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Dynamics of mechanical waves in periodic grapheme nanoribbon assemblies.

Scarpa F, Chowdhury R, Kam K, Adhikari S, Ruzzene M - Nanoscale Res Lett (2011)

Bottom Line: The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures.We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length).The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk.

View Article: PubMed Central - HTML - PubMed

Affiliation: Advanced Composites Centre for Innovation and Science, University of Bristol, BS8 1TR Bristol, UK. f.scarpa@bristol.ac.uk.

ABSTRACT
We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs) of the type (8,0) and (0,8) using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length). We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk.

No MeSH data available.


Related in: MedlinePlus

Wave dispersion along the zigzag and armchair directions for a (8,0) GNR with length 15.854 nm. (a) Continuous green line is referred to the Hamiltonian minimized versus d. Continuous red line is for the Hamiltonian minimized both for d and l. (b) Comparison of wave dispersions along the zigzag direction (continuous blue line) and armchair (continuous red line). The Hamiltonians are minimized for d only.
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Figure 2: Wave dispersion along the zigzag and armchair directions for a (8,0) GNR with length 15.854 nm. (a) Continuous green line is referred to the Hamiltonian minimized versus d. Continuous red line is for the Hamiltonian minimized both for d and l. (b) Comparison of wave dispersions along the zigzag direction (continuous blue line) and armchair (continuous red line). The Hamiltonians are minimized for d only.

Mentions: The 1D wave propagation analysis has been carried out on (8,0) nanoribbons with a length of 15.854 nm along the zigzag direction, and 15.407 nm along the armchair direction for the (0,8) cases. The hybrid FE models have been subjected to simply supported (SS) conditions, clamping the relevant DOFs in the middle location of the ribbons, and allowing, therefore, to apply the relations (12) using a set of constraint equations. The wave dispersion characteristics for the propagation along the zigzag edge of the nanoribbons for the first Brillouin zone [32] are shown in Figure 2. The mode shapes associated to the first four pass-stop bands (Figure 3) are typical of periodic SS structural beams under bending deformation [40], while from our observations the out-of-plane torsional modes appear for the 5th and 6th wave dispersion characteristics.


Dynamics of mechanical waves in periodic grapheme nanoribbon assemblies.

Scarpa F, Chowdhury R, Kam K, Adhikari S, Ruzzene M - Nanoscale Res Lett (2011)

Wave dispersion along the zigzag and armchair directions for a (8,0) GNR with length 15.854 nm. (a) Continuous green line is referred to the Hamiltonian minimized versus d. Continuous red line is for the Hamiltonian minimized both for d and l. (b) Comparison of wave dispersions along the zigzag direction (continuous blue line) and armchair (continuous red line). The Hamiltonians are minimized for d only.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211848&req=5

Figure 2: Wave dispersion along the zigzag and armchair directions for a (8,0) GNR with length 15.854 nm. (a) Continuous green line is referred to the Hamiltonian minimized versus d. Continuous red line is for the Hamiltonian minimized both for d and l. (b) Comparison of wave dispersions along the zigzag direction (continuous blue line) and armchair (continuous red line). The Hamiltonians are minimized for d only.
Mentions: The 1D wave propagation analysis has been carried out on (8,0) nanoribbons with a length of 15.854 nm along the zigzag direction, and 15.407 nm along the armchair direction for the (0,8) cases. The hybrid FE models have been subjected to simply supported (SS) conditions, clamping the relevant DOFs in the middle location of the ribbons, and allowing, therefore, to apply the relations (12) using a set of constraint equations. The wave dispersion characteristics for the propagation along the zigzag edge of the nanoribbons for the first Brillouin zone [32] are shown in Figure 2. The mode shapes associated to the first four pass-stop bands (Figure 3) are typical of periodic SS structural beams under bending deformation [40], while from our observations the out-of-plane torsional modes appear for the 5th and 6th wave dispersion characteristics.

Bottom Line: The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures.We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length).The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk.

View Article: PubMed Central - HTML - PubMed

Affiliation: Advanced Composites Centre for Innovation and Science, University of Bristol, BS8 1TR Bristol, UK. f.scarpa@bristol.ac.uk.

ABSTRACT
We simulate the natural frequencies and the acoustic wave propagation characteristics of graphene nanoribbons (GNRs) of the type (8,0) and (0,8) using an equivalent atomistic-continuum FE model previously developed by some of the authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE models developed. The acoustic wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic mechanical structures. We show that the thickness and equilibrium lengths do depend on the specific vibration and dispersion mode considered, and that they are in general different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 nm for equilibrium length). We also show the dependence of the wave dispersion characteristics versus the aspect ratio and edge configurations of the nanoribbons, with widening band-gaps that depend on the chirality of the configurations. The thickness, average equilibrium length and edge type have to be taken into account when nanoribbons are used to design nano-oscillators and novel types of mass sensors based on periodic arrangements of nanostructures.PACS 62.23.Kn · 62.25.Fg · 62.25.Jk.

No MeSH data available.


Related in: MedlinePlus