ISSN 10637834, Physics of the Solid State, 2012, Vol. 54, No. 8, pp. 1723–1727. © Pleiades Publishing, Ltd., 2012. Original Russian Text © A.I. Podlivaev, L.A. Openov, 2012, published in Fizika Tverdogo Tela, 2012, Vol. 54, No. 8, pp. 1614–1618.
FULLERENES
Isomers of C46 Fullerene with Carbyne Chains A. I. Podlivaev and L. A. Openov* National Research Nuclear University “MEPhI,” Kashirskoe sh. 31, Moscow, 115409 Russia email:
[email protected] Received February 8, 2012
Abstract—The dynamics of the processes of isomerization and decomposition of C46 fullerene has been stud ied by computer simulation in the realtime regime. At an intermediate stage of evolution of the cluster (before it loses the spheroidal shape), isomers in which groups of adjacent pentagons and hexagons of C–C bonds are connected to each other with two, four, and sixatomic carbyne chains have been revealed. An analysis of the potential energy hypersurface has demonstrated that the isomers are quite stable and some of them can be observed experimentally. DOI: 10.1134/S1063783412080252
1. INTRODUCTION Hybridization of four valence orbitals of carbon atoms (2S, 2Px, 2Py, 2Pz) allows each of atoms to par ticipate in formation from one to four covalent bonds. It is the reason why carbon has many allotropic modi fications that are different in structure and electronic properties. The most known of them are diamond (sp3 hybridization, coordination number z = 4), graphite (sp2, z = 3), and carbyne [1] (sp, z = 2). Recently, much attention has been concentrated on carbon nanostructures such as fullerenes [2], nanotubes [3], and graphene [4], in which the C–C bonds form a pat tern from pentagons and hexagons; i.e., the sp2 hybrid ization (z = 3) takes place. Of great interest is continuous searching for new bulk and lowdimensional carbon allotropes. For example, the Cco–C8 phase close to diamond in hard ness has been identified recently [5]. Graphene deriv atives such as graphyne and graphdiyne in which hexa gons from C–C bonds are connected to each other by means of two and fouratomic carbon chains with a polyin structure were predicted and synthesized (Fig. 1) [6–8]. It was suggested in [9, 10] that similar chains can be composite elements of fullerenelike spheroidal clus ters that connect C–C pentagons and hexagons to each other. A rectilinear theoretical approach to solv ing the problem of the possible existence of such clus ters is an analysis of the energy gain of corresponding structures [9, 10], namely, search for the atomic con figurations that correspond to the local minima of the potential energy of a cluster as a function of the coor dinates of the cluster atoms. However, in this work, we did not initially pose this problem. We studied the ways of decomposing the C46 fullerene (Fig. 2) that is of interest, first, due to its lower thermodynamic stability as compared to its nonclassic isomer C46 with one tet
ragon [11] (it is an exclusion to the rule) and, second, due to fact that this cluster has new channels of defect formation that are absent in C60, C70, and other fullerenes with higher symmetry [12]. The appearance of isomers with two, four, and sixatomic carbyne chains at the intermediate stage of evolution of heated C46 fullerene is an unexpected result. The aim of this work is to study the structure of these isomers and transition between them and also to calculate the energy barriers preventing their decomposition. 2. CALCULATION METHODS The numerical simulation of the time evolution of C46 fullerene was performed by the molecular dynam ics method with the time step t0 = 2.72 × 10–16 s, assuming that the total energy (the sum of the poten tial and kinetic energies) is constant, which corre sponds to the microcanonical ensemble (in more detail, see [13, 14]). The “dynamic” temperature that is a measure of the energy of relative motion of atoms [15] was taken to be T = 2500–2800 K. These condi tions are sufficient to initiate defect formation [12] for a time corresponding to ~106 moleculardynamics steps. To calculate the energies of atomic configurations formed during the process of cluster evolution and to determine the forces acting on atoms, we used a non orthogonal tightbinding model [16] that ranks below ab initio approaches in accuracy but requires much lower consumptions of computer resources, and, because of this, allows us to study evolution of a system from ~100 atoms for macroscopic (on atomic scale) times of ~10 ns and also to analyze in detail the poten tial energy hypersurface Epot near various atomic con figurations. The model was successfully used to study
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(b)
Fig. 2. C46 fullerene.
of numerical simulation, the dynamics of develop ment of a defect structure is substantially dependent on the first defect type. In this work, we focus attention on the sequence of formation of new and new defects that we observed when simulating evolution of C46 fullerene; the sequence leads, first, to the formation of isomers with twoatomic carbyne chains and then to appearance of isomers with four and sixatomic chains.
