Fullerenes C C and C can be considered

Fullerenes C24, C30, and C36 can be considered to be perfect fullerenes with a threefold symmetry. The symmetry can be easily discovered looking at their graphs. The fullerenes C26, C28, C32, and C34 are imperfect. By analogy with crystal physics, it ck2 inhibitor can be said that the reason for imperfection is connected with the fact that the fullerenes have extra ‘interstitial’ dimers or ‘vacant’ dimers. The structure of fullerene C36 is rather interesting. It has two triangles around a polar axis. Each triangle surrounded by three hexagons forms a cluster. The clusters are separated by a zigzag ring of twelve atoms which create an equator. It is worth noting that all equator atoms are former dimer atoms. Although any hexagon of fullerene C36 is capable of embedding a dimer, but a hexagon with not only two neighboring mutually antithetic pentagons but one pentagon and a mutually antithetic trigon is more likely to do so. It is connected with the well-known fact; the less is the fullerene surface, the less is its energy. A local curvature is defined by the sum of adjacent angles having a common vertex. The less is the sum, the larger is the curvature, and therefore the more is the local stress concentration. Even the first embedding of a dimer into such a hexagon increases the sum from 300 to 330º, and thus the configuration becomes more stable. The process of growth of fullerene C36 leads to forming imperfect fullerenes C38, C42, and C46, semi-perfect fullerenes C40, C44, and perfect fullerene C48. The imperfect fullerenes have an odd number of dimers; the semi-perfect fullerenes, as well as the perfect one, have an even number. The final high-symmetry fullerene C48 has the same structure as the one of fullerene C48 which was grown out of fullerene C20[6]. It contains clusters of eighteen atoms in the polar areas; each cluster is composed of six pentagons around a hexagon. This means that there the principle of equifinality holds in this case; a nucleus of fullerenes can be different, but the final structure is the same. Therefore, the further growth of fullerene C48 formed in the second branch will not differ from that of the first branch.
Introduction Up to now the fullerene-formation mechanism has remained a controversial point. Research suggests that fullerene assemblage originates of individual atoms and C2-dimers, and, probably, of very small clusters. In Refs. [1,2] we have exhaustively investigated a dimer mechanism of fullerene growing. According to it, a carbon dimer embeds either into a hexagon or a pentagon of an initial fullerene. This leads to stretching and breaking the covalent bonds which are parallel to arising tensile forces. In both cases there arises a new atomic configuration and there is a mass increase of two carbon atoms. However, the above-stated mechanisms of fullerene growth are not unique. Fullerenes can be imagined to grow by reacting with each other, similar to a bubble growth in the soap solution. This possibility was demonstrated by the example of such reactions as and through the use of a new molecular dynamics that takes into consideration both atomic and electronic degrees of freedom simultaneously, especially the excited electronic states created by electronic transitions [3–6]. Fullerenes and nanotubes are formed at high temperatures and the new molecular dynamics, termed ‘charged-bond’ molecular dynamics, accounts for this factor properly. At first this molecular dynamics was developed as a rather sophisticated design, but later Transfection obtained a strict theoretical basis [7]. Any molecular dynamics needs input data. For mini-fullerenes (up to C20) the number of possible configurations is not very large, but as one passes to midi-fullerenes (C20–C60) one obtains a monstrous size of isomers. It is clear that there is no big sense in studying all of them, so it is desirable to restrict their number to the most stable. In this respect, it makes sense to use geometric modeling as a first step of a computer simulation and further theoretical analysis [8]. We suppose that the geometric modeling will allow us to envision a possible way of growing carbon clusters from the very beginning and thereby to decrease the number of configurations being worthy of further study.