1. Testing the mechanism Step 1 Where will the C 2 attack?

2. The colours show the range of the attractive potential - green most attractive. The intense region is next to the shifted pentagon and its next neighbouring hexagon towards the tube tip. The favoured attack site for C 2 is next to the shifted pentagon.

3. New mechanism for C 2 ingestion Based on a mechanism proposed by Endo and Kroto in the early 90s for C 2 ingestion into nanotube caps / fullerenes. Mechanism for fullerene/nanotube growth without the aid of catalysts. New mechanism contains less steps and more stable intermediaries.

4. Growth mechanism applied to a nanotube tip (other end H terminated) Schlegel diagram shows equivalent for C 76 Starting with one pentagon displaced Pentagons blue Heptagons grey

5. Addition of C 2 unit

6. C 2 ingestion in fullerenes and nanotube caps Summary of work to date by Chris Ewels, Alberto Zobelli, Greg Van Lier, Harry Kroto

7. Pseudorotation

9. Vertical slice through total electrostatic potential for the tip through the shifted pentagon. The colours show the range of the attractive potential from -0.014 to -0.01 (-0.014 being the most attractive value). The potential exhibits an intense region next to the shifted pentagon and its next neighbouring hexagon towards the tube tip. The favoured attack site for C 2 is next to the shifted pentagon.

10. Vertical slice through total electrostatic potential for the tip through the shifted pentagon. The colours show the range of the attractive potential from -0.014 to -0.01 (-0.014 being the most attractive value). The potential exhibits an intense region next to the shifted pentagon and its next neighbouring hexagon towards the tube tip. The favoured attack site for C 2 is next to the shifted pentagon.

11. Vertical slice through total electrostatic potential for the tip through the shifted pentagon. The colours show the range of the attractive potential from -0.014 to -0.01 (-0.014 being the most attractive value). The potential exhibits an intense region next to the shifted pentagon and its next neighbouring hexagon towards the tube tip. The favoured attack site for C 2 is next to the shifted pentagon.

12. Vertical slice through total electrostatic potential for the tip through the shifted pentagon. The colours show the range of the attractive potential from -0.014 to -0.01 (-0.014 being the most attractive value). The potential exhibits an intense region next to the shifted pentagon and its next neighbouring hexagon towards the tube tip. The favoured attack site for C 2 is next to the shifted pentagon.

13. C 2 ingestion in fullerenes and nanotube caps Summary of work to date by Chris Ewels, Alberto Zobelli, Greg Van Lier, Harry Kroto

14. C 2 ingestion in fullerenes and nanotube caps Summary of work to date by Chris Ewels, Alberto Zobelli, Greg Van Lier, Harry Kroto

15. New mechanism for C 2 ingestion Based on a mechanism proposed by Endo and Kroto in the early 90s for C 2 ingestion into nanotube caps / fullerenes. Mechanism for fullerene/nanotube growth without the aid of catalysts. New mechanism contains less steps and more stable intermediaries.

16. New mechanism for C 2 ingestion Based on a mechanism proposed by Endo and Kroto in the early 90s for C 2 ingestion into nanotube caps / fullerenes. Mechanism for fullerene/nanotube growth without the aid of catalysts. New mechanism contains less steps and more stable intermediaries.

17. Original C 2 ingestion The new mechanism is simpler (less steps) and notably the initial addition step is metastable, whereas in this old mechanism it involves adding C 2 across a bond. Also the new mechanism never requires of over- coordinated C atoms whereas this older mechanism has a number of steps with either 2- or 4- fold coordinated atoms.

18. New mechanism starts with C 2 addition next to the displaced pentagon, adding across an existing hexagon. This is followed by a single ‘Stone-Wales’ bond rotation of a neighbouring bond, which restores the initial structure but with the displaced pentagon rotated by one. This is shown in more detail in the next slides. Pentagons : Light grey Heptagons : Dark grey

19. Growth mechanism applied to a nanotube tip (other end H terminated) Schlegel diagram shows equivalent for C 76 Starting with one pentagon displaced Pentagons blue Heptagons grey

20. Addition of C 2 unit

22. This opens two bonds, leading to formation of paired pentagon and neighbouring heptagon.

23. Rotating a neighbouring bond by 90 degrees (dotted lines show newly forming bonds, double strikes show two bonds which break)

24. Leads to a return to the ideal cap structure with one displaced pentagon, however the displaced pentagon has now rotated one step around the cap.

