Catalyst volume to surface area constraints for nucleating carbon nanotubes

In this Article, we describe a carbon nanotube formation model in which sp2 carbon hemispheres form the embryonic caps from which a nanotube can grow. This requirement leads to a single wall carbon nanotube formation window concomitant with our systematic experimental findings, which show upper and lower diameter limits. Further, the successful formation of a nucleation cap (hemisphere) is governed by catalyst particle volume to surface area considerations. Single wall carbon nanotubes are only obtained when both the nanotube formation window and the precipitating catalyst size distribution cross over. The extent to which these two windows overlap establishes the mean diameter and diameter distribution of the obtained single wall carbon nanotubes.     

Carbon nanotubes in benzene: internal and external solvation

The structure and dynamics of benzene inside and outside of single-walled carbon nanotubes (SWNTs) in the (n,n) armchair configuration are studied via molecular dynamics computer simulations. Irrespective of the nanotube diameter, benzene molecules form cylindrical solvation shell structures on the outside of the nanotubes. Their molecular planes near the SWNTs in the first external solvation shell are oriented parallel to the nanotube surface, forming a π-stacked structure between the two. By contrast, the benzene distributions in the interior of the SWNTs are found to vary markedly with the nanotube diameter. In the case of the (7,7) and (8,8) nanotubes, internal benzene forms a single-file distribution, either in a vertex-to-vertex (n = 7) or face-to-face (n = 8) orientation between two neighboring molecules. Inside a slightly wider (9,9) nanotube channel, however, a cylindrical single-shell distribution of benzene arises. A secondary solvation structure, which begins to appear inside (10,10), develops into a full structure separate from the first internal solvation shell in (12,12). The ring orientation of internal benzene is generally parallel to the nanotube wall for n = 9-12, while it becomes either slanted with respect to (n = 7), or perpendicular to (n = 8), the nanotube axis. The confinement inside the small nanotube pores exerts a strong influence on the dynamics of benzene. Both translational and rotational dynamics inside SWNTs are slower and more anisotropic than in liquid benzene. It is also found that reorientational dynamics of internal benzene deviate dramatically from the rotational diffusion regime and change substantially with the nanotube diameter.     

Model of carbon nanotube growth through chemical vapor deposition

This Letter outlines a model to account for the catalyzed growth of nanotubes by chemical vapor deposition. It proposes that their formation and growth is an extension of other known processes in which graphitic structures form over metal surfaces at moderate temperatures through the decomposition of organic precursors. Importantly, the model also states that the form of carbon produced depends on the physical dimensions of the catalyzed reactions. Experimental data are presented that correlate nanotube diameters to the size of the catalyst particles. Nanotube stability as a function of nanotube type, length and diameter are also investigated through theoretical calculations.     

Theoretical Study on Mechanism of Cycloadditional Reaction Between Dichloro-Germylidene and Formaldehyde

Mechanism of the cycloadditional reaction between singlet dichloro-germylidene and formaldehyde has been investigated with MP2/6-31G^* method, including geometry opti-mization, vibrational analysis and energies for the involved stationary points on the poten-tial energy surface. From the potential energy profile, we predict that the cycloaddition reaction between singlet dichloro-germylidene and formaldehyde has two competitive dom-inant reaction pathways, going with the formation of two side products (INT3 and INT4), simultaneously. Both of the two competitive reactions consist of two steps, two reactants firstly form a three-membered ring intermediate INT1 and a twisted four-membered ring intermediate INT2, respectively, both of which are barrier-free exothermic reactions of 41.5 and 72.3 kJ/mol; then INT1 isomerizes to a four-membered ring product P1 via transition state TS1, and INT2 isomerizes to a chlorine-transfer product P2 via transition state TS2,with the barriers of 2.9 and 0.3 kJ/mol, respectively. Simultaneously, P1 and INT2 further react with formaldehyde to form INT3 and INT4, respectively, which are also barrier-free exothermic reaction of 74.9 and 88.1 kJ/mol.     

Semiconductor quantum dot-inorganic nanotube hybrids

A synthetic route for preparation of inorganic WS(2) nanotube (INT)-colloidal semiconductor quantum dot (QD) hybrid structures is developed, and transient carrier dynamics on these hybrids are studied via transient photoluminescence spectroscopy utilizing several different types of QDs. Measurements reveal efficient resonant energy transfer from the QDs to the INT upon photoexcitation, provided that the QD emission is at a higher energy than the INT direct gap. Charge transfer in the hybrid system, characterized using QDs with band gaps below the INT direct gap, is found to be absent. This is attributed to the presence of an organic barrier layer due to the relatively long-chain organic ligands of the QDs under study. This system, analogous to carbon nanotube-QD hybrids, holds potential for a variety of applications, including photovoltaics, luminescence tagging and optoelectronics.     

Ab Initio Study on the Mechanism of Cycloaddition Reaction between Silylene Carbene （H_2Si=C：） and Acetone

The mechanism of cycloaddition reaction between singlet silylene carbene and acetone has been investigated with CCSD(T)//MP2/6-31G method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. One consists of two steps: (1) the two reactants (R1, R2) firstly form a four-membered ring intermediate (INT4) through a barrier-free exothermic reaction of 585.9 kJ/mol; (2) Then intermediate (INT4) isomerizes to CH3-transfer product (P4.1) via a transition state (TS4.1) with energy barrier of 5.3 kJ/mol. The other is as follows: on the basis of intermediate (INT4) created between R1 and R2, intermediate (INT4) further reacts with acetone (R2) to form the intermediate (INT5) through a barrier-free exothermic reaction of 166.3 kJ/mol; Then, intermediate (INT5) isomerizes to a silicic bis-heterocyclic product (P5) via a transition state (TS5), for which the barrier is 54.9 kJ/mol. The presented rule of this reaction: the [2+2] cycloaddition effect between the π orbital of silylene carbene and the π orbital of π-bonded compounds leads to the formation of a four-membered ring intermediate (INT4); The unsaturated property of C atom from carbene in the four-membered ring intermediate (INT4) results in the generation of CH3-transfer product (P4.1) and silicic bis-heterocyclic compound (P5).     

Theoretical study of the mechanism of cycloaddition reaction between dichloro-germylidene and acetaldehyde

The mechanism of the cycloadditional reaction between singlet dichloro-germylidene(R1) and (acetaldehyde(R2) has been investigated with MP2/6-31G* method, including geometry optimization, vibrational analysis and energies for the involved stationary points on the potential energy surface. From the potential energy profile, we predict that the cycloaddition reaction between singlet dichloro-germylidene and acetaldehyde has two competitive dominant reaction pathways. Going with the formation of two side products (INT3 and INT4), simultaneously. The two competitive reactions both consist of two steps: (1) two reactants firstly form a three-membered ring intermediate (INT1) and a twisted four-membered ring intermediate (INT2), respectively, both of which are barrier-free exothermic reactions of 44.5 and 63.0 kJ/mol; (2) then INT1 and INT2 further isomerize to a four-membered ring product (P1) and a chlorine-transfer product (P2) via transitions (TS1 and TS2), respectively, with the barriers of 9.3 and 1.0 kJ/mol; simultaneously, P1 and INT2 react further with acetaldehyde(R2) to give two side products (INT3 and INT4), respectively, which are also barrier-free exothermic reaction of 65.4 and 102.7 kJ/mol.     

碳离子碰撞单壁碳纳米管的动力学

采用分子动力学方法研究了碳离子碰撞碳纳米管中顶位、键中心和六元环中心的动力学过程。通过分析低、中、高3种入射能分别对碰撞过程的影响,探索了典型缺陷形成的微观演化过程。研究结果表明,碰撞碳纳米管中不同空间位置,其碰撞结果差异较大,其中顶位碰撞阈能最低,约为20 eV;碰撞六元环中心时碳管会发生严重变形,损伤最为严重。通过分析入射离子动能,碳纳米管热动能、质心动能以及势能随时间的演化规律,阐述了碰撞过程中的能量转移机制。     

碳离子碰撞单壁碳纳米管的动力学

采用分子动力学方法研究了碳离子碰撞碳纳米管中顶位、键中心和六元环中心的动力学过程。通过分析低、中、高3种入射能分别对碰撞过程的影响,探索了典型缺陷形成的微观演化过程。研究结果表明,碰撞碳纳米管中不同空间位置,其碰撞结果差异较大,其中顶位碰撞阈能最低,约为20 e V;碰撞六元环中心时碳管会发生严重变形,损伤最为严重。通过分析入射离子动能,碳纳米管热动能、质心动能以及势能随时间的演化规律,阐述了碰撞过程中的能量转移机制。     

Adsorption and diffusion of molecular nitrogen in single wall carbon nanotubes

Using molecular simulation, the adsorption and self-diffusion of diatomic nitrogen molecules inside a single wall carbon nanotube have been studied over a range of nanotube diameters (8.61-15.66 A) and loadings at temperatures of 100 and 298 K. Nitrogen adsorption energy is found to increase as the nanotube diameter is reduced toward the molecular diameter of nitrogen. A discrete organization of the nitrogen into adsorbed layers is observed at high loadings that follows a regular progression determined primarily by geometric considerations. The formation of an adsorbate core at the center of the nanotube is found to increase the self-diffusion of nitrogen. A "wormlike" phase is found for the adsorbed nitrogen in the (15, 0) carbon nanotube at high loadings and at 100 K.     

Theoretical study of mechanism of forming a silapolycyclic compound between methylenesilylene and acetone

The mechanism of the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD(T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming a silapolycyclic compound between singlet methylenesilylene and acetone has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (I) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 46.2 kJ/mol; (II) intermediate (INT1) then isomerizes to a planar four‐membered ring product (P3) via transition state (TS3) with an energy barrier of 47.1 kJ/mol; (III) planar four‐membered ring product (P3) further reacts with acetone (R2) to form an intermediate (INT4), which is also a barrier‐free exothermic reaction of 40.0 kJ/mol; (IV) intermediate (INT4) isomerizes to a silapolycyclic compound (P4) via transition state (TS4) with an energy barrier of 57.0 kJ/mol. Second dominant reaction pathway consists of three steps: (I) the two reactants (R1, R2) first form a four‐membered ring intermediate (INT2) through a barrier‐free exothermic reaction of 0.5 kJ/mol; (II) INT2 further reacts with acetone (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 45.4 kJ/mol; (III) intermediate (INT5) isomerizes to a silapolycyclic compound (P5) via transition state (TS5) with an energy barrier of 49.3 kJ/mol. P4 and P5 are isomeric compounds. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Investigation of possible structures of silicon nanotubes via density-functional tight-binding molecular dynamics simulations and ab initio calculations

We show, computationally, that single-walled silicon nanotubes (SiNTs) can adopt a number of distorted tubular structures, representing respective local energy minima, depending on the theory used and the initial models adopted. In particular, "gearlike" structures containing alternating sp(3)-like and sp(2)-like silicon local configurations have been found to be the dominant structural form for SiNTs via density-functional tight-binding molecular dynamics simulations (followed by geometrical optimization using Hartree-Fock or density function theory) at moderate temperatures (below 100 K). The gearlike structures of SiNTs deviate considerably from, and are energetically more stable than, the smooth-walled tubes (the silicon analogues of single-walled carbon nanotubes). They are, however, energetically less favorable than the "string-bean-like" SiNT structures previously derived from semiempirical molecular orbital calculations. The energetics and the structures of gearlike SiNTs are shown to depend primarily on the diameter of the tube, irrespective of the type (zigzag, armchair, or chiral). In contrast, the energy gap is very sensitive to both the diameter and the type of the nanotube.     

交流放电法合成多种形态的碳纳米管

碳纳米管的发现［１］引起了科学界的广泛重视,人们对于这种新型材料在纳米导线、高强纤维、超导等方面的应用寄予厚望．目前,合成碳纳米管的方法主要是采用不等径石墨棒直流放电,在阴极上得到含有碳纳米管的沉积物［２］．对于碳纳米管的应用,有关的理论研究［３］及...     

Theoretical study on the mechanism of cycloaddition reaction between dimethyl germylidene and formaldehyde

The cycloaddition mechanism of the reaction between singlet dimethyl germylidene and formaldehyde has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated with CCSD (T)//MP2/6-31G* method. From the potential energy profile, we predict that the cycloaddition reaction between singlet dimethyl germylidene and formaldehyde has two dominant reaction pathways. First dominant reaction pathway consists of three steps: (1) the two reactants (R1, R2) firstly form an intermediate INT1a through a barrier-free exothermic reaction of 43.0 kJ/mol; (2) INT1a then isomerizes to a four-membered ring compound P1 via a transition state TS1a with an energy barrier of 24.5 kJ/mol; (3) P1 further reacts with formaldehyde(R2) to form a germanic heterocyclic compound INT3, which is also a barrier-free exothermic reaction of 52.7 kJ/mol; Second dominant reaction pathway is as following: (1) the two reactants (R1, R2) firstly form a planar four-membered ring intermediate INT1b through a barrier-free exothermic reaction of 50.8 kJ/mol; (2) INT1b then isomerizes to a twist four-membered ring intermediate INT1.1b via a transition state TS1b with an energy barrier of 4.3 kJ/mol; (3) INT1.1b further reacts with formaldehyde(R2) to form an intermediate INT4, which is also a barrier-free exothermic reaction of 46.9 kJ/mol; (4) INT4 isomerizes to a germanic bis-heterocyclic product P4 via a transition state TS4 with an energy barrier of 54.1 kJ/mol.     

Ab initio Study of Mechanism of Forming Germanic Hetero-Polycyclic Compound between Germylene Carbene (H2Ge=C: ) and Formaldehyde

The mechanism of the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by CCSD (T)//MP2/6‐31G* method. From the potential energy profile, we predict that the cycloaddition reaction of forming germanic hetero‐polycyclic compound between singlet germylene carbene and formaldehyde has two competitive dominant reaction pathways. First dominant reaction pathway consists of four steps: (1) the two reactants (R1, R2) first form an intermediate (INT1) through a barrier‐free exothermic reaction of 117.5 kJ/mol; (2) intermediate (INT1) then isomerizes to a four‐membered ring compound (P2) via a transition state (TS2) with an energy barrier of 25.4 kJ/mol; (3) four‐membered ring compound (P2) further reacts with formaldehyde (R2) to form an intermediate (INT3), which is also a barrier‐free exothermic reaction of 19.6 kJ/mol; (4) intermediate (INT3) isomerizes to a germanic bis‐heterocyclic product (P3) via a transition state (TS3) with an energy barrier of 5.8 kJ/mol. Second dominant reaction pathway is as follows: (1) the two reactants (R1, R2) first form an intermediate (INT4) through a barrier‐free exothermic reaction of 197.3 kJ/mol; (2) intermediate (INT4) further reacts with formaldehyde (R2) to form an intermediate (INT5), which is also a barrier‐free exothermic reaction of 141.3 kJ/mol; (3) intermediate (INT5) then isomerizes to a germanic bis‐heterocyclic product (P5) via a transition state (TS5) with an energy barrier of 36.7 kJ/mol.     

Theoretical study of mechanism of cycloaddition reaction between dichloro‐germylene carbene (Cl2GeC:) and aldehyde

The mechanism of the cycloaddition reaction between singlet dichloro‐germylene carbene and aldehyde has been investigated with MP2/6‐31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by zero‐point energy and CCSD (T)//MP2/6‐31G* method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. The channel (A) consists of four steps: (1) the two reactants (R1, R2) first form an intermediate INT2 through a barrier‐free exothermic reaction of 142.4 kJ/mol; (2) INT2 then isomerizes to a four‐membered ring compound P2 via a transition state TS2 with energy barrier of 8.4 kJ/mol; (3) P2 further reacts with aldehyde (R2) to form an intermediate INT3, which is also a barrier‐free exothermic reaction of 9.2 kJ/mol; (4) INT3 isomerizes to a germanic bis‐heterocyclic product P3 via a transition state TS3 with energy barrier of 4.5 kJ/mol. The process of channel (B) is as follows: (1) the two reactants (R1, R2) first form an intermediate INT4 through a barrier‐free exothermic reaction of 251.5 kJ/mol; (2) INT4 further reacts with aldehyde (R2) to form an intermediate INT5, which is also a barrier‐free exothermic reaction of 173.5 kJ/mol; (3) INT5 then isomerizes to a germanic bis‐heterocyclic product P5 via a transition state TS5 with an energy barrier of 69.4 kJ/mol. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Carbon nanotube formation and growth via particle-particle interaction

Carbon nanotubes are observed to form under a wide range of temperatures, pressures, reactive agents, and catalyst metals. In this paper we attempt to rationalize this body of observations reported in the literature in terms of fundamental processes driving nanotube formation. Many of the observed effects can be attributed to the interaction of three key processes: surface catalysis and deposition of carbon, diffusive transport of carbon, and precipitation effects. A new nanotube formation mechanism is proposed that describes the nanotube structures observed experimentally in a premixed flame and can account for certain shortcomings of the prevailing mechanism that has been repeatedly applied to explain nanotube formation in nonflame environments. The interacting particle model (IPM) attributes the initiation of nanotube growth to the physical interaction between catalyst particles. Coalescence of two (or more) catalyst particles leads to partial blocking of the particle surface, causing a disparity in carbon deposition over the particle surface. The resulting concentration gradient generates a net diffusive flux toward the interparticle contact point. Dimers that separate in this condition can support continuous nanotube growth between the particles. The model can also be extended to multiple particles to account for more complex morphologies. The IPM is consistent with many of the structures observed in the flame-produced material. The validity of the model is evaluated through analysis of diffusion dynamics and a force analysis of particle binding and separation. The IPM is also discussed in relation to identifying the requirements and best conditions to support nanotube growth in the premixed flame. The formation of nanotubes between particles as described by the IPM indicates that a single mechanism cannot completely describe nanotube synthesis; more likely, multiple pathways exist with varying rates that depend on specific process conditions.     

Theoretical study of mechanism of cycloaddition reaction between singlet dichlorosilylene carbene (Cl<Subscript>2</Subscript>Si=C:) and formaldehyde

The mechanism of the cycloaddition reaction between singlet dichlorosilylene carbene (Cl₂Si=C:) and formaldehyde has been investigated with MP2/6-31G* method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. The energies of the different conformations are calculated by Zero-point energy and CCSD (T)//MP2/6-31G* method. From the potential energy profile, it can be predicted that the reaction has two competitive dominant reaction pathways. The first dominant reaction pathway consists of two steps: (1) the two reactants (R1, R2) firstly form a four-membered ring intermediate (INT4) through a barrier-free exothermic reaction of 387.9 kJ/mol; (2) intermediate (INT4) then isomerizes to H-transfer product (P4.2) via a transition state (TS4.2) with energy barrier of 4.7 kJ/mol. The second dominant reaction pathway as follows: on the basis of intermediate (INT4) created between R1 and R2, intermediate (INT4) further reacts with formaldehyde (R2) to form the intermediate (INT5) through a barrier-free exothermic reaction of 158.3 kJ/mol. Then, intermediate (INT5) isomerizes to a silicic bis-heterocyclic product (P5) via a transition state (TS5), for which the barrier is 40.1 kJ/mol.     

Entropy of single-file water in (6,6) carbon nanotubes

We used molecular dynamics simulations to investigate the thermodynamics of filling of a (6,6) open carbon nanotube (diameter D = 0.806 nm) solvated in TIP3P water over a temperature range from 280 K to 320 K at atmospheric pressure. In simulations of tubes with slightly weakened carbon-water attractive interactions, we observed multiple filling and emptying events. From the water occupancy statistics, we directly obtained the free energy of filling, and from its temperature dependence the entropy of filling. We found a negative entropy of about -1.3 k(B) per molecule for filling the nanotube with a hydrogen-bonded single-file chain of water molecules. The entropy of filling is nearly independent of the strength of the attractive carbon-water interactions over the range studied. In contrast, the energy of transfer depends strongly on the carbon-water attraction strength. These results are in good agreement with entropies of about -0.5 k(B) per water molecule obtained from grand-canonical Monte Carlo calculations of water in quasi-infinite tubes in vacuum under periodic boundary conditions. Overall, for realistic carbon-water interactions we expect that at ambient conditions filling of a (6,6) carbon nanotube open to a water reservoir is driven by a favorable decrease in energy, and opposed by a small loss of water entropy.     

Theoretical studies of mechanisms of cycloaddition reaction between difluoromethylene carbene and acetone

Mechanisms of the cycloaddition reaction between singlet difluoromethylene carbene and acetone have been investigated with the second‐order Møller–Plesset (MP2)/6‐31G* method, including geometry optimization and vibrational analysis. Energies for the involved stationary points on the potential energy surface (PES) are corrected by zero‐point energy (ZPE) and CCSD(T)/6‐31G* single‐point calculations. From the PES obtained with the CCSD(T)//MP2/6‐31G* method for the cycloaddition reaction between singlet difluoromethylene carbene and acetone, it can be predicted that path B of reactions 2 and 3 should be two competitive leading channels of the cycloaddition reaction between difluoromethylene carbene and acetone. The former consists of two steps: (i) the two reactants first form a four‐membered ring intermediate, INT2, which is a barrier‐free exothermic reaction of 97.8 kJ/mol; (ii) the intermediate INT2 isomerizes to a four‐membered product P_2b via a transition state TS2b with an energy barrier of 24.9 kJ/mol, which results from the methyl group transfer. The latter proceeds in three steps: (i) the two reactants first form an intermediate, INT1c, through a barrier‐free exothermic reaction of 199.4 kJ/mol; (ii) the intermediate INT1c further reacts with acetone to form a polycyclic intermediate, INT3, which is also a barrier‐free exothermic reaction of 27.4 kJ/mol; and (iii) INT3 isomerizes to a polycyclic product P₃ via a transition state TS3 with an energy barrier of 25.8 kJ/mol. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007