X-ray scattering studies of the structure of aqueous hydroxy-propylcellulose solutions

X-ray diffraction studies have been undertaken on aqueous solutions of hydroxy propylcellulose (HPC) over a wide range of the scattering vector Q. The experiments revealed only modest differences in local structure on a distance scale ca. 5–300 Å despite the fact that they covered concentrations generally interpreted as ranging from the isotropic (35.1 wt %) to the anisotropic liquid crystalline (LC) phase (53.5 wt %). Several models were used to interpret the small-angle scattering data, and each gave similar structural parameters and extrapolated intensities ( Q → 0) for both solutions. Peaks were observed with d-spacings ca. 12–17 Å in both materials. Wide-angle x-ray scattering (WAXS) showed slightly increased local order over a size range ca. 5–20 Å for the anisotropic solution, and this is consistent with a greater intensity of the 13 Å peak in this material. It is difficult to reconcile these findings with an interpretation of the LC state involving major differences with the isotropic phase and a high degree of orientational order extending over long length scales.     

Theory of light scattering from vesicles

The scattering and depolarization of light from spherical membrane systems, vesicles, is calculated in a new succinct formalism appropriate to spherical systems and the rotations of anisotropic elements composing them. The results of Tinker (1972) and Mishima (1980, 1981) are readily derived within this formalism and there is a considerable saving in numerical computation. The problem of fluctuations in the molecular packing of the component phospholipid molecules is also addressed.     

Calculation of the glory scattering with anisotropic molecule-atom interactions in sudden approximation

For specified rotational states glory phenomena are investigated in sudden approximation under influence of angle dependent terms in the intermolecular potential. The distance at which the intermolecular potential is probed by the anisotropic glory undulation is R ≈ 0.96 R_m, for LJ 12-6 potentials, i.e. the well defined probing distance nearly coincides with the classical turning point of the glory ray. For a specific choice of the ratio of anisotropy parameters, q_2,12/q_2,6, ≈ 1.5, the anisotropic glory changes sign. Quenching of the state averaged glories practically disappears for q_2,12/q_2,6 ≈ 2 (e.g. for NO-Ar). The method of calculation is tested against a full partial wave treatment.     

Small-angle scattering of polarized light. I. comparison of theoretical predictions for isotropic and anisotropic spheres

This paper describes small angle light scattering (SALS) calculations and compares the results for isotropic and anisotropic spheres. For isotropic spheres the exact Mie theory is compared with the Rayleigh-Gans-Debye (RGD) and the anomalous diffraction (AD) approximations in order to study the validity of the approximations. For anisotropic spheres the RGD is compared with the AD approximation. A study of SALS in the RGD approximation shows that the first-order intensity maximum corresponding to a lobe of the four-leaf clover pattern is not only a function of the sphere diameter but also depends on the isotropic and the anisotropic refractive index of the sphere. The practical implications of this are discussed.     

Low-angle x-ray scattering from crazes and fracture surfaces in polystyrene

Both crazes and fracture surfaces in glassy polymers produce a low-angle scattering of x-rays. Scattering patterns are anisotropic and often show considerable streaking. In the one case (polystyrene) studied extensively so far, detalied analysis suggests that the craze is approximated as a collection of spheroidal or irregular-shaped voids surrounded by material with anisotropic density distribution arising from its orientation in the stress direction. The void dimension is about 90–115 Å and the specific internal surface area about 170 m²/cm³ of craze. These results and those from electron microscopic studies are reasonably consistent.     

