Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theoretical study of the nucleation/growth process of carbon clusters under pressure

We used molecular dynamics and the empirical potential for carbon LCBOPII to simulate the nucleation/growth process of carbon clusters both in vacuum and under pressure. In vacuum, our results show that the growth process is homogeneous and yields mainly sp(2) structures such as fullerenes. We used an argon gas and Lennard-Jones potentials to mimic the high pressures and temperatures reached during the detonation of carbon-rich explosives. We found that these extreme thermodynamic conditions do not affect substantially the topologies of the clusters formed in the process. However, our estimation of the growth rates under pressure are in much better agreement with the values estimated experimentally than our vacuum simulations. The formation of sp(3) carbon was negligible both in vacuum and under pressure which suggests that larger simulation times and cluster sizes are needed to allow the nucleation of nanodiamonds.     

Dangling bond-induced graphitization process on the (111) surface of diamond nanoparticles

The intrinsic mechanism of graphitization occurring on the (111) surface of nanodiamonds (NDs) during the transformation from NDs into bucky diamonds are explored using density functional theory (DFT) computations in conjunction with density functional based tight-binding simulations. The DFT results indicate that dangling bonds (DBs) on the ND surfaces play an important role in the graphitization process, and the orientation of the DBs on different ND surfaces determines whether there will be a graphitization process or not. Moreover, a criterion is proposed to estimate rupturing of the C-C bonds between different layers on the [111] direction in the NDs and is verified to be applicable to illustrate the phase transformation from sp(3) into sp(2) bonding structures. The energy contributions of the four-coordinated carbon atoms located at different positions on the (111) surface are exhibited for the first time and discussed in detail to gain a clear picture for the transition from NDs into bucky diamonds. The outcome may provide a deeper understanding on the influence of DBs upon the transformation from sp(3) into sp(2) bonding structures.     

Hypercoordinated carbon in C-doped boron fullerenes: a quantum chemical study

The structures and stability of C-doped boron fullerenes with the three-dimensional arrangement of non-classical pentacoordinated quasi-flat carbon centers were studied using the density functional theory (DFT) B3LYP/6-311+G(d,p) method. The doping with carbon atoms in apical positions above the five-membered rings stabilizes the spherical boron fullerene forms due to multicenter interactions of p_z-orbitals of the carbons and adjacent boron atoms. Increasing in the size of the fullerene cluster is accompanied by change in the bonding pattern and by flattening of the hypercoordinated carbon centers. Endohedral metal atoms significantly affect on the structure and stability of the fullerene systems with hypercoordinated carbon centers.     

Phase stability of nanocarbon in one dimension: nanotubes versus diamond nanowires

Since their discovery in 1990, the study of sp2 bonded carbon nanotubes has grown into a field of research in it's own right; however the development of the sp3 analog, diamond nanowires, has been slow. A number of theoretical models have been proposed to compare the relative stability of diamond and graphite at the nanoscale; and more recently, to compare nanodiamonds and fullerenes. Presented here is a study of the phase stability of nanocarbon in one-dimension. The structural energies of carbon nanotubes and diamond nanowires have been calculated using density functional theory within the generalized gradient approximation, and used to determine the atomic heat of formation as a function of size.     

Application of carbon-based nanomaterials in sample preparation: A review

In this paper, a broad overview on the applications of different carbon-based nanomaterials, including nanodiamonds, fullerenes, carbon nanotubes, graphene, carbon nanofibers, carbon nanocones-disks and nanohorns, as well as their functionalized forms, in sample preparation is provided. Particular attention has been paid to graphene because many papers regarding its application in this research field are becoming available. The distinctive properties, derivatization methods and application techniques of these materials were summarized and compared. According to their research status and perspective, these nanomaterials were classified in four groups (I: graphene and carbon nanotubes; II: carbon nanofibers; III: fullerenes; and IV: nanodiamonds, carbon nanocones/disks and carbon nanohorns) and characteristics and future trends of every group were discussed.     

