Role%20of%20Nanomechanics%20in%20Computational%20Nanotechnology

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Role of Nanomechanics in Computational
Nanotechnology

• N Chandra, S Namilae and C Shet

Collaborators Leon van Dommelen (ME/FSU)
Ashok Srinivasan (CS/FSU)
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Computational Modeling in Nanotechnology

• By nature, humans live, work and play in the
  macroscale. But they have the unique ability to
  think in the nanoscale.
• Control must inherently come from the MACROSCALE
  because that is the scale where humans reside.
• MANY PATHS TO FOLLOW
• Biochemistry Custom protein design
• Chemistry Molecular recognition
• Physics Scanning probe microscopy
• Computing Molecular modeling
• Engineering Molecular electronics
• Engineering Quantum electronic devices
• Engineering Nanocomposites
• Engineering Nanomaterials engineering

...thorough control of the structure of matter
at the molecular level. It entails the ability to
build molecular systems with atom-by-atom
precision, yielding a variety of nanomachines.
These capabilities are sometimes referred to as
molecular manufacturing.
- K. Eric
Drexler, 1989
To manipulate things which we cannot see without
the unaided eye but indeed understand, we must
employ predictive methods
Computational Tools.
If you cant model it, you cant build it!
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The Scale of Things -- Nanometers and More
Things Natural
Things Manmade
MicroElectroMechanical devices 10 -100 mm wide
Red blood cells
Pollen grain
Zone plate x-ray lensOutermost ring spacing
35 nm
Atoms of silicon spacing tenths of nm
Office of Basic Energy Sciences Office of
Science, U.S. DOE Version 03-05-02
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Nanomechanics Issues
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Mechanics at atomic scale
Stress-strain required for local behavior
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Carbon Nanotubes

• Carbon Nanotubes ? Graphite sheet rolled into a
  tube
• Length 100 nm to few ?m Diameter 1 nm
• Chirality based on rolling direction
• Found as single wall and Multi wall tubes

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Carbon Nanotubes (CNTs)

• CNTs can span 23,000 miles without failing due to
  its own weight.
• CNTs are 100 times stronger than steel.
• Many times stiffer than any known material
• Conducts heat better than diamond
• Can be a conductor or insulator without any
  doping.
• Lighter than feather.

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Defects in carbon nanotubes (CNT)

• Mechanical properties
• stiffness Reduction.
• Plastic deformation and fracture
• Enhanced Chemical activity
• Electrical properties
• Formation of Y-junctions
• End caps
• Other applications
• Hydrogen storage, sensors etc

• Defect types
• Point defects e.g Vacancy
• Topological defects e.g. 5-7-7-5 defect
• Hybridization defects

1Ref D Srivastava et. al. (2001)
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Stress at atomic scale

• Definition of stress at a point in continuum
  mechanics assumes that homogeneous state of
  stress exists in infinitesimal volume surrounding
  the point
• In atomic simulation we need to identify a volume
  inside which all atoms have same stress
• In this context different stresses- e.g. virial
  stress, atomic stress, Lutsko stress,Yip stress

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Virial Stress
Stress defined for whole system
For Brenner potential
Includes bonded and non-bonded interactions
(foces due to stretching,bond angle, torsion
effects)
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BDT (Atomic) Stresses
Based on the assumption that the definition of
bulk stress would be valid for a small volume ??
around atom ?
- Used for inhomogeneous systems
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Lutsko Stress
- fraction of the length of ?-? bond lying inside
the averaging volume

• Based on concept of local stress in
• statistical mechanics
• used for inhomogeneous systems
• Linear momentum conserved

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Averaging volume for nanotubes

• No restriction on shape of averaging volume
  (typically spherical for bulk materials)
• Size should be more than two cutoff radii
• Averaging volume taken as shown

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Strain calculation in nanotubes

• Defect free nanotube ? mesh of hexagons
• Each of these hexagons can be treated as
  containing four triangles
• Strain calculated using displacements and
  derivatives shape functions in a local coordinate
  system formed by tangential (X) and radial (y)
  direction of centroid and tube axis
• Area weighted averages of surrounding hexagons
  considered for strain at each atom
• Similar procedure for pentagons and heptagons

Updated Lagrangian scheme is used in MD
simulations
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Elastic modulus of defect free CNT
-Defect free (9,0) nanotube with periodic
boundary conditions
-Strains applied using conjugate gradients
energy minimization

• All stress and strain
• measures yield a Youngs
• modulus value of 1.002TPa

• Values in literature range
• from 0.5 to 5.5 Tpa. Mostly
• around 1Tpa

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Local elastic moduli of CNT with defects

• Type I defect ? E 0.62 TPa

• Type II defect ? E0.63 Tpa

• Reduction in stiffness in the presence of defect
  from 1 Tpa
• -Initial residual stress indicates additional
  forces at zero strain
• -Analogous to formation energy

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Stress and Strain profiles
Note the stress and strain amplification
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Bond angle and bond length effects

• Pentagons experiences maximum bond angle change
  inducing considerable longitudinal strains in
  facets ABH and AJI
• Though considerable shear strains are observed in
  facets ABC and ABH, this is not reflected when
  strains are averaged for each of hexagons

