact that the reduced vertical compression for a large θ reduces the deformation of the CNT, while the rolling of the CNT for large θ does not cause much deformation. The decreasing behavior of bs in Figure 6b is opposite to that found for CNTs colliding along their axes, in which case the axis of the CNT is bent for large θ and therefore bs increases due to the increase in θ. τv in Figure 6c increases from 5.0 to 8.5 ps as θ is increased from 0° to 75°. This behavior is again attributed to the rolling of the CNT for a large θ of 60° or 75°. The τv’s are much larger than the τs’s (typically by more than 20 times). The τv’s are similar to those of the CNTs colliding along their axes.27 In addition to the default Vp of 5 km/s, we considered a typical speed used in the CNT cold spraying experiments, Vp ) 700 m/s. Snapshots taken at impact for θ ) 0° and 75° are shown in Figure 7a and b, respectively. After impact, the CNT for θ ) 0° bounces off the surface (Figure 7c, snapshot taken after 5.1 ps), but the CNT with θ ) 75° binds to the surface (Figure 7d, snapshot taken after 18.92 ps). This can be explained as follows. Because of its relatively low speed, the CNT does not penetrate into the surface or flatten out to make wide contact with the surface. The contact area for θ ) 0° is especially limited, in that only the bottom C atoms of the wall touch the surface throughout the collision. By analyzing the MD trajectory, we found that the nearest C-Si distance for θ ) 0° is about 0.25 nm, which is too large for covalent bonding to occur. The CNT spends approximately 0.75 ps physisorbed to the surface (with a nearest C-Si distance of 0.25 nm) and is then reflected from the surface. For θ ) 75°, however, the bottom of the CNT wall smoothly approaches the surface, and the CNT slightly rolls over along the surface as soon as it touches the surface. The resulting smooth vertical landing anchors the bottom of the CNT to the surface, and its subsequent rolling increases the area of contact between the CNT and the surface. With this increased area of contact, the CNT eventually transfers enough energy that it can bind to the surface. The nearest C-Si distance is 0.175 nm, which is similar to that for Vp ) 5 km/s (the CNT is thus chemisorbed). Also plotted in Figure 7 are the rmsd (e) and Tv (f) for θ ) 0° (solid lines) and 75° (dotted lines). As with Vp ) 5 km/s, both the rmsd and the Tv increase initially

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Figure 8. Fragmentation of CNT and sputtering of Si atoms for Vp ) 15 km/s. The incident angle is varied as θ ) 0° (a and c) and 45° (b and d). The Si atoms are drawn small. Shown in (a) and (b) are snapshots taken at 1.54 and 0.56 ps after impact, respectively. Drawn in (c) and (d) are fragments of the CNT bound to the surface for θ ) 0° (c) and 45° (d), respectively. The snapshots in (c) and (d) are taken at 10.73 ps after impact.

Figure 7. Collision of CNT with Vp ) 700 m/s for two limiting angles of incidence. The incidence angle θ is varied as 0° (a and c) and 75° (b and d). Shown in (a) and (b) are snapshots taken at impact for θ ) 0° and 75°, respectively. Shown in (c) and (d) are snapshots taken at 5.1 ps after impact for θ ) 0° and 18.92 ps after impact for θ ) 75°, respectively. The arrows in (a)-(c) represent the direction of motion of the CNT. We also plot the time variation of the rmsd (e) and the vibrational temperature Tv (f). The solid and dotted lines in (e) and (f) are the results obtained from collisions with θ ) 0° and 75°, respectively.

after impact (time zero) and later decrease. Because of the large fluctuations of the rmsd and Tv, pronounced maxima after impact (as in Figure 5) do not exist, especially for Tv. The relaxation of the rmsd and of Tv cannot be approximated as exponential decays, as in the case of Figure 5. Regardless of θ, the rmsd in Figure 7e completely recovers (within fluctuations) its original value after several ps. The rmsd’s for θ ) 0° and 75° approach 0.03 and 0.04 nm on average, respectively, which are nearly identical to that of an isolated CNT (0.03 nm is obtained by averaging over a 20 ps time period). Note that the presence of an underlying surface for θ ) 75° increases the rmsd of CNT by 0.01 nm per atom. Tv at long times approaches the temperature of surface (356 K for θ ) 75°) when it remains on the surface, but not if it bounces off (312 K for θ ) 0°, i.e., the CNT is lower in temperature). In short, the CNT with Vp ) 700 m/s elastically recovers from its initial deformation and increases in vibrational temperature. At its maximal deformation, the height of the CNT is compressed by 18.8% of its diameter for θ ) 0° and by 5.7% for θ ) 75°. It was observed above that, in the case of θ ) 0°, the CNT sticks to the surface at Vp ) 5 km/s, but bounces off at Vp ) 700 m/s. By varying Vp for θ ) 0°, we found that the lower threshold speed for deposition via collision is 1.1 km/s for θ ) 0°. At this speed, the CNT reached temperatures of up to 575 K, and its bs was 0.04 nm, which is slightly larger than 0.03

