Dynamic Topology of Fullerene Coalescence

Atomic rearrangements leading to the coalescence of fullerene cages are revealed by topological analysis. Paths found for nanotubes and ${\mathrm{C}}_{60}$ consist exclusively of Stone-Wales bond rotations. Computed intermediate states show gradual evolution from separate clusters to completely fused coherent units. Molecular dynamics simulations follow the predicted routes, overcome the nucleation barrier, and reach a final annealed state. While the overall behavior resembles macroscopic sintering, the nanoscale neck undergoes quantized changes in diameter and crystalline order.