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Evolution of stress and strain
Strain and stress evolution at 1,3,5 and 7
applied strains Stress based on BDT stress
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Effect of Diameter and Chirality
More pronounced effect with variation in chirality
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Residual stress at zero strain

• Stress is present at zero strain values.
• This corresponds to stress due to curvature
• It is found to decrease with increasing diameter
• Basis for stress calculation ? graphene sheet

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Functionalized Nanotubes and Nanotube composite
Interfaces
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Issues in Nanotube composites

• Controlling alignment during processing
• Homogeneous distribution (spatial)
• Orientation control (directional)
• Processing induced residual stresses
• Interface bonding (at atomic level)
• Load transfer
• Fracture/load shedding

Strong Interfaces By Chemical Bonding ?
Interface ? Bounding surface with physical /
chemical / mechanical discontinuity
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Chemical bonding at CNT- matrix interfaces

• Wagner et.al. (1998) ? indirect measurement of
  interface strength 500MPa
• Qian et.al. (2002) significant load transfer
  across interface in CNT-polystyrene composites
• Eitan et. al (2003) report carboxylization of CNT
  and predict covalent bonding with epoxy matrix
• Gong and coworkers (2000) improved composite
  properties by coating nanotubes with surfactants
• Frankland et. al.(2002) based on MD simulation
  suggest increased interface strength with
  chemical bonding

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Functionalized nanotubes

• Objective
• Study Deformation of functionalized nanotubes
• Study deformation on nanotubes in composites

• Change in hybridization (SP2 to SP3)
• Experimental reports of different chemical
  attachments
• Application in composites, medicine, sensors

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Simulation Parameters

• Various nanotubes with hydrocarbon attachments,
  vinyl and butyl in central portion
• Temperature 77K and 3000K
• Applied displacement at both ends at 0.05A/1000
  steps
• Lutsko stress computed on volume shown

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Functionalized nanotubes contd

• Increase in stiffness observed by functionalizing
• 20 attachments show about 10 increase in local
  elastic modulus

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Local Stiffness of functionalized CNTs
 

• Stiffness increase is more for higher number of
  chemical attachments
• Stiffness increase higher for longer chemical
  attachments

 
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Contour plots
Stress contours with one chemical attachment.
Stress fluctuations are present
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Radius variation

• Increased radius of curvature at the attachment
  because of change in hybridization
• Radius of curvature lowered in adjoining area

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Defect evolution and onset of plastic deformation

• Defect evolution starts at about 7 strain
• (10,10) CNT T3000K

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Evolution of defects in functionalized CNT

• Defects Evolve at much lower strain of 4.5 in
  CNT with chemical attachments
• Onset of plastic deformation at lower strain.
  Reduced fracture strain

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Multi scale model (I Molecular dynamics)
(10,10) CNT with varying no of hydrocarbon
attachments Applied displacements at 300K
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Interfacial shear
Interfacial shear measured as reaction force of
fixed atoms
Max load
Typical interface shear force pattern. Note zero
force after Failure (separation of chemical
attachment)
After Failure
250,000 steps
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Debonding and Rebonding of Interfaces
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Variation in interface behavior
Homogenization ?
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Force distribution along the interface
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Bonding and Rebonding in CNT pullout test
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Bonding and Rebonding in CNT pullout test
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Multi scale approach (II FEM/cohesive zone
model)

• Assumptions
• Nanotubes deform in linear elastic manner
• Interface character completely determined by
  traction-displacement plot

CZM enables modeling of surfaces before and after
fracture
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Preliminary result Numerical pull-out test

• Pull out of nanotube from polymer matrix modeled
  with CZM/ atomically informed interface
  characteristics

Scaled up version of the previous test nanotube
length 2 microns
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Shear Lag Studies
Contours of Normall Stress s22 at d 0.72 nm
Contours of Shear s12 Stress at d 0.72 nm
Contours of Normal Stress s22 at d 12 nm
Contours of Shear s12 Stress at d 12 nm
separation
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Applications of the multiscale model
Composite effective properties
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Summary

• Local kinetic and kinematic measures are
  evaluated for nanotubes at atomic scale
• There is a considerable decrease in stiffness at
  5-7-7-5 defect location in different nanotubes
• Defect-defect interactions
• Functionalization of nanotubes results in
  increase in stiffness
• Onset of inelastic deformation characterized by
  evolution of topological defects occurs at lower
  strains in functionalized tubes
• Interface constitutive behavior has been modeled
  using MD and this information is passed to
  continuum model using CZM

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Interaction between defects

• Stiffness reduction in defects placed at
  different distances along length
• Defects placed close to each other experience
  more loss of stiffness
• If distance between the defects is greater than
  42 A i.e. 30l , it does not effect stiffness

Variation of stiffness loss with spacing of two
interacting defects, placed along the length of
the tube.
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Non-interacting Defects

• Reduction in stiffness increases linearly with
  number of defects when distance between them gt
  30l
• Linear damage model predicts this

Variation in stiffness loss for with the number
of non-interacting defects placed along the
length of the carbon nanotube.
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Prediction of Reduction in stiffness
A simple damage like model predicts reduction in
stiffness when number of defects are present