Carbon Nanotori Research Articles

Synthesis of Sb688-: Crafting a Homoatomic Antimony Nanotorus.

Pure-element cyclic molecules have garnered extensive attention owing to their intriguing structures and promising applications. Among these, carbon-based cyclic molecules such as cyclo[n]carbon (Cn, n = 10-26) and carbon nanotori have ignited significant interest in both experimental and theoretical investigations. However, systematic investigations of analogous cyclic counterparts of heavier main-group elements are limited, with only a few known by theoretical studies. Furthermore, these corresponding cyclic structures lack synthetic examples in the condensed phase, primarily attributed to their high reactivity resulting from lone electron pairs and the absence of electronic delocalization, which typically aids in stabilizing the structure. In this work, we introduce the pioneering synthesis of a pure antimony-based inorganic nanotorus, denoted as Sb688-, facilitated by the incorporation of C60 for oxidation by utilizing wet-chemistry methodologies. The unique nanotorus structure was meticulously examined via single-crystalline X-ray diffraction, unveiling its composition of 68 antimony atoms and forming a tubular structure with approximate dimensions of 18.5 × 18.4 Å2 in a square shape. Theoretical calculations further revealed that the nanotorus structure, characterized by 16 delocalized electrons distributed across eight 3c-2e σ bonds, effectively saturated the eight two-coordinated Sb atoms within the cluster. This study unveils an innovative approach to synthesizing cyclic compounds solely from pure elements, departing from traditional methods dependent on chemical vapor deposition or surface synthesis, and heralds a profound paradigm shift in physical science.

Numerical Analysis of the Influence of a Magnetic Field on the Group Dynamics of Iron-Doped Carbon Nanotori

Columnar phases consisting of a group of carbon toroidal molecules (C120, C192, C252, C288) are studied numerically. Each nanotorus was previously doped with an iron atom. This made it possible to use an external magnetic field as a tool for influencing both an individual molecule and a linear fragment of the columnar phase. A high-precision scheme for calculating the dynamics of large molecules with a rigid frame structure is proposed to solve the problem. The group dynamics of nanotori clusters under the influence of an external magnetic field has been studied using classical molecular dynamics methods. The influence of the molecular cluster size, temperature, magnetic moment of the molecule, and magnetic field direction on the collective behavior of iron-doped toroidal molecules with different contents of carbon atoms is analyzed. Molecular dynamics calculations showed that systems of nanotori doped with a single iron atom retain a columnar structure both in the absence and in the presence of an external magnetic field. The columnar fragment behaves as a stable linear association of molecules even at sufficiently high values of magnetic induction, performing a coordinated collective orbital rotation around a common center of mass on a nanosecond time scale.

Atom-bond-connectivity (ABC) indices of graphene sheets, zigzag single walled carbon nanotubes and single walled carbon nanotori

Abstract Atom-bond-connectivity (ABC) indices are obtained in analytical forms for graphene sheets, zigzag single walled carbon nanotubes (SWCNTs), and single walled carbon nanotori in terms of number of rings (r) that measures the length and the number of hexagons in between two rings (h) that dictates the width of the concerned systems. The procedures followed for ABC index have been used to obtain the expressions of augmented Zagreb and Randić indices for such systems. Logarithm of ABC indices of zigzag SWCNTs are found to correlate linearly well with the bond dissociation energies per C–C bond and the Young’s moduli of said SWCNTs with fixed number of rings (r) but varying number of hexagons (h) in between two successive rings. The plot of logarithm of ABC index versus Young’s modulus of such SWCNTs in varying both r and h simultaneously is not a straight line but fits well with the sigmoidal (Boltzmann) curve. Wiener index, one of the important distance based index, has recently been found to have similar correlations with the concerned properties of such systems. Similar plots would appear for the said properties of the zigzag SWCNTs with other degree-based indices like augmented Zagreb and Randić indices, as have been indicated from their respective expressions obtained.

Design of High-Frequency Carbon Nanotube-Carbon Nanotorus Oscillators for Energy Harvesting: A Molecular Dynamics Study.