Reactivity Differences between Carbon Nano Onions (CNOs) Prepared by Different Methods

The carbon nanoparticles obtained from either arcing of graphite under water or thermal annealing of nanodiamonds are commonly called carbon nano onions (CNOs), or spherical graphite, as they are made of concentric fullerene cages separated by the same distance as the shells of graphite. A more careful analysis reveals some dramatic differences between the particles obtained by these two synthetic methods. Physicochemical methods indicate that the CNOs obtained from nanodiamonds (N‐CNOs) are smaller and contain more defects than the CNOs obtained from arcing (A‐CNOs). These properties explain the enhanced reactivity of the N‐CNOs in cycloaddition and oxidation reactions, as well as in reactions involving radicals. Given the easier functionalization of the N‐CNOs, they are the most obvious choice for studying the potential applications of these multi‐shelled fullerenes.     

M4 @Si28 (M=Al,Ga): metal-encapsulated tetrahedral silicon fullerene

It is known that silicon fullerenes cannot maintain perfect cage structures like carbon fullerenes. Previous density-functional theory calculations have shown that even with encapsulated species, nearly all endohedral silicon fullerenes exhibit highly puckered cage structures in comparison with their carbon counterparts. In this work, we present theoretical evidences that the tetrahedral fullerene cage Si(28) can be fully stabilized by encapsulating a tetrahedral metallic cluster (Al(4) or Ga(4)). To our knowledge, this is the first predicted endohedral silicon fullerene that can retain perfectly the same cage structure (without puckering) as the carbon fullerene counterpart (T(d)-C(28) fullerene). Density-functional theory calculations also suggest that the two endohedral metallosilicon fullerenes T(d)-M(4)@Si(28) (M=Al and Ga) can be chemically stable because both clusters have a large highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap ( approximately 0.9 eV), strong spherical aromaticity (nucleus-independent chemical shift value of -36 and -44), and large binding and embedding energies.     

Transformation of three-dimensional three-connected silicon nets in SrSi2

Dimorphic SrSi₂ is the first compound for which the two simplest three-dimensional three-connected nets are found in its polymorphs. The cubic net of three-connected silicon atoms (SrSi₂ type of structure) can be transformed into the tetragonal one (α-ThSi₂ type of structure) by a high-pressure-high-temperature treatment. The tetragonal phase is quenchable. Heating of this phase to 600–700°C at ambient pressure results in transformation into the cubic one. At a heating rate of 20°C/min complete transformation can be achieved within 5 min in a DTA apparatus. The energy of transformation has been obtained from the peak areas of the DTA curves to ?1.6 ± 0.3 kcal/mole. Although the transformation between the three-dimensional three-connected sets in SrSi₂ must be formally classified as a reconstructive one, a relatively small entropy change (ΔS = 1 ·₁ cal/deg · mole) has been calculated from the change in molar volume and p-T equilibrium conditions. Therefore, structural relations between the cubic and the tetragonal nets are discussed.     

毫秒脉冲激光合成超细纳米金刚石

通过热力学和动力学的基本理论, 分析了毫秒脉冲激光照射石墨悬浮液合成超细纳米金刚石的机理. 在毫秒脉冲激光与石墨颗粒相互作用形成的碳蒸气羽中, 通过碳蒸气凝聚形成了金刚石核. 与纳秒脉冲激光相比, 毫秒脉冲激光具有较低的功率密度和较长的脉宽, 为金刚石核的生长提供了较小的过冷度, 使得金刚石核的生长速率减小; 而较小的生长速率也为金刚石表面形成sp2杂化结构提供了机会, 它可以有效降低金刚石核的表面能, 促使金刚石核稳定, 但表面的sp2杂化也阻止了金刚石核的外延. 以上两个原因决定了毫秒激光辐照石墨颗粒过程中只能获得超细的纳米金刚石.     

Simulating the thermal behavior and fragmentation mechanisms of exohedral and substitutional silicon-doped C60

