Mechanical stability of Mechanical stability of SWCNSWCN

Ana ProykovaAna ProykovaHristo IlievHristo Iliev

University of Sofia, Department of Atomic University of Sofia, Department of Atomic PhysicsPhysics

Singapore, February 6, 2004Singapore, February 6, 2004

Outline of talkOutline of talk

• MotivationMotivation• Discovery -> production of CNTDiscovery -> production of CNT• Modeling procedureModeling procedure

– Molecular DynamicsMolecular Dynamics

• ResultsResults - - Simulations done at various speeds for Simulations done at various speeds for

two lengths (stress and stretch)two lengths (stress and stretch)

• ConclusionsConclusions

CNT declared to be the CNT declared to be the ultimate high strength fibersultimate high strength fibers

• How does the CNT shape change How does the CNT shape change under compression? under compression?

• Does a CNT relax after being Does a CNT relax after being released from the compression?released from the compression?

• Can active adsorption centers be Can active adsorption centers be created under mechanical created under mechanical deformation? (meaning – do some deformation? (meaning – do some bonds break?)bonds break?)

Discovery 1991 S. IijimaDiscovery 1991 S. Iijima

• The tubes are still in the labsThe tubes are still in the labs• Why? Fundamental problems or Why? Fundamental problems or

normal time lagnormal 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

ReminderReminder

• For a tube (n,m) there is a rule:For a tube (n,m) there is a rule:

If (n-m) = 3 If (n-m) = 3

then the tube is metallic,then the tube is metallic,

elseelse

semiconducting semiconducting

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

A 4-wall (0.34 – 0.36 nm A 4-wall (0.34 – 0.36 nm spacing)spacing)

and a single wall CNT and a single wall CNT

PRODUCTION PRODUCTION and and PURIFICATIONPURIFICATION

• MWNT - MWNT - arc discharge or by thermal arc discharge or by thermal decomposition of hydrocarbons (700-800C)decomposition of hydrocarbons (700-800C)

• SWNT - arc discharge method in the SWNT - arc discharge method in the presence of catalystspresence of catalysts

• SWNT are contaminated with magnetic SWNT are contaminated with magnetic catalyst particlescatalyst particles

• Sedimentation of suspensions: sediment – Sedimentation of suspensions: sediment – nanotubes; suspension – nanoparticles nanotubes; suspension – nanoparticles (EPF-Lausanne group, Dept. of Physics, J.-(EPF-Lausanne group, Dept. of Physics, J.-P.Salvetat)P.Salvetat)

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

Models and simulationsModels 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 Molecular Dynamics is simply solving Newton's equations of motion for atoms and Newton's equations of motion for atoms and

molecules.molecules. This requires:This requires:

CALCULATIONS OF FORCES (POTENTIALS) - - - from CALCULATIONS OF FORCES (POTENTIALS) - - - from first principles and/or from experimental data. For first principles and/or from experimental data. For our carbon modeling we used the potential of our carbon modeling we used the potential of

Brenner [Phys.Rev.B 42 (1990) 9458]Brenner [Phys.Rev.B 42 (1990) 9458] METHODS FOR INTEGRATING EQUATIONS OF MOTION METHODS FOR INTEGRATING EQUATIONS OF MOTION

- - - fast, converging algorithms and computer time- - - fast, converging algorithms and computer time

TECHNIQUES FOR VISUALIZATION OF RESULTS - - - TECHNIQUES FOR VISUALIZATION OF RESULTS - - - 3D visualization and animation 3D visualization and animation

Molecular Dynamics Molecular Dynamics ModelingModeling• Equations of motion are solved for Equations of motion are solved for

each particle at a series of time stepseach particle at a series of time steps• Calculates the evolution of a system Calculates the evolution of a system

of particles over time of particles over time FF = m = m aa• Forces come from the potential energy Forces come from the potential energy

functionfunction

F F = - = - ∂∕∂r [U(r)]∂∕∂r [U(r)]Various integration techniques exist – Various integration techniques exist –

stability versus speed problemstability versus speed problem

Molecular Dynamics codeMolecular Dynamics code

• Constant energy, constant volume – Constant energy, constant volume – micro-canonical ensemblemicro-canonical ensemble

• Velocity Verlet algorithm for Velocity Verlet algorithm for integrating the equationsintegrating the equations

• Stress (stretch) are simulated with Stress (stretch) are simulated with changes of the velocity at every time changes of the velocity at every time stepstep

• Uses modified Brenner potential Uses modified Brenner potential (based on Tersoff potential)(based on Tersoff potential)

Tersoff potentialsTersoff potentials

• The family of potentials developed by Tersoff The family of potentials developed by Tersoff based on the concept of based on the concept of bond orderbond order: the : the strength of a bond between two atoms is not strength of a bond between two atoms is not constant, but depends on the local constant, but depends on the local environment. This idea is similar to that of the environment. This idea is similar to that of the ``glue model'' for metals, to use the ``glue model'' for metals, to use the coordination of an atom as the variable coordination of an atom as the variable controlling the energy. controlling the energy.

• In semiconductors, the focus is on bonds In semiconductors, the focus is on bonds rather than atoms: that is where the electronic rather than atoms: that is where the electronic charge is sitting in covalent bonding. charge is sitting in covalent bonding.