The objective of this study is to examine the feasibility of using carbon-based nanostructures as nano-oscillators for future nanoelectromechanical applications such as energy harvesting devices and vibration sensing. The proposed nano-oscillator is comprised of a carbon nanotube (CNT) oscillating through a fixed carbon nanotorus molecule. For the first time in the literature, molecular dynamics (MD) simulations in conjunction with the Tersoff-Brenner (TB) and 6-12 Lennard-Jones (LJ) potential functions are adopted to determine the molecular interactions of the introduced nanodevice. To simulate the oscillatory behavior, two different schemes, namely, rigid and flexible, are considered. A detailed parametric study is performed to investigate the effects of rigidity, flexibility, and size of nanostructures as well as initial velocity on the force distribution and time histories of displacement and velocity of the core. Numerical results reveal that unlike the rigid oscillators, the flexible oscillators damp out within a few cycles. It is shown that the escape velocity of the flexible scheme is ∼6 times greater than that of the rigid scheme. The operating frequency and the generated power of rigid and flexible schemes under different system parameters are also calculated and compared. It is demonstrated that with increasing the ratio of nanotube-to-nanotorus diameter, the operating frequencies of both schemes decrease, while the generated powers do not behave monotonically. For a determined system parameter, it is observed that the flexible scheme provides higher operating frequencies compared to the rigid one. Moreover, considering that the initial velocity of the system is identical to the escape velocity, the generated power of the flexible scheme is calculated to be ∼14 times greater than that of the rigid scheme.

Structural characterization of nanomaterials C4C8

Topological indices are the numerical parameters of molecular graphs that characterise their behaviour and are mathematical invariant that preserves chemical and material properties. In a QSAR/QSPR study, physico-chemical properties and topological indices are studied. In this research, we shall calculate forgotten topological, inverse sum, the general sum connectivity and the first multiplicative atom–bond connectivity indices of carbon nanotube and nanotorus. The main motivation here is the molecular graphs of the nano-chemical compound nanotubes and nanotorus. While the central and latest point of convergence of our discussion is to provide a ‘ graphical trend and relative comparison’ of these derived topological descriptors of these materials that will make them more useful and comparative for chemists, nano and material scientists and would open a new graphical horizon towards material sciences and chemical engineering.

On multiplicative universal Zagreb and its subsequent indices of C4C8 carbon nanostructures

Mathematical chemistry studies the chemical structure of molecules. Topological indices are numerical values which associates the chemical structure with the physical and chemical properties. Multiplicative Universal Zagreb indices are generalized degree-based topological indices which gave rise to several indices like first and second multiplicative, Zagreb and hyper-Zagreb indices, multiplicative sum and product conductivity indices. This research is designed to study the first and second multiplicative Universal Zagreb indices of carbon nanostructures (carbon nanosheet, nanotube and nanotorus) of the same chemical formula [Formula: see text] We also depict the values of first and second multiplicative, Zagreb and hyper-Zagreb indices as well as multiplicative sum and product connectivity indices for the mentioned structures. The graphical comparison for each of the multiplicative Zagreb indices is presented for all the carbon nanostructures with the same chemical formula [Formula: see text]

Flip effect of carbon nanotori

Flip effect of carbon nanotori

Carbon Nanotori Reinforced Lubricants in Plastic Deformation Processes

This research presents the effects of carbon nanotori structures (CNst) dispersed as reinforcement for metal-working and metal-forming lubricants. Synthetic (SL) and deep drawing (DD) nanolubricants were prepared following a two-step method at 0.01 wt.%, 0.05 wt.%, and 0.10 wt.% filler fractions. Slight increases in viscosity (<6%) for nanolubricants were observed as filler fraction was increased through various measured temperatures. Tribological behavior of nanolubricants displayed superb improvements under antiwear and extreme pressure conditions. The load carrying capacity (poz) increased by 16% and 22% at merely 0.01 wt.% CNst reinforcement and up to 73% and 107% at 0.10 wt.% filler fraction for SL and DD nanolubricants, respectively, compared to conventional materials. Additionally, at 0.10 wt.% wear scar evaluations showed a highest benefit of 16% and 24%, for SL and DD nanolubricants, respectively. This enhancement is attributed to diverse mechanisms such as rolling/sliding and load bearing effects, tribofilm formation, and CNst tribosintering behavior (at high pressures) onto metallic surfaces due to nanostructures size and morphology and their interlayer relationship among conventional lubricants.

Numerical study of rotational dynamics of carbon nanotori during intermolecular interaction

The group dynamics of the motion of a toroidal carbon molecules is investigated using the approaches of classical mechanics. The model of pair interaction of non-polar particles is used to describe the motion of molecules. The ability of group of nanotori to perform coordinated and directed movements caused by the van der Waals forces is analyzed. The influence of the speed of rotation of molecules on the emergence and suppression of group movement is studied.

Molecular Dynamics Study of Collective Behavior of Carbon Nanotori in Columnar Phase

Supramolecular interaction of carbon nanotori in a columnar phase is described using the methods of classical molecular dynamics. The collective behavior and dynamic properties of toroidal molecules arising under the action of the van der Waals forces are studied. The conditions under which columnar structures based on molecular tori become unstable and rearrange into another structure are investigated. The reasons for the appearance of two types of directed rotational motion from the chaotic motion of molecules are discussed.

