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Nanometer-Scale Indentation
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(1) System Setup
- Probes:
- Capped (10,10) tubules
- Two-shell, capped tubule
- Nanotube Bundle
- inner tube is (10,10)
- outer tube is (15,15)
- Tubule lengths of 5.0, 8.1, 13.4 nm
- Surfaces:
- Hydrogen-terminated diamond (111) surface
- Graphene sheet where the outer atoms are held rigid.
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(2) Nanometer-Scale Indentation of Diamond
Tubule deforms by inversion of the cap, buckling, and slip. Same mechanisms are seen for all tube lengths considered.
a) Effect of Tube Length on Buckling Force
The Euler buckling force varies with changes to the length of the tube. In other words,
increasing the length of the nanotubule tip will result in a gentler probe that can be pushed against a softer surface without damaging it,
though the modulus of the tube will not change. 
| CNT Length (nm) | # Buckles | Buckling force (nN) | Modulus (TPa) |
| Indent | Free space | Indent | Free space | Indent | Free space |
| 5.0 | 1 | 1 | 82 | 85 | 1.2 | 1.3 |
| 6.2 | - | 2 | - | 102 | - | 0.6 |
| 7.3 | - | 2 | - | 100 | - | 0.8 |
| 8.1 | 2 | 2 | 79 | 110 | 0.8 | 1.0 |
| 9.8 | - | 2 | - | 120 | - | 1.7 |
| 12.3 | - | 3 | - | 130 | - | 1.3 |
| 13.4 | 2 | 3 | 85 | 120 | 2.3 | 1.4 |
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(3) Nanometer-Scale Indentation of Graphene
On indentation the graphene deforms to form a "well-like" structure.
Tubule deforms by inversion of the cap, buckling, and slip. Same mechanisms are seen for all tube lengths considered.
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(4) Nanometer-Scale Indentation with a Multiwalled Nanotube
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(5) Conclusions
- Single-walled tube:
- Nanotube tips buckle than slip to relieve applied stress during indentation.
- Number of buckles depend on tubule length.
- Deformation mechanisms depend on the reactivity of the surface but do not depend on surface rigidity.
- Buckling force is weakly dependent on tubule length, strongly dependent on degrees of freedom available to the tip.
- Modified buckling force equation works well when buckling is the only mechanism available to relieve applied stress.
- Nanotube bundle:
- Mechanisms are the same as for a single tubule.
- Maximum buckling force of a tubule bundle tip is inversely proportional to the rigidity of the surface.
- Maximum buckling force is not a simple summation of the corresponding number of individual tubules.
- Multi-walled tube:
- Mechanism is the same as for a single-walled tubule.
- Multi-walled tubule is stiffer than comparably sized single-walled tubule.
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We provide open source codes for MD simulations: C-H REBO MD code, C-F-H REBO MD code, and C-O-H REBO MD code.
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