Mechanical stability of SWCN

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Mechanical stability of SWCN

• Ana Proykova
• Hristo Iliev
• University of Sofia, Department of Atomic Physics
• Singapore, February 6, 2004

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Outline of talk

• Motivation
• Discovery -gt production of CNT
• Modeling procedure
• Molecular Dynamics
• Results
• - Simulations done at various speeds for two
  lengths (stress and stretch)
• Conclusions

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CNT declared to be the ultimate high strength
fibers

• How does the CNT shape change under compression?
• Does a CNT relax after being released from the
  compression?
• Can active adsorption centers be created under
  mechanical deformation? (meaning do some bonds
  break?)

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Discovery 1991 S. Iijima

• The tubes are still in the labs
• Why? Fundamental problems or normal time lag
  between discoveries and their exploitation
• Developments around mechanical properties of
  CNTs, both from a fundamental point of view and
  in the direction of applications

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• Carbon nanotubes (CNT), like whiskers, are
  single crystals of high aspect ratio which
  contain only a few defects ? excellent mechanical
  properties to CNT
• The secret is in the intrinsic strength of the
  carbon carbon sp2 bond

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Reminder

• For a tube (n,m) there is a rule
• If (n-m) 3
• then the tube is metallic,
• else
• semiconducting

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There are many possibilities to form a cylinder
with a graphene sheet the most simple way of
visualizing this is to use a "de Heer abacus" to
realize a (n,m) tube, move n times a1 and m times
a2 from the origin to get to point (n,m) and
roll-up the sheet so that the two points
coincide...
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A 4-wall (0.34 0.36 nm spacing) and a single
wall CNT
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PRODUCTION and PURIFICATION

• MWNT - arc discharge or by thermal
  decomposition of hydrocarbons (700-800C)
• SWNT - arc discharge method in the presence of
  catalysts
• SWNT are contaminated with magnetic catalyst
  particles
• Sedimentation of suspensions sediment
  nanotubes suspension nanoparticles
  (EPF-Lausanne group, Dept. of Physics,
  J.-P.Salvetat)

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The catalytic method is suitable for the
production of either single and multi-wall or
spiral CNT. An advantage is that it enables
the deposition of CNT on pre-designed
lithographic structures, producing ordered arrays
which can be used in applications such as
thin-screen technology, electron guns
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Models and simulations

• Most numerical studies are based on a macroscopic
  classical continuum picture that provides an
  appropriate modeling except at the region of
  failure where a complete atomistic description
  (involving bond breaking in real chemical
  species) is needed

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Nanotubes offer the possibility of checking
the validity of different macroscopic and
microscopic models

• When models bridging different scales are worked
  out we will be able to analyze and optimize
  material properties at different
• levels of approximation eventually leading
• to the theoretical synthesis of novel
  materials

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Need for a hierarchy of models for conceptual
understanding

• Classical molecular dynamics simulations with
  empirical potentials bridging mesoscopic and
  microscopic modeling help to elucidate several
  relevant processes at the atomic level

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Molecular Dynamics is simply solving Newton's
equations of motion for atoms and molecules. This
requires

• CALCULATIONS OF FORCES (POTENTIALS) - - - from
  first principles and/or from experimental data.
  For our carbon modeling we used the potential of
  Brenner Phys.Rev.B 42 (1990) 9458
• METHODS FOR INTEGRATING EQUATIONS OF MOTION - - -
  fast, converging algorithms and computer time
• TECHNIQUES FOR VISUALIZATION OF RESULTS - - - 3D
  visualization and animation

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Molecular Dynamics Modeling

• Equations of motion are solved for each particle
  at a series of time steps
• Calculates the evolution of a system of particles
  over time F m a
• Forces come from the potential energy function
• F - ?/?r U(r)
• Various integration techniques exist stability
  versus speed problem

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Molecular Dynamics code

• Constant energy, constant volume
  micro-canonical ensemble
• Velocity Verlet algorithm for integrating the
  equations
• Stress (stretch) are simulated with changes of
  the velocity at every time step
• Uses modified Brenner potential (based on Tersoff
  potential)

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Tersoff potentials

• The family of potentials developed by Tersoff
  based on the concept of bond order the strength
  of a bond between two atoms is not constant, but
  depends on the local environment. This idea is
  similar to that of the glue model'' for metals,
  to use the coordination of an atom as the
  variable controlling the energy.
• In semiconductors, the focus is on bonds rather
  than atoms that is where the electronic charge
  is sitting in covalent bonding.

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At first sight, a Tersoff potential has
the appearance of a pair potential. However, it
is not a pair potential because B_ij (next slide)
is not a constant. In fact, it is the bond order
for the bond joining i and j
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R and A mean repulsive''
andattractive'' The basic idea is that the bond
ij is weakened by the presence of other bonds ik
involving atom i. The amount of weakening is
determined by where these other bonds are placed.
Angular terms appear necessary to construct a
realistic model.
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Brenners contribution

• The empirical form of the Brenner potential has
  been adjusted to fit thermodynamic properties of
  graphite and diamond, and therefore can describe
  the formation and/or breakage of carbon-carbon
  bonds. In the original formulation of the
  potential, its second derivatives are
  discontinuous.

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Brenner hydrocarbon potential

• Based on Tersoffs covalent bonding formalism
  with bij term represents the bond order
  essentially, the strength of the attractive
  potential is modified by the atoms local
  environment, i.e. CH-H differs from CH3-H

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(A)dvantages and (D)isadvantages of the
Brenner-Tersoff potential

• (A) Simple, allows a good fit to experimental
  data worked out for hydrocarbons, carbon
• (A) reactivity is mimicked well
• (D) non-bonded repulsion, dispersion, torsion
  are left out
• (D) too robust objects!

