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Coarse graining of carbon nanotubes

Since molecular dynamics simulations are computationally expensive for the simulation of whole devices, we propose a coarse-grained simulation of carbon nanotubes (CNTs) based on the dissipative particle dynamics method (DPD).

The coarse-graining of a representative graphene sheet. Solid dots represent the lumped particles. The solid arrow represents the axis of the tube. The dashed arrow represents the wrapping of the graphene to form a tube. This model is equivalent to an armchair nanotube with a chirality of (6,6) Figure 1 
Illustration of the coarse-graining for a single DPD particle. Figure 2 
TEM image of two adhering CNTs after growth by chemical vapour deposition. Courtesy Department of Physical Electronics, The Iby and Aladar Fleischman Faculty of Engineering, School of Electrical Engineering, Tel-Aviv University, Israel Figure 3 
Simulation result for two DPD-CNTs. The vertical bars on the right end of the CNTs indicate the anchoring to a substrate; top: Initial configuration of the DPD-CNTs; bottom: Configuration after t = 30 ns. The angle 2theta, the zipping length l = 27 nm PLUSMINUS 1 nm and the distance of the fixed ends 2DELTA = 11 nm can be used to compute the binding energy. Figure 4 
A spectral analysis of the first three vibration modes of a slacked (black and dark grey lines) and a taut (light grey line) double-clamped tube of length 57 nm at 300 K. The clamping distance of the slacked tube is 99% of its natural length. The taut tube is neither strained nor compressed. Figure 5 
The first resonance frequency of a 57nm tube versus temperature. Empty circles are the simulation results, and the solid line is a theoretical prediction. Figure 6 

Coarse-graining procedure

Figures 1 and 2 show a schematic representation of the coarse graining procedure of a carbon nanotube by grouping 24 carbon atoms. Figure 1 shows the coarse-graining of a representative graphene sheet. Solid dots represent the lumped particles. The solid arrow represents the axis of the tube. The dashed arrow represents the wrapping of the graphene to form a tube. This model is equivalent to an armchair nanotube with a chirality of (6,6). Figure 2 clarifies the coarse-graining for a single DPD-particle.

Simulation of tube-tube interactions

Figure 3 shows a TEM image of two adhering CNTs after growth by chemical vapour deposition. Courtesy Department of Physical Electronics, The Iby and Aladar Fleischman Faculty of Engineering, School of Electrical Engineering, Tel-Aviv University, Israel.

Figure 4 shows the simulation result for two DPD-CNTs. The vertical bars on the right end of the CNTs indicate the anchoring to a substrate. On top, the Initial configuration of the DPD-CNTs is shown. The configuration after t = 30 ns is shown at the bottom. The angle 2θ, the zipping length l = 27 nm ± 1 nm and the distance of the fixed ends 2Δ = 11 nm can be used to compute the binding energy. The obtained value matches well with microscopic predictions.

Simulation of CNT-resonators

Figure 5 shows the spectral analysis of the first three vibration modes of a slacked (black and dark grey lines) and a taut (light grey line) double-clamped tube of length 57 nm at 300 K. The clamping distance of the slacked tube is 99% of its natural length. The taut tube is neither strained nor compressed. It is clearly visible that for a slacked tube, the resonance peaks in the spectrum have broadened considerably.

Figure 6 shows the first resonance frequency of a 57 nm tube versus temperature. Empty circles are the simulation results, and the solid line is a theoretical prediction.

Relevant publications:

  • O. Liba, D. Kauzlarić, Y. Hanein, A. Greiner, J. G. Korvink, Investigation of the mechanical properties of bridged nanotube resonators by dissipative particle dynamics simulation. Int. J. Multiscale Comp. Eng., 6:549–562, 2008.
  • O. Liba, D. Kauzlarić, Z. R. Abrams, Y. Hanein, A. Greiner, J. G. Korvink, A dissipative particle dynamics model of carbon nanotubes. Molecular Simulation 34:737–748, 2008.
  • O. Levy, Y. Hanein, D. Kauzlarić, A. Greiner, J. G. Korvink, Reduced molecular model for the mechanics of carbon nanotubes. Proceedings of the APCOM07, Kyoto, Japan 357–362, 2007.

Contact person:

David Kauzlarić

Collaboration partners

Orly Liba, Yael Hanein, School of Electrical Engineering, Department of Physical Electronics, The Iby and Aladar Fleischman Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel
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