Structures, thermal behavior, and fragmentation mechanisms of exohedral and substitutional silicon-doped C(60) containing 1-12 Si atoms are investigated by extensive molecular-dynamics simulations. A nonorthogonal tight-binding model is used to mimic the interatomic interactions in the doped fullerenes. Beginning from the minimum-energy structures, the temperature of the doped fullerenes is slowly increased until fragmentation takes place. A correlation can be established between the exohedral and substitutional structures and the corresponding fragmentation mechanisms and fragmentation temperatures. Exohedral C(60)Si(m) fullerenes fragment into two homonuclear pieces, the Si(m) cluster and the C(60) fullerene that remains intact. In contrast, the substitutional C(60-m)Si(m) heterofullerenes undergo structural transformations, including the partial unraveling of the cage, prior to fragmentation. Then, ejection of atoms or small molecules takes place from the distorted structures. The slow heating rate used, combined with long simulation runs, allows us to determine the fragmentation temperature of exohedral and substitutional Si-doped fullerenes as a function of the number of silicon atoms. Substitutional Si-doped fullerenes exhibit much higher fragmentation temperatures (1000-1500 K higher) than the exohedral fullerenes. This can be understood from the different bonding of the Si atoms in both structures.     

First-principles study of hydrogen storage on Li12C60

Solid state materials capable of storing hydrogen with high gravimetric (9 wt %) and volumetric density (70 g/L) are critical for the success of a new hydrogen economy. In addition, an ideal storage system should be able to operate under ambient thermodynamic conditions and exhibit fast hydrogen sorption kinetics. No materials are known that meet all these requirements. While recent theoretical efforts showed some promise for transition-metal-coated carbon fullerenes, later studies demonstrated that these metal atoms prefer to cluster on the fullerene surface, thus reducing greatly the weight percentage of stored hydrogen. Using density functional theory we show that Li-coated fullerenes do not suffer from this constraint. In particular, we find that an isolated Li(12)C(60) cluster where Li atoms are capped onto the pentagonal faces of the fullerene not only is very stable but also can store up to 120 hydrogen atoms in molecular form with a binding energy of 0.075 eV/H(2). In addition, the structural integrity of Li(12)C(60) clusters is maintained when they are allowed to interact with each other. The lowest energy structure of the dimer is one where the Li atom capped on the five-member ring of one fullerene binds to the six-member ring of the other. The binding of hydrogen to the linking Li atom and the potential of materials composed of Li(12)C(60) building blocks for hydrogen storage are discussed.     

Versatile fullerenes as sensor materials

The last century outstanding discovery of fullerenes (or C₆₀), as they are popularly called ‘buckyball’ structured molecules with icosahedral spherical structure, consists of 60 sp^2-hybridized carbon atoms. These fullerenes have created immense applications in various fields, such as catalysts, sensors, photocatalysts, energy production, and storage materials. Fullerenes because of their improved conductivity, charge transfer, and photophysical properties have gained considerable attention, particularly in sensor area. The activity of sensors depends upon the interactions between fullerene and the sensing material. Among all the types of fullerenes, C₆₀ has been extensively used. This review is an attempt to cover different aspects of fullerene-based sensing devices, wherein fullerenes act as important component (s) of the sensor device because of their electron-accepting properties. We will discuss the fullerene-based sensors for diverse applications as strain/gas sensors, electrochemical sensors, and optical sensors as much effort has been recently made to detect different analytes such as gases, volatile organic compounds, metal ions, anions, and biomolecules.     

Isomerization kinetics of carbon clusters 1. Potential of interatomic interaction

Formation of fullerenes — spherical carbon clusters C₆₀ and clusters of other sizes — during condensation of carbon vapors has not yet received theoretical explanation. Recent experimental works concerned with cluster formation in carbon vapors have established that during condensation carbon atoms form rings and then polycyclic clusters, which are precursors of fullerenes. Theoretical investigation of the spontaneous formation of fullerenes from polycyclic rings calls for a simple model of the potential of interatomic interaction of carbon, which would allow fast calculations of bond energies and statistical sums of the clusters. We use the modified Brenner potential, which was developed for hydrocarbon molecules. The parameters of the potential are refitted according to the results of quantum chemical calculations. Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Institute of Computation Technologies, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No.4, pp. 664–670, July–August, 1996. Translated by I. Izvekova     

C60 buckminsterfullerene high yields unraveled

Recently Irle, Morokuma, and collaborators have carried out a series of quantum chemical molecular dynamics simulations of carbon clustering. The results of these computer experiments are that carbon clusters of size greater than 60 atoms are rapidly formed, anneal to giant fullerenes, and then these fullerenes shrink. The simulation could not be carried to long enough times for the shrinking to reach C60, but they propose reasonably that this shrinking process ultimately forms buckminsterfullerene. However, these simulations do not reveal the force driving the shrinking process. Here, this driving force for shrinking is found to be reactions in which C2 is swapped between fullerenes. The key element is that for typical fullerenes the equilibrium constants for such C2 interchanges are near unity, resulting in expansion of the breadth of the fullerene distribution in an annealing process. When fullerenes of 60 or 70 atoms are populated by shrinking, they fall into the local energy minimum of buckminsterfullerene or D5h C70. This simple mechanism accounts for the high yields (>20%) of buckminsterfullerene that can be achieved in pure carbon systems.     

