1. Effect of Defects in the Mechanical Properties of Carbon Nanotubes PHY 472 / Lehigh University Instructor: Prof. Slava V. Rotkin By: Paul A. Belony, Jr.

2. Common Defects observed in CNT’s  Main types of defects 3 main groups 3 main groups Point defectsPoint defects Topological defectsTopological defects Hybridization defectsHybridization defects  Subgroups Vacancies (PD) Vacancies (PD) Metastable atoms Metastable atoms Pentagons (TD) Pentagons (TD) Heptagons (TD) Heptagons (TD) Stone–Wales (SW or 5–7–7–5) (TD) Stone–Wales (SW or 5–7–7–5) (TD) Fictionalization (HD) (sp 3 bonds) Fictionalization (HD) (sp 3 bonds) Discontinuities of walls Discontinuities of walls Distortion in the packing configuration of CNT bundles Distortion in the packing configuration of CNT bundles Etc… Etc…

3. Stone-Wales (5-7-7-5) Defects Stone-Wales defect is:  Composed of Two Pentagon-Heptagon pairs  Formed by rotating a sp 2 bond by 90 0  In other words, formed when bond rotation in a graphitic network transforms four hexagons into two pentagons and two heptagons, which is accompanied by elongation of the tube structure along the axis connecting the pentagons, and shrinking along the perpendicular direction

4. Main Mechanical Properties affected by Defects  Stiffness  Ultimate Strength  Ultimate Strain  Flexibility  Buckling and robustness under high pressure CNT’s are among the most robust materials CNT’s are among the most robust materials High Elastic Modulus (order of 1 TPa) High Elastic Modulus (order of 1 TPa) High Strength (range up to 100’s of GPa) High Strength (range up to 100’s of GPa)

5. Main effects on Stiffness Changes in stiffness observed. Stiffness decrease with topological defects and increase with fictionalization Defect generation and growth observed during plastic deformation and fracture of nanotubes Qiang Lu and Baidurya Battacharya Deepak Srivastava etal.

6. SWNTs with more defects are likely to break at smaller strains and have less strength as well. Force–displacement curves of nanotubes with various average numbers of defects.  the Young modulus can be calculated as the initial slope of the force–displacement curve;  The ultimate strength is calculated at the maximum force point, σ U = (F max )/A, where F is the maximum axial force, A is the cross section area  the ultimate strain, which corresponds to the ultimate strength, is calculated as ε U = (ΔL U )/L, where L is the original tube length. Force-Displacement curves are used in order to show the response of the SWNTs under loading Reduced units: 1 time ru = 0.03526 ps 1 force ru = 1.602 nN 1 displacement ru = 1 Ǻ

7. Types of stresses  virial stress  atomic (BDT) stress  Lutsko stress  Yip stress i, j  indices in Cartesian coordinate systemΑ, β  atomic indices Ω tot  total volume L α,β  fraction of the length of αβ bond inside the averaging volume

8. Belytschko et al. Force-Deflection curve for a model of zigzag NT (Normalized to Stress vs. Strain) ۩ The applied force is computed by summing the interatomic forces for the atoms along the end of the nanotube where the displacement is prescribed. ۩ The stress is calculated from the cross- sectional area S = πdh (h is the chosen interlayer separation of graphite) Evolution of cracks in the NT Bond-breaking spreads sideways after the initially weakened bond failed Crack formation in a [40, 40] armchair NT with SW defect (evolution from left to right 12.5 – 12.8 ps) The crack grows in the direction of maximum shear

9. Elastic modulus before defect -Defect free (9,0) nanotube with periodic boundary conditions -Strains applied using conjugate gradients energy minimization - All stress and strain measures yield a Young’s modulus value of 1.002TPa

10. 5-7-7-5 Defect on CNTs  The graph shows the graph for Lutsko stress profile for (9,0) zigzag NT with (5-7-7-5) defect  The defected region facilitates Stress amplification  When applied strains increase, this amplification reduces  A different situation is observed for (n,n) armchair NT; there is a decrease in stress at the defect region

11. Contour plots of the longitudinal strain ε 33 strain and stress σ 33 near the defected region drawn at different applied strain levels. a)Strain contours at an applied strain of 1%.b) Stress contours at an applied strain of 1%. c)Strain contours at an applied strain of 3%.d) Stress contours at an applied strain of 3%. e)Strain contours at an applied strain of 5%. f) Stress contours at an applied strain of 5%. g)Strain contours at an applied strain of 8%.h) Stress contours at an applied strain of 8%. N. Chandra, S. Namilae and C. Shet

12. NT possess residual forces at zero strain (even when defect free) At about 1 TPa there’s a reduction of stiffness away from the defect-free straight line

13. Measuring Mechanical Properties  Use of Atomic Force Microscopy (AFM) For individual CNTsFor individual CNTs A)3D representation of the adhesion of a SWNT to an alumina ultra-filtration (tube is clamped allowing mechanical testing) B)How AFM works in schematic way (a load F is applied to the suspending portion of the NT with length L. So the max deflection d is topologically measured L. Forro etal.

14. Fracture process of a (6, 6) SWNT with three SW defects: (a)crack initiation and propagation (A–I); (b)(b) corresponding force time history.

15. Diameter dependence The slope of the graphs seem to be very close to each other for different curvature of the NTs So, stiffness values of various tubes of same SW defect but different diameters do not change significantly Stiffness in the range of 0.61TPa to 0.63TPa for different (n,0) tubes Curvature is not significantly affected by Mechanical properties of SW defect

16. Charality Dependence There’s a significant change in the measured stiffness when the charality varies

17.  Defects can occur in the form of atomic vacancies.  High levels of such defects can lower the tensile strength by up to 85%.  Due to the almost one-dimensional structure of CNTs, the tensile strength of the tube is dependent on the weakest segment of it in a similar manner to a chain, where a defect in a single link will greatly diminish the strength of the entire chain.

18. Summary  Mechanical behavior of defects such as 5-7-7-5 defect is examined  A considerable decrease in stiffness at 5-7-7-5 defect location in different nanotubes is observed  Changes in diameter don’t affect the decrease in stiffness significantly  Changes in chirality have different effect on stiffness

19. (10,10) NT under 10% strain STM images and corresponding atomic positions for a C2 dimer absorbed into different nanotubes: (a) and (b) show a (10,10) tube; (c) and (d) a (17,0) tube. All under a 10% strain (tip at 10.5 eV.) Heterojunction 7-5-5-7