Nanomechanics and Kinky Chem

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Modeling and Design of Carbon Nanotube
Materials and Devices
M. Meyyappan NASA Ames Research Center
Contributors Deepak Srivastava, M. Anantram
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Simulation Techniques

• Large scale Classical Molecular Dynamics
  Simulations on a Shared
• Memory Architecture Computer

• Tersoff-Brenner reactive many-body potential for
  hydrocarbons
• with long range LJ(6-12) Van der Walls
  interactions
• Parallel implementation on a shared memory
  Origin2000

• Quantum Molecular Dynamics Simulations

• Tight-binding MD in a non-orthogonal atomic
  basis
• Previous parametrization silicon and carbon (M.
  Menon and K. R
• Subbaswami, Phys. Rev. B 1993-94.
• Extended to heteroatomic systems including C, B,
  N, H

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Spatio-Temporal Resolution
Finite element for homogeneous, Continuum
description
bulk continuous media
Mesoscopic dynamics for non-homogeneous
1000,000,000 atoms or grid
Atomistic MD, many-body force fields
1000,000 atoms
Semi-emirical, tight-binding MD
1000 atoms
ab-initio, structure, energetics
100 atoms
Molecular Dynamics
Experiments
Long time structural
KMC, TDMC
Hyperdynamics
up to 100s of ns
up to sec, hours
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Modulus of Carbon Nanotubes
It is a measure of the strength and stiffness
against small axial stretching and compression
strains as well as nonaxial bending and torsion
strains Observed properties of CNTs come from
the strength of in-plane C-C bonds in graphene
sheet and facile out-of-plane deformation of the
structure For large diameter of small
curvature CNT, the modulus, strength and
stiffness should be comparable with the in-plane
modulus strength of graphene sheet In
tubular geometry, elastic strain energies are
also affected by the instrinsic curvature of the
surface. The elastic energy of a SWNT scales as
1/(Radius)2
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Modulus of CNTs (Continued)
For axial strains, the Youngs modulus of SWNT
is where E is strain energy, V is the
nanotube volume Bending stiffness is where
L is the length, C is the curvature of the bent
nanotube ( ?/L where ? is bending
angle) Torsion stiffness is here ? is the
torsion angle shear strain ? R?/L
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Nanomechanics of Nanomaterials

• Nanotubes are extremely strong highly elastic
  nanofibers

High value of Youngs Modulus (1.2 -1.3 T Pa
for SWNTs)
Elastic limit up to 10-15 strain

• Dynamic response under axial compression,
  bending torsion

• redistribution of strain
• sharp buckling leading to bond rupture
• SWNT is stiffer than MWNT

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Nanomechanics of Nanomaterials
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Nanomechanics of Nanotubes - Classical MD (II)
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Nanotubes in Composites
Experiment buckling and collapse of nanotubes
embedded in polymer composites.
Buckle, bend and loops of thick tubes..
Local collapse or fracture of thin tubes.
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Stiffness and Plasticity of Compressed C Nanotubes
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Plastic Collapse of an (8,0) Carbon Nanotube
Quantum Molecular Dynamics

• D. Srivastava, M. Menon and K. Cho, Phys. Rev.
  Lett. (1999)

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Plastic Collapse by Design

• Tube plastically collapses at the location of
  the defect
• New types of heterojunctions can be created
• Quantum dot effect in one dimensional system

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Carbon-based Electronics
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Nanotube Electronics (Basics)
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Trends in Device Miniaturization
Down scaling of semiconductor technology
Molecular devices
Smaller and Faster Devices
Conventional
New
Hybrid
- Ultra Small MOSFET - Interference based
devices - Resonant tunneling diodes - Single
electron transistors
- Carbon nanotube - Molecular diodes - DNA?
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Conventional Methods of Device Modeling

• Electrons are waves. de Broglie wavelength of an
  electron is,
• h/p,
• where p is the momentum
• Device dimensions are much larger than the
  electron wave length
• Transit time through the device is much larger
  than the scattering time
• Diffusion equation for semiconductors

Diffusive
Ballistic Phase-coherent
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• Electrons behave as waves rather than particles
• Schrodingers wave equation
• Poisson equation still important
• Landauer-Buttiker Scattering theory
• In this theory,
• Current,
• T(E) Transmission probability
  for an electron to traverse
• the device at energy E
• fLEFT(E) occupancy factor /
  probability for an electron to be
• incident from the left
  contact (Fermi- dirac factor)