nm. Visual inspection shows that the structure of the CNT is virtually unchanged from its original structure. Unlike for the threshold Vp for deposition of a CNT, the determination of the threshold bs for a plastic deformation is rather subtle. As seen above, choosing 0.03 nm as the threshold of bs is too strict. As Vp was increased from 1.1 to 2 and 3 km/s, bsslightly increased, from 0.04 to 0.051 and 0.058 nm, respectively. CNTs with these bs’s retained the cylindrical structure of an isolated CNT. When Vp reached 4 km/s, the CNT became noticeably flattened in its radial cross section, especially the part touching the surface. Increasing Vp from 3 to 4 km/s almost doubled bs to a value of 0.1 nm, close to that for Vp ) 5 km/s (0.12 nm). It is therefore reasonable to set the threshold bs for plastic deformation as 0.06 nm, at least for θ ) 0°. As Vp was increased from 1.1 to 2, 3, 4, and 5 km/s, the maximum of Tv also increased from 569 K to 575, 751, 1264, 1783, and 2945 K, respectively. The threshold temperature corresponding to the plastic deformation is therefore 1783 K. Interestingly, this temperature threshold is close to that reported in experimental studies (2000 °C)44,45 for plastic deformation of a single-walled CNT (with a diameter of 12 nm) under a tensile load. We also considered a Vp of 15 km/s, which is 3 times larger than the default speed, but still 10 times less than the typical speed in an ion beam experiment.46 Figure 8 shows snapshots taken at 1.54 ps (a) and 10.73 ps (c) after impact for θ ) 0° and taken at 0.56 ps (b) and 10. 73 ps (d) after impact for θ ) 45°. The Si atoms are drawn small to clarify the structure of the CNT. The CNT penetrates as much as 2.38 and 1.63 nm below the surface for θ ) 0° and 45°, respectively. Complete fragmentation of the CNT occurs for this high Vp. After impact, the CNT for θ ) 0° is nearly immersed below the surface, and the surface locally bulges due to this immersion. The structure of the CNT is completely broken, but most of the C atoms (376 out of 384) stay trapped below the surface (Figure 8c). Only a small fraction of the C (8 out of 384) atoms escape into vacuum, and those C atoms that are scattered or Si atoms that are sputtered are in the form of individual atoms. For θ ) 45°, 18% of the C atoms are scattered into vacuum (Figure 8b). Si atoms are sputtered as well. The scattered atoms are either individual atoms or small clusters of pure or mixed atoms: there were 53 atomic C atoms, one C2, one C3, one C4, one C8, one SiC, one SiC2, and one SiC3 in the fragments. These fragments show a distribution in size narrower than that obtained from