At first sight, a Tersoff At first sight, a Tersoff potential has the appearance potential has the appearance of a pair potentialof a pair potential.. However, it However, it is not a pair potential because is not a pair potential because B_B_ijij (next slide) (next slide) is not a is not a constant. In fact, it is the bond constant. In fact, it is the bond order for the bond joining order for the bond joining ii and and jj ::

RR and and AA mean ``repulsive'' mean ``repulsive'' and``attractive'' The basic idea is that and``attractive'' The basic idea is that the bond the bond ijij is weakened by the is weakened by the presence of other bonds presence of other bonds ikik involving involving atom atom ii. The amount of weakening is . The amount of weakening is determined by where these other determined by where these other bonds are placed. Angular terms bonds are placed. Angular terms appear necessary to construct a appear necessary to construct a

realistic model.realistic model.

Brenner’s contributionBrenner’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 Brenner hydrocarbon potentialpotential• Based on Tersoff’s covalent bonding Based on Tersoff’s covalent bonding

formalism with formalism with bbijij term represents the term represents the “bond order” – essentially, the strength of “bond order” – essentially, the strength of the attractive potential is modified by the the attractive potential is modified by the atom’s local environment, atom’s local environment, i.e. CH-H differs from CH3-H

ij

ijAijijRijcij rVbrVrfV )()()( / 21

nn nij ijb

(A)dvantages and (A)dvantages and (D)isadvantages of the (D)isadvantages of the Brenner-Tersoff potentialBrenner-Tersoff potential• (A) – Simple, allows a good fit to (A) – Simple, allows a good fit to

experimental data; worked out for experimental data; worked out for hydrocarbons, carbonhydrocarbons, carbon

• (A) – reactivity is mimicked well(A) – reactivity is mimicked well

• (D) – non-bonded repulsion, (D) – non-bonded repulsion, dispersion, torsion are left out 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 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

Simulations of dynamics: axial Simulations of dynamics: axial compression for 30 compression for 30 fsfs

Total energy of (10,10) Total energy of (10,10) armchair CNT-800 atoms – armchair CNT-800 atoms – stress/release stress/release relaxation/explosion in a small relaxation/explosion in a small boxbox

[10 ,10] armchair nanotube – [10 ,10] armchair nanotube – smashed smashed

5000 atoms CNT smashed5000 atoms CNT smashed

Small and large strainsSmall 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 ~ 5000 atoms SWCNT under stretch – potential energystretch – 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 - rescaledKinetic energy - rescaled

Carbon nanotubes also exhibit Carbon nanotubes also exhibit charge induced structural charge induced structural deformations. Tube tends to deformations. Tube tends to expand under negative charging.expand under negative charging.

Single-wall nanotubes (10,10) growth – Single-wall nanotubes (10,10) growth – DFT, Jaguar code [W.Deng, J. Che, X. DFT, Jaguar code [W.Deng, J. Che, X. Xu, T. Cagin, W. Goddard,III, Pasadena, Xu, T. Cagin, W. Goddard,III, Pasadena, USA]USA]

Mechanism: metal catalysts atom absorbed at the Mechanism: metal catalysts atom absorbed at the growth edge will block the adjacent growth site of growth edge will block the adjacent growth site of pentagon and thus avoid the formation of defect. pentagon and thus avoid the formation of defect. Metal catalysts can also anneal the existed defects.Metal catalysts can also anneal the existed defects.

Efforts to produce highly defective CNTs

5–7 ring defects in graphitecreated by rotating a C–C bond

in the hexagonal network by 90°

- low energy defect

Back to mechanical Back to mechanical propertiesproperties• 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?How to make stiff polymers?

• Orient them! More order - more Orient them! More order - more energy is necessary to ‘melt’ them!energy is necessary to ‘melt’ them!

• Add nanotubes and make compositesAdd nanotubes and make composites

It is a good job to synthesize a stiff material

Stiff materialStiff 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: The future: organized structure. organized structure. The first stage is induced, then The first stage is induced, then self-organization occursself-organization occurs

This we know from clusters This we know from clusters tootoo

The future: The future: Neural tree with 14 symmetric Y-junctions can be trained to perform complex switching and computing functions

ConclusionConclusion

• Modification of the potential used are Modification of the potential used are needed to control the stiffness of a needed to control the stiffness of a SWNT with defects and doped atomsSWNT with defects and doped atoms

• MolDyn describes the trendsMolDyn describes the trends

• DFT explains the growthDFT explains the growth

• More work on realistic casesMore work on realistic cases

Group members:Group members:

• M.ScM.Sc. . StoyanStoyan PisovPisov, Ass. Prof. , Ass. Prof.

• Dr. Rossen RadevDr. Rossen Radev ( (postdocpostdoc) Monte ) Monte CarloCarlo

• M.ScM.Sc. . EvgeniaEvgenia P. P. DaykovaDaykova, Ph.D. Student, Ph.D. Student• B.Sc. B.Sc. HristoHristo IlievIliev, Ph.D. Student, Ph.D. Student• B.Sc. Peter B.Sc. Peter GeorgievGeorgiev, M.Sc. Student, M.Sc. Student• Mr. Mr. KalinKalin ArsovArsov, Undergraduate Student, Undergraduate Student• M.ScM.Sc. Ivan P. . Ivan P. DaykovDaykov, Ph.D. Student (Cornell , Ph.D. Student (Cornell

USA/UoS) USA/UoS)

AcknowledgementsAcknowledgements

• EU – grants for mobility, resources EU – grants for mobility, resources (TRACS)(TRACS)

• NSF – USANSF – USA

• NSF – BulgariaNSF – Bulgaria

• U of Sofia – Scientific GrantsU of Sofia – Scientific Grants

http://cluster.phys.uni-sofia.bg:808http://cluster.phys.uni-sofia.bg:8080/0/

• anap@phys.uni-sofia.bganap@phys.uni-sofia.bg

Thank you for listeningThank you for listening