Light scattering from swollen textured polymer network composites

Light scattering from a swollen textured heterogeneous polymer network is discussed using example of a network composite filled by spherical inclusions anisotropically distributed in the matrix. The dependence of the scattering intensity on the Fourier transform of the correlation function dry-state shear moduli fluctuations has been established. H_v scattering patterns from uniaxial textures and their ratio with the composite anisotropy parameter are analyzed. The sensitivity of the H_v scattering pattern on restrictions during the swelling is emphasized. © 1993 John Wiley & Sons, Inc.     

Small-Angle light scattering from an anisotropic sphere: Anisotropy and size effects

The recently developed theory of light scattering from an anisotropic sphere (taken as a model for a spherulite) summarizes all information obtainable from such scattering system when the Rayleigh-Gans-Debye approximation is appropriate. The commonly used procedure of size determination from the maximum of the H_v intensity is tested for a number of models differing in radius size, inherent anisotropy δn and mean refractive index ¯n. It has been confirmed, that the parameter (¯n - 1)/δn plays the decisive role in the angular dependence of the H_v intensity and the influence of that parameter on the size determination and resulting accuracy is specified. The results differ for positive and negative spherulites and the stabilizing role of increasing spherulite size in accuracy of procedure is demonstrated. It has been shown that the RGD approximation is appropriate especially for the case of homogeneous spherulite texture (thus implying, that the refractive index of the surrounding is close to the average refractive index of a single spherulite). The results extrapolated outside of the RGD approximation display invariable U_max position for isotropic contribution with increasing sphere size in contrast to the oscillatory character of U_max predicted by the LM solution. It is proposed to construct the anisotropic solution under an approximation recently suggested for thin anisotropic shell. © 1994 John Wiley & Sons, Inc.     

Scattering of light by deformed three-dimensional spherulites

A theoretical calculation of the H_v light-scattering patterns for deformed three-dimensional spherulites is presented. Affine deformation is assumed. The optic axis of the scattering element is allowed to lie at an arbitrary angle ß to the radius which is permitted to change in the course of the deformation in a manner that may depend upon the angular location in the spherulite. The consequences of twisting of the optic axis about the spherulite radius are also explored.     

Light scattering from crystalline superstructure in tubular-extruded polybutene-1 films

Light scattering from polybutene-1 films prepared by tubular extrusion was studied in order to investigate its crystalline superstructure and the deformation mechanism. Analysis of the light-scattering patterns together with electron micrographs, indicate the existence of sheaflike crystalline superstructures. The sheaves are aligned nearly side by side with their axes preferentially oriented perpendicular to the machine direction. The H_v scattering patterns exhibit a “butterfly” appearance. Analysis of the patterns in terms of scattering and azimuthal angles at which the scattering intensity is a maximum yields information on the size and shape of the sheaflike texture. The information should be of importance in studies of anisotropic crystal growth caused by molecular orientation in the melt and of the deformation mechanism of the texture. The deformation behavior should be representative of that of different parts of spherulites, at least qualitatively; the deformation of the texture along the machine and transverse directions corresponds to deformation of equatorial and meridional regions of a spherulite, respectively.     

Formation of band textures in hydroxypropylcellulose liquid crystals

Upon shearing, some polymeric liquid crystals develop a particular texture, called “band texture,” consisting of fine equidistant black lines as viewed between crossed polarizers. In mesomorphic hydroxypropylcellulose–water solutions, these bands are due to relaxation of the shear. The band texture appears after shearing at low shear rates and seems to exist during shearing at high shear rates (> 200 S^?1). In the latter case, the steady-state first normal-stress difference is negative. The bands relax in a few minutes and parts of the bands form elongated domains. This texture gives a H_v light-scattering pattern which can be interpreted by the theory of scattering by anisotropic rods. These domains lose their elongated shape with time.     

Untersuchungen zu den Anisotropie- und Dichtefluktuationen im Polymethylmethacrylat mit Hilfe der Lichtstreuung

Zusammenfassung DieV _r - undH _r -Komponenten des an verschieden vorbehandelten Polymethylmethacrylat-Proben gestreuten Lichtes wurden mit Hilfe eines Lichtstreuphotometers in Abhängigkeit vom Streuwinkel und von der Temperatur gemessen. Aus der Höhe der winkel- und temperaturunabhängigenH _v -Komponente wurde eine obere Grenze von 28 Å für die Größe der im PMMA vorhandenen anisotropen Strukturen errechnet. Tatsächlich dürften sie jedoch wesentlich kleiner sein. Flüssigkeiten mit isotropen Molekülen wie z.B. Tetrachlorkohlenstoff verursachen nämlich bereits eine ähnlich hoheH _v -Komponente.Neben den geringen Anisotropiefluktuationen liegen Dichtefluktuationen vor, die zu einer Winkelabhängigkeit derV _v -Komponente führen. Verantwortlich hierfür sind niedermolekulare Bereiche und Löcher mit Dimensionen von 1000–3000 Å. Zusätzlich sind thermische Dichtefluktutionen vorhanden. Bei großen Streuwinkeln kommt etwa die Hälfte der gestreuten Intensität durch sie zustande.

