Inverse Diameter Research Articles

Hypersonic Vibrations of Ag@SiO2(Cubic Core)−Shell Nanospheres

The intriguing optical and catalytic properties of metal-silica core-shell nanoparticles, inherited from their plasmonic metallic cores together with the rich surface chemistry and increased stability offered by their silica shells, have enabled a wide variety of applications. In this work, we investigate the confined vibrational modes of a series of monodisperse Ag@SiO(2) (cubic core)-shell nanospheres synthesized using a modified Stöber sol-gel method. The particle-size dependence of their mode frequencies has been mapped by Brillouin light scattering, a powerful tool for probing hypersonic vibrations. Unlike the larger particles, the observed spheroidal-like mode frequencies of the smaller ones do not scale with inverse diameter. Interestingly, the onset of the deviation from this linearity occurs at a smaller particle size for higher-energy modes than for lower-energy ones. Finite element simulations show that the mode displacement profiles of the Ag@SiO(2) core-shells closely resemble those of a homogeneous SiO(2) sphere. Simulations have also been performed to ascertain the effects that the core shape and the relative hardness of the core and shell materials have on the vibrations of the core-shell as a whole. As the vibrational modes of a particle have a bearing on its thermal and mechanical properties, the findings would be of value in designing core-shell nanostructures with customized thermal and mechanical characteristics.

Growth and population structure of the tree species Malouetia tamaquarina (Aubl.) (Apocynaceae) in the central Amazonian floodplain forests and their implication for management

The long-term success of forest management depends primarily on the sustainability of timber production. In this study we analyse the population structure, tree age and wood increment of Malouetia tamaquarina (Aubl.) (Apocynaceae) to define a species-specific minimum logging diameter (MLD) and felling cycle by modelling volume growth. Contrary to other timber species in the nutrient-rich white-water floodplains forests (várzea), M. tamaquarina grows in the subcanopy of old-growth várzea forests. The wood of this species is utilized by local inhabitants in the floodplains for handicraft. In 35 plots of 25 m × 50 m we measured diameter at breast height (DBH) and tree height of all trees taller than 150 cm height. From 37 individuals with DBH > 15 cm we sampled two cores by increment borers to determine the wood density, tree age and diameter increment rates. In the management area of a várzea settlement with about 150 ha recently harvested trees of M. tamaquarina have been recorded and DBH was measured. The species presents an inverse J-shaped diameter distribution indicating that the species is obviously regenerating in the old-growth forests. Tree-ring analysis indicates a mean age of 74.5 years for a DBH of 22.7 cm for a studied population comprising 37 trees with maximum ages of up to 141 years for an individual with a DBH of 45.7 cm. The tree species has low annual diameter increment rates (3.16 ± 0.6 mm) despite a low wood density (0.36 ± 0.05 g cm −3). The volume growth model indicates a MLD of 25 cm and a felling cycle of 32.4 years. In the management area 35 trees with a mean DBH of 24 cm were recorded, similar to the defined MLD. The abundance of trees above the MLD is 2.7 trees ha −1, or 405 trees, when extrapolated to the whole management area. Considering a felling cycle of 32.4 years (annual production unit of 4.63 ha) this results in total of 12.5 harvestable trees, almost three times less than actually harvested. The actual practice of harvesting M. tamaquarina risks the overexploitation of this slow-growing species.

Diameter dependence of interwall separation and strain in multiwalled carbon nanotubes probed by X-ray diffraction and Raman scattering studies

We have made a systematic study on the diameter dependent spectral features in X-ray diffraction (XRD) and Raman scattering studies of multiwalled carbon nanotubes (MWCNTs) of various diameters in the range 5−100 nm. High resolution transmission electron microscopy (HRTEM) imaging reveals a systematic decrease in the interwall separation from 3.8 Å down to 3.2 Å as the diameter of nanotubes increases from 5.8 nm to 63.2 nm. Analysis of the XRD patterns shows an exponential decrease in d 002 interlayer spacing with increasing tube diameter, in close agreement with the HRTEM results. Further, XRD profile line width shows inverse diameter dependence and exponential increase in intensity as the diameter of the MWCNTs increases. Raman spectra of different diameter nanotubes show different evolutions of metallic and semiconducting components in the G-band, as found from spectral deconvolution. The frequency and full width at half maximum (FWHM) of the semiconducting component of the G − band gradually decreases as the tube diameter increases. Ratio of intensities of G − band to D-band first shows a sharp fall as the tube diameter increases from 7 nm to 15 nm and then slowly increases with increasing diameter. On the other hand, G′ mode frequency shows large up shift when average diameter is increased from 7 nm to 15 nm and then saturates for higher diameter tubes. Analysis of Raman and XRD data reveals that the lowest diameter (7 nm) MWCNTs have features similar to those of the single walled nanotubes, while the spectral features are distinctly different for higher diameter MWCNTs due to the interaction among tube walls that is very significant for large diameter MWCNTs. Observed diameter dependence of the spectral features is explained in terms of nanotube curvature and atomic vibrations involving interaction among the walls in MWCNTs. The present study demonstrates the power of XRD for nondestructive evaluation of diameter distribution and interwall separation in MWCNTs with wide range of diameters.