25. Pseudorotation

26. C 76 The same process works in fullerenes, starting from C 76. We have calculated the structure energies for C 76 up to C 86 by this mechanism, i.e. one complete circuit of the cap through C 2 addition.

27. C 76 + C 2

28. C 78

29. We have traced this process in our calculations in the entire series from C 76 to C 86, i.e. through the addition of 5 C 2 pairs, returning the displaced pentagon to its original position and adding a complete ring of hexagons around the ‘waist’ of the fullerene. C 86

30. 3D isosurfaces of the electrostatic potential, with the isosurface created for different values of the potential. These show, that the attractive potential is associated with the tip rather than the tube walls

31. 3D isosurfaces of the electrostatic potential, with the isosurface created for different values of the potential. These show, that the attractive potential is associated with the tip rather than the tube walls

32. Increasing the cut-off shows the electrostatic potential is strongest on the one side of the tube tip:

33. Increasing the cut-off still further shows that the most intense region of the electrostatic potential is located just over the shared bond between the shifted pentagon and its hexagon neighbour

34. Model requires C 2 addition across the hexagon marked with the red arrow, i.e. neighbouring the region of high potential

36. Increasing the cut-off still further shows that the most intense region of the electrostatic potential is located just over the shared bond between the shifted pentagon and its hexagon neighbour (these three images show the same potential value from different orientations): Our model requires C 2 addition across the hexagon marked with the red arrow, i.e. neighbouring the region of high potential

37. Testing the mechanism Step 2 What is the barrier for the subsequent bond rotation? From structure (c) to (e) And what is the energy difference between these two?

38. DFTB results for different ‘Stone Wales’ bond rotations (description next slides)

39. Initial C 2 addition After Stone-Wales rotation removes excess heptagons and pentagons

40. DFTB results for different ‘Stone Wales’ bond rotations (description next slides) Graphite with one Stone - Wales defect in it Perfect graphite

41. DFTB results for different ‘Stone Wales’ bond rotations Fullerene : C 76 + C 2 giving C 78 : this C 78 is the structure on the right. The structure on the left is C 78 after Stone Wales rotation, i.e. the cap is reconstructed to give the stable five pentagon structure with one pentagon displaced. Graphite : This is a large sheet of flat graphene, Stone Wales rotating a single C-C bond in the sheet. Cap:This is the same displaced pentagon structure as for the fullerene, but instead in the cap of a nanotube, with the other end of the nanotube hydrogen terminated (as seen in some of the other images). These are DFTB results (density functional tight binding) determined using the deMon code by Alberto Zobelli (unpublished) using a ‘nudged elastic band’ algorithm to determine the barrier. Since they are density functional tight binding the barriers may be overestimated slightly compared to better DFT results (which are currently underway).

42. DFTB results for different ‘Stone Wales’ bond rotations Thus the barrier in normal graphite to ‘undo’ a Stone-Wales defect is roughly 4eV, releasing around 4eV in the process. In contrast for the C 2 addition case there is very little energy release (energy of start structure <1eV higher than end structure) and the barrier is much higher at around 6eV. This is true both for the fullerenes and also for the nanotube cap case. Note: The reaction path should be read ‘backwards’ – i.e. the right hand end of the x-axis corresponds to the structure with the C 2 just added, the left hand end of the x-axis corresponds to the structure after the Stone-Wales bond rotation has removed the excess heptagons and pentagons. Likewise for the perfect graphite case, the right hand end of the x-axis is graphite with a Stone-Wales bond rotation in it, the left hand end of the x-axis is perfect graphite. I have shown this with labelling on the graphs now.

43. When can we apply this? Smallest fullerene possible with displaced pentagon and no paired pentagons is C 76.

44. Information on structure energies and rotation barriers to follow for C n, n=76-86, likewise for the nanotube caps. Greg is currently working on the background bibliography … to follow …