Fig. 1. Fragments of layers of (a) graphyne and (b) graph dine.
various carbon and hydrocarbon nanostructures [17, 18]. Heights U of the energy barriers preventing the transitions between various isomers of C46 cluster were found by analyzing the potential energy Epot as a func tion of coordinates of all atoms in the vicinity of cor responding metastable configurations that correspond to local minima of Epot. In this case, we used the method of searching for a saddle point in the normal coordinates [19, 20]. 3. RESULTS AND DISCUSSION Since C46 fullerene (Fig. 2) has a comparatively low symmetry, it contains many (unlike, e.g., C60 fullerene) nonequivalent C–C bonds with various local surroundings. Because of this, there are also very many different channels of defect formation in C46 fullerene [12], and, according to an analysis of the data
The first defect forms as a result of breaking of one (common for two hexagons) C–C bond, and a deca gonlike “window” forms on the fullerene surface (Fig. 3). At the next stage, the C–C bond common for pentagons and hexagons neighboring with the window is broken, and, as a result, two adjacent windows (decagonlike and nanogonlike) appear. Then, new windows continue to form by the above mechanism, until they will completely occupy the “lateral surface” of the cluster along its equator (Fig. 3), and two poles consisted of pentagons and hexagons of C–C bonds remain at its top and bottom (Fig. 4). As a result, we have C46 isomer with eight windows (one decagonlike and seven nanogonlike) and two poles connected by means of eight twoatomic chains (here and in what follows, we indicate the number of atoms in carbon chains with no considering atoms belonging to the poles). We shall call such isomers graphynefullerenes with an eye the fact that they contain elements of the graphyne structure (Fig. 1a). The carbyne chains binding the poles of graphynefullerene have a polyin structure, as is the case in graphyne: the length of cen
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Fig. 4. Various types of poles in graphynefullerenes.
Fig. 3. Sequence of formation of defect isomers of the C46 fullerene that is completed by formation of graphyne fullerene.
tral C–C bonds in the chains are 1.255–1.265 Å, while the bond lengths between edge chain atoms and atoms located in the poles are 1.426–1.461 Å (the scatter of bond lengths of each type is due to nonequivalence of chains because of asymmetry of the poles). These bond lengths are close to the corresponding values in graphyne [7]. Figure 5 (AA' region) shows the results of calcula tion of the potential energy of a C46 cluster along the reaction coordinate connecting a perfect fullerene with graphynefullerene and passing through the con figuration with different numbers of windows (Fig. 3). It is seen that intermediate isomers with the numbers of windows 1–5 and 7 are metastable, and their ener gies increase with the number of windows. To open each new window, it is necessary to overcome an energy barrier whose heights Unm (for the transition of the isomer with n windows to the isomer with m win dows) are U01 = 3.00 eV, U12 = 0.65 eV, U23 = 0.58 eV, U34 = 0.73 eV, U45 = 0.61 eV, U57 = 2.00 eV, and U78 = 0.04 eV (the isomer with six windows is not metasta ble). The summary barrier height for the transition of the C46 fullerene to graphynefullerene (configuration with eight windows) is U08 = 6.86 eV. Note that barrier height for the inverse transition is quite high (U80 = 1.75 eV), i.e., the C46 graphynefullerene formed dur ing thermal evolution of the initial fullerene must retain its structure for a fairly long time (sufficient for its experimental detection) PHYSICS OF THE SOLID STATE
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The C46 graphynefullerene (Fig. 3) is not the only possible isomer. It has several isomers close in energy that are different in pole structure formed, as a rule, by four or five (more rarely, three or six) pentagons and hexagons from C–C bonds (Fig. 4). The common property of all the isomers is the existence of eight diatomic chains connecting two poles. When simulat ing the dynamics of the C46 cluster, we observed repeated transitions between various isomers. Each of the transitions occurs as a result of synchronous or successive breaking of several C–C bonds in the poles and their vicinities and subsequent formation of new bonds. In this case, the structure of each of the poles is changed, so that the number of diatomic chains con necting the poles is unchanged. Sometimes, the two poles change their places. The variation of the poten tial energy of the C46 cluster during transitions between various graphynefullerene isomers is shown in Fig. 5 (region A'A''). It is seen that the energy barriers of the transitions are Ugf ≈ 1 eV; i.e., they are lower than the barrier U80 for