We investigate vibration modes and their Raman activity of single-walled carbon nanotubes that are bent within their intrinsic elastic limits. By implementing novel boundary conditions for density-functional based tight-binding, and using non-resonant bond polarization theory, we discover that Raman activity can be induced by bending. Depending on the degree of bending, high-energy Raman peaks change their positions and intensities significantly. These effects can be explained by migration of nodes and antinodes along tube circumference. We discuss the challenge of associating the predicted spectral changes with experimental observations.
A simple empirical model and approach are introduced for calculation of the vibrational spectra of arbitrary single wall carbon nanotubes. Differently from the frequently used force constants description, the model employs only invariant quantities such as variations of lengths and angles. All the salient qualitative features of vibrational spectra of nanotubes naturally follow from the vibrational Hamiltonian of graphene upon its isometric mapping onto a cylindrical surface and without any ad hoc corrections. A qualitative difference with previous results is found in a parabolic, rather than …
We report a detailed study of the vibrational properties of BN single-walled nanotubes and of the BN monolayer. Our results have been obtained from a well-established Tight-Binding model complemented with an electrostatic model to account for the long-range interactions arising from the polar nature of the material, and which are not included in the Tight-Binding model. Our study provides a wealth of data for the BN monolayer and nanotubes, such as phonon band structure, vibrational density of states, elastic constants, etc. For the nanotubes we obtain the behavior of the optically active mode…
We have developed a pair-potential approach for the evaluation of van der Waals interaction between carbon nanotubes in bundles. Starting from a continuum model, we show that the intertube modes range from $5 cm^{-1}$ to $60 cm^{-1}$. Using a non-orthogonal tight-binding approximation for describing the covalent intra-tube bonding in addition, we confirme a slight chiral dependance of the breathing mode frequency and we found that this breathing mode frequency increase by $\sim$ 10 % if the nanotube lie inside a bundle as compared to the isolated tube.
Vibration reduction is of great importance in various engineering applications, and a material that exhibits good vibration damping along with high strength and modulus has become more and more vital. Owing to the superior mechanical property of carbon nanotube (CNT), new types of vibration damping material can be developed. This paper presents recent advancements, including our progresses, in the development of high-damping macroscopic CNT assembly materials, such as forests, gels, films, and fibers. In these assemblies, structural deformation of CNTs, zipping and unzipping at CNT connection …
A study based on ab initio calculations is presented on the estructural, elastic, and vibrational properties of single-wall carbon nanotubes with different radii and chiralities. We use SIESTA, an implementation of pseudopotential-density-functional theory which allows calculations on systems with a large number of atoms per cell. Different quantities like bond distances, Young moduli, Poisson ratio and the frequencies of different phonon branches are monitored versus tube radius. The validity of expectations based on graphite is explored down to small radii, where some deviations appear relat…
Carbon nanotube (CNT) have been known to increase the heat transfer at the solid-liquid interfaces, but have a limitation due to the interfacial thermal resistance. Vibrational mismatch at the interface leads to this interfacial thermal resistance, which plays an important role in energy transfer at the boundary. Negligible work has been reported on the influence of CNT diameter on the resistance through the vibrational mismatch study. Molecular dynamics simulations have been performed to investigate the effect of CNT diameter on interfacial resistance between carbon nanotube (CNT) and water m…
We calculated the effects of structural distortions on the electronic structure of carbon nanotubes. The key modification of the electronic structure brought about by bending a nanotube involves an increased mixing of $σ$ and $π$-states. This mixing leads to an enhanced density-of-states in the valence band near the Fermi energy region. While in a straight tube the states accessible for electrical conduction are essentially pure C($2p_π$)-states, they acquire significant C($2sp_σ$) character upon bending. Bending also leads to a charge polarization of the C-C bonds in the deformed region remin…
We study 23 to 30 nm long suspended single-wall carbon nanotube quantum dots and observe both their stretching and bending vibrational modes. We use low-temperature DC electron transport to excite and measure the tubes' bending mode by making use of a positive feedback mechanism between their vibrations and the tunneling electrons. In these nano-electro-mechanical-systems (NEMS), we measure fundamental bending frequencies $f_{bend}\approx$ 75 - 280 GHz, and extract quality factors $Q \sim 10^{6}$. The NEMS' frequencies can be tuned by a factor of two with tension induced by mechanical breakjun…
Vibrational energy transfer from photo-excited single-wall carbon nanotubes (SWCNTs) to coupled proteins is a key to engineer thermally induced biological reactions such as photothermal therapy. Here, we explored vibrational energy transfer from the photo-excited SWCNTs to different adsorbed biological materials by means of a femtosecond pump-probe technique. We show that the vibrational relaxation time of the radial breathing modes (RBMs) in SWCNTs significantly depends on the structure of coupled materials, i.e. proteins or biopolymers, indicating the vibrational energy transfer is governed …
We present a lattice dynamics study of the vibrations of a linear chain of Xe adsorbates in groove positions of a bundle of carbon nanotubes. The characteristic phonon frequencies are calculated and the adsorbate polarization vectors discussed. Comparison of the present results with the ones previously published shows that the adsorbate vibrations cannot be treated as completely decoupled from the vibrations of carbon nanotubes and that a significant hybridization between the adsorbate and the tube modes occurs for phonons of large wavelengths.
