A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

Pressure-induced Raman-active radial breathing mode transition in single-wall carbon nanotubes

Using classical constant-pressure molecular dynamics simulations and the force constants model, radial breathing mode (RBM) transition of single-wall carbon nanotubes under hydrostatic pressure is reported. With the pressure increased, the RBM shifts linearly toward higher frequency, and the RBM transition occurs at the same critical pressure as the structural transition. The group theory indicates that the RBMs are all Raman-active; however, due to the effect of the frequency transition and the electronic structure change for tube radial deformation, the Raman intensity of the modes becomes so weak as not to be experimentally detected, which is in agreement with a recent experiment by S. Lebedkin [Phys. Rev. B 73, 094109 (2006)]. Furthermore, the calculated RBM transition pressure is well fitted to the cube of diameter (similar to 1/d(3)).

Interaction of H-2 with transition metal homonuclear dimers Cu-2, Ag-2, Au-2 and heteronuclear dimers PdCu, PdAg and PdAu

The reaction mechanisms of the H-2 with the homonuclear dimers M-2 (Cu, Ag, Au) and the heteronuclear dimers PdM (M = Cu, Ag, Au) were studied by use of density functional theory. For the H-2 reactions with homonuclear dimers M-2 (Cu, Ag, Au), it was found that it is easier for Au-2 to dissociate the hydrogen molecule compared with Cu-2 and Ag-2. For H-2 reactions with the heteronuclear dimers PdM (M = Cu, Ag, An), the hydrogen molecule can be easily dissociated at Pd site, rather than at noble metal site.

Electronic structures of Al2W, AlW2 clusters and their anions

Possible structures for Al2W and AlW2 clusters and their anions were presented and studied by use of density functional theory B3LYP at various spin multiplicities. The proposed three structures are triangular form with C-2v symmetry; linear structure with D (infinity h) symmetry; and linear structure with C (infinity v) symmetry. The calculated results indicate that structures with C-2v symmetry are the most stable for both neutral clusters and their anions. For Al2W, C-2v Symmetry at spin multiplicity 5 is the ground state, while for its anion, doublet is the lowest. For AlW2 and its anion, doublet and triplet are the ground states, respectively.

Density functional study of the second row transition metal dimers

Equilibrium geometries, vibrational frequencies and dissociation energies of the second row transition metal dimers (from Y-2 to Cd-2 except Tc-2) ere studied by use of density functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, SVWN, MPW1PW91 and PBE1PBE. The accuracy DFT methods is found to be highly dependent on the functional employed, in particular for vibrational frequency and dissociation energy. In most cases, the predicted bond distance is in general agreement with experiment and previous theoretical results. For van der Waals dimer Cd-2, B3LYP and BLYP have excellent performance in predicting the bond distance. For Ag-2, all density functional methods used in this study perform well in producing the bond distance, vibrational frequency and dissociation energy.

Structural stability and electronic state of transition metal trimers

Ground state geometries were searched for transition metal trimers Sc-3, Y-3, La-3, Lu-3, Ti-3, Zr-3, and Hf-3 by density functional methods. For all the studied trimers, our calculation indicates that the ground state geometries are either equilateral triangle (Zr-3 and Hf-3) or near equilateral triangle (Ti-3, Sc-3, Y-3, La-3, and Lu-3). For rare earth trimers Sc-3, Y-3, La-3, and Lu-3, isosceles triangle (near equilateral triangle) at quartet state is the ground state. Isosceles triangle at doublet state is the competitive candidate for the ground state. For Zr-3 and Hf-3, equilateral triangle at singlet state is the most stable. For Ti-3, isosceles triangle (near equilateral triangle) at quintet state gives the ground state. For Sc-3, Zr-3, and Hf-3, where experimental results are available, the predicted geometries are in agreement with experiment in which the ground state is equilateral triangle (Zr-3) or fluxional (Sc-3 and Hf-3). For Y-3, the calculated geometry is in agreement with experimental observation and previous theoretical study that Y-3 is a bent molecule for the ground state.

Electronic structures of hafnium dimer and trimer by density functional theory

Equilibrium geometries, vibrational frequencies and dissociation energies of hafnium dimer and trimer were studied by density functional methods B3LYP, BLYP, B3PW91, BHLYP, BP86, B3P86, mPW1PW91 and PBE1PBE. The results indicate that singlet is the ground state both for hafnium dimer and for trimer. For hafnium dimer, the calculated bond distance is less sensitive to the methods used. Except at BHLYP level, the calculated vibrational frequency is comparable to the experimental value. For hafnium trimer, equilateral triangle with D-3h symmetry is slightly favored compared with isosceles triangle with C-2v, symmetry except at BHLYP level. This conclusion is in agreement with experiment in which the ground state of Hf-3 is fluxional and low-spin or closed shell is preferred.

