Angular Distribution Functions Research Articles

Tagging photons with gold nanoparticles as localized absorbers in optical measurements in turbid media

We analyze a role of a localized inclusion as a probe for spatial distributions of migrating photons in turbid media. We present new experimental data and two-dimensional analysis of radiance detection of a localized absorptive inclusion formed by gold nanoparticles in Intralipid-1% when the target is translated along the line connecting the light source and detector. Data are analyzed using the novel analytical expression for the relative angular photon distribution function for radiance developed by extending the perturbation approach for fluence. Obtained photon maps allow predicting conditions for detectability of inclusions for which proximity to the detector is essential.

The dynamical study of O(1D) + HCl(v = 0, j = 0) reaction at hyperthermal collision energies

BackgroundsThe quasi-classical trajectory calculations for O(1D) + HCl → OH + Cl (R1) and O(1D) + HCl → ClO + H (R2) reactions have been performed at hyperthermal collision energies (60.0, 90.0, and 120.0 kal/mol) on the 1A' state. Reaction probabilities and integral cross sections are calculated. The product rotational distributions for the two channels, and the product rotational alignment parameters are investigated. Also, the alignment and the orientation of the products have been predicted through the angular distribution functions (concerning the initial/final velocity vector, and the product rotational angular momentum vector). To have a deeper understanding of the natures of the vector correlation between reagent and product relative velocities, a natural generalization of the differential cross section __PDDCS00, is calculated.ResultsThe OH + Cl channel is the main product channel and is observed to have essentially isotropic rotational distributions. The ClO + H channel is found to be clearly rotationally polarized.ConclusionsThe dynamical, especially the stereodynamical characters are quite different for the two channels of the title reaction. Most reactions occur directly, except for R2 reaction at the collision energies of 60.0 and 120.0 kcal/mol. The alignment and orientation effects are weak/strong for R1/R2 reaction. The well structure on the potential energy surface and hyperthermal collision energies might result in the dynamical effects.

Structural characteristics of liquid SiC during quenching process

AbstractQuenching process of liquid silicon carbide (SiC) is simulated with Tersoff potential by using molecular dynamic. Structural characteristics of SiC are analyzed by radial distribution function, angular distribution function, coordination number, and Voronoi polyhedron index. Results show that both heteronuclear and homonuclear bonds exist and no atomic segregation occurs during the quench process. The bond angles of silicon and carbon atoms are distributed at around 109° and 120°, respectively. The average coordination number is <4. Threefold carbon atoms and fourfold silicon atoms link together and ultimately form a random network of amorphous structure. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A New Central Angle Estimation Method of Bistatic MIMO Radar

Based on the theory that the steering vectors of coherently distributed targets for bistatic MIMO radar possess a property called Hadamard product rotational invariance (HPRI), a novel central angle estimation algorithm is derived. The proposed algorithm has the advantage of no searching and easily pair the estimated angles. Furthermore, it can deal with different coherently distributed targets with different angular distribution functions or unknown angular distribution functions. Simulation results show the proposed method is effective.

Inertial Particles in Homogeneous Shear Turbulence: Experiments and Direct Numerical Simulation

The properties of the transport of heavy inertial particles in a uniformly sheared turbulent flow have been investigated by combining experimental and numerical data at particle Stokes number St ≈ 0.3 ÷ 0.5 respectively. As in isotropic turbulence, particles are observed to avoid zones of intense enstrophy and to cluster in strain-dominated regions, resulting in highly intermittent spatial distributions. Moreover, the anisotropy of the mean flow is found to imprint a clear preferential orientation of the particle clusters in the direction of the maximum mean strain. These features are observed both in the numerics and in the experiments, and have been consistently quantified by a number of complementary statistical tools, such as the Voronoi tessellations and the pair correlation function. The latter quantity has been generalized in the form of the Angular Distribution Function and has allowed to evaluate the anisotropy content of the particle field at each scale. The behavior of this observable exhibits the same trend in the two datasets and suggests that, owing to increased inertia, the particle distribution starts to recover isotropy at scales smaller than the carrier velocity field. A proper rescaling of the two datasets in terms of their respective values of the shear scale allows to account for differences in the Reynolds number of experiments and numerics in the range of scales dominated by the mean shear.

Solvation properties and behaviour of lutetium(III) in aqueous solution—A quantum mechanical charge field (QMCF) study

This work presents the first ab initio molecular dynamics study of trivalent lutetium in aqueous solution. The hybrid quantum and molecular mechanics simulation has been carried out on Hartree-Fock level and the results were compared to extended X-ray absorption fine structure and X-ray diffraction data. In addition to the structural characterisation via radial and angular distribution functions, the influence of the ion on the surrounding solvent was further investigated by local-density-corrected three-body distribution functions and frequency calculations. The obtained results for the mean Lu-O bond distance and force constant were in very good agreement with the literature. Furthermore, deeper insight into the dynamics and geometry of the solvation shell and the number of involved solvent molecules was obtained.

Structure and dynamics of the Th4+-ion in aqueous solution – An ab initio QMCF-MD study

An ab initio quantum mechanical charge-field molecular dynamics simulation of the tetravalent thorium ion in aqueous environment is presented. Including the first and second hydration shell in the quantum mechanical treatment to enhance accuracy, this study yields very good results for a wide range of characteristics, as compared to experimental data. 20ps of simulation time were used to investigate structural and dynamical properties of the hydrate by numerous methods, including radial and angular distribution functions, three-body distribution functions, ligand exchange analysis and vibrational spectra. The hydrate proved stable during the simulation and did not show hydrolysis. The first solvation shell was found to be a very flexible one, with a number of intrashell ligand rearrangements occurring along the simulation. The data of the simulation also indicated the existence of a third hydration layer. Vibrational analysis yielded an average ion–oxygen frequency of 420cm−1, which is in excellent agreement with experimental data.

Dynamics of ligand exchange mechanism at Cu(II) in water: An ab initio quantum mechanical charge field molecular dynamics study with extended quantum mechanical region

Ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) were successfully applied to Cu(II) embedded in water to elucidate structure and to understand dynamics of ligand exchange mechanism. From the simulation studies, it was found that using an extended large quantum mechanical region including two shells of hydration is required for a better description of the dynamics of exchanging water molecules. The structural features characterized by radial distribution function, angular distribution function and other analytical parameters were consistent with experimental data. The major outcome of this study was the dynamics of exchange mechanism and reactions in the first hydration shell that could not be studied so far. The dynamical data such as mean residence time of the first shell water molecules and other relevant data from the simulations are close to the results determined experimentally. Another major characteristic of hydrated Cu(II) is the Jahn-Teller distortion which was also successfully reproduced, leading to the final conclusion that the dominating aqua complex is a 6-coordinated species. The ab initio QMCF-MD formalism proved again its capabilities of unraveling even ambiguous properties of hydrated species that are far difficult to explore by any conventional quantum mechanics/molecular mechanics (QM/MM) approach or experiment.

The photoelectron angular distribution of water clusters

The angular distribution of photoelectrons emitted from water clusters has been measured by linearly polarized synchrotron radiation of 40 and 60 eV photon energy. Results are given for the three outermost valence orbitals. The emission patterns are found more isotropic than for isolated molecules. While a simple scattering model is able to explain most of the deviation from molecular behavior, some of our data also suggest an intrinsic change of the angular distribution parameter. The angular distribution function was mapped by rotating the axis of linear polarization of the synchrotron radiation.

Effective permittivity and third-order nonlinear susceptibility for a dilute composite consisting of partially aligned nanorods

The expected permittivity and third-order nonlinear susceptibility of a composite consisting of semiconductor nanorods (NRs) dispersed in a polymer host are derived using a generalized Maxwell Garnett model under various NR axis orientation statistics, achieved by an aligning electric field. The semiconductor NRs are analyzed as prolate spheroids and modeled as more realistic capsule shapes. From the angular distribution function of the NRs, the composite macroscopic characteristics are found for low filling fractions. As the alignment field strength increases, the composite optical properties asymptotically converge toward the nematic case. Aligning fields of order 107  V/m are required for the optical properties to increase to half the value between random orientation and nematic array composites.

The R3-carbon allotrope: a pathway towards glassy carbon under high pressure

Pressure-induced bond type switching and phase transformation in glassy carbon (GC) has been simulated by means of Density Functional Theory (DFT) calculations and the Stochastic Quenching method (SQ) in a wide range of pressures (0–79 GPa). Under pressure, the GC experiences a hardening transition from sp- and sp2-type to sp3-type bonding, in agreement with previous experimental results. Moreover, a new crystalline carbon allotrope possessing R3 symmetry (R3-carbon) is predicted using the stochastic SQ method. The results indicate that R3-carbon can be regarded as an allotrope similar to that of amorphous GC. A very small difference in the heat of formation and the coherence of the radial and angular distribution functions of GC and the R3-carbon structure imply that small perturbations to this crystalline carbon allotrope may provide another possible amorphization pathway of carbon besides that of quenching the liquid melt or gas by ultra-fast cooling.