We have generated and detected the radial-breathing mode of coherent lattice vibrations in single-walled carbon nanotubes using ultrashort laser pulses. Because the band gap is a function of diameter, these diameter oscillations cause ultrafast band gap oscillations, modulating interband excitonic resonances at the phonon frequencies (3-9 THz). Excitation spectra show a large number of pronounced peaks, mapping out chirality distributions in great detail.
In this paper we present the results on Raman-active modes calculation in achiral $(n,n)$ and $(n,0)$ carbon nanotubes (CNTs). vibrational spectra are derived as the eigenvalues of corresponding dynamical matrix at the $Γ$-point of Brillouin zone. Diagonal components and $α_{xy} (=α_{yx})$ are the only non-zero components of polarization tensor. Selection rules for Raman-active modes are determined by direct estimations of matrix elements responsible for the intensities of corresponding vibrational transitions. Few $E_{2g}$ modes can be non-Raman-active because of their ``fine'' vibrational st…
We study the influence of structural lattice fluctuations on the elastic electron transport in single-wall carbon nanotubes within a density-functional-based scheme. In the linear response regime, the linear conductance is calculated via configurational averages over the distorted lattice. Results obtained from a frozen-phonon approach as well as from molecular dynamics simulations are compared. We further suggest that the effect of structural fluctuations can be qualitatively captured by the Anderson model with bond disorder. The influence of individual vibrational modes on the electronic tra…
We have calculated the effects of structural distortions of armchair carbon nanotubes on their electrical transport properties. We found that the bending of the nanotubes decreases their transmission function in certain energy ranges and leads to an increased electrical resistance. Electronic structure calculations show that these energy ranges contain localized states with significant $σ$-$π$ hybridization resulting from the increased curvature produced by bending. Our calculations of the contact resistance show that the large contact resistances observed for SWNTs are likely due to the weak …
The electrical and chemical properties of carbon nanotubes vary significantly with different chirality and diameter, making the experimental determination of these structural properties important. Here, we show that the vibrational density of states (VDOS) contains information on the structure of carbon nanotubes, particularly at low frequencies. We show that the diameter and chirality of the nanotubes can be determined from the characteristic low frequency $L$ and $L'$ modes in the VDOS. For zigzag nanotubes, the $L$ peak splits into two peaks giving rise to another low energy $L"$ peak. The …
The structural, electronic, optical and vibrational properties of the collapsed (10,10) single-walled carbon nanotube bundle under hydrostatic pressure have been studied by the first-principles calculations. Some features are observed in the present study: First, a collapsed structure is found, which is distinct from both of the herringbone and parallel structures obtained previously. Secondly, a pseudo-gap induced by the collapse appears along the symmetry axis \textit{$Γ$X}. Thirdly, the relative orientation between the collapsed tubes has an important effect on their electronic, optical and…
In this paper, we proposed a lattice dynamic treatment for the total potential energy for single-walled carbon nanotubes (SWCNT's) which is, apart from a parameter for the non-linear effects, extracted from the vibrational energy of the planar graphene sheet. Based upon the proposal, we investigated systematically the relaxed lattice configuration for narrow SWCNT's, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties respected to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consisten…
A new formula for elastic bending modulus of monolayer graphene is derived analytically from an empirical potential for solid-state carbon-carbon bonds. Two physical origins are identified for the non-vanishing bending modulus of the atomically thin graphene sheet, one due to the bond angle effect and the other resulting from the bond order term associated with dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers are simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tange…
The facile synthesis and electronic properties of two-dimensional hybrid organic-inorganic perovskites (2D HOIPs) make these self-assembled systems an important class of energy materials. The basic building blocks of these materials include inorganic lattice frameworks that often consist of lead-halide octahedra and organic molecules possessing ammonium functional groups. Understanding the coupling between the inorganic and organic layers is key to unraveling how the electronic properties of 2D HOIPs relate to their structures. In this work, we leverage Raman spectroscopy measurements and firs…