Quantitative Determination of the Size Dependence of Surface Plasmon Resonance Damping in Single Ag@SiO2 Nanoparticles

The optical extinction spectra of single silver nanoparticles coated with a silica shell were investigated in the size range 10-50 nm. Measurements were performed using the spatial modulation spectroscopy technique which permits independent determination of both the size of the metal nanoparticle under study and the width of its localized surface plasmon resonance (LSPR). These parameters can thus be directly correlated at a single particle level for the first time. The results show a linear increase of the width of the LSPR with the inverse diameter in the small size regime (less than 25 nm). For these nanoparticles of well-controlled environment, this can be ascribed to quantum confinement of electrons or, classically, to increase of the electron surface scattering processes. The impact of this effect was measured quantitatively and compared to the predictions by theoretical models.

Quasiparticle interference and Landau level spectroscopy in graphene in the presence of a strong magnetic field

We present a calculation of the modulation in the Local Density Of electronic States (LDOS) caused by an impurity in graphene in the presence of external magnetic field. We focus on the spatial Fourier Transform (FT) of this modulation around the impurity. The FT due to the low energy quasiparticles are found to be nonzero over the reciprocal lattice corresponding to graphene. At these lattice spots the FT exhibits well-defined features at wavevectors that are multiples of the inverse cyclotron orbit diameter (see Figure 2) and is cut off at the wavevector corresponding to the energy of observation. Scanning Tunneling Spectroscopy (STS) on graphene and the energy-resolved FT fingerprint obtained therefrom may be used to observe the quasiparticle interference of Dirac particles in graphene in the presence of magnetic field.

Wave propagation through elastic granular and granular auxetic materials

AbstractThe wave propagation through a material with a granular micro‐structure is investigated. The simplest such medium is the granular medium of equal spheres. The theory demonstrates that for long wavelengths the micro‐structured material exhibits modes of wave motion that are also found for a traditional medium (that is, a medium that satisfies simple continuum stress equilibrium laws and no consideration for particle spin and moment of inertia of the particles is accounted for). However, an extra shear wave and rotational oscillatory particle motion are also found. The limit of a traditional material is obtained by letting tangential contact stiffnesses vanish. Towards higher wave numbers the micro‐structure reveals itself in the shear wave speeds by displaying strongly anomalous behaviour compared to a traditional isotropic, elastic medium. An expansion in terms of structural sums (these are sums over the contact interaction weighed with a string of branch vectors) is explored. The lowest order non‐trivial terms (second order structural sums) yield basic behaviour, but a higher order expansion (including fourth order sums) shows a more pronounced anomaly for wave numbers approaching the inverse particle diameter. Yet higher order terms capture more information than can possibly be present in a granular medium and it is senseless to examine these. The theory is relevant to granular materials and granular auxetics. In the latter case the tangential contact stiffness needs to exceed the normal stiffness, which is not possible for ordinary solid contacts, but can be achieved with special arrangements.

Measurement and Estimation of Organic-Liquid/Water Interfacial Areas for Several Natural Porous Media

The objective of this study was to quantitatively characterize the impact of porous-medium texture on interfacial area between immiscible organic liquid and water residing within natural porous media. Synchrotron X-ray microtomography was used to obtain high-resolution, three-dimensional images of solid and liquid phases in packed columns. The image data were processed to generate quantitative measurements of organic-liquid/water interfacial area and of organic-liquid blob sizes. Ten porous media, comprising a range of median grain sizes, grain-size distributions, and geochemical properties, were used to evaluate the impact of porous-medium texture on interfacial area. The results show that fluid-normalized specific interfacial area (A) and maximum specific interfacial area (Am) correlate very well to inverse median grain diameter. These functionalities were shown to result from a linear relationship between effective organic-liquid blob diameter and median grain diameter. These results provide the basis for a simple method for estimating specific organic-liquid/water interfacial area as a function of fluid saturation for a given porous medium. The availability of a method for which the only parameter needed is the simple-to-measure median grain diameter should be of great utility for a variety of applications.

Binding Energy of Metal Oxide Nanoparticles

Current models for the binding energy of nanoparticles generally predict a linear dependence on the inverse particle diameter for spherical clusters or, equivalently, on the inverse of the cube root of the number of particles in the cluster. We have tested this assumption on the simple oxides MgO, CuO, and TiO2 and for the complex oxide FeTiO3. We find that a linear dependence is not observed for these materials despite the fact that it generally occurs for simple metals. Instead, using first principles, density functional theory calculations to calculate the binding energy of these materials, we find an approximately quadratic dependence on the inverse of the particle size, in direct contradiction to current assumptions. This nonlinear dependence of the binding energy has substantial implications on physical properties that depend on the cohesive energy, particularly in the small particle regime.

Numerical Study of the Size-Dependent Melting Mechanisms of Nickel Nanoclusters

Molecular dynamics simulations were used to investigate the size-dependent melting mechanism of nickel nanoclusters of various sizes. The melting process was monitored by the caloric curve, the overall cluster Lindemann index, and the atomic Lindemann index. Size-dependent melting temperatures were determined, and the correct linear dependence on inverse diameter was recovered. We found that the melting mechanism gradually changes from dynamic coexistence melting to surface melting with increasing cluster size. These findings are of importance in better understanding carbon nanotube growth by catalytic chemical vapor deposition as the phase state of the catalyst nanoparticle codetermines the growth mechanism.

Relaxation in the Exciton Fine Structure of Semiconductor Nanocrystals

A spectroscopic study is reported of relaxation in the exciton fine structure of CdSe nanorods measured using ultrafast cross-polarized heterodyned third-order transient grating (CPH-3TG) spectroscopy. The CPH-3TG spectroscopy probes the dynamics of population transfer between states accompanying exciton spin flip (radiationless transitions in the exciton fine structure associated with changes in the sign of the total angular momentum). Analysis of the data enabled elucidation of pathways for exciton fine structure relaxation (EFSR) involving all of the exciton fine structure states. The mechanism and origin of the EFSR dynamics in CdSe nanorods are discussed in the exciton state picture with an analogy to molecular radiationless transition processes such as internal conversion and intersystem crossing. Key conclusions are that the fast transitions are between states with total angular momentum of ±1 and ∓2 and that the rate of this transition follows an inverse diameter to the fourth power size dependence, which originates from the Dresselhaus spin−orbit coupling effect.

Micro-Brillouin Study of the Eigenvibrations of Single Isolated Polymer Nanospheres

The localized acoustic modes of single isolated polymethyl methacrylate (PMMA) and polystyrene nanospheres have been studied by micro-Brillouin light scattering. The measured mode frequencies are analyzed on the basis of the Lamb theory formulated for a sphere under free boundary conditions. By measuring light scattering from single isolated particles, placed atop a piece of polished silicon wafer, the free-surface conditions are almost experimentally realized. The observed spectral peaks are attributed to localized eigenvibrations whose frequencies scale as inverse sphere diameter, in accordance with Lamb's theory. The Young's moduli and Poisson ratios of the polymer spheres studied have been evaluated from fits to the experimental data. We have demonstrated that micro-Brillouin spectroscopy is a powerful technique for probing the acoustic dynamics and mechanical properties of nanostructures.

Size-dependent characterization of embedded Ge nanocrystals: Structural and thermal properties

