Particle size analysis of polymer latexes by light scattering. V. The significance of an assumed distribution in the analysis of angular scattering data

In the analysis of light scattering data from polymer latex systems or other systems of spherical particles, it is necessary to assume a particle size distribution function. Theoretical angular scattering functions based on the assumed distribution and representing a wide range of size distribution parameters are compared to experimental data in order to obtain a best fit. In previous work, it has been shown that as the polydispersity increases beyond certain limits the uncertainty in the assignment of the size distribution parameters (i.e., the best fit) increases. This report is concerned with the analysis of angular scattering from unimodal systems and simulated cases where theoretical scattering functions for wide, negatively skewed distributions are used as “experimental data,” are analyzed by utilizing four different distribution functions. These functions represent different degrees of skewness and include negatively, positively, and normally skewed distributions. The results from the use of the various distribution functions are discussed with respect to the uncertainly in the assignment of distribution parameters resulting from the loss of structure in the angular scattering pattern due to increased polydispersity. Scattering data from the bimodal distribution are analyzed by assuming a unimodel distribution, and the consequences of this assumption are assessed.     

The importance of polarization for electron scattering in the intermediate energy region

The angular dependence of electron scattering from the helium atom and the hydrogen molecule for small scattering angles in the 34 – 100 eV impact energy range is explained in terms of the first Born approximation and the polarized Born approximation. The theoretical results compare favorably with the experimental data for both elastic and inelastic scattering. New experimental and theoretical results are presented.     

Angular intensity distribution of a molecular oxygen beam scattered from a graphite surface

The scattering of the oxygen molecule from a graphite surface has been studied using a molecular beam scattering technique. The angular intensity distributions of scattered oxygen molecules were measured at incident energies from 291 to 614 meV with surface temperatures from 150 to 500 K. Every observed distribution has a single peak at a larger final angle than the specular angle of 45° which indicates that the normal component of the translation energy of the oxygen molecule is lost by the collision with the graphite surface. The amount of the energy loss by the collision has been roughly estimated as about 30-41% based on the assumption of the tangential momentum conservation during the collision. The distributions have also been analyzed with two theoretical models, the hard cubes model and the smooth surface model. These results indicate that the scattering is dominated by a single collision event of the particle with a flat surface having a large effective mass. The derived effective mass of the graphite surface for the incoming oxygen is 9-12 times heavier than that of a single carbon atom, suggesting a large cooperative motion of the carbon atoms in the topmost graphene layer.     

Photoelectron angular distribution in valence shell ionization of heteroaromatic molecules studied by the continuum multiple scattering xalpha method

Photoelectron angular distributions are calculated for the valence shell ionization of heteroaromatic molecules of pyridine, pyrazine, pyrimidine, pyrrole, and furan by the continuum multiple scattering Xalpha method. The asymmetry parameters exhibit strong energy dependences in ionization from pi orbitals but are almost invariant in ionization from sigma orbitals, in good agreement with experimental results. The asymmetry parameters in ionization from nonbonding orbitals appear generally higher than those in ionization from bonding orbitals. These features are interpreted in terms of the Coulomb phase and photoelectron angular distribution in the molecular frame.     

Hyperthermal Ar atom scattering from a C(0001) surface

Experiments and simulations on the scattering of hyperthermal Ar from a C(0001) surface have been conducted. Measurements of the energy and angular distributions of the scattered Ar flux were made over a range of incident angles, incident energies (2.8-14.1 eV), and surface temperatures (150-700 K). In all cases, the scattering is concentrated in a narrow superspecular peak, with significant energy exchange with the surface. The simulations closely reproduce the experimental observations. Unlike recent experiments on hyperthermal Xe scattering from graphite [Watanabe et al., Eur. Phys. J. D 38, 103 (2006)], the angular dependence of the energy loss is not approximated by the hard cubes model. The simulations are used to investigate why parallel momentum conservation describes Xe scattering, but not Ar scattering, from the surface of graphite. These studies extend our knowledge of gas-surface collisional energy transfer in the hyperthermal regime, and also demonstrate the importance of performing realistic numerical simulations for modeling such encounters.     