Radial Deformation of Carbon Nanotubes the MD simulation of a C240 fullerene colliding against a hard wall (which ranged from 1 to more than 50).47 Moreover, diatomic C2 is known to be the major product for the fragmentation by electron impact48 or laser irradiation.49 This discrepancy might be due to a shortcoming of the empirical Tersoff potential. To be conclusive, however, we first need to obtain a reliable statistics on the size distribution by running many more MD trajectories (typically 1000 trajectories are run). Such investigation is beyond the scope of the current work and left as future work. The damage (bulging) of the surface is asymmetric for θ ) 45° (Figure 8b and d). The C and Si atoms are scattered in the same horizontal direction (from right to left) as the incident CNT. For both cases in Figure 8, the nearest C-Si distance is 0.15 nm, which is less than the value of 0.175 nm found for Vp ) 5 km/s and 700 m/s. Figure 8c and d shows the fragmented CNTs remaining on the surface for θ ) 0° and 45°, respectively. The structure of the CNT is completely amorphous. We considered a clean silicon surface corresponding to ultra high vacuum conditions. Under ambient conditions, the surface Si atoms can be terminated by various functional groups, such as -H or -OH. Investigation of the effects of this surface termination is beyond the scope of this work. However, we did consider the effect of hydrogen (H) termination on the Si surface. In the case of Vp ) 700 m/s, the CNT is scattered from the H-terminated surface for both θ ) 0° and 75°. In the case of Vp ) 5 km/s, the CNT for a low θ penetrates and binds to the surface, but it bounces off for a high θ. Hence, H-termination of the surface is more likely to cause the CNT to bounce. However, with a sufficiently large Vp (above 5 km/s), the CNT is likely to penetrate below the surface and be deposited, even if the surface is terminated by H or other groups. 4. Discussion and Conclusion With the help of a molecular beam, the orientation and energy of organic molecules can be controlled with unprecedented accuracy.28-31 Supersonic spray techniques are beginning to be applied to the deposition of CNTs on a surface.25,26 Despite this experimental progress, the deformation of CNTs after supersonic collisions with a surface is not well understood at the molecular level. In principle, various orientations of the CNT are possible under experimental conditions, but we focused here on the case where the sidewall of the CNT impacts with its axis parallel to the surface. This contrasts with our previous investigation27 of the collision of a CNT along its long axis. While long axis collisions can easily bend nanotubes, parallel impacts lead to more efficient conversion of translational energy to thermal energy, leading to more serious nanotube restructuring mainly along its radial direction. We focused on the theoretical investigation on the radial deformation of CNT in supersonic collisions. Because the present collision geometry is a fraction of geometries possible in experiment, our work cannot mimic the cold spray experiment to the full extent. However, we studied an elementary molecular process, which seems crucial in the deformation of CNT in the cold spray experiment. Our simulation is relevant to a collision of CNT mainly involving a deformation in its radial cross section. Any collision of CNT with its axis forming an angle less than 45° with respect to the surface plane is likely to fall in this category, which is a significant portion of the possible geometries. To corroborate this, we simulated a CNT moving along the surface normal direction with its axis tilted by 45°. This collision led to results similar to those from the radial collision considered in this work (see Supporting Information, Figure S4). The CNT deposited on the surface did not show

J. Phys. Chem. C, Vol. 114, No. 29, 2010 12571 any significant bending of its long axis. Instead, the height and width in the radial cross section of CNT changed significantly. The radial cross section in this case resembled that in the radial collision with an incidence angle of 45° (Figure 1d). The height and width were 0.51 and 1.01 nm, respectively, which are virtually identical to those obtained from the corresponding radial collision (0.61 and 0.92 nm, respectively). A tilt angle higher than 45° should give results even closer to those in the radial collision. Collisions with a supersonic speed of 5 km/s can produce a sudden (within 0.3 ps) and drastic (complete flattening temporarily) deformation of the CNT. Permanent deformation of the CNT from a perfect cylinder is inevitable in this case with the diameter of the CNT compressed vertically (widened horizontally) by 7-35% at the completion of the collision. The CNT with this projectile speed temporarily heats up to temperatures more than 2000 °C. Interestingly, previous experiments reported that a single-walled CNT (with a diameter of 12 nm) plastically deforms under a tensile load at temperatures higher than 2000 °C.44,45 Thus, we see that 5 km/s collisions lead to sufficient heating to produce plastic deformation. Low velocity (700 m/s) collisions tend to be weakly inelastic, with the nanotube either bouncing from the surface or sticking to it without structural damage. In this range of velocities (700 ms to 5 km/s), the CNTs have remarkable elasticity in their radial deformation, with the diameter of the CNT momentarily shrinking by up to 60% and then recovering (partially or completely) its cylindrical shape within a time scale of less than one-half a picosecond. Plastic deformations were found to be important for 4 km/s velocities or higher. If the projectile speed is increased to 15 km/s, the CNT loses its ability to recover from the deformation, and its inherent structure is completely destroyed. At the typical speed (700 m/s) reached in a cold spraying experiment, our single-walled CNT remained intact in structure (regardless of whether its collision is radial or axial). The experimental fracture observed25 for a multiwalled CNT was not seen. Therefore, the present CNT, which is smaller in both length and diameter than the experimental one, is mechanically robust and is not vulnerable to bending of its axis or radial collapse at this speed. To emulate the spray experiment closely, however, we need to consider the multiwalled CNTs. Such a CNT is likely to suffer more impact due to the bumping of walls against each other, thereby raising the temperature high enough for plastic behavior and reaction with surface silicon atoms. While it is not possible to simulate the actual (40-70 nm diameter) CNTs studied in the experiment, our simulations show (see Supporting Information) that multiwalled CNTs indeed have an increased temperature after impact as compared to a singlewalled CNT. In particular, for a three-walled CNT (2.1 nm diameter) whose innermost part is the same as the present CNT, we observed that the maximum temperature is 17 K higher than that of a single-walled CNT (see Figure S2 in the Supporting Information). This temperature increases as nanotube diameter grows, as the force exerted on the CNT when it collides with the surface scales with nanotube mass. Indeed for a five-wall CNT (3.5 nm diameter), the temperature increases by an additional 14 K (see Figure S2). Simple linear scaling of temperature increase with nanotube diameter fits the results accurately, leading to temperatures in the 843-1214 K range for 40-70 nm tubes, which is high enough for significant restructuring. We also checked the temperature versus diameter for long CNTs as follows. We elongated multiwalled CNTs in Figure S2 so that their axes have the same length as the side length of the simulation box in the Y direction. We then imposed

