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).
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.
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.
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.
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