A combination of conventional and synchrotron-based techniques has been used to characterize the size-dependent structural and thermal properties of Ge nanocrystals (NCs) embedded in a silica $(a{\text{-SiO}}_{2})$ matrix. Ge NC size distributions with four different diameters ranging from 4.0 to 9.0 nm were produced by ion implantation and thermal annealing as characterized with small-angle x-ray scattering and transmission electron microscopy. The NCs were well represented by the superposition of bulklike crystalline and amorphous environments, suggesting the formation of an amorphous layer separating the crystalline NC core and the $a{\text{-SiO}}_{2}$ matrix. The amorphous fraction was quantified with x-ray-absorption near-edge spectroscopy and increased as the NC diameter decreased, consistent with the increase in surface-to-volume ratio. The structural parameters of the first three nearest-neighbor shells were determined with extended x-ray-absorption fine-structure (EXAFS) spectroscopy and evolved linearly with inverse NC diameter. Specifically, increases in total disorder, interatomic distance, and the asymmetry in the distribution of distances were observed as the NC size decreased, demonstrating that finite-size effects govern the structural properties of embedded Ge NCs. Temperature-dependent EXAFS measurements in the range of 15--300 K were employed to probe the mean vibrational frequency and the variation of the interatomic distance distribution (mean value, variance, and asymmetry) with temperature for all NC distributions. A clear trend of increased stiffness (higher vibrational frequency) and decreased thermal expansion with decreasing NC size was evident, confirming the close relationship between the variation of structural and thermal/vibrational properties with size for embedded Ge NCs. The increase in surface-to-volume ratio and the presence of an amorphous Ge layer separating the matrix and crystalline NC core are identified as the main factors responsible for the observed behavior, with the surrounding $a{\text{-SiO}}_{2}$ matrix also contributing to a lesser extent. Such results are compared to previous reports and discussed in terms of the influence of the surface-to-volume ratio in objects of nanometer dimensions.

The Scaling of the Effective Band Gaps in Indium−Arsenide Quantum Dots and Wires

Colloidal InAs quantum wires having diameters in the range of 5-57 nm and narrow diameter distributions are grown from Bi nanoparticles by the solution-liquid-solid (SLS) mechanism. The diameter dependence of the effective band gaps (DeltaE(g)s) in the wires is determined from photoluminescence spectra and compared to the experimental results for InAs quantum dots and rods and to the predictions of various theoretical models. The DeltaE(g) values for InAs quantum dots and wires are found to scale linearly with inverse diameter (d(-1)), whereas the simplest confinement models predict that DeltaE(g) should scale with inverse-square diameter (d(-2)). The difference in the observed and predicted scaling dimension is attributed to conduction-band nonparabolicity induced by strong valence-band-conduction-band coupling in the narrow-gap InAs semiconductor.

Analysis of the Relationship between Reaction Energies of Electrophilic SWNT Additions and Sidewall Curvature: Chiral Nanotubes

The relationship of reaction energies for CH2/NH/O exo- and endo-[2 + 1] cycloadditions to chiral single-walled carbon nanotube (SWNT) sidewalls with the inverse tube diameter (1/d) was investigated using density functional theory (DFT) and density functional tight binding (DFTB) methods. We considered additions to the three nonequivalent C−C bond types t (bond most parallel to tube axis), d (“diagonal” bond, slightly skewed), and p (bond most perpendicular to tube axis), using hydrogen-terminated (2n,n) SWNT model systems with n = 2−8. Exoadditions are classified into two types, one where the original C−C bond is broken (exo(l)), and one where it remains intact (exo(s)) in the addition complex. Endoadditions are found to always belong to the latter (endo(s)) type. It is found that (a) exoadditions are more exothermic than endo additions, and (b) that exoadditions are more exothermic with larger bond-tube axis angle (p > d > t). A nearly perfect linear relationship between the total reaction energy ΔE and...

Radiation-pressure-driven vibrational modes in ultrahigh-Q silica microspheres

Quantitative measurements of the vibrational eigenmodes in ultrahigh-Q silica microspheres are reported. The modes are excited via radiation-pressure-induced dynamical backaction of light confined in the optical whispering-gallery modes of the microspheres (i.e., via the parametric oscillation instability). Two families of modes are studied and their frequency dependence on sphere size investigated. The measured frequencies are in good agreement both with Lamb's theory and numerical finite-element simulation and are found to be proportional to the sphere's inverse diameter. In addition, the quality factors of the vibrational modes are studied.