Scattering of O2 from AL111

Experimental results are presented for the scattering of well-defined beams of molecular oxygen incident on clean Al(111). The data consist of scattered angular distributions measured as a function of incident angle, and for fixed incident angle, the dependence on surface temperature of the angular distributions. The measurements are interpreted in terms of a scattering theory that treats the exchange of energy between the translational and rotational motions of the molecule and the phonons of the surface using classical dynamics. The dependence of the measured angular distributions on incident beam angle and temperature is well explained by the theory. Rotational excitation and quantum excitation of the O(2) internal stretching mode are briefly discussed.     

The dynamics of the Cl+n-C4H10-->HCl (v',j') + C4H9 reaction at 0.32 eV

Rotational state resolved center-of-mass angular scattering and kinetic energy release distributions have been determined for the HCl (v' = 0, j' = 0-6) products of the reaction of chlorine with n-butane using the photon-initiated reaction technique, coupled with velocity-map ion imaging. The angular and kinetic energy release distributions derived from the ion images are very similar to those obtained previously for the Cl plus ethane reaction. The angular distributions are found to shift from forward scattering to more isotropic scattering with increasing HCl rotational excitation. The kinetic energy release distributions indicate that around 30% of the available energy is channeled into internal excitation of the butyl radical products. The data analysis also suggests that H-atom abstraction takes place from both primary and secondary carbon atom sites, with the primary site producing rotationally cold, forward scattered HCl (v' = 0) products, and the secondary site yielding more isotropically scattered HCl (v' = 0) possessing higher rotational excitation. The mechanisms leading to these two product channels are discussed in the light of the present findings, and in comparison with studies of other Cl plus alkane reactions.     

Crossed beams and theoretical studies of the dynamics of hyperthermal collisions between Ar and ethane

Crossed molecular beams experiments and classical trajectory calculations have been used to study the dynamics of Ar+ethane collisions at hyperthermal collision energies. Experimental time-of-flight and angular distributions of ethane molecules that scatter into the backward hemisphere (with respect to their original direction in the center-of-mass frame) have been collected. Translational energy distributions, derived from the time-of-flight distributions, reveal that a substantial fraction of the collisions transfer abnormally large amounts of energy to internal excitation of ethane. The flux of the scattered ethane molecules increased only slightly from directly backward scattering to sideways scattering. Theoretical calculations show angular and translational energy distributions which are in reasonable agreement with the experimental results. These calculations have been used to examine the microscopic mechanism for large energy transfer collisions ("supercollisions"). Collinear ("head-on") or perpendicular ("side-on") approaches of Ar to the C-C axis of ethane do not promote energy transfer as much as bent approaches, and collisions in which the H atom is "sandwiched" in a bent Ar...H-C configuration lead to the largest energy transfer. The sensitivity of collisional energy transfer to the intramolecular potential energy of ethane has also been examined.     

Interacting resonances in the F+H2 reaction revisited: complex terms, Riemann surfaces, and angular distributions

We study the effect of overlapping resonances on the angular distributions of the reaction F+H2(v=0,j=0)-->HF(v=2,j=0)+H in the collision energy range from 5 to 65 meV, i.e., under the reaction barrier. Reactive scattering calculations were performed using the hyperquantization algorithm on the potential energy surface of Stark and Werner [J. Chem. Phys. 104, 6515 (1996)]. The positions of the Regge and complex energy poles are obtained by Pade reconstruction of the scattering matrix element. The Sturmian theory is invoked to relate the Regge and complex energy terms. For two interacting resonances, a two-sheet Riemann surface is contracted and inverted. The semiclassical complex angular momentum analysis is used to decompose the scattering amplitude into the direct and resonance contributions.     

The concept of mass angular scattering power and its relation to the diffusion constant

An understanding of the scattering of high energy charged particle beams by tissue is required in radiotherapy since the particle trajectories determine the pattern of radiation dose deposition in patients. Numerical calculations of radiation dose often utilize energy dependent values of the angular scattering power. However, the physics literature is replete with confused interpretations of the concept of angular scattering power and its relation to the single scattering cross section for the medium or the diffusion constant in the diffusional limit. The purpose of this article is to clarify these notions.     