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Transport in Molecular Structures - Interplay
between Chemistry and Physics

• Quantum chemistry tools (perform energy
  minimization) or Molecular Dynamics (MD) are used
  to find chemically and mechanically stable /
  preferable structures
• Schrodinger equation describes electron flow
  through the device
• Poissons equation gives the self-consistent
  potential profile

Chemically Mechanically Stable
Structures Energy Minimization, quantum chemistry
(hundred atoms) Molecular Dynamics simulations
(millions of atoms) Number of atoms ?? accuracy
Current, Electron Density Schrodingers equation
/ non equilibrium Greens function
Potential (Voltage) Profile Poissons equation
New Devices
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Resonant Tunneling Diode
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Example Resonant Tunneling Diode
Current
Voltage

• Negative differential resistance
• Peak to valley ratio should be large

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Graphene

• Blue box unit cell of graphene
• a1 a2 lattice vectors
• r1, r2 r3 - bond vectors
• Two atoms per unit cell

• Applying of Blochs theorem
• For graphene, symmetry dictates that t1t2t3

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Graphene
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Graphene
a1
a1
a2
a2
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eikfeik(f2p)
Graphene to Nanotube

• Y eikxxikyy (u v)

• Example, (6,0) zigzag tube,

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Nanotube Wavefunction
p - integer
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Summary of Main Electronic Properties

• Metallic nanotubes
• n-m 3integer
• Semiconducting tubes
• Bandgap a 1/Diameter
• Armchair tubes are truly metallic
• Other metallic tubes have a tiny curvature
  induced bandgap

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Summary of Main Electronic Properties
Armchair tubes do not develop a band gap
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Shapes in Nature

• Nanohorns
• Torus

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Armchair Nanotube Bands

• Close to E0, only two sub-bands, (6.5 kW)
• At higher energies,
  (
• Low bias record (multi-wall nanotube)
  (500W)

• Can subbands at the higher energies be accessed
  to drive large currents through these molecular
  wires?

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Quantum Conductance Experiment

• Frank et. al, Science 280 (1998)

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Quantum Conductance Experiment (cont.)

• VAPPLIED
• VAPPLIED 200mV, slow increase

• E 120meV, non-crossing bands open
• At E2eV, electrons are injected into about 80
  subbands
• Yet the conductance is 5 e2/h

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Semiclassical Picture

• The strength of the two processes are determined
  by
• Tunneling distance, Barrier height (DENC),
  Scattering
• DENC a 1/Diameter. So the importance of Zener
  tunneling increases with increase in nanotube
  diameter.

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Semiclassical Picture (cont.)

• The differential conductance is not comparable to
  the increase in the number of subbands. (20,20)
  nanotube 35 subbands at 3.5eV
• Two classes of experiments with order of
  magnitude current that differs by a factor of 5!
• Our ballistic calculations agree with increase in
  conductance

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Summary (Current Carrying Capacity of Nanotubes)

• Nanotubes are the best nanowires, at present!
• However, Bragg reflection limits the current
  carrying capacity of nanotubes
• Large diameter nanotubes exhibit Zener tunneling
• Conductance much larger than 4e2/h is difficult

Phys. Rev. B 62, 4837 (2000)
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Band Structure
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2-Point Nanotube Heterojunctions
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T-Shaped Nanotubes
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Two Dimensional Molecular "Networks"
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Nanoelectronics with Doping
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Nanoelectronics with Doping
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Multi-wall Y-Junction Carbon Nanotubes
Experimental Synthesis of Multi-wall Carbon
Nanotube Y-Junctions (2000)
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Transport in Y-Junction Carbon Nanotubes
Rectification and Ballistic Quantum Transport in
Carbon Nanotube Y junction
V 0 V 0
2
3
I
1
I
1
V 0
3
A Andriotis, M. Menon, D. Srivastava and, L.
Chernozatonski, submitted, Phys. Rev. Lett. (2001)
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Rectification in Y-junction Nanotube has a
Strong Dependence on the Strunctural Symmetry
A Andriotis, M. Menon, D. Srivastava and L.
Chernozatonski, submitted, Appl. Phys. Lett.
(2001)
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Nanotube Devices
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Nano Electromechanical Effects (NEMS)
Mechanical deformation alter the electronic
deformation of nanotubes effect is chirality
dependent
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CNT Conductance Decreases with Deformation
Tombler et. al, Nature 405, 769 (2000) showed
that the conductance of SWNT decreases when
deformed by AFM tip.
Tombler et al, Nature 405, 769 (2000)
Stretching of bonds Opens bandgap in most
nanotubes Phys. Rev. B, vol. 60 (1999)
What is the conductance decrease due to?
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Model to Explain the Experimental Observation
1) AFM Deformation
2) Bending
Structure
Relaxation Central 150 atoms were relaxed using
DFT and the remaining 2000 atoms were relaxed
using a universal force field
Density of states and conductance were computed
using four orbital tight-binding method with
various parametrizations
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Bond Length Distribution Conductance
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AFM Deformed versus Stretched
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What Happens to Other Chiralities?

