Mechanical stability of SWCN Ana Proykova Hristo Iliev University of Sofia, Department of Atomic Physics Singapore, February 6, 2004

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

CNT declared to be the ultimate high strength fibers How does the CNT shape change under compression? How does the CNT shape change under compression? Does a CNT relax after being released from the 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?) 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 The tubes are still in the labs Why? Fundamental problems or normal time lag 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: For a tube (n,m) there is a rule: If (n-m) = 3 then the tube is metallic, elsesemiconducting

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

Molecular Dynamics Modeling Equations of motion are solved for each particle at a series of time steps 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 Calculates the evolution of a system of particles over time F = m a Forces come from the potential energy function 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 Constant energy, constant volume – micro-canonical ensemble Velocity Verlet algorithm for integrating the equations Velocity Verlet algorithm for integrating the equations Stress (stretch) are simulated with changes of the velocity at every time step Stress (stretch) are simulated with changes of the velocity at every time step Uses modified Brenner potential (based on Tersoff potential) 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. 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. 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 carbon- carbon bonds. In the original formulation of the potential, its second derivatives are discontinuous.

Brenner hydrocarbon potential Based on Tersoff’s covalent bonding formalism with b ij term represents the “bond order” – essentially, the strength of the attractive potential is modified by the atom’s local environment, Based on Tersoff’s covalent bonding formalism with b ij 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

(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) – Simple, allows a good fit to experimental data; worked out for hydrocarbons, carbon (A) – reactivity is mimicked well (A) – reactivity is mimicked well (D) – non-bonded repulsion, dispersion, torsion are left out (D) – non-bonded repulsion, dispersion, torsion are left out (D) – too robust objects! (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 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. 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 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 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! Orient them! More order - more energy is necessary to ‘melt’ them! Add nanotubes and make composites 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 self- organization occurs

This we know from clusters too

The future: The future: Neural tree with 14 symmetric Y- junctions 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 Modification of the potential used are needed to control the stiffness of a SWNT with defects and doped atoms MolDyn describes the trends MolDyn describes the trends DFT explains the growth DFT explains the growth More work on realistic cases More work on realistic cases

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

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

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