Scattering of hyperthermal argon atoms from clean and D-covered Ru(0001) surfaces

Hyperthermal Ar atoms were scattered from a Ru(0001) surface held at temperatures of 180, 400 and 600 K, and from a Ru(0001)-(1×1)D surface held at 114 and 180 K. The resultant angular intensity and energy distributions are complex. The in-plane angular distributions have narrow (FWHM ≤ 10°) near-specular peaks and additional off-specular features. The energy distributions show an oscillatory behavior as a function of outgoing angle. In comparison, scattered Ar atoms from a Ag(111) surface exhibit a broad angular intensity distribution and an energy distribution that qualitatively tracks the binary collision model. The features observed for Ru, which are most evident when scattering from the clean surface at 180 K and from the Ru(0001)-(1×1)D surface, are consistent with rainbow scattering. The measured TOF profiles cannot be adequately described with a single shifted Maxwell-Boltzmann distribution. They can be fitted by two components that exhibit complex variations as a function of outgoing angle. This suggests at least two significantly different site and∕or trajectory dependent energy loss processes at the surface. The results are interpreted in terms of the stiffness of the surface and highlight the anomalous nature of the apparently simple hcp(0001) ruthenium surface.     

Angular scattering using parameterized S matrix elements for the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction: an example of Heisenberg's S matrix programme

A neglected topic in the theory of reactive scattering is the use of parameterized scattering (S) matrix elements to calculate differential cross sections (DCSs). We construct four simple parameterizations, whose moduli are smooth step-functions and whose phases are quadratic functions of the total angular momentum quantum number. Application is made to forward glory scattering in the DCS of the H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction at a translational energy of 1.81 eV, where v and j are vibrational and rotational quantum numbers respectively. The parameterized S matrix elements can reproduce the forward scattering for centre-of-mass reactive scattering angles up to 30° and can identify the total angular momenta (equivalently, impact parameters) that contribute to the glory. The theoretical techniques employed to analyze structure in the DCS include: nearside-farside theory, local angular momentum theory--in both cases incorporating resummations of the partial wave series representation of the scattering amplitude--and the uniform semiclassical theory of forward glory scattering. Our approach is an example of Heisenberg's S matrix programme, in which no potential energy surface is used. Our calculations for the DCS using the four parameterized S matrix elements are counterexamples to the following universal statements often found in the chemical physics literature: "every molecular scattering investigation needs detailed information about the interaction potential," and "an accurate potential energy surface is an essential element in carrying out simulations of a chemical reaction". Both these statements are false.     

Depth and angular profiles of inelastic low-energy electron scattering in condensed molecular samples

Angular distributions of electrons scattered elastically and inelastically from cold solid molecular films of ethylene and nitrogen in various proportions, grown from the gas phase at different temperatures, have been studied by high-resolution electron energy loss spectroscopy. The probing depth of dipole and impact scattering has been investigated by covering the sample by overlayers of argon of increasing thickness. The angular distribution measured for elastically and inelastically dipole-scattered electrons was found to be peaked about the specular direction for all surface conditions studied, while a diffuse angular distribution was possible for electrons that underwent dipole-forbidden scattering. These results allow us to identify favorable conditions for monitoring the composition of a solid sample during the course of reactions occurring under exposure to low-energy electrons.     

A study of measured neutron elastic differential neutron cross sections for 23Na

Elastic neutron scattering angular distributions from ²³Na have been measured for incident neutron energies between 1.0 and 4.0 MeV at the University of Kentucky Accelerator Laboratory using neutron time-of-flight techniques for the scattered neutrons. This is an energy region in which existing data are very sparse. Measurements are compared with the predictions of the light particle-induced reaction code TALYS. The calculations reproduce forward angle scattering but have difficulty with relative minima in the differential cross section and large-angle scattering.     

The elastic scattering on jellium clusters

The following calculations are based on the local density approximation potential (LDA) of W. Ekardt for the spherical jellium-background model (SJBM). Taking into account the smooth shape of the potential, the WKB approximation was used to calculate the energy and angular dependence of the electron scattering cross-sections fo rsmall Na clusters. The number of phase shifts needed to describe the scattering in the range of energies <4.5 eV increases with the size of cluster. The calculated elastic electron scattering cross-sections for the Na clusters, corresponding to the shell closings (8, 20, 40), are exhibiting a pronounced peak structure, correlated with resonance states. The computed peaks of the angular dependences of the cross-sections on energy are shifted to small angles with increasing the cluster size. The absence of fragmentation at these small electron energies presents a challenge for the experimentalists.     

