An approach to multi-body interactions in a continuum-atomistic context: Application to analysis of tension instability in carbon nanotubes

The tensile strength of single-walled carbon nanotubes (CNT) is examined using a continuum-atomistic (CA) approach. The strength is identified with the onset of the CNT instability in tension. The focus of this study is on the effects of multi-body atomic interactions. Multiscale simulations of nanostructures usually make use of two- and/or three-body interatomic potentials. The three-body potentials describe the changes of angles between the adjacent bonds – bond bending. We propose an alternative and simple way to approximately account for the multi-body interactions. We preserve the pair structure of the potentials and consider the multi-body interaction by splitting the changing bond length into two terms. The first term corresponds to the self-similar deformation of the lattice, which does not lead to bond bending. The second term corresponds to the distortional deformation of the lattice, which does lead to bond bending. Such a split of the bond length is accomplished by means of the spherical–deviatoric decomposition of the Green strain tensor. After the split, the continuum-atomistic potential can be written as a function of two bond lengths corresponding to the bond stretching and bending independently. We apply an example exponential continuum-atomistic potential with the split bond length to the study of tension instability of the armchair and zigzag CNTs. The results of the study are compared with those obtained by Zhang et al. (2004. J. Mech. Phys. Solids 52, 977–998) who studied tension instability of carbon nanotubes by using the Tersoff–Brenner three-body potential, and with recent experimental results on the tensile failure of single walled carbon nanotubes.     

EPR and Optical Absorption Study of Cr3+-Doped Dipotassium Tetrachloropalladate

X-band electron paramagnetic resonance (EPR) study of Cr³⁺-doped dipotassium tetrachloropalladate single crystal is done at liquid nitrogen temperature. EPR spectrum shows two sites. The spin-Hamiltonian parameters have been evaluated by employing hyperfine resonance lines observed in EPR spectra for different orientations of crystal in externally applied magnetic field. The values of spin-Hamiltonian and zero-field splitting (ZFS) parameters of Cr³⁺ ion-doped DTP for site I are: g _x  = 2.096 ± 0.002, g _y  = 2.167 ± 0.002, g _z  = 2.220 ± 0.002, D = (89 ± 2) × 10^?4 cm^?1, E = (16 ± 2) × 10^?4 cm^?1. EPR study indicates that Cr³⁺ ion enters the host lattice substitutionally replacing K⁺ ion and local site symmetry reduces to orthorhombic. Optical absorption spectra are recorded at room temperature. From the optical absorption study, the Racah parameters (B = 521 cm^?1, C = 2,861 cm^?1), cubic crystal field splitting parameter (Dq = 1,851 cm^?1) and nephelauxetic parameters (h = 2.06, k = 0.21) are determined. These parameters together with EPR data are used to discuss the nature of bonding in the crystal.     

Optimized AC conductivity correlated to structure,morphology and thermal properties of PVDF/PVA/Nafion composites

Polyvinylidene fluoride (PVDF) and polyvinyl alcohol (PVA) composites were prepared by controlled loading of Nafion (5 to 15 wt%) by solution casting using water and dimethylformamide (DMF) as a solvent. The surface morphology of composite analyzed by atomic force microscopy (AFM) reveals the presence of Nafion ionomers. The increase in interlayer spacing of modified PVDF/PVA polymer system as a function of Nafion was detected by X-ray diffraction (XRD). The major change in Fourier transform infrared (FTIR) spectroscopy confirms the chemical bond C=O stretching around 1,700 cm^?1 due to Nafion. Differential scanning calorimetry (DSC) demonstrates the thermal stability of polymer composites and the decrease in melting temperature (T _m). The optimized AC conductivity (σ) of the prepared composite was evaluated by using an impedance analyzer as a function of temperature (40 to 150 °C) at constant 30-MHz frequency. The highest conductivity of 1.3?×?10^?2 S m^?1 was observed at 80 °C for 10 wt% of Nafion and correlated with structure, morphology and thermal properties of modified PVDF/PVA/Nafion composites. The experimental results may be useful for sensors, fuel cells and battery application domains.     

Stochastic stability of a fractional viscoelastic column under bounded noise excitation

The stability of a viscoelastic column under the excitation of stochastic axial compressive load is investigated in this paper. The material of the column is modeled using a fractional Kelvin–Voigt constitutive relation, which leads to that the equation of motion is governed by a stochastic fractional equation with parametric excitation. The excitation is modeled as a bounded noise, which is a realistic model of stochastic fluctuation in engineering applications. The method of stochastic averaging is used to approximate the responses of the original dynamical system by a new set of averaged variables which are diffusive Markov vector. An eigenvalue problem is formulated from the averaged equations, from which the moment Lyapunov exponent is determined for the column system with small damping and weak excitation. The effects of various parameters on the stochastic stability and significant parametric resonance are discussed and confirmed by simulation results.     

