“…A myriad of chemical models for the formation of fullerene have been proposed and can be categorized into two groups: pathways that start from large carbon aggregates that degrade into fullerene (“size-down”) and pathways that start from small carbon aggregates and condense into fullerene (“size-up”). The “size-down” pathways that have been proposed include the degradations of graphene, , graphene nanoflakes, carbon nanotubes, and giant fullerenes. , The “size-up” pathways proposed include the fullerene road, pentagon road, closed network growth, − and ring coalescence and annealing. ,, All of the “size-up” pathways except the ring coalescence and annealing model progress from smaller carbon aggregates to larger fullerenes through the steady incorporation of C 2 fragments. In contrast, the ring coalescence and annealing model proposes the addition of medium-sized (C 12 –C 20 ) cyclic polyynes, and subsequent annealing through a cascading radical mechanism, resulting in fullerenes .…”