• Metallic zigzag nanotubes develop largest bandgap
  with tensile strain.
• All other chiralities develop bandgap that varies
  with chirality (n,m).
• Experiments on a sample of metallic tubes will
  show varying decrease in conductance.
• Some semiconducting tubes will show an increase
  in conductance upon crushing with an AFM tip.

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Summary (Electromechanical Switch)

• Metallic nanotubes develop a bandgap upon strain.
  Detalied simulations show that this is a
  plausible explanation for the recent experiment
  on electromechanical properties by Tombler et al,
  Nature (2000)
• In contrast, we expect nanotube lying on a table
  to behave differently. A drastic decrease in
  conductance is expected to occur only after sp3
  type hybridization occurs between the top and
  bottom of the nanotube.

Suspended in air
Table Experiment
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Mechano-Chemical Effects Kinky Chemistry
Cohesive Energy
Binding Energy
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Functionalization of Nanotubes
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Mechano-Chemical Effects Kinky Chemistry
SEM images of MWNTs dispersed on a V-ridged
Formvar substrate
D. Srivastava, J. D. Schall, D. W. Brenner, K. D.
Ausman, M. Feng and R. Ruoff, J. Phys. Chem. Vol.
103, 4330 (1999).
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H Storage in Nanotubes
Experimental Observations

• A. C. Dillon et. al. Nature (1997)
• fractional weight of H2 5-10
• Y. Ye et. al. Appl. Phys. Letters (1999)
• adsorption in crystaline ropes of SWNTs 8
  - at 80K and 12MPa
• Chen et. al. Science (1999)
• Li doped and K doped MWNTs, 14-20 - ambient
  press and RT
• C. Liu et. al., Science (1999)
• storage in SWNTs 4.2 at room temperature and
  10MPa

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H Storage in Nanotubes - Physisorption
Modeling and Simulations

• Q. Wang and K. Johnson et. al., J. Chem. Phys.
  (1999)
• - Monte Carlo methods with quantum effects
• - Results are in agreement with activated carbon
  data
• - Storage and absorption is much less as
  reported above by experiments
• - Only mechanism is H2 adsorption via
  physisorption

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H Storage in Nanotubes - Physisorption
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H Storage in Nanotubes - Physisorption
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H Storage in Nanotubes - Chemisorption and Hybrid
Mechanisms
Consider 5 Competing Mechanisms in Metal Doped
Nanotubes

• Chemisorption of H/Nanotube (?)
• Surface Diffusion of H/Nanotube (?)
• Recombination H-Nanotube H H2 (?)
• Catalytic Dissociation of H2 (?)
• Physi/Chemisorption (?)
• Physisorption (Investigated in Detail) (?)

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H Chemisorption on Graphene Sheet
Effective Potential Energy Surface H/Graphene
Sheet
Binding Energy 1.38 eV Diffusion Barrier
0.50eV
Computed on a grid with full dynamics of
surface C atoms and H atom normal to the
surface
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H Chemisorption and Diffusion on (10,10) Carbon
Nanotube
H Chemisorbed on the outside Barrier 0.83 eV
H Chemisorbed on the inside Barrier 0.33 eV
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Diffusion Rate Constant via Wave-Packet
Dynamics and Flux-Flux Correlation Function
Formalism
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H Chemisorption and Diffusion Comparison
H/(10,10) nanotube (outside) Diffusion Barrier
0.83eV H/Graphene Sheet Diffusion Barrier
0.50eV (10,10) nanotube (inside) Diffusion
Barrier 0.33eV
Anisotropy in the diffusion on the in and
ouside of a nanotube Magnitude of anisotropy
will be inversely proportional to the diameter
of the nanotube
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Molecular Machines and Laser Motor
J. Han, A Globus and R. Jaffe
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Molecular Machines and Laser Motor