Higher-order stochastic averaging to study stability of a fractional viscoelastic column

Stochastic stability of a fractional viscoelastic column axially loaded by a wideband random force is investigated by using the method of higher-order stochastic averaging. By modelling the wideband random excitation as Gaussian white noise and real noise and assuming the viscoelastic material to follow the fractional Kelvin–Voigt constitutive relation, the motion of the column is governed by a fractional stochastic differential equation, which is justifiably and uniformly approximated by an averaged system of Itô stochastic differential equations. Analytical expressions are obtained for the moment Lyapunov exponent and the Lyapunov exponent of the fractional system with small damping and weak random fluctuation. The effects of various parameters on the stochastic stability of the system are discussed.     

Selective injection locking of a multi-mode semiconductor laser to a multi-frequency reference beam

Injection locking is a well known and commonly used method for coherent light amplification. Usually injection locking is obtained on a single-mode laser injected by a single-frequency seeding beam. In this work we show that selective injection locking of a single-frequency may also be achieved on a multi-mode semiconductor laser injected by a multi-frequency seeding beam, if the slave laser provides sufficient frequency filtering. This selective injection locking condition depends critically on the frequency detuning between the free-running slave emission frequency and each injected frequency component. Stable selective injection locking to a set of three seeding components separated by 1.2 GHz is obtained. This system provides an amplification up to 37 dB of each component. This result suggests that, using distinct slave lasers for each frequency line, a set of mutually coherent high-power radiation modes can be tuned in the GHz frequency domain.     

Proportional odds frailty model and stochastic comparisons

In this paper, we present some distributional properties of the survival and frailty distribution involved in the proportional odds (PO) frailty model. Stochastic orderings are studied for this proportional odds frailty model. It is showed that negative dependence arises in the PO frailty model as opposed to the proportional hazard frailty model.     

A foldamer-based chiroptical molecular switch that displays complete inversion of the helical sense upon anion binding

Chiral indolocarbazole dimers fold into a helical conformation by virtue of intramolecular hydrogen bonds, as demonstrated by (1)H NMR and CD spectra and optical rotations. In particular, the optical properties of the dimers were found to be extremely sensitive to the nature of the solvent, depending on whether they are folded or not. The helical sense of the dimers can be reversibly switched by binding sulfate ion, which gives rise to complete inversion of the CD spectra. The binding mode and absolute stereochemistry of the sulfate complexes was unequivocally determined by single-crystal X-ray structures, which are all consistent with the CD and (1)H NMR spectra in solution.     

Hybrid density functional∕molecular mechanics studies on activated adsorption of oxygen on zeolite supported gold monomer

Density functional theory calculations on oxygen adsorption over gas phase and faujasite supported Au monomer has been studied using hybrid quantum mechanics∕molecular mechanics method, surface integrated molecular orbital molecular mechanics implemented in GAMESS package. Three different oxidation states of Au (0, +1, +3) and three different adsorption modes viz., top, bridge, and dissociative adsorption of oxygen have been considered in our calculations. Redshift in the ν(O-O) value from that in gas phase O(2) indicates activation of O(2) upon adsorption over faujasite supported gold monomer. The activation of O(2) is an important step in the catalytic oxidation of CO. The presence of adsorbed O(2) increases the interaction of the Au monomer with the faujasite support. In faujasite supported cationic Au monomer, O(2) preferably remains bridge bonded to Au rather than being dissociated.     

KINETIC EFFECTS OF SURFACTANT / POLYMER MIXTURES UPON ACIDIC HYDROLYSIS OF HYDROXAMIC ACIDS

The influence of surfactant / polymer (polyethylene glycol, PEG, mol. wt. = 400) mixtures upon the acidic hydrolysis of two N-substituted hydroxamic acids, i.e., R(CO). N(OH)R' : R = C₆H₅, R' = C₆H₅;4-CH₃C₆H₄ has been studied using cationic (CTAB, TTAB and CPC) and nonionic (TX-100 and Brij-35) surfactants. An inhibitory effect was observed. The results have been explained by Porinoy - Menger model. The critical aggregation concentration and polymer saturation point of the corresponding systems have also been measured with the conductivity and surface tension methods.