Multiscale modeling strategy to solve fullerene formation mystery

Abstract

Since fullerene formation occurs under conditions where direct observation of atomic-scale reactions is not possible, modeling is the only way to reveal atomistic mechanisms which can lead to selection of abundant fullerene isomers (like C 60 -I h ). In the present paper we review the results obtained for different atomistic mechanisms by various modeling techniques. Although it seems that atomic-scale processes related to odd fullerenes (such as growth by consecutive insertions of single carbon atoms and rearrangements of the sp 2 structure promoted by extra sp atoms) provide the main contribution to selection of abundant isomers, at the moment there is no conclusive evidence in favor of any particular atomistic mechanism. Thus, the following multiscale modeling strategy to solve the mystery of the high yield of abundant fullerene isomers is suggested. On the one hand, sets of reactions between fullerene isomers can be described using theoretical graph techniques. On the other hand, reaction schemes can be revealed by classical molecular dynamics simulations with subsequent refinement of the activation barriers by ab initio calculations. Based on the reaction sets with the reaction probabilities derived in this way, the different atomistic mechanisms of abundant fullerene isomer selection can be compared using kinetic models.

Role of Graphitic Bowls in Temperature Dependent Fullerene Formation

“…Also at low temperatures, if a highly curved bowl with large side chains is initially formed, a fast chain incorporation to complete fullerene from a chain network is common. This is similar to previous reports self-organization or ring coalescence mechanisms with the more highly curved bowls being transitory. In this case as the sp 2 network forms into a bowl, a C chain spanning the structure remains present (Figure b inserts).…”

“…From here, the sp junctions acted as nucleation sites for more complicated isoforms. This is extremely similar to observations for carbon nanotube and graphene nucleation on metal substrates. , Further, the formation of these chain networks is eerily similar to those found in the initial parts of the fullerene road mechanism, though no small fullerene ever forms, and to the ring coalescence and self-organization mechanism, though only initially. Finally, given we have the formation of fullerene at such a small size, the SHG mechanism is not necessary for C 60 formation (though not excluded).…”

“…With this model, the lowest energy structures above C 30 are thought to be fullerenes with clusters adding directly to these fullerenes up to C 60 . The ring coalescence and self-organization mechanisms involve the formation of chain networks that then coalesce directly into fullerene structures (albeit, ring coalescence involves oxygen). These 2 mechanisms do not involve bowl structures and generally assume fullerenes form directly from chain networks.…”

Quantum‐chemical approaches in the study of fullerene and its derivatives by the example of the most typical cycloaddition reactions: A review

“…It is important that the very existence of a stable, highly symmetric 3D fullerene molecule was predicted theoretically [106] and described by quantum-chemical calculations [107] long before the experimental discovery of C 60 . Later, the structure of fullerene was studied from a fundamental point of view in a number of works [106][107][108][109][110][111][112][113]. In fact, Lee et al [108] used the B3LYP/6-31(d) method to study the ionic forms of C 60 and C 70 fullerenes.…”

“…The data presented in the article can be used to further improve the fullerene model. In 2021, the same group of scientists published a comprehensive review on the methods used to solve the puzzle of fullerene formation [113]. It conducts the main results and proposes a further strategy using a multiscale approach that combines various modeling techniques such as atomistic modeling, kinetic models and graph techniques.…”