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The mechanical properties of a solid must
ultimately depend on the strength of its
interatomic bonds

• imagine an experiment, where a perfect rod of a
  given material is stressed axially under the
  force F - the rod length l at rest will vary by
  dl. The macroscopic stiffness, F/dl, is directly
  related to the stiffness of the atomic bonds. In
  a simple harmonic model, the Young modulus
  Yk/r_o,
• kspring constant, r_o is the inter-atomic
  distance

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This distance does not vary much for different
bonds

• k does (between 500 and 1000 N/m for
  carboncarbon bond and between 15 and 100 N/m for
  metals and ionic solids
• A low mass density is also often desirable for
  applications.
• Most polymers are made of carbon and have low
  density

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Elastic properties versusbreaking strength

• Establishing the elastic parameters is easier
  then predicting the way a bond can break
• The fracture of materials is a complex phenomenon
  that requires a multiscale description involving
  microscopic, mesoscopic and macroscopic modeling

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Simulations of dynamics axial compression for 30
fs
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Total energy of (10,10) armchair CNT-800 atoms
stress/release relaxation/explosion in a small box
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10 ,10 armchair nanotube smashed
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5000 atoms CNT smashed
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Small and large strains

• It is also worth controlling that the material
  does not break at too small strain as can happen
  with ceramics.
• The theoretical strength of a material is
  0.1v(YG/r_o ), where G is the free surface
  energy and r _o is the equilibrium spacing
  between the planes to be separated

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5000 atoms SWCNT under stretch potential
energy
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Tensile strength of materials with some
inelastic behavior and fracture toughness are
inversely related

• An increase in toughness is generally achievable
  at the expense of tensile strength.
• Roughly speaking crack propagation allows stress
  to relax in the material under strain thus,
  blocking cracks favors an earlier catastrophic
  rupture

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Kinetic energy - rescaled
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Carbon nanotubes also exhibit charge induced
structural deformations. Tube tends to expand
under negative charging.
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Single-wall nanotubes (10,10) growth DFT,
Jaguar code W.Deng, J. Che, X. Xu, T. Cagin, W.
Goddard,III, Pasadena, USA
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Mechanism metal catalysts atom absorbed at the
growth edge will block the adjacent growth site
of pentagon and thus avoid the formation of
defect. Metal catalysts can also anneal the
existed defects.
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Efforts to produce highly defective CNTs
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57 ring defects in graphitecreated by rotating
a CC bond in the hexagonal network by 90- low
energy defect
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Back to mechanical properties

• The highest Youngs modulus of all the different
  types of composite tubes considered (BN, BC_3 ,
  BC_2 N, C_3 N_4, CN)
• The conventional definition of the Young modulus
  involves the second derivative of the energy with
  respect to the applied strain. This definition
  for an SWNT requires adopting a convention for
  the thickness of the carbon layer
• in order to define a volume for the object.

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The stiffness of an SWNT can be defined via
S_o - the surface area at a zero strain
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computed value of 0.43 nm corresponds to 1.26
TPa modulus

• Slight dependence of Y on the tube diameter - Ab
  initio calculations
• Generally, the computed ab initio Young modulus
  for both C and BN nanotubes agrees well with the
  values obtained by the TB calculations and with
  the trends given by the empirical TersoffBrenner
  potential.

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a new mechanism for the collapse

• immediate graphitic to diamond-like bonding
  reconstruction at the location of the collapse
  due to relaxation of energy Srivastava D, Menon
  M, Kyeongjae C.
• Phys Rev Lett 199983(15)29736
• We do not see it in open-end nanotubes

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How to make stiff polymers?

• Orient them! More order - more energy is
  necessary to melt them!
• Add nanotubes and make composites
• It is a good job to synthesize a stiff material

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Stiff material

• It is therefore important to be able to align
  nanotubes in order to make stiff macroscopic
  ropes
• We have learned that a continuous rope of
  infinitely long CNTs would exhibit unrivalled
  mechanical properties
• without alignment, per formances in terms of
  strength and stiffness are far away from what is
  currently reached with traditional carbon fibers

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The future organized structure. The first stage
is induced, then self-organization occurs
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This we know from clusters too
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The future Neural tree with 14 symmetric
Y-junctions can be trained to perform complex
switching and computing functions
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Conclusion

• Modification of the potential used are needed to
  control the stiffness of a SWNT with defects and
  doped atoms
• MolDyn describes the trends
• DFT explains the growth
• More work on realistic cases

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Group members

• M.Sc. Stoyan Pisov, Ass. Prof.
• Dr. Rossen Radev (postdoc) Monte Carlo
• M.Sc. Evgenia P. Daykova, Ph.D. Student
• B.Sc. Hristo Iliev, Ph.D. Student
• B.Sc. Peter Georgiev, M.Sc. Student
• Mr. Kalin Arsov, Undergraduate Student
• M.Sc. Ivan P. Daykov, Ph.D. Student (Cornell
  USA/UoS)

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Acknowledgements

• EU grants for mobility, resources (TRACS)
• NSF USA
• NSF Bulgaria
• U of Sofia Scientific Grants

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http//cluster.phys.uni-sofia.bg8080/

• anap_at_phys.uni-sofia.bg
• Thank you for listening