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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

Comparison between MM (full markers) and hybrid-FE (empty markers) natural frequencies for (8,0) SLGSs with different widths.
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Figure 1: Comparison between MM (full markers) and hybrid-FE (empty markers) natural frequencies for (8,0) SLGSs with different widths.

Mentions: Figure 1 shows the comparison between the MM simulations and the results from the hybrid FE models for a (8,0) nanoribbon at different lengths (6.03, 12.18, 18.34 and 24.49 nm). The equilibrium lengths are l = 0.142 nm for all cases considered. For the flexural modes the hybrid FE approach identifies a bond thickness d of 0.077 nm, with only a 3% difference from the analogous thickness value assocoated to the first torsional mode is considered. The identified thickness value compares well with the 0.074-0.099 nm found by some of the authors in uni-axial tensile loading cases related to single layer graphene sheets [13], with the 0.0734 nm in uni-axial stretching using first generation Brenner potential [25], and the 0.0894 nm identified by Kudin et al using ab initio techniques [38]. Gupta and Batra [39] find a thickness of 0.080 nm for the ω11 frequency of a fully clamped single layer graphene sheet (SLGS) with dimensions 3.23 nm × 2.18 nm, combining a MD simulation and results from the continuum elasticity of plates. It is worth to notice that these results are significantly different from the usual 0.34 nm inter-atomic layer distance adopted by the vast majority of the research community in nanomechanical simulations. The percentage difference between our MM and hybrid FE natural frequencies is on average around 3 for all the flexural modes. The torsional frequencies for the nanoribbons with the lowest aspect ratio provide a higher error (5%), suggesting that the assumption of equal in-plane and out-of-plane torsional stiffness with the AMBER model in Equation 1 leads to a slightly lower out-of-plane torsional stiffness of the nanoribbon.


Dynamics of mechanical waves in periodic grapheme nanoribbon assemblies.

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

Comparison between MM (full markers) and hybrid-FE (empty markers) natural frequencies for (8,0) SLGSs with different widths.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Comparison between MM (full markers) and hybrid-FE (empty markers) natural frequencies for (8,0) SLGSs with different widths.
Mentions: Figure 1 shows the comparison between the MM simulations and the results from the hybrid FE models for a (8,0) nanoribbon at different lengths (6.03, 12.18, 18.34 and 24.49 nm). The equilibrium lengths are l = 0.142 nm for all cases considered. For the flexural modes the hybrid FE approach identifies a bond thickness d of 0.077 nm, with only a 3% difference from the analogous thickness value assocoated to the first torsional mode is considered. The identified thickness value compares well with the 0.074-0.099 nm found by some of the authors in uni-axial tensile loading cases related to single layer graphene sheets [13], with the 0.0734 nm in uni-axial stretching using first generation Brenner potential [25], and the 0.0894 nm identified by Kudin et al using ab initio techniques [38]. Gupta and Batra [39] find a thickness of 0.080 nm for the ω11 frequency of a fully clamped single layer graphene sheet (SLGS) with dimensions 3.23 nm × 2.18 nm, combining a MD simulation and results from the continuum elasticity of plates. It is worth to notice that these results are significantly different from the usual 0.34 nm inter-atomic layer distance adopted by the vast majority of the research community in nanomechanical simulations. The percentage difference between our MM and hybrid FE natural frequencies is on average around 3 for all the flexural modes. The torsional frequencies for the nanoribbons with the lowest aspect ratio provide a higher error (5%), suggesting that the assumption of equal in-plane and out-of-plane torsional stiffness with the AMBER model in Equation 1 leads to a slightly lower out-of-plane torsional stiffness of the nanoribbon.

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