A comparison of tribological properties of nanolubricants containing carbon nanotori and additional additives

This work presents the effects of five inorganic nanoparticles as additives, i.e., CNp (carbon nanotori particles), TiO2, MoS2, MoO3, and HcNT (halloysite clay nanotubes), in three different lubricants (oil-based, grease, and water-based). Nanolubricants were prepared by adding 1 wt% particles into each type of lubricant. Tribological properties of nanolubricants were determined and compared under anti-wear (AW) and extreme pressure (EP) conditions. CNp showed a decrease in coefficient of friction (COF) by 22% when added to water-based lubricant. Additionally, CNp demonstrated an improvement in limiting pressure of seizure (poz) of 74%, 52%, and 1621% for oil-based lubricant, grease, and water-based lubricant, respectively. Comparing 1 wt% CNp added to water-based lubricant with oil-based lubricant and grease, the improvements become outstanding under EP conditions. An increase in poz by 2479% compared to oil-based lubricant, and 789% compared to grease, was observed. In addition, a decrease of 66–69% in average wear scar diameter (AWSD) was obtained in comparison to oil-based lubricant and grease. Tribological mechanisms of carbon nanotori provide a rolling/sliding effect under AW conditions, and a load-bearing effect under EP conditions.

Dynamic state of columnar structures formed on the basis of carbon nanotori

In this work, the integral potential of the C180 nanotori is constructed. The angular corrections in the law of distribution of the interaction energy are found, which turned out to be valid for all tori with a small inner radius. Using this potential, a characteristic fragment of a columnar crystal structure was calculated. The amplitude-frequency characteristics of vibrations and angular vibrations of a typical torus of the structure located in the center of the selected elementary fragment have been determined.

Energy stability and electronic properties of carbon nanotorus at a localized breaking of interatomic bonds: computer modeling

This paper is devoted to the study of the dynamic processes that occur in the carbon nanotorus during localized breaking of interatomic bonds, and to the analysis of the influence of these processes on the electronic properties of carbon nanotorus. The object of research is a carbon nanotorus with chirality indices (13, 0) with a diameter of 20 nm and a thickness of 1 nm obtained as a result of defect-free folding of a zigzag carbon nanotube of appropriate geometric dimensions into a ring. The behavior of the nanotorus is modeled by the molecular dynamics method using a modified Brenner potential to describe the interaction between atoms. It is shown that over time, the nanotorus straightens into a nanotube, while maintaining energy stability. It is found that the process of nanotorus straightening is accompanied by the appearance of deformation wave-like bends propagating at a speed of 200 m/s along the atomic network of the structure. These bends lead to deformation of the nanotorus and numerous local breaks in the bonds between atoms. However, broken bonds are restored within a few femtoseconds before the structure relaxes in energy, therefore, in general, the atomic framework of the nanotorus remains defect-free after rectification. The results of calculating the distribution of the density of electronic states (DOS) of a nanotorus by the self-consistent charge density functional tight-binding (SCC-DFTB) quantum method showed that at the moment of localized breaking of interatomic bonds around the circumference of the tubular framework, the nanotorus loses its semiconductor properties, becoming a gapless conductor. The discovered physical phenomenon explains the process of nanotorus formation during synthesis accompanied by multiple ruptures of the nanotori and reverse closure of the nanotubes into the nanotori.

On Three Constructions of Nanotori

There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized honeycomb tori. Altshuler showed that his method gives all non-isomorphic nanotori, but this was not known for the other two constructions. Here, we show that these three approaches are equivalent and give explicit formulas that convert parameters of one construction into the parameters of the other two constructions. As a consequence, we obtain that the other two approaches also construct all nanotori. The four parameters construction is mainly used in chemistry and physics to describe carbon nanotori molecules. Some properties of the nanotori can be predicted from these four parameters. We characterize when two different quadruples define isomorphic nanotori. Even more, we give an explicit form of all isomorphic nanotori (defined with four parameters). As a consequence, infinitely many 4-tuples correspond to each nanotorus; this is due to redundancy of having an “extra” parameter, which is not a case with the other two constructions. This result significantly narrows the realm of search of the molecule with desired properties. The equivalence of these three constructions can be used for evaluating different graph measures as topological indices, etc.

Tensor and Cartesian products for nanotori, nanotubes and zig–zag polyhex nanotubes and their applications to 13C NMR spectroscopy

We have developed novel topological techniques to generate distance degree vector sequences (DDS) and distance degree scalar sequences(SS) of tensor and Cartesian products of graphs. We establish that the tensor products of two distance degree regular graphs is distance degree regular. We apply the mathematical techniques thus developed for both tensor and Cartesian products to enumerate NMR signals and intensity patterns through the partitioning of equivalence classes accomplished by the use of distance degree vector sequences. In particular the techniques are applied to several nano materials such as carbon nanotori, monocyclic cylindrical nanotubes and zig–zag polyhex carbon nanotubes. It is shown that DDS sequences satisfactorily partition carbon vertices into equivalence classes for these nanomaterials. We also demonstrate applications of the developed techniques to diagrammatic representations of energy decompositions in molecular interactions.