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the periodic boundary conditions in simulation. This way, we simulated three-, five-, and seven-walled tubes. The three- and five-walled tubes are the same in diameter as those in Figure S2. The outermost diameter for the newly simulated sevenwalled CNT was 4.89 nm. In Figure S3, we plot the diameter of CNT versus the maximum in the vibrational temperature TV. The slope from the fit of data was 13.97 K/nm, similar to but slightly larger than that without the periodic boundary conditions. A linear extrapolation in this case gives temperature of 1398 K for the CNT with a diameter of 70 nm, showing the results for short CNTs are valid for long CNTs. It should also be noted that in the experiment, the velocities have a broad distribution, and metal particles are sprayed with the CNTs. This would allow even higher temperatures to be achieved upon impact with the surface. Possible defects in the CNTs could be another aspect to be included to emulate the experiment. Previous theoretical work50,51 has shown that certain defects can dramatically reduce the fracture strength of a CNT. Consideration of an increased diameter, defects, and multi walls in the CNT as well as the presence of metal particles is likely to achieve conditions more commensurate with the experiments. Insights and molecular details from this work are expected to shed light on the design and interpretation of experiments utilizing the controlled collision of CNTs with surfaces. Acknowledgment. This study was supported by a Korea Research Foundation Grant funded by the Korean Government (MEST) (no. 2009-0089497), by the National Science Foundation (CCI Grant CHE-0943639), and by the Army Research Office (MURI Grant #W911NF-09-1-0541). Supporting Information Available: Effects of the van der Waals interaction between the carbon and silicon atoms (Figure S1). Collision of a multiwalled CNT with a silicon surface (Figure S2). Collisions of infinitely long CNTs (Figure S3). Collision of a CNT moving along the direction of surface normal with its axis tilted (Figure S4). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Iijima, S. Nature 1991, 354, 56. (2) Minary-Jolandan, M.; Yu, M.-F. J. Appl. Phys. 2008, 103, 073516. (3) Palaci, I.; Fedrigo, S.; Brune, H.; Klinke, C.; Chen, M.; Riedo, E. Phys. ReV. Lett. 2005, 94, 175502. (4) Yu, M.-F.; Kowalewski, T.; Ruoff, R. S. Phys. ReV. Lett. 2000, 85, 1456. (5) Zhu, C.; Guo, W.; Yu, T. X.; Woo, C. H. Nanotechnology 2005, 16, 1035. (6) Jeng, Y.-R.; Tsai, P.-C.; Fang, T.-H. J. Chem. Phys. 2005, 122, 224713. (7) Yu, M.-F.; Lourie, O.; Dyer, M. J.; Moloni, K.; Kelly, T. F.; Ruoff, R. S. Science 2000, 287, 637. (8) Marques, M. A.; Troiani, H. E.; Miki-Yoshida, M.; Jose-Yacaman, M.; Rubio, A. Nano Lett. 2004, 4, 811. (9) Dumitrica, T.; Hua, M.; Yakobson, B. I. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 6105. (10) Harrison, J. A.; Stuart, S. J.; Robertson, D. H.; White, C. T. J. Phys. Chem. B 1997, 101, 9682. (11) Wang, Y.; Wang, X.-X.; Ni, X.-G.; Wu, H.-A. Comput. Mater. Sci. 2005, 32, 141. (12) Liew, K. M.; Wong, C. H.; Tan, M. J. Appl. Phys. Lett. 2005, 87, 041901.

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