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Exploring Carbon Nanotubes and Graphene: Structure, Hybridization, and Electronic Properties

This lecture delves into the physical structure and bond hybridization of carbon nanotubes (CNTs) and graphene. It discusses the versatility of hybridization types, including sp1, sp2, and sp3, emphasizing their significance in understanding the mechanical and electronic properties of these nanoscale materials. The insights into their electronic structures, derived from key literature, help elucidate the origins of CNT and graphene's unique characteristics. The lecture aims to provide a comprehensive understanding of the effects of hybridization on material properties.

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Exploring Carbon Nanotubes and Graphene: Structure, Hybridization, and Electronic Properties

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  1. ECE 802-604:Nanoelectronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

  2. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  3. sp1 hybridization • Use orthonormality • sp2 hybridization: • Get help from directions • Use orthonormality VM Ayres, ECE802-604, F13

  4. sp2 hybridization: 1 VM Ayres, ECE802-604, F13

  5. sp2 hybridization: 1 Example: how many valence (bonding) electrons do you get in: sp1 hybridization? sp2 hybridization? VM Ayres, ECE802-604, F13

  6. sp2 hybridization: Answer: sp = sp1 hybridization: 2e- per C: linear bonding sp2 hybridization: 3e- per C: trigonal bonding sp sp sp sp sp2 sp2 sp2 VM Ayres, ECE802-604, F13

  7. sp2 hybridization: VM Ayres, ECE802-604, F13

  8. sp2 hybridization: VM Ayres, ECE802-604, F13

  9. sp2 hybridization: VM Ayres, ECE802-604, F13

  10. sp2 hybridization: VM Ayres, ECE802-604, F13

  11. sp2 hybridization: VM Ayres, ECE802-604, F13

  12. sp2 hybridization: VM Ayres, ECE802-604, F13

  13. sp2 hybridization: VM Ayres, ECE802-604, F13

  14. sp2 hybridization: VM Ayres, ECE802-604, F13

  15. sp2 hybridization: VM Ayres, ECE802-604, F13

  16. sp2 hybridization: VM Ayres, ECE802-604, F13

  17. sp2 hybridization: VM Ayres, ECE802-604, F13

  18. sp2 hybridization: VM Ayres, ECE802-604, F13

  19. sp2 hybridization: VM Ayres, ECE802-604, F13

  20. sp2 hybridization: VM Ayres, ECE802-604, F13

  21. sp2 hybridization: VM Ayres, ECE802-604, F13

  22. sp2 hybridization: VM Ayres, ECE802-604, F13

  23. sp2 hybridization: VM Ayres, ECE802-604, F13

  24. sp2 hybridization: VM Ayres, ECE802-604, F13

  25. sp2 hybridization: VM Ayres, ECE802-604, F13

  26. sp2 hybridization: VM Ayres, ECE802-604, F13

  27. VM Ayres, ECE802-604, F13

  28. sp2 hybridization: VM Ayres, ECE802-604, F13

  29. sp2 hybridization: VM Ayres, ECE802-604, F13

  30. sp2 hybridization: VM Ayres, ECE802-604, F13

  31. sp2 hybridization: VM Ayres, ECE802-604, F13

  32. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  33. VM Ayres, ECE802-604, F13

  34. Expect: 180º Get: 180º F VM Ayres, ECE802-604, F13

  35. Expect: 90º Get: 104.5º “Explanation”: Mutual repulsion of the H atoms “Plausible”: H2S, H2Se = 92º, 90º Greater separation of H around larger S and Se atoms H O H VM Ayres, ECE802-604, F13

  36. Expect: 90º pyramid Get: 107.5º pyramid “Explanation”: Mutual repulsion of the H atoms “Plausible”: H3P, H3As = 92º, 90º Greater separation of H around larger P and As atoms H H N H VM Ayres, ECE802-604, F13

  37. Expect: 90º CH2, like H2O H C H VM Ayres, ECE802-604, F13

  38. Expect: 90º CH2, like H2O Get: CH4 tetrahedron CH4 is impossible in this p-orbital picture. H C H VM Ayres, ECE802-604, F13

  39. sp3 Hybrid orbital picture VM Ayres, ECE802-604, F13

  40. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  41. sp3: • Diamond • methane • alkane VM Ayres, ECE802-604, F13

  42. sp2: • Benzene • Graphene • CNT (curvature) • fullerene (curvature) • Polyacetylene: non-trigonal: linear VM Ayres, ECE802-604, F13

  43. Division of structural and electronic properties in linear sp1 that makes both effective: VM Ayres, ECE802-604, F13

  44. Diamond sp3: no division. Great structural strength but wide bandgap electronic properties VM Ayres, ECE802-604, F13

  45. Division of structural and electronic properties in trigonal sp2 makes both effective: All Structure: s-bonds Electronic: p-bonds VM Ayres, ECE802-604, F13

  46. Structure: s-bonds Electronic: p-bonds p* -conduction band e- ECE, PHY -anti-bonding e- CHM Electronic: Delocalized p e- p -valence band e- ECE, PHY -bonding e- CHM VM Ayres, ECE802-604, F13

  47. Structure: s-bonds Electronic: p-bonds p* -conduction band e- ECE, PHY -anti-bonding e- CHM Electronic: Delocalized p e- p -valence band e- ECE, PHY -bonding e- CHM VM Ayres, ECE802-604, F13

  48. Lecture 20, 05 Nov 13 Carbon Nanotubes and Graphene Carbon nanotube/Graphene physical structure Carbon bond hybridization is versatile : sp1 (Lec19), sp2, and sp3 (HW05) More motivation for bond hybridization CNT/Graphene electronic properties sp2: origin of CNT/Graphene mechanical and electronic structures sp2: electronic structure: 1st: polyacetylene 2nd:graphene: R. Saito, G. Dresselhaus and M.S. Dresselhaus Physical Properties of Carbon Nanotubes A. Beiser, Modern Physics E. Anderson, Quantum Mechanics VM Ayres, ECE802-604, F13

  49. Game plan: E VM Ayres, ECE802-604, F13

  50. Rules for finding the electronic structure (p. 21): 1 Find Unit cell “a” 2 Find k: 3 Find H and S elements Det [H – SI] =0 4 Solve for E(k) VM Ayres, ECE802-604, F13

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