Nanomechanics of Carbon Nanotubes and Silicon Nanowires via … · 2009-07-28 · Nanomechanics of...
Transcript of Nanomechanics of Carbon Nanotubes and Silicon Nanowires via … · 2009-07-28 · Nanomechanics of...
Nanomechanics of Carbon Nanotubes and Silicon Nanowires via Objective Molecular ModelingIlia Nikiforov, Dong-Bo Zhang, Traian Dumitrică. University of Minnesota.
12 13 14 15 16Stra
in E
nerg
y (b
LUE)
and
Der
ivat
ive
w/ R
espe
ct to
Ang
le (G
REE
N)
Bending Angle (deg)
Second-order discontinuity in energy signals onset of buckling
in CNTs
(5,5)(10,10)
(15,15)
(20,20)
(25,25)
(30,30)
0
50
100
150
200
250
0 0.5 1 1.5 2 2.5Crit
ical
Rad
ius
of C
urva
ture
(nm
)
Radius (nm)
MWCNTs buckle at higher curvatures than SWCNTs of the
same diameter
SWCNTMWCNT
1. Goals
3. Objective Molecular Dynamics
Replaces PBC over a large translational cell with Objective Boundary Conditions over a small objective cell:Repetition Rule = Translation + Rotation
2. Chiral Systems: Examples from Nanostructures and Biology
SiGe/Si Nanowires
Tobacco Mosaic Virus1. nucleic acid (RNA)2. capsomer 3. capsid
4. Symmetry-Adapted DFT-based Tight-Binding
Xi,ζ = Xi +ζT , i = 1,...,N t
Xi,ζ1ζ 2= R2
ζ 2 R1ζ1 Xi +ζ1T1, i = 1,2
Z → T1,R1(θ1)Ch /d → R2 (θ2)
Fi = −∇X iV (Xi,ζ 1ζ 2
)
numberquantumhelicalnumberquantumangularNl a
1,...,0
→<≤−→−=
πκπ
αn, lκ ∝ζ 1 = 0
Ns −1∑ e
ζ 2 = 0
Na −1∑
ilθ 2ζ 2 + iκζ 1
αn,ζ1ζ 2
H(lκ)C( j,lκ) = Ei(lκ)S(lκ)C( j,lκ), j =1,...,Nobjele
Schroedinger Equation in Matrix Form:
(4,2) CNT
References:• T. Dumitrica and R. D. James, Objective Molecular Dynamics, Journal of the Mechanics and Physics of Solids 55,
2206 (2007).• D.-B. Zhang, M. Hua, and T. Dumitrica, Journal of Chemical Physics 128, 084104 (2008).Carbon and Boron-Nitride Nanotubes
“Translational” and “Helical-Angular” Representation ofCarbon Nanotubes
References:• S. S. Alexandre, M. S. C. Mazzoni, and H. Chachama, Stability, geometry, and electronic structure of the boron
nitride B36N36 fullerene, Applied Physics Letters 75, 1 (1999).
6. Application: Electromechanical Characterization of Carbon
Nanotubes in Torsion
Stra
in E
nerg
y (e
V/a
tom
)
(a)
Ban
d ga
p (e
V)
(b) (c)
The objective methodology allows us to derive the nonlinear elastic response of CNTs in torsion from a density-functional-based tight-binding model. Figures below reveal a sharply contrasting behavior in the electronic response. The critical strain εc beyond which CNTs behave nonlinearly, the most favorable rippling morphology, and the twist- and morphology-related changes in fundamental band gap are identified. Results are assistive for experiments performed on CNT-pedal devices.
In single-walled CNTs the band gap variations are dominated by rippling.
Band gap of multi-walled CNTs exhibits an unexpected insensitivity.
References:• D.-B. Zhang, R.D. James, and T. Dumitrica, Physical Review B (at press).
The research objective of this project is to develop amultiscale computational methodology based on a symmetry-adapted scheme. This objective will be achieved by pursuingthe following specific aims:Create a versatile symmetry-adapted density functionaltheory-based modeling capability by implementing the helicalboundary conditions into an existing density functional theorycomputational solver;Bridge the density functional theory description with finitedeformation continuum for the single-walled carbonnanotubes;Establish a dynamic mesoscopic model of the few-layerthick SiGe/Si and ZnO nanobelts.
CNTs
5. Application: Linear and non-Linear Elasticity of Carbon Nanotubes
Tight-Binding treatment under objective boundary conditions makes possible to compute the linear and non-linear elastic mechanical response of nanotubes
Young’s modulus Ys, and Shear modulus Gs as a function of NT diameter. Calculations were carried out on the “Helical-Angular” cell.
px ,ζ1ζ 2
px ,00
Tight-Binding solution is represented in terms of“Helical-Angular” Adapted Bloch Sums:
BNNTs
The objective method allows for efficient treatment of pure bending in quasi-one-dimensional structures. Figures bellow illustrate how it can be applied to study buckling in carbon nanotubes.
References:• D.-B. Zhang and T. Dumitrica, Applied Physics Letters 93, 031919 (2008).• I. Nikiforov, D-B. Zhang and T. Dumitrica, In progress.