Determination of static microstructure of dilute and concentrated suspensions of anisotropic particles by ultra-small-angle X-ray scattering

Ultra-small-angle X-ray scattering was performed on suspensions of anisotropic polystyrene particles of varying degrees of anisotropy. The wave vector dependence of particle form factors is well described by a model developed by Debye for the scattering from fused spheres. As volume fraction is raised, all suspensions undergo a disorder/order phase transition. The scattering from disordered and ordered suspensions of anisotropic particles is the same as that of spheres up to volume fractions of 0.45, suggesting that, in the dilute crystalline phase, the anisotropic particles order into a rotator or plastic crystal phase, where the particle centers of mass are ordered, but the particle directors are randomly distributed. Further increase in particle volume fraction leads to differences in scattering between homonuclear dicolloids and spheres, implying that the homonuclear dicolloids form a body-centered tetragonal phase with both positional and directional order. This conclusion is supported by real-space imaging of dried films of the particles.     

Electron scattering states for low-energy spectroscopies

In contrast to bound-state calculations for the valence band regime, the continuous states of half-space systems have not attained a level where a broad variety of methods ensures large applicability and sufficient accuracy for the needs of highly resolved spectroscopy. The multiple-scattering procedure works well in the high-energy range, but lacks either accuracy or convenience when applied to lower energies, where the anisotropic parts of the potential are strongly effective. The concept of Bloch-wave procedures in its original form is less well adapted to scattering boundary conditions, but requires additional theoretical adjustment, such as matching conditions, which often leads to an ill-posed boundary problem of the elliptic equation. The solution then suffers from instabilities preventing the development of stand-alone algorithms. The current state of the subject together with some promising solutions will be presented. Consideration will be given to the multiple scattering approach with anisotropic potentials and to the Bloch-wave development relying on pseudopotential, as well as on singular-potential formulations. The importance and quality of procedures is estimated through a comparison with very low energy electron diffraction (VLEED), low-energy electron diffraction (LEED) and total current spectroscopy (TCS) experiments.     

Correction factors for sizing weakly anisotropic transparent fibers using light scattering

Correction factors defined as the ratio of the true size parameter and the size parameter deduced from Fraunhofer diffraction theory are presented for weakly anisotropic transparent fibers. These correction factors enable the Fraunhofer diffraction approximation to be used for sizing weakly anisotropic fibers from light-scattering measurements. Fibers in the diameter range 4–50 μm and refractive index range 1.45–1.56 are considered. It is shown that for fibers having birefringence ?0.005 ≤ Δm ≤ 0.01, the diameters may be obtained to within 9% accuracy if the fiber diameter lies between 4 and 50 μm.     

On the shape of the Q-branch of Raman scattering spectra in dense media. Theory

A nonadiabatic quasi-classical impact theory of the Q-band shape for isotropic and anisotropic Raman scattering by linear rotors has been developed. With our previous results this allows us to obtain upper and lower estimates of the contribution of collisional rotational relaxation to the Raman line broadening.     

Depolarization of light scattering by atomic and molecular solutions with strongly anisotropic translational-orientational fluctuations

Translational-orientational fluctuations are shown to raise or lower the depolarization of light scattered by solutions according to the structure of the near-order region of anisotropic molecules. In solutions of atoms, translational fluctuations induce anisotropic scattering already described in the bi-molecular radial correlations approximation; in accordance with the latest experiments, this scattering undergoes an increase or decrease depending on ternary radial correlations. A general expression for the effective optical anisotropy of the near-order region in solutions is applied to the dilute case permitting, in a novel manner, determination of both the value and sign of the anisotropy for isolated solute molecules.     

Isotropic and anisotropic scattering from polyethylene during crystallization

A light-scattering method for determining the optical anisotropy of large molecules is considered in detail. An application of the method is demonstrated to linear polyethylene while isothermally crystallizing in p-xylene solution. The polyethylene crystals formed are characterized as anisotropic thin discs having an optical anisotropy of 0.4–0.6.     

Suppressed forward scattering in photoelectron holography

The anisotropic nature of photoelectron source waves may be exploited to suppress forward scattering in photoelectron diffraction. Theoretical simulations show that this is the case for a geometry where the scattered electrons are measured close to a node of the electron source wave. As a consequence the quality of holographic reconstructions from such data improves considerably. The optimum geometry between the excitation source and the electron analyzer is evaluated quantitatively for the case of Mg K excited C1s electrons in CO molecules.     