Large energy transfer in hyperthermal heavy-atom—surface scattering: A study of Hg/MgO(100)

Large energy transfer to the solid was observed for Hg scattering from single-crystal MgO(100) in the 1–10 eV range. The final velocity distribution was narrow. The scattering angular distribution was narrow and slightly supraspecular. Classical trajectory calculations using a model solid constructed out of a hundred layers resulted in a double maximum compression travelling wave. This model reproduced the large energy transfer and its dependence on incident energy.     

Vibrational excitation of SF6 scattering from graphite

We have observed vibrationally excited sulfur hexafluoride molecules in direct inelastic scattering from hot graphite surfaces. The vibrational temperature for the scattered flux has been determined by probing the effect of internal temperature on electron-induced fragmentation observed in mass spectra. The vibrational excitation depends on incident translational energy, E_tr, and a maximum temperature increase of 50 K is reached in direct scattering at E_tr = 2.5 eV. No effect of surface temperature has been observed at 950–1400 K. Inelastic angular distributions are reproduced by a collision complex model, and the experimental results are related to existing models for vibrational excitation.     

Rainbows and glories in the angular scattering of the state-to-state F + H2 reaction at E(trans)=0.04088 eV

State-of-the-art differential cross sections (DCSs) have been reported by Wang et al. [Proc. Nat. Acad. Sci. (U.S.), 2008, 105, 6227] for the state-to-state F + H(2)→ FH + H reaction using fully quantum-state-selected crossed molecular beams. We theoretically analyze the angular scattering of this reaction, in order to quantitatively understand the physical content of structure in the DCSs. Three transitions are studied, v(i)=0, j(i)=0, m(i)=0 → v(f)=3, j(f)=0, 1, 2, m(f)=0 at a translational energy of 0.04088 eV, where v, j, m are the vibrational, rotational and helicity quantum numbers respectively for the initial and final states. The input to our analyses consists of accurate quantum scattering (S) matrix elements computed for the Fu-Xu-Zhang potential energy surface, as used by Wang et al. in a computational simulation of their experimental DCSs. We prove that the pronounced peak at forward angles observed in the experimental and simulated DCSs for all three transitions is a glory. At larger angles, it is demonstrated that the 000 → 300 and 000 → 310 DCSs both possess a broad farside rainbow, which is accompanied by diffraction oscillations. We confirm the conjecture of Wang et al. that these diffraction oscillations arise from nearside-farside (NF) interference. We find that the reaction is N dominant for all three transitions. The theoretical techniques used to analyze the angular scattering include uniform semiclassical theories of glory and of rainbow scattering. We also make the first application of a semiclassical formula that is uniform for both glory + rainbow scattering. In addition, structure in the DCSs is analyzed using NF theory and local angular momentum theory, in both cases with three resummations of the partial wave series for the scattering amplitude. We make the first explicit application of the Thiele rational interpolation formula to extract the position and residue of the leading Regge pole from a set of S matrix elements, thereby making contact with complex angular momentum theories of DCSs, which interpret the angular scattering in terms of Regge resonances. Our calculations complement the exit-valley vibrationally-adiabatic analysis of Wang et al.     

Quasiclassical trajectory study of the vibrational quenching of hydroxyl radicals through collision with O atoms

The collisional removal of vibrationally excited OH radicals by O atoms is studied by the quasiclassical trajectory method. To evaluate the effect of different topological features on the scattering processes two different global potential energy surfaces, DMBE IV and TU, are used. Results for reactive, exchange, and inelastic scattering probabilities are reported for central collisions (with zero total angular momentum) with a fixed relative translational energy for vibrational levels of OH ranging from nu=1 to v=8. Vibrational state distributions of product molecules are also compared on the two potential energy surfaces. Both surfaces predict higher probabilities for reaction than for exchange or inelastic scattering. The vibrational state distributions of the product diatomic molecules are different on the two surfaces. In particular, the two surfaces give substantially different probabilities for multiquantum OH vibrational relaxation transitions OH(v)+O-->OH(v')+O.     

Ultra-low energy elastic scattering in a system of three He atoms

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold.