Mechanical stability of SWCN
Ana Proykova
Hristo Iliev
University of Sofia, Department of Atomic Physics
Singapore, February 6, 2004
Outline of talk
• Motivation
• Discovery -> production of CNT
• Modeling procedure
– Molecular Dynamics
• Results
- Simulations done at various speeds for two
lengths (stress and stretch)
• Conclusions
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?)
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
• 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
Reminder
• For a tube (n,m) there is a rule:
If (n-m) = 3
then the tube is metallic,
else
semiconducting
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...
A 4-wall (0.34 – 0.36 nm spacing)
and a single wall CNT
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 (EPFLausanne group, Dept. of Physics, J.-P.Salvetat)
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
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
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
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
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
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
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)
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.
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 :
R and A mean ``repulsive'' and``attractive''
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.
Brenner’s 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 carboncarbon bonds. In the original formulation
of the potential, its second derivatives are
discontinuous.
Brenner hydrocarbon potential
• Based on Tersoff’s covalent bonding formalism
with bij term represents the “bond order” –
essentially, the strength of the attractive
potential is modified by the atom’s local
environment, i.e. CH-H differs from CH3-H
Vij 
f (r )V

 
j i
c
ij
R
(rij )  bijVA (rij )

bij  1   
n

n n / 2
ij
(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!
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 Y=k/r_o,
k=spring constant, r_o is the inter-atomic distance
This distance does not vary much
for different bonds
• k does (between 500 and 1000 N/m for
carbon–carbon 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
Elastic properties versus
breaking 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
Simulations of dynamics: axial
compression for 30 fs
Total energy of (10,10) armchair
CNT-800 atoms – stress/release
relaxation/explosion in a small box
[10 ,10] armchair nanotube –
smashed
5000 atoms CNT smashed
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
0.1√(Y*G/r_o ), where G is the free
surface energy and r _o is the equilibrium
spacing between the planes to be
separated
~ 5000 atoms SWCNT under
stretch – potential energy
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
Kinetic energy - rescaled
Carbon nanotubes also exhibit charge
induced structural deformations. Tube
tends to expand under negative
charging.
Single-wall nanotubes (10,10) growth – DFT,
Jaguar code [W.Deng, J. Che, X. Xu, T.
Cagin, W. Goddard,III, Pasadena, USA]
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.
Efforts to produce highly defective
CNTs
5–7 ring defects in graphite
created by rotating a C–C bond in
the hexagonal network by 90°
- low energy defect
Back to mechanical properties
• The highest Young’s 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.
The stiffness of an SWNT can be defined via S_o the surface area at a zero strain
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 Tersoff–Brenner
potential.
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 1999;83(15):2973–6
• We do not see it in open-end nanotubes
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
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
The future: organized structure. The
first stage is induced, then selforganization occurs
This we know from clusters too
The future:
Neural tree with 14 symmetric Yjunctions can be trained to perform
complex switching and computing
functions
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
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)
Acknowledgements
• EU – grants for mobility, resources
(TRACS)
• NSF – USA
• NSF – Bulgaria
• U of Sofia – Scientific Grants
http://cluster.phys.uni-sofia.bg:8080/
• anap@phys.uni-sofia.bg
Thank you for listening