Mechanical stability of SWCN

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

2. 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

3. 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?)

4. 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 mechanicalproperties of CNTs, both from a fundamental point of view and in the direction of applications

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

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

7. 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...

8. A 4-wall (0.34 – 0.36 nm spacing) and a single wall CNT

9. 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)

12. 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

13. Models and simulations • Most numerical studies are based on a macroscopic classical continuum picture that provides an appropriate modelingexcept at the region of failure where a complete atomisticdescription (involving bond breaking in real chemicalspecies) is needed

14. 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 andoptimize material properties at different levels of approximation eventually leading to the theoretical synthesis ofnovel materials

15. Need for a hierarchy of modelsfor conceptual understanding • Classical molecular dynamics simulations with empirical potentials bridging mesoscopic and microscopic modeling help toelucidate several relevant processes at the atomic level

16. 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

17. 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

18. 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)

19. 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.

20. 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:

21. 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.

22. Brenner’s contribution • The empirical form of the Brenner potential has been adjustedto fit thermodynamic properties of graphite and diamond,and therefore can describe the formation and/or breakageof carbon-carbon bonds. In the original formulation ofthe potential, its second derivatives are discontinuous.

23. 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

24. (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!

25. The mechanical properties of a solid must ultimatelydepend on the strength of its interatomic bonds imagine an experiment, where a perfect rodof a givenmaterial is stressed axially under the force F - the rodlengthl at rest will vary by dl. The macroscopicstiffness, F/dl, is directly related to the stiffness of theatomic bonds. In a simple harmonic model, the Young modulus Y=k/r_o, k=spring constant, r_o is the inter-atomic distance

26. This distance does not vary much for differentbonds • kdoes (between 500 and 1000 N/m for carbon–carbonbond and between 15 and 100 N/m for metals and ionicsolids • A low mass density is also oftendesirable for applications. • Most polymers are made ofcarbonand have low density

27. 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

28. Simulations of dynamics: axial compression for 30 fs

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

31. [10 ,10] armchair nanotube – smashed

32. 5000 atoms CNT smashed

33. Small and large strains • It is alsoworth controlling that the material does not break at toosmall strain as can happen with ceramics. • The theoretical strength of a material is 0.1√(Y*G/r_o), where Gis thefree surface energy and r_o is the equilibrium spacing betweenthe planes to be separated

34. ~ 5000 atoms SWCNT under stretch – potential energy

35. Tensile strength of materials with someinelastic behavior and fracture toughness are inverselyrelated • An increase in toughness is generally achievableat the expense of tensile strength. • Roughly speaking crackpropagation allows stress to relax in the material understrain; thus, blocking cracks favors an earlier catastrophic rupture

36. Kinetic energy - rescaled

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

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

39. 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.

40. Efforts to producehighly defective CNTs

41. 5–7 ring defects in graphitecreated by rotating a C–C bond in the hexagonalnetwork by 90°- low energy defect

42. Back to mechanical properties • The highest Young’s modulus of all the different types of compositetubes considered (BN, BC_3 , BC_2 N, C_3 N_4, CN) • The conventional definition of the Young modulusinvolves the second derivative of the energy with respectto the applied strain. This definition for an SWNT requiresadopting a convention for the thickness of the carbon layer in order to define a volume for the object.

43. The stiffness of an SWNTcan be defined via S_o - the surface area at a zero strain

44. 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 forboth C and BN nanotubes agrees well with the valuesobtained by the TB calculations and with the trends givenby the empirical Tersoff–Brenner potential.

45. a new mechanism for the collapse • immediate graphitic to diamond-likebonding 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

46. 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

47. Stiff material • It is therefore important to be able to align nanotubes in order to make stiff macroscopic ropes • We have learnedthat a continuous rope of infinitely longCNTs would exhibit unrivalled mechanical properties • without alignment, performances in terms of strength and stiffness are far awayfrom what is currently reached with traditional carbonfibers

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

49. This we know from clusters too

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