the inverse transition of the gra phynefullerene to the fullerene. The decomposition of the graphynefullerene starts from its transition to an isomer that has one large 13 member window on its lateral surface, and its poles are connected by not only diatomic but also two triatomic chains. Then, the number of large windows (among them 12, 15, and 16member windows) increases; as a result, fouratomic and sixatomic chains occur instead of triatomic chains, and the number of penta gons and hexagons in the poles decreases to one– three. The process is accompanied by an increase in the potential energy of the cluster (Fig. 5, region A''A'''). The isomers forming at this stage of evolution of the cluster differ by both the pole structure and the number of two, four and sixatomic chains binding the poles; because of this, we cannot suggest that the graphynefullerene transform to a new class of car bynefullerenes (e.g., they may be graphdiyne fullerenes if their poles are bound only by fouratomic chains (Fig. 1b). The isomers with five diatomic, two
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higher as compared to barriers Ugf ≈ 1 eV for transitions between its various isomers. Since the barrier U80 = 1.75 eV for the reserve transition of the graphyne fullerene to the initial fullerene is also higher than Ugf (see above), it may be suggested that the space of atomic coordinates contains a particular graphyne fullerene valley, in which metastable configurations of graphynefullerenes with various structure of poles are located (Fig. 5, region A'A'').
Epot, eV
12
8
... 7
4 12 0 A
3
45
8
9
...
A' A'' A''' Reaction coordinate, arb. units
4. CONCLUSIONS The C46 graphynefullerenes under study differ from fullereneynes (according to the terminology from [9]) and carbynefullerenes, according to terminology from [10]) by that the diatomic carbyne chains bind two groups from several adjacent pentagons and hexagons that we call poles, not individual pentagons and/or hexagons. We underline that we did not guess atomic configurations of such graphynefullerenes but we detected them during the computer experiment on studying evolution of the initial C46 fullerene during its heating. Although these clusters are less stable from the thermodynamic standpoint than perfect C46 fullerene, they correspond to fairly deep (~1 eV) local minima of energy as a function of atomic coordinates; i.e., they can be synthesized and detected. It is of interest that a metastable isomer of similar type was observed when simulating thermal evolution of a C20 fullerene, in which role of poles is played by parallel pentagons bound to each other by five diatomic carbyne chains [21]. Note that the simula tion of decomposition of C60 and C36 did not reveal isomers with chain elements [22, 23]. The tendency of formation of such isomers seems to be dependent to any degree on the number of atoms in the initial fullerene and/or its symmetry. In the future, it would be interesting to study the possibility of formation of carbynefullerenes with longer chains and to consider twodimensional carbynographene nanostructures.
Fig. 5. Variations of the potential energy Epot of the C46 fullerene during formation of graphynefullerenes, their subsequent evolution, and decomposition. The energy of perfect fullerene is taken as the reference point. Region AA' corresponds to successive formation on the cluster surface of eight windows separated by diatomic carbyne chains (Fig. 3). The numerals from 1 to 8 denote the numbers of windows (there is no isomer with six windows). The isomer with eight windows is graphynefullerene consisting of two poles (Fig. 4) bound by eight diatomic chains. Region A'A'' corresponds to the transitions between various isomers of graphynefullerene different in the pole structure. In region A''A''', the pole size decreases and the chains binding them are elongated, which leads in the end to the cluster decom position. 9 is the isomer shown in Fig. 6. The asterisk is the atomic configuration after decomposition.
ACKNOWLEDGMENTS We are thankful to M.M. Maslov for assistance in this work and discussion of the results. One of the authors (L. A. O.) is grateful to collaborators of the “LeDa” Center for warm reception and moral sup port. This study was supported by the Russian Founda tion for Basic Research (project no. 120200561).
Fig. 6. C46 isomer with five diatomic, two fouratomic, and one sixatomic carbon chains.
fouratomic, and one sixatomic chains are more fre quent than other. In the end, it is precisely one of such isomers (Fig. 6) that losses its spheroidal shape that is no longer recovered during subsequent evolution of the cluster. From Fig. 5, it is seen that the barrier for decompo sition of graphynefullerene U ≈ 2 eV is substantially
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Translated by Yu. Ryzhkov