Mechanisms underlying two kinds of surface effects on elastic constants

ABSTRACT Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample: elastic modulus either decreases or increases with decreas- ing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the mi- crostructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, resulting in the decrease of the elastic moduli with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coor- dination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair po- tential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface re- spectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one- dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.

A thin liquid film and its effects in an atomic force microscopy measurement

Recently, it has been observed that a liquid film spreading on a sample surface will significantly distort atomic force microscopy (AFM) measurements. In order to elaborate on the effect, we establish an equation governing the deformation of liquid film under its interaction with the AFM tip and substrate. A key issue is the critical liquid bump height y(0c) at which the liquid film jumps to contact the AFM tip. It is found that there are three distinct regimes in the variation of y(0c) with film thickness H, depending on Hamaker constants of tip, sample and liquid. Noticeably, there is a characteristic thickness H* physically defining what a thin film is; namely, once the film thickness H is the same order as H* , the effect of film thickness should be taken into account. The value of H* is dependent on Hamaker constants and liquid surface tension as well as tip radius.

Investigation of facilitated ion-transfer reactions at high driving force by scanning electrochemical Microscopy

The kinetics of facilitated ion-transfer (FIT) reactions at high driving force across the water/1,2-dichloroethane (W/DCE) interface is investigated by scanning electrochemical microscopy (SECM). The transfers of lithium and sodium ions facilitated by dibenzo-18-crown-6 (DB18C6) across the polarized W/DCE interface are chosen as model systems because they have the largest potential range that can be controlled externally. By selecting the appropriate ratios of the reactant concentrations (Kr c(M)+/c(DB18C6)) and using nanopipets as the SECM tips, we obtained a series of rate constants (k(f)) at various driving forces (Delta(O)(W) phi(ML+)(0') - Es, Delta(O)(W) phi(ML+)(0') is the formal potential of facilitated ion transfer and Es is the potential applied externally at the substrate interface) based on a three-electrode system. The FIT rate constants k(f) are found to be dependent upon the driving force. When the driving force is low, the dependence of 1n k(f) on the driving force is linear with a transfer coefficient of about 0.3. It follows the classical Butler-Volmer theory and then reaches a maximum before it decreases again when we further increase the driving forces. This indicates that there exists an inverted region, and these behaviors have been explained by Marcus theory.

Kinetics and Force Dependence of P-selectin/PSGL-1 Interactions Measured by AFM

Leukocytes roll along the endothelium of postcapillary venules in response to inflammatory and thrombotic processes. The rolling under hydrodynamic shear forces is a first step in directing leukocytes out of the blood stream into sites of inflammation and is mediated by the selectins, a family of extended, modular, and calcium-dependent lectin receptors. The interactions between P-, E-or L-selectins and their count.

Influences of Hydration Force and Elastic Strain Energy on the Stability of Solid Film in a Very Thin Solid-on-Liquid Structure

Since hydration forces become very strong at short range and are particularly important for determining the magnitude of the adhesion between two surfaces or interaction energy, the influences of the hydration force and elastic strain energy due to hydration-induced layering of liquid molecules close to a solid film surface on the stability of a solid film in a solid-on-liquid (SOL) nanostructure are studied in this paper. The liquid of this thin SOL structure is a kind of water solution. Since the surface forces play an important role in the structure, the total free energy change of SOL structures consists of the changes in the bulk elastic energy within the solid film, the surface energy at the solid-liquid interface and the solid-air interface, and highly nonlinear volumetric component associated with interfacial forces. The critical wavelength of one-dimensional undulation, the critical thickness of the solid film, and the critical thickness of the liquid layer are studied, and the stability regions of the solid film have been determined. Emphasis is placed on calculation of critical values, which are the basis of analyzing the stability of the very thin solid film.

A Quantitative Analysis of the Effect of Laser Transformation Hardening on Crack Driving Force in Steels

A mechanical model of a laser transformation hardening specimen with a crack in the middle of the hardened layer is developed to quantify the effects of the residual stress and hardness gradient on crack driving force in terms of J-integral. It is assumed

A Discussion on Modeling Shape Memory Alloy Embedded in A Composite Laminate as Axial Force and Elastic Foundation

In this paper, the possible error sources of the composite natural frequencies due to modeling the shape memory alloy (SMA) wire as an axial force or an elastic foundation and anisotropy are discussed. The great benefit of modeling the SMA wire as an axial force and an elastic foundation is that the complex constitutive relation of SMA can be avoided. But as the SMA wire and graphite-epoxy are rigidly bonded together, such constraint causes the re-distribution of the stress in the composite. This, together with anisotropy, which also reduces the structural stiffness can cause the relatively large error between the experimental data and theoretical results.

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.