Are diamond nanoparticles cytotoxic?

Finely divided carbon particles, including charcoal, lampblack, and diamond particles, have been used for ornamental and official tattoos since ancient times. With the recent development in nanoscience and nanotechnology, carbon-based nanomaterials (e.g., fullerenes, nanotubes, nanodiamonds) attract a great deal of interest. Owing to their low chemical reactivity and unique physical properties, nanodiamonds could be useful in a variety of biological applications such as carriers for drugs, genes, or proteins; novel imaging techniques; coatings for implantable materials; and biosensors and biomedical nanorobots. Therefore, it is essential to ascertain the possible hazards of nanodiamonds to humans and other biological systems. We have, for the first time, assessed the cytotoxicity of nanodiamonds ranging in size from 2 to 10 nm. Assays of cell viability such as mitochondrial function (MTT) and luminescent ATP production showed that nanodiamonds were not toxic to a variety of cell types. Furthermore, nanodiamonds did not produce significant reactive oxygen species. Cells can grow on nanodiamond-coated substrates without morphological changes compared to controls. These results suggest that nanodiamonds could be ideal for many biological applications in a diverse range of cell types.     

Quantum-chemical models of the annealing of open shell carbon clusters during the synthesis of fullerenes

It is shown that a model for assembling fullerenes from polycyclic carbon clusters, supplemented by consideration of the Stone-Wales transformation on open shell hot clusters, predicts the formation of fullerenes with an almost even distribution of pentagonal cells on their surface. The possibility of this transformation on an open shell cluster itself establishes the maximally proper assembling rate and determines its limiting condition.     

Pb12 2-: plumbaspherene

Although Si or Ge is not known to form empty cage clusters such as the fullerenes, we recently found a unique 12-atom icosahedral tin cluster, Sn12 2- (stannaspherene). Here we report photoelectron spectroscopy and theoretical evidence that Pb12 2- is also a highly stable icosahedral cage cluster and bonded by four delocalized radial pi bonds and nine delocalized on-sphere sigma bonds from the 6p orbitals of the Pb atoms. Following Sn12 2-, we coin a name, plumbaspherene, for the highly stable and nearly spherical Pb12 2- cluster, which is expected to be stable in solution and the solid state. Plumbaspherene has a diameter of approximately 6.3 A with an empty interior volume large enough to host most transition metal atoms, affording a new class of endohedral clusters.     

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

热辅助存储磁盘硅掺杂非晶碳薄膜氧化的ReaxFF反应力场分子动力学模拟

Heat-assisted magnetic recording (HAMR) is one of the promising ways to extend the magnetic recording area density to 1 Tb·in^-2 in hard disk drives (HDDs).High temperature induced by laser heating can cause carbon overcoat (COC) oxidation.Reactive molecular dynamics (MD) simulations are performed to investigate the oxidation process of silicon-doped amorphous carbon (a-C:Si) films for HAMR application.The atomic details of the structure evolution and oxidation process are investigated, and, the oxidation mechanism of the a-C:Si film is clarified.The effect of the duration of laser irradiation on the oxidation of the a-C:Si film is investigated.The oxidation occurs during heating and the beginning of cooling process.Both volume expansion during heating process and cluster of carbon atoms during cooling process increase the rate of sp² carbon.Because of the decrease in the amount of unsaturated silicon atoms and low diffusion coefficient of atomic oxygen, the oxidation rate of the a-C:Si film decreases with laser irradiation cycles.The molecular oxygen is the oxidant due to surface defect of a-C:Si film.The atomic strains break the O-O bonds in Si-O-O-Si linkages and rearrange the surface oxide layers, and process the oxidation of the a-C:Si film.