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Summary TheV _v andH _v components of the light scattered by polymethylmethacrylate samples, which had been subjected to different pretreatments, were measured as a function of the scattering angle and temperature with the help of a light scattering photometer. An upper limit of 28 Å for the size of the anisotropic structures present in PMMA was calculated from the height of the angle- and temperature-independentH _v component. They may however be essentially smaller. In fact, fluids with isotropic molecules, for example carbon tetrachloride, give rise to a similarly highH _v component.In addition to the slight anisotropy fluctuations, density fluctuations are present, which lead to an angular dependence of theV _v component. Lower molecular regions and holes with dimensions of 1000–3000 Å are responsible for this. There exist also thermal fluctuations. Approximately half of the scattered light intensity at large scattering angles is caused by them.

     

Morphology of a liquid-crystalline polyester film

Morphological studies are reported for a thermotropic liquid crystalline polyester. Small angle light scattering studies were carried out as a function of temperature using H_v and V_v polarization with photographic as well as photometric techniques. No scattering was observed from a thin film cast from a dilute solution of the polymer in a highly volatile solvent. When the film was heated, scattering of light was observed above the glass transition temperature of the polyester. The scattering was found to be azimuthally dependent with V_v intensities being much higher than the corresponding H_v intensities. The size of the morphological features responsible for SALS patterns were calculated and were found not to change significantly with temperature ranging from glass transition temperature to the solid-nematic transition temperature of the polyester. The WAXS pattern of solution cast polymer was representative of an amorphous structure. Solution cast films heat treated under various conditions (all above the T_g of the polymer) contained crystalline as well as amorphous structures. The maximum apparent crystallinity for annealed samples was of the order of 30%.     

Deformation of polybutene-1 spherulites

The deformation of fresh and aged polybutene-1 spherulitic samples has been investigated by microscopic observation, interferometry, studying macroscopic and spherulitic birefringence changes, and study of light-scattering patterns. The spherulite deformation is not affine, the microscopic deformation ratio being less than the macroscopic deformation ratio of the sample and greater in the equatorial regions of the spherulite than in the polar regions. The deviation from affine deformation is less for fresh spherulites than for the aged, where void formation occurs in the equatorial part of the spherulite. This gives rise to large scattering by this part of the spherulite and to form birefringence. The spherulite birefringence and its change with elongation is dependent upon the degree of aging of the sample. The spherulite birefringence is more negative for the aged sample. In the polar regions of the spherulite, this negative birefringence decreases and turns positive at higher elongations, characteristic of a reorientation of the crystals with their optic axes turning from being perpendicular to parallel to the spherulite radius. The spherulite birefringence in the equatorial direction becomes somewhat more negative on stretching a fresh sample but less negative on stretching an aged one. Spherulite distortion and orientation changes are apparent from the light-scattering patterns of films possessing small spherulites. The changes in V_v and H_v scattering patterns upon stretch are different for the fresh and aged samples. The V_v patterns of the fresh samples decrease in intensity with time after stretching a fresh sample with the H_v patterns do not.     

Changes in light scattering from poly(ethylene terephthalate) and nylon 6 films upon stretching in relation to the deformation mechanism

Unoriented T-die flat films of nylon 6 and PET films annealed at 90°C were stretched in water at 80°C. Amorphous PET films were stretched in water at 65–75°C. Changes in the light scattering patterns from these samples upon stretching were investigated. One of the observed LS patterns from the stretched samples is the H_v eight-leaf pattern consisting of four lobes and streaks. In the nylon 6 and heat-treated PET showing this pattern, spherulitic patterns can be seen in polarization microscopy. The microscopic spherulitic superstructure may possibly be the factor responsible for producing the lobe-and-streak pattern. On the other hand, many microscopic eight-leaf patterns can be observed in amorphous unannealed PET showing the lobe-and-streak pattern. These microscopic patterns are due to retardation at stress concentrations around impurities and nuclei. The superstructure giving these microscopic patterns must be the origin of the lobe-and-streak pattern from unannealed PET. Another scattering pattern, the V_v cruciform pattern, was observed in both stretched nylon 6 and unannealed PET. This pattern is due to an orientation change across the slip lines observed under a polarizing microscope. It is noted (1) that the appearance of the slip lines in PET coincides with the occurrence of oriented crystallization on stretching, (2) that the lobe-and-streak pattern from PET in which orientation crystallization has taken place is fairly stable to heat treatment and does not disappear until just before melting, and (3) that the superstructures produced at low stretching seem to be deformed on further stretching, in accordance with affine deformation theory.     

The scattering of light from thin polymer films: Multiple scattering. II. Effect of depolarization

A procedure is described to include the effect of depolarization of the originally plane-polarized incident light beam as it passes through a thin polymer sample on the intensity of multiple light scattering. The multiple scattering gives rise to “polarization scrambling” in which, for example, H_v scattering measurements involve multiple scattered rays which may have undergone some V_v scattering. These phenomena reduce the angular dependence of scattering since large intensities originally occurring at small values of θ are rescattered so as to enhance intensities at other angles. Correction factors for both H_v and V_v scattering are presented.     