Optical assessment of silicon nanowire arrays fabricated by metal-assisted chemical etching

Silicon nanowire (SiNW) arrays were prepared on silicon substrates by metal-assisted chemical etching and peeled from the substrates, and their optical properties were measured. The absorption coefficient of the SiNW arrays was higher than that for the bulk silicon over the entire region. The absorption coefficient of a SiNW array composed of 10-μm-long nanowires was much higher than the theoretical absorptance of a 10-μm-thick flat Si wafer, suggesting that SiNW arrays exhibit strong optical confinement. To reveal the reason for this strong optical confinement demonstrated by SiNW arrays, angular distribution functions of their transmittance were experimentally determined. The results suggest that Mie-related scattering plays a significant role in the strong optical confinement of SiNW arrays.

Densification of the packing structure under vibrations

Two packing structures with the maximum packing densities of 0.64 and 0.74 for the amorphous state and crystalline state, respectively, were numerically reproduced in the packing densification of equal spheres subjected to onedimensional and three-dimensional vibrations using the discrete element method (DEM), and the results were physically validated. These two packing structures were analyzed in terms of coordination number (CN), radial distribution function (RDF), angular distribution function (ADF), and pore size distribution (Voronoi/Delaunay tessellation). It is shown that CN distributions have the peak values of 7 and 12 for the amorphous state and crystalline state, respectively. RDF and ADF distributions show isolated peaks and orientation preferences for the crystalline state, indicating the long range and angle correlation among particles commonly observed in the crystalline state. Voronoi/Delaunay tessellation also shows smaller and narrower pore size distribution for the crystalline state.

Theoretical study of stereodynamics for the D′ + DS(v = 0, j = 0) → D′D + S abstraction reaction

Quasiclassical trajectory (QCT) calculations have been performed for the abstraction reaction, D′ + DS(v = 0, j = 0) → D′D + S on a new LZHH potential energy surface (PES) of the adiabatic 3A″ electronic state [Lü et al. 2012 J. Chem. Phys. 136 094308]. The collision energy effect on the integral cross section and product polarization are studied over a wide collision energy range from 0.1 to 2.0 eV. The cross sections calculated by the QCT procedure are in good accordance with previous quantum wave packet results. The three angular distribution functions, P(θr), P(φr), and P(θr, φr), together with the four commonly used polarization-dependent differential cross sections ((2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21−/dωt)) are obtained to gain insight into the chemical stereodynamics of the title reaction. Influences of the collision energy on the product polarization are exhibited and discussed.

The effect of anodizing temperature on structural features and hexagonal arrangement of nanopores in alumina synthesized by two-step anodizing in oxalic acid

Nanoporous anodic aluminum oxide (AAO) layers were synthesized by a two-step self-organized anodization in 0.3M oxalic acid under various anodizing conditions. The influence of anodizing temperature on the structural features and pore arrangement of AAO was investigated. With increasing anodizing temperature, an increase of the pore diameter and porosity of AAO, as well as a decrease of the cell wall thickness and barrier layer thickness were observed. Notwithstanding, the interpore distance and pore density were found to be almost constant independently of the anodizing temperature.A degree of pore order was studied on the basis of the fast Fourier transform (FFT) images, Delaunay triangulations (defect maps), pair distribution functions (PDF) and the angular distribution functions (ADF). For anodizations carried out at 30V, it was found that the better nanopore order in AAO is observed, the higher temperature is applied. It can be explain in terms of the faster reorganization of pores at the metal/oxide interface occurring during the oxide growth at elevated temperatures. On the other hand, no direct effects of the anodizing temperature on the regularity of nanoporous AAO were found for anodizations carried out at higher potentials. A significant increase of the pore circularity with increasing temperature was observed for all studied potentials. The highest values of the FFT-based, PDF and ADF-derived regularity ratios, as well as the lowest percentage of defects and the highest circularity of pores were obtained for samples anodized at 40V independently of the anodizing temperature.