Binding energy, vapor pressure, and melting point of semiconductor nanoparticles

Current models for the cohesive energy of nanoparticles generally predict a linear dependence on the inverse particle diameter for spherical clusters, or, equivalently, on the inverse of the cube root of the number of atoms in the cluster. Although this is generally true for metals, the authors find that for the group IV semiconductors, C, Si, and Ge, this linear dependence does not hold. Instead, using first principles, density functional theory calculations to calculate the binding energy of these materials, they find a quadratic dependence on the inverse of the particle size. Similar results have also been obtained for the metallic group IV elements Sn and Pb. This is in direct contradiction to current assumptions. Further, as a consequence of this quadratic behavior, the vapor pressure of semiconductor nanoparticles rises more slowly with decreasing size than would be expected. In addition, the melting point of these nanoparticles will experience less suppression than experienced by metal nanoparticles with comparable bulk binding energies. This nonlinearity also affects sintering or Ostwald ripening behavior of these nanoparticles as well as other physical properties that depend on the nanoparticle binding energy. The reason for this variation in size dependence involves the covalent nature of the bonding in semiconductors, and even in the “poor” metals. Therefore, it is expected that this result will hold for compound semiconductors as well as the elemental semiconductors.

Intermediate-frequency Raman modes for the lower optical transitions of semiconducting single-walled carbon nanotubes

A new class of intermediate-frequency modes (IFMs) associated with the ${E}_{22}^{S}$ and ${E}_{11}^{S}$ optical transitions of bundled HiPco single-walled carbon nanotubes (SWNTs) have been investigated via tunable laser (700\char21{}$985\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$) resonance Raman spectroscopy. ``Steplike'' dispersive behavior was observed for these IFMs, along with associated clusters of radial breathing mode (RBM) overtones at higher frequencies. While the excitation profiles of both RBM and RBM overtones follow a classical behavior predicted by resonance Raman theory, significant differences are observed for the IFM excitation profiles. The observed IFM maxima were found to obey a resonance behavior based on a combination of the ${E}_{22}^{S}$ and${E}_{11}^{S}$ transition energies, scaled by the inverse diameter of the respective nanotube. Only IFMs for the $\mathrm{mod}(n\ensuremath{-}m,3)=2$ nanotubes are visible, with intensities found to obey the family-based chiral angle dependence similar to previously reported electron-phonon interaction patterns observed for the RBM.

Vibrational properties of single-walled gold nanotubes from first principles

The vibrational modes, especially the radial breathing modes (RBMs), of single-walled gold nanotubes (SWGTs) have been calculated using the density-functional theory in the generalized gradient approximation, taking into account the gold's relativistic effect. It is found that the maximal frequency of the SWGTs are comparable to that of bulk gold, but its vibrational density of states is quite different. Although the RBM frequencies of the SWGTs are found to depend on both of their diameters and chiral symmetries, a linear variation of them with the inverse tube diameters is still found to hold approximately. It is also found that the scalar relativistic effect increases their bond strength, but shortens greatly their bond lengths, and the tube diameter, increasing so their RBM frequency significantly.

Direct probe of excitonic and continuum transitions in the photocurrent spectroscopy of individual carbon nanotube p-n diodes

The authors show that a carbon nanotube p-n diode is a very sensitive probe of optical transitions in individual single-walled carbon nanotubes. In the photocurrent spectra, an alternating sequence of resonant peaks from dissociation of excitons and exciton-phonon bound states, for the lowest and higher electronic subbands, is observed. At an intermediate energy, the onset of continuum is observed that allows measurement of exciton binding energies. Both the binding energy and the onset of continuum follow the inverse diameter relation as expected from general theory of optical transitions in nanotubes.

Exciton-photon, exciton-phonon matrix elements, and resonant Raman intensity of single-wall carbon nanotubes

Within the framework of the tight-binding model, we have developed exciton-photon and exciton-phonon matrix elements for single-wall carbon nanotubes. The formulas for first-order resonance and double-resonance Raman processes are discussed in detail. The lowest-energy excitonic state possesses an especially large exciton-photon matrix element compared to other excitonic states and continuum band states because of its localized wave function with no node. Unlike the free-particle picture, the photon matrix element in the exciton picture shows an inverse diameter dependence but no tube type or chirality dependences. As a result, the optical absorption intensity shows a strong diameter dependence but no tube type or chirality dependences. Moreover, the continuum band edge can be determined from the wave function or exciton-photon matrix element. For the radial breathing mode (RBM) and $G$-band modes, the phonon matrix elements in the exciton and free-particle pictures are almost the same. As a result, the intensity for the Kataura plots for the RBM or $G$-band modes by the exciton and free-particle pictures show similar family patterns. However, the excitonic effect has greatly increased the diameter dependence and magnitude of the intensities for the RBM and $G$ band by enhancing the diameter dependence and magnitude of the photon matrix element. Therefore, excitons have to be considered in order to explain the strong diameter dependence of the Raman signal observed experimentally.