Constrained anisotropic dipole oscillator strength distribution techniques,and reliable results for anisotropic and isotropic dipole molecular properties,with applications to H2 and N2

Summary Constrained anisotropic dipole oscillator strength distribution techniques are discussed and applied to obtain reliable results for a wide variety of the anisotropic and isotropic dipole properties of H₂ and N₂. These include the dipole oscillator strength sumsS _k, k=2, 1, –1/2(–1/2) –2, –3, –4, ..., the logarithmic dipole sumsL _k and mean excitation energiesI _k, k=2(–1) – 2, and, as a function of wavelength, the dynamic polarizability and the associated anisotropy, the total depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. The anisotropic components of the DOSD for a molecule are obtained from a given recommended isotropic DOSD by using a constrained least squares procedure and a series of known anisotropic constraints. Assuming that sufficient input is available, the constrained DOSD approach used in this paper is the only available method for the reliable evaluation ofall the relevant anisotropic and isotropic dipole properties for a wide variety of atoms and molecules.This research was supported by a grant from the Natural Sciences and Engineering Research Council of CanadaOn leave from Department of Physics, Meerut University, Meerut, India     

Small-angle light scattering from hedrites,ovoids, and spiral ovoids. II. Experimental

Procedures for obtaining hedrites, ovoids, and spiral ovoids in polyoxymethylene are described. Results of morphological studies on these structures by optical and electron microscopy are presented. Small-angle light scattering studies on single isolated supermolecular structures are described. The V_v and H_v diffraction patterns obtained experimentally are discussed in the light of theoretical results of Part I of this study.     

Light scattering by anisotropic elliptical objects

The small-angle light scattering in H_v and V_v modes is calculated for elliptical disks with the use of an elliptical coordinate system. The method is general for all degrees of ellipticity, from a circular disk to rodlike extensions, and permits the definition of any desired dipole orientations. The solution is obtained by computer-assisted numeric integration. Two models are considered, an “elliptical” one an “affine deformation” one differing in the orientation of scattering dipoles. The calculated patterns show a significant dependence of the distribution of the scattered intensity on the size and the elliptical axial ratio in both models, permitting the determination of both the size and the degree of ellipticity of the disk from its patterns. In addition, the differences between the calculated results for the two models are sufficiently large to permit the selection of the experimentally appropriate model, at least within the range of moderate degree of ellipticity.     

Small-angle light scattering from hedrites,ovoids, and spiral ovoids. I. Theoretical considerations

Taking into consideration results of our microscopy studies and data given in the literature on the structure of hedrites, ovoids, and spiral ovoids, we have developed optical models for these morphological entities. These models are applied to calculations of small-angle scattered light intensity distributions for these structural elements. Analytic formulae computed for the V_v and H_v scattering patterns contain terms dependent only on azimuthal angle μ and vertical angle θ. For hedrites and ovoids, equations are derived relating the characteristic points of scattered light intensity patterns to structural parameters. The corresponding diagrams of light intensity distributions are given.     

Study of the molecular conformation of an aromatic polyamide–hydrazide by intrinsic viscosity

The persistence length of poly(terephthaloyl p-amino benzhydrazide) (X-500) in dimethyl sulfoxide (DMSO) has been determined from intrinsic viscosities measured for several whole-polymer samples. An approximate correction is applied for excluded volume effects, and these corrected values are fitted using the viscosity treatments of Yamakawa and Fujii and of Eizner and Ptitsyn. Both give for the persistence length of X-500 values in the range 30–35 Å. Revised treatment of our previous light scattering data for the same polymer yields 49 Å for the persistence length. Thus the chain extension of X-500 falls between those of para-linked polyamides and those of typical freely coiling macromolecules. Phase diagram studies indicate the solubility of X-500 in DMSO decreases with rising temperature, and can be increased by the addition of LiCl. No anisotropic phase is found in DMSO at the highest volume fraction of polymer, v₂ = 0.19, which can be obtained with 4 g/dl LiCl. The critical concentration of X-500 needed for the appearance of the anisotropic phase depends upon solvent since Morgan reported an anisotropic phase for this polymer in 100% H₂SO₄ when v₂ ≈ 0.13.     

A lattice theory of light scattering from disordered spherulites

A lattice theory of orientational disorder in two-dimensional spherulites is developed in which the orientation direction of the optic axis in lattice cells is allowed statistically to deviate from its mean value in a manner correlated with the orientation in neighboring cells. The H_v light scattering patterns arising from such disordered spherulites deviate from the patterns for perfect spherulites in that there is excess intensity at both small and large scattering angles and the intensity at the maximum is lower. A comparison of the calculated scattering angular dependence with that which is experimentally measured permits assignment of values of correlation parameters. A consequence of this disorder is that the spherulite birefringence is reduced below that calculated on the basis of perfect crystalline orientation in agreement with experiment.     

Small-angle light scattering by random assemblies of incomplete spherulites. I. Sheaflike textures

The calculation of the scattering from a sheaflike sector of a two-dimensional spherulite has been carried