1 / 20

ELASTIC PROPERTIES OF NANOTUBES

ELASTIC PROPERTIES OF NANOTUBES. Nanotube learning seminar series SZFKI. B.Sas, T. Williams 12 September 2005. HOW TO LEARN ABOUT ELASTICITY OF CNT. • Approaches 1. Experimental: i) “Macroscopic” mechanical measurements ii) Microscopic spectroscopic measurements 2. Modelling:

lyle-bates
Download Presentation

ELASTIC PROPERTIES OF NANOTUBES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ELASTIC PROPERTIES OF NANOTUBES Nanotube learning seminar series SZFKI B.Sas, T. Williams 12 September 2005

  2. HOW TO LEARN ABOUT ELASTICITY OF CNT • Approaches 1. Experimental: i) “Macroscopic” mechanical measurements ii) Microscopic spectroscopic measurements 2. Modelling: i) Continuum elasticity ii) Phonon dispersion and anharmonicity 3. Comparison with ab initio calculation

  3. GPa σzz 30 - E=350GPa δL/L % 0 - 0 10

  4. Tensile Loading of Ropes of SWNTs (Yu et al PRL 2000) E=1000GPa

  5. L y σxx=f/2πR x x 2-D ELASTICITY δR Uniaxial force F=0 2R F=f L+δL L δWp=δWel 2πR fδL=∫σxxuxxdS= 2 πRLσxxδL/L σxx=f/2πR Euxx= σxx uyy=δR/R= -σP uxx σP=(K-μ)/(K+μ) E=4K μ/(K+ μ) E3-D=E2-D /wall thickness

  6. (2-D Elasticity) BENDING MODEL F=0 F=f 2R d L compression [E3-DE2-D/wall thickness] dilatation

  7. d [nm] 4 - 2 - F [nN] E3-D=1000GPa E2-D=300Nm-1

  8. COMPARISON WITH STEEL STEEL 100 0.1 0.1 100 8 10 CNT 1000 10 100 50 0.6 5000 Young mod E3-D Strain limit stress limit filling factor density stress limit cable [GPa] [%] [GPa] [%] [g cm-2] [Kg force mm-2] Hung by Φ500μm CNT thread

  9. Micro-Mechanical Manipulations • Rotational actuators based on carbon nanotubes (Nature, 2003.) Electrostatic motor.

  10. (ω0- ωPn)ω0(ω0+ωPn) RAMAN EFFECT FOR BEGINNERS I ω0 ω0 ω0-ωph α,ωph dipole emission cosω0t , cos(ω0±ωPn)t excitation Eincosω0t ω0 24000cm-1 25000cm-1

  11. Graphene phonons

  12. ħω0 RAMAN FOR BEGINNERS II CLASSICAL QUANTUM m,e u x κ=mω2el ħωel Eincosω0t g Dipole:

  13. RAMAN III APPLIED STRESS ustatic≠0 ⇒intensity change by δωel ⇒ reveals by δωPn ⇒ lifts phonon mode degeneracies by symmetry reduction Ustatic=0 ustatic≠0

  14. m = 0 1 2 3 4 Eg A2u Sanchez-Portal et al.

  15. L σyy 2πR y σxx x Hydrostatic pressure Capped ends 2-D ELASTICITY δR 2R L L-δL P=0 P=p δWp=δWel πR2pδL=∫σxxuxxdS= 2 πRLσxxδL/L 2πRLpδR=∫σyyuyydS=2 πRL σyyδR/R σxx=pR/2 σyy=pR uyy/uxx=2 if σP=0

  16. L 2πR σyy y σxx x 2-D ELASTICITY Hydrostatic pressure P=p Capped ends σxx=pR/2 ; σyy=0 uxx=pR/2E ; uyy=-σPpR/2E + σxx=0 ; σyy=pR uxx=-σPpR/E; uyy=pR/E = σxx=pR/2 ; σyy=pR uxx=(1-2σP)pR/2E ; uyy=(2-σP)pR/2E uyy/uxx = (2-σP)/(1-2σP)

More Related