Angle-resolved evolution of the composition of Cr–Al–C thin films deposited by sputtering of a compound target

The composition of multi-element thin films deposited by magnetron sputtering of a compound target may significantly differ from the target composition. Differences in the sputter emission characteristics (angle and energy distributions) and transport of the sputtered species through the gas phase for different elements were shown to be responsible for this phenomenon (Neidhardt et al 2008 J. Appl. Phys. 104 063304). The evolution of the composition of Cr–Al–C thin films deposited by magnetron sputtering of a compound target is investigated as a function of the deposition pressure. The pressure was varied from 0.2 to 3.0 Pa, corresponding to a pressure–distance product range 1.4–21.0 Pa cm. Additionally, the influence of the angle between the target normal and the line between the target and the substrate on the composition is investigated in the range 0°–67.5°. Good agreement between the experimental data and an extended Monte Carlo model based on dynamic (TRIDYN) and static transport of ions in matter (TRIM) simulations is observed for a ternary compound target with a mass ratio of the target constituents of up to 4.3. Furthermore, the influence of the surface binding energies (SBEs) of the target constituents on the thin-film composition is discussed. The simulations indicate that scattering within the collision cascades in a compound target rather than the SBEs determine the character of the angular distribution functions of the sputtered species and, consequently, the thin-film composition. The extended Monte Carlo model employed here predicts variations in composition between the compound target and the as-deposited thin films as the pressure–distance product and the angular orientation of the film with respect to the substrate are varied.

Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts

Molecular dynamic simulations of aqueous solutions containing Me4NCl and an inorganic salt, NaCl, MgCl2 or CaCl2, have been performed at room temperature. Flexible models have been employed for the Me4N+-ions and the water molecules. The hydration of the ions has been discussed on the basis of the radial and angular distribution functions. The geometrical arrangement of the water molecules in the coordination shell has been deduced form the distributions of the angles between two vectors connecting the ion and an oxygen and of the angles between three oxygens. The addition of Me4N+ does not influence noticeably the size and structure of the cationic hydration shells, but it affects remarkably their persistence, causing a fast exchange of the water molecules between the shell and the bulk solvent.

Hydration structure of salt solutions from ab initio molecular dynamics

The solvation structures of Na(+), K(+), and Cl(-) ions in aqueous solution have been investigated using density functional theory (DFT) based Car-Parrinello (CP) molecular dynamics (MD) simulations. CPMD trajectories were collected for systems containing three NaCl or KCl ion pairs solvated by 122 water molecules using three different but commonly employed density functionals (BLYP, HCTH, and PBE) with electron correlation treated at the level of the generalized gradient approximation (GGA). The effect of including dispersion forces was analyzed through the use of an empirical correction to the DFT-GGA scheme. Special attention was paid to the hydration characteristics, especially the structural properties of the first solvation shell of the ions, which was investigated through ion-water radial distribution functions, coordination numbers, and angular distribution functions. There are significant differences between the present results obtained from CPMD simulations and those provided by classical MD based on either the CHARMM force field or a polarizable model. Overall, the computed structural properties are in fair agreement with the available experimental results. In particular, the observed coordination numbers 5.0-5.5, 6.0-6.4, and 6.0-6.5 for Na(+), K(+), and Cl(-), respectively, are consistent with X-ray and neutron scattering studies but differ somewhat from some of the many other recent computational studies of these important systems. Possible reasons for the differences are discussed.

Self-assembly of spherical colloidal particles with off-centered magnetic dipoles

Fluids of spherical colloids possessing an off-centered embedded magnetic dipole were investigated by using Monte Carlo simulations. Systems of colloids with different strengths and directions of the embedded dipole moment confined in a 2D space without and with an external magnetic field applied were considered. The fluids were characterized by radial distribution functions, angular distribution functions, cluster data, and energetic data. In the absence of an external field, the colloids form dimers and trimers at sufficiently large magnetic moment without the tendency of forming chains of colloids as appearing in systems with particles possessing a central magnetic dipole. In the presence of an external field, chains of colloids aligned in a zigzag fashion were formed for a field parallel to the plane of the particles, whereas the colloidal ordering was suppressed in the presence of a field perpendicular to that plane. The findings agree surprisingly well with the recent experimental observations on fluids containing spherical polymer colloids with embedded single-domain magnetic hematite cubes (S. Sacanna, L. Rossi, and D. J. Pine, J. Am. Chem. Soc., 2012, 134, 6112).

Structural Properties of Liquid SiC during Rapid Solidification

The rapid solidification of liquid silicon carbide (SiC) is studied by molecular dynamic simulation using the Tersoff potential. The structural properties of liquid and amorphous SiC are analyzed by the radial distribution function, angular distribution function, coordination number, and visualization technology. Results show that both heteronuclear and homonuclear bonds exist and no atomic segregation occurs during solidification. The bond angles of silicon and carbon atoms are distributed at around 109° and 120°, respectively, and the average coordination number is <4. Threefold carbon atoms and fourfold silicon atoms are linked together by six typical structures and ultimately form a random network of amorphous structure. The simulated results help understand the structural properties of liquid and amorphous SiC, as well as other similar semiconductor alloys.