Inorganic nanorings and nanotori: State of the art

Abstract

Topologically Unique Molecular Nanocarbons.

As new forms of carbon are unearthed, they invariably transform the scientific landscape. Numerous researchers have been inspired to discover the unique characteristics of these fascinating materials, consistently leading to the development of important technological innovations in materials science. Recently, studies on the preparation of molecular nanocarbons (small molecule analogues of larger carbon nanostructures) by precision organic synthesis have attracted much attention. Cycloparaphenylene (CPP), the substructure of carbon nanotubes (CNTs), is the oldest of such organic molecules, and since 2008 the successful synthesis of CPP dramatically advanced the synthetic chemistry of molecular nanocarbons. In fact, as pioneering research, we succeeded in producing carbon nanotubes using seed CPP molecules in 2013. This method represented an important landmark in the quest for controlling the diameter of CNTs via utilization of a well-defined small molecule as a template. Other avenues of research on graphene nanoribbons and partial structures of fullerenes such as corannulene and sumanene are also highly active at the current time. On the other hand, carbon forms with nontrivial topologies, i.e., topological nanocarbons, are virtually unexplored. In addition to the 3D network structures represented by the Mackay crystal, many topologically complex structures have been envisioned. To date, there is no rational approach toward the bottom-up synthesis of these carbon structures. As with the case of fullerenes and CNTs, access to these unique carbon structures should undoubtedly revolutionize a wide range of sciences. This Account highlights our efforts toward the synthesis of topologically unique molecular nanocarbons. Starting from CPP as the topologically simple subunit, we have successfully created novel molecular nanocarbons that have more complexed topologies. The first topic is carbon nanobelts, fully fused cylinder-shaped molecular nanocarbons representing the segment structure of armchair-type CNTs. The second topic is carbon nanocages, molecular nanocarbons having a "three-holed" topology representing the joint unit of branched CNTs. The third and fourth topics are all-benzene catenanes consisting of two CPP rings and an all-benzene trefoil knot topologically related to a carbon nanotorus. The world of nanocarbon molecules is only limited by our imagination and creativity. As history has proved, the synthesis of new forms of carbon and topologically complex molecules has always subsequently led to new fields and applications associated with their unforeseen properties and functions.

Organometallic complexes of carbon nanotori.

New organometallic complexes of carbon nanotori were designed and theoretically described by means of density functional theory. After a systematic structural search, it was found that energetically favorable complexes were formed by the metal atoms Cr and Ni, both located at the center of a nanotorus with diameter around 5Å and 120 carbon atoms. The nature of the metal-nanotorus interaction shows a partial polar-covalent character, different from those found in other well-known organometallic compounds. Interactions were studied through molecular orbitals and thermodynamic stability. Ten bonds are set up between the metal atom and nanotorus, confirmed by electron density topology analysis, showing ten bond critical points among the metal atoms and the surrounding carbon atoms. The response of the induced electron current caused by a magnetic field perpendicular to the nanotorus was analyzed to explain the electron delocalization and aromaticity of the complexes. Only in the case of the chromium complex, the electron density is fully delocalized on the whole complex. According to a geometry-based index of aromaticity, interaction with the metal atom only changes the aromatic character of the carbon rings slightly. Also, induced currents were used to elucidate the presence of a ferrotoroidal behavior. The isolated nanotorus and its compound with a single Ni atom have well-defined ferrotoroidal behavior because they present broken symmetries and could help to design a topological insulator. Meanwhile, the nanotorus with a Cr atom at the center lacks ferrotoroidal behavior as a consequence of the absence of magnetic vortices. Graphical abstract Organometallic complex of carbon nanotoruswith chromium and induced currents on it by applying an external magnetic field.

A Review of Geometry, Construction and Modelling for Carbon Nanotori

After the discovery of circular formations of single walled carbon nanotubes called fullerene crop circles, their structure has become one of the most researched amongst carbon nanostructures due to their particular interesting physical properties. Several experiments and simulations have been conducted to understand these intriguing objects, including their formation and their hidden characteristics. It is scientifically conceivable that these crop circles, nowadays referred to as carbon nanotori, can be formed by experimentally bending carbon nanotubes into ring shaped structures or by connecting several sections of carbon nanotubes. Toroidal carbon nanotubes are likely to have many applications, especially in electricity and magnetism. In this review, geometry, construction, modelling and possible applications are discussed and the existing known analytical expressions, as obtained from the Lennard-Jones potential and the continuum approximation, for their interaction energies with other nanostructures are summarised.

Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

ABSTRACTIn this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.