Zero-angle depolarized light scattering of a colloidal polymer

The potential of zero-angle depolarized scattering for measuring the size distributions of optically anisotropic particles is considered. To illustrate the method, an analysis of Fluon, a teflon latex suspension, is presented. Homodyne correlation functions having signal-to-noise characteristics every bit as good as conventional unpolarized finite-angle measurements enabled confident application of a smoothed exponential sampling algorithm to obtain the decay rate distribution, which was converted to a size distribution with certain approximations. The size distribution obtained from light scattering agrees well with that from electron microscopy.     

The effect of interference between anisotropic scattering entities on the light scattering from polymer films. I. Case of no impingement

Equations are developed for describing the effect of interspherulitic interference on the scattering of light by anisotropic spherulites. These are used to account for the variation in V_V and H_H scattered intensity during the course of spherulitic crystallization. The scattering depends upon the number of spherulites, their size, their anisotropy, the difference between one of their polarizabilities and that of the surroundings, and the radial distribution function of spherulite centers.     

Light scattering and x-ray characterization of amylose films

Small-angle light scattering (SALS) in the solid state and x-ray diffraction were used to investigate the development of anisotropic structure in water-cast amylose films prepared under various conditions. The conditions investigated were different temperatures and relative humidities maintained during the drying of the films and different aging times and temperatures of the amylose solution prior to the casting of films. As revealed by SALS, the predominant morphology developing in these films was based on rod-like scattering units of considerable size. At times, a low degree of spherulitic character was also evident in the films. All four experimental conditions affected the development of anisotropic structure, with the aging time and temperature producing the most noticeable effects. Increasing aging time and/or decreasing aging temperature markedly increased the rod-like morphology of the films. On the other hand, crystallite sizes as measured by x-ray diffraction remained constant at 24–28 Å, indicating no influence on the part of experimental conditions. These findings are discussed in the light of starch retrogradation.     

Light scattering in binary and ternary (polymer) solutions with specific interactions

Concentration dependence of basic light-scattering quantities in three binary low-molecular and two ternary polymer solutions was studied. Depolarization ratio alone may serve as a sensitive measure of presence of specific interactions. Experimental data of anisotropic scattering in low-molecular mixtures were in harmony with the idea that the parameters determining molecular orientation should be considered as continuous probability variables; in the case of polymer solutions specific interactions do not influence the anisotropic scattering.The presence of specific interactions with the formation of a minimum on the course of isotropic scattering is characterized. Transition from one solution structure to another with a local maximum on the course of composition light scattering is indicated.     

Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Liquid crystal electrohydrodynamics in the presence of a magnetic field: the dynamic scattering transition

We have studied electrohydrodynamic convection in the nematic liquid crystal MMBA in the conduction regime in the presence of a competing magnetic field. This field substantially alters the behaviour of the system, causing a metastable surface deformation and travelling waves. The magnetic field also alters the transition between the two dynamic scattering modes so that both states retain anisotropic ordering. A scaling relation is found describing this hysteretic transition. We report the existence of a stable mixed state of DSM 1 and DSM 2.     

Liquid crystal electrohydrodynamics in the presence of a magnetic field: the dynamic scattering transition

We have studied electrohydrodynamic convection in the nematic liquid crystal MMBA in the conduction regime in the presence of a competing magnetic field. This field substantially alters the behaviour of the system, causing a metastable surface deformation and travelling waves. The magnetic field also alters the transition between the two dynamic scattering modes so that both states retain anisotropic ordering. A scaling relation is found describing this hysteretic transition. We report the existence of a stable mixed state of DSM 1 and DSM 2.     

A simple representation of small-angle light scattering from an anisotropic sphere

An explicit form of Mueller's phenomenological matrix has been derived which characterizes the small-angle light scattering from an anisotropic sphere when the requirements of the Rayleigh-Gans approximation are fulfilled.