A continuous model of double-walled carbon nanotube (DWCNT) low-frequency dynamics was constructed. In the frame of the approach proposed formation of a DWCNT low-frequency phonon spectrum from the ones of corresponding single-walled carbon nanotubes (SWCNTs) was considered. Environmental influence on the individual DWCNT phonon spectrum was studied. A combined method of van der Waals interlayer coupling coefficients evaluation was proposed, and it is based on Raman spectroscopy data and known values of graphite elastic moduli. Also DWCNT low-temperature specific heat was calculated. In the mo…
Recently, a new type of two-dimensional layered material, i.e. C3N, has been fabricated by polymerization of 2,3-diaminophenazine and used to fabricate a field-effect transistor device with an on/off current ratio reaching 5.5E10 (Adv. Mater. 2017, 1605625). Here we have performed a comprehensive first-principles study mechanical and electronic properties of C3N and related derivatives. Ab inito molecular dynamics simulation shows that C3N monolayer can withstand high temperature up to 2000K. Besides high stability, C3N is predicted to be a superior stiff material with high Young's modulus (10…
We use ab initio density functional calculations to study the chemical functionalization of single-wall carbon nanotubes and graphene monolayers by silyl (SiH3) radicals and hydrogen. We find that silyl radicals form strong covalent bonds with graphene and nanotube walls, causing local structural relaxations that enhance the sp3 character of these graphitic nanostructures. Silylation transforms all carbon nanotubes into semiconductors, independent of their chirality. Calculated vibrational spectra suggest that specific frequency shifts can be used as a signature of successful silylation.
We propose to use the damping signal of an oscillating cantilever in dynamic atomic force microscopy as a noninvasive tool to study the vibrational structure of the substrate. We present atomically resolved maps of damping in carbon nanotube peapods, capable of identifying the location and packing of enclosed Dy@C82 molecules as well as local excitations of vibrational modes inside nanotubes of different diameter. We elucidate the physical origin of damping in a microscopic model and provide quantitative interpretation of the observations by calculating the vibrational spectrum and damping of …
Moiré patterns are additional, long-range periodicities in twisted crystalline bilayers. They are known to fundamentally change the electronic states of the layers, but similar effects on their mechanical and vibrational properties have not been discussed so far. Here we show that the Moiré potential shifts the radial breathing mode in double walled carbon nanotubes (DWCNTs). The change of frequency is expected to be proportional to the shift in optical transition energies, which are induced by the Moiré patterns. To verify our model we performed resonant Raman scattering on purified and sorte…
In many applications, viscoelastic properties of reinforced composites need to be determined prior to their real service life. Such properties can be assured by destructive and non-destructive tests. In this paper, a novel non-destructive test (NDT) method based on flexural free vibration is introduced to investigate the viscoelastic properties of fiber-reinforced composites. Three different types of industrial fibers (carbon, glass, and hemp) and an unsaturated polyester resin were selected to produce bar-shaped composites via pultrusion technique. These composite bars were used in a simple N…
We develop a continuous theory of low-frequency dynamics for nanotubes with truly two-dimensional (2D) walls constituted by single-atom monolayer. In this frame topological bending elasticity of the monolayer is not related to its vanishing macroscopic thickness. The proposed approach predicts completely new sound dispersions and radius dependences of non-resonant Raman-active modes frequencies in single-walled carbon nanotubes (SWCNT). Resulting relations are suitable for nanotubes identification and more complete or alternative characterization. The theory is also applied to describe the low…
The electronic and vibrational density of states of a semiconducting carbon nanotube in a crossed junction was investigated by elastic and inelastic scanning tunneling spectroscopy. The strong radial compression of the nanotube at the junction induces local metallization spatially confined to a few nm. The local electronic modifications are correlated with the observed changes in the radial breathing and G-band phonon modes, which react very sensitively to local mechanical deformation. In addition, the experiments reveal the crucial contribution of the image charges to the contact potential at…
The capabilities of the mechanical resonator-based nanosensors in detecting ultra-small mass or force shifts have driven a continuing exploration of the palette of nanomaterials for such application purpose. Based on large-scale molecular dynamics simulations, we have assessed the applicability of a new class of carbon nanomaterials for the nanoresonator usage, i.e., the single wall carbon nanotube (SWNT) network. It is found that the SWNT networks inherit the excellent mechanical properties from the constituent SWNTs, possessing a high natural frequency. However, although a high quality facto…
Prevalence of electronic gadgets has been on the rise and among several considerations that are important for furthering frontiers of utility of new gadgets is mechanical flexibility of electronic systems. Flexible electronics require functional materials to be held by flexible substrates that can be bent to small radii of curvature. In addition, the functionality of the active material has to remain intact during the process of bending. There have been challenges in the transfer process of functional materials onto flexible substrates as well as challenges in maintaining the functionality of …
The molecular dynamics method is used to study the process of development of dynamic instability of a thin film, leading to its destruction. The calculations are performed for a thin (5 atomic layers) $fcc$ aluminum film using the interatomic interaction potential tested by comparing the numerical results with the analytical ones obtained in the framework of elasticity theory. For this purpose, an original approach is developed, which allows one to calculate the dispersion law of long-wave phonons in ultrathin films using the molecular dynamics method. The temperatures ($< 600 K$) at which the…
A simple macroscopic continuum elasticity theory (CET) is used to calculate the structure relaxation of single-wall carbon nanotube (SWNT), an analytic formula is obtained. We also expand an atomic scale three-parameter empirical model [ T. Lenosky {\emph et al.} Nature 355, 333(1992)] in order to correctly describe the bond-length change effects. The structure relaxation of SWNT expected by the model is good in agreement with our CET results, and very well consistent with the previous calculation from a first principles local density function approximation. Using the expanded Lenosky model, w…
We present a procedure for determining independently the lattice structure and the vibrational properties of the same individual nano-object. For the example of an individual single-walled carbon nanotube we demonstrate the determination of the structural indices (n,m) of the nanotube by electron diffraction and of the frequencies of vibrational modes by micro-Raman spectroscopy. The precise and independent determination of both structure and mode frequencies allows for direct and unambiguous verification of molecular dynamical calculations and of conclusions drawn from Raman-only experiments.
We report on single-wall carbon nanotube (SWCNT) specific $^{13}$C isotope enrichment. The high temperature annealing of isotope enriched fullerenes encapsulated in SWCNTs yields double-wall carbon nanotubes (DWCNTs) with a high isotope enrichment of the inner wall. The vibrational spectra evidences that no carbon exchange occurs between the two walls. The method facilitates the identification of the Raman signal of the outer and inner tubes. Nuclear magnetic resonance proves the significant contrast of the isotope enriched SWCNTs as compared to other carbon phases, and provides information on…
We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory…
This work considers the g-tensor anisotropy induced by the flexural thermal vibrations in one-dimensional structures and its role in electron spin relaxation. In particular, the mechanism of spin-lattice relaxation via flexural modes is studied theoretically for localized and delocalized electronic states in semiconducting carbon nanotubes in the presence of magnetic field. The calculation of one-phonon spin-flip process predicts distinctive dependencies of the relaxation rate on temperature, magnetic field and nanotube diameter. Comparison with the spin relaxation caused by the hyperfine inte…
Vibrational properties of composites based on single-walled carbon nanotubes (SWNTs) and conducting polymers of the type polyaniline (PANI) and poly (3,4-ethylene dioxythiophene) (PEDOT) are reported. For PANI-functionalized SWNTs, the intensity increase of the Raman band at 178 cm-1, associated with radial breathing modes of SWNTs bundles, indicates an additional roping of nanotubes due to the presence of the polymer. The interaction of this composite with NH4OH solution involves an internal redox reaction between PANI and SWNTs. Thus, the polymer chain undergoes a transition from the semi-ox…
The nonlinear mechanical response of carbon nanotubes, referred to as their "buckling" behavior, is a major topic in the nanotube research community. Buckling means a deformation process in which a large strain beyond a threshold causes an abrupt change in the strain energy vs. deformation profile. Thus far, much effort has been devoted to analysis of the buckling of nanotubes under various loading conditions: compression, bending, torsion, and their certain combinations. Such extensive studies have been motivated by (i) the structural resilience of nanotubes against buckling and (ii) the subs…
The heat flux autocorrelation functions of carbon nanotubes (CNTs) with different radius and lengths is calculated using equilibrium molecular dynamics. The thermal conductance of CNTs is also calculated using the Green-Kubo relation from the linear response theory. By pointing out the ambiguity in the cross section definition of single wall CNTs, we use the thermal conductance instead of conductivity in calculations and discussions. We find that the thermal conductance of CNTs diverges with the CNT length. After the analysis of vibrational density of states, it can be concluded that more low …
We use an atom-atom potential between carbon atoms to obtain an interaction potential between nanotubes (assumed rigid), thereby calculating the cohesive energy of a bunch of nanotubes in hexagonal two dimensional packing. The model proposed is quite similar to our earlier work on fullerenes and organic molecular crystals. The results for inter-nanotube distances, energy per unit length, bulk modulus and phonons for inter-nanotube vibrations are obtained and compared with available data from measurements and other available calculations. We also model formation of multi-wall nanotubes. We find…
A natural embodiment for multifunctional materials combining energy-storing capabilities and structural mechanical properties are layered structures, similar to both laminate structural composites and electrochemical energy storage devices. A structural composite with integrated electric double layer capacitive storage is produced by resin infusion of a lay up including woven glass fabric used as mechanical reinforcement, carbon nanotube non-woven fabrics as electrodes/current collectors and a polymer electrolyte. The energy-storing layer is patterned with holes, which after integration form r…
We present the first low-temperature thermodynamic investigation of the controlled physisorption of He$^{4}$ gas in carbon single-wall nanotube (SWNT) samples. The vibrational specific heat measured between 100 mK and 6 K demonstrates an extreme sensitivity to outgassing conditions. For bundles with a few number of NTs the extra contribution to the specific heat, C$_{ads}$, originating from adsorbed He$^{4}$ at very low density displays 1D behavior, typical for He atoms localized within linear channels as grooves and interstitials, for the first time evidenced. For larger bundles, C$_{ads}$ re…
The bending of a carbon nanotube is studied by considering the structural evolution of a carbon nanotorus from elastic deformation to the onset of the kinks and eventually to the collapse of the walls of the nanotorus. The changes in the electronic properties due to {\it non-local} deformation are contrasted with those due to {\it local} deformation to bring out the subtle issue underlying the reason why there is only a relatively small reduction in the electrical conductance in the former case even at large bending angles while there is a dramatic reduction in the conductance in the latter ca…
Lattice vibrations of the wurtzite-type AlN have been studied by Raman spectroscopy under high pressure up to the structural phase transition at 20 GPa. We have shown that the widely debated bond-bending E_2^1 mode of w-AlN has an abnormal positive pressure shift up to the threshold of the phase transition, whereas in many tetrahedral semiconductors the bond-bending modes soften on compression. This finding disagrees with the results of ab initio calculations, which give a "normal" negative pressure shift. Combination of high dynamical and low thermodynamical stability of AlN breaks the correl…
The excess low-frequency vibrational spectrum, called boson peak, and non-affine elastic response are the most important particularities of glasses. Herein, the vibrational and mechanical properties of polymeric glasses are examined by using coarse-grained molecular dynamics simulations, with particular attention to the effects of the bending rigidity of the polymer chains. As the rigidity increases, the system undergoes a glass transition at a higher temperature (under a constant pressure), which decreases the density of the glass phase. The elastic moduli, which are controlled by the decreas…
Printed electronics rely on the deposition of conductive liquid inks, typically onto polymeric or paper substrates. Among available conductive fillers for use in electronic inks, carbon nanotubes (CNTs) have high conductivity, low density, processability at low temperatures, and intrinsic mechanical flexibility. However, the electrical conductivity of printed CNT structures has been limited by CNT quality and concentration, and by the need for nonconductive modifiers to make the ink stable and extrudable. This study introduces a polymer-free, printable aqueous CNT ink, and presents the relatio…
High pressure Raman experiments on Boron Nitride multi-walled nanotubes show that the intensity of the vibrational mode at ~ 1367 cm-1 vanishes at ~ 12 GPa and it does not recover under decompression. In comparison, the high pressure Raman experiments on hexagonal Boron Nitride show a clear signature of a phase transition from hexagonal to wurtzite at ~ 13 GPa which is reversible on decompression. These results are contrasted with the pressure behavior of carbon nanotubes and graphite.
Energy exchanges between orderly intertube axial motion and vibrational modes are studied for isolated systems of two coaxial carbon nanotubes at temperatures ranging from 300 K to 500 K. It is found that the excess intertube van der Waals energy, depleted from the intertube axial motion, is primarily stored in low-frequency mechanical modes of the oscillator for an extended period of time, and furthermore, such an energy exchange may be reversible. A new nanoscale tribological phenomenon of negative friction is reported for the first time in concentric cylindrical carbon nanotube oscillators.
External loads typically have a indirect influence on phonon curves, i.e., they influence the phonon curves by changing the state about which linearization is performed. In this paper, we show that in nanotubes, the axial load has a direct first-order influence on the long-wavelength behavior of the transverse acoustic (TA) mode. In particular, when the tube is force-free the TA mode frequencies vary quadratically with wave number and have curvature (second derivative) proportional to the square-root of the nanotube's bending stiffness. When the tube has non-zero external force, the TA mode fr…
We present a theoretical study of the intrinsic quality factor of the fundamental flexural vibration in a carbon nanotube and its dependence on temperature, radius, length and tension. In particular, we examine three- and four-phonon decays of the fundamental flexural mode within quantized elasticity theory. This analysis reveals design principles for the construction of ultrasensitive nanotube mass sensors: under tensions close to the elastic limit, intrinsic losses allow for \emph{single yoctogram} mass resolution at room temperature, while cooling opens the possibility of \emph{sub-yoctogra…
Using the first principles calculations we have studied the vibrational modes and Raman spectra of a (10, 10) single-walled carbon nanotube (SWNT) bundle under hydrostatic pressure. Detailed analysis shows that the original radial breathing mode (RBM) of the SWNT bundle disappears after the structural phase transition (SPT). And significantly a RBM-like mode appears at about 509 cm^{-1}, which could be considered as a fingerprint of the SPT happened in the SWNT bundle, and further used to determine the microscopic structure of the bundle after the SPT.
Similar to the carbon nanotube fabricated from graphene sheet, a black phosphorus nanotube (BPNT) also can theoretically be produced by curling the rectangular single-layer black phosphorus (SLBP). In present study, the effect of thermal vibration of atoms on the failure of a BPNT is investigated using molecular dynamics simulations. Two types of double-shell BPNTs, which are obtained by curling the rectangular SLBP along its armchair/pucker direction and zigzag direction (in-plane normal) respectively, are involved in simulation. At finite temperature, a bond on the outer shell of tube is und…
Recent studies of single-walled carbon nanotubes (CNTs) in aqueous media have showed that water can significantly affect the tube mechanical properties. CNTs under hydrostatic compression can preserve their elastic properties up to large pressure values, while exhibiting exceptional resistance to mechanical loadings. It was experimentally observed that CNTs with encapsulated linear carbon chains (LCCs), when subjected to high hydrostatic pressure values, present irreversible red shifts in some of their vibrational frequencies. In order to address the cause of this phenomenon, we have carried o…
Direct Realization of Near-Ideal Carbyne in Ultrathin Boron Nitride Nanotubes
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Center for the Science of Materials Berlin, Humboldt-Universität zu Berlin（柏林材料科学中心）；Politecnico di Milano（米兰理工大学）；Huzhou Normal University（湖州师范学院）
We theoretically demonstrate that at a finite temperature, an effective wall thickness of a single walled carbon nanotube (SWNT) should be $W=W_s+W_d$, where $W_s$ is the static thickness defined as the extension of the outmost electronic orbit and $W_d$ the dynamic thickness due to thermal vibration of atoms. Both molecular simulations and a theoretical analysis show that $W_d$ is proportional to $\sqrt{T}$. We find that the increase of dynamic thickness with temperature is the main mechanism of Raman spectrum shift. The introduction of dynamic thickness changes some conclusions about the You…
