Theory for the Growth of Fullerenes

Abstract

In view of recent experiments we extend our previous growth model for fullerene formation. It becomes clear how a high efficiency of C₆₀ formation is achieved. We estimate the size dependence of intermediate structures along the most efficient growth route and furthermore the stability of Si_2o, Ge_2o vs. the unstable C_20-

Notes

Like in chemisorption one may describe bond formation using the Arrhenius law.

From using exp(−β/kT) for adding a pentagon next to a pentagon of a polyhedra we get the avoidance rule for pentagons for C_60- Of course, two n. n. p may result if this closes deformed structures and enough lowering of surface energy is achieved this way.

One estimates using previous results n_c ∽ 13, thus bicycling at n ≳ 26. Then, the structure (ring - C_N - ring), should occur for n ≳ 35, N ∼ 10. For larger rings C_n the polycyclic transitions and C_N formation is more effective.

From p_n+1 = qp_n and p′_n+1 = (1 — q)p_n , where p′_n+1 refers to bad polyhedra, one gets Pn+1 = IPn + ?(1 - q)Pn and thus q_eH = (2–9)q.

Assuming that for combined growth, first C_N-chain, then addition of C₂ C₃ to get C₆₀, one has f_n =1 for first steps, then f_n < 1.

For geometrical, bond-length reason one estimates that on the surface of the sphere with Rmin ∽ 3Å there is space for 69 C-atoms, 25 Si-atoms, and 26 Ge-atoms, which already is in fair agreement with C₆₀, Si₂₀, Ge₂₀. Hence, C₂₀ involves a much larger bending energy Δε_bend than C₆₀ and consequently Δε_bend > Aebond, since Aebend = Ae_bond holds just for C₆₀ In conclusion, C₂₀ is for energetic reasons not possible.

Note, C_n ^-rings are stiffer due to the excess electron. This explains the observation that C₆₀ growth is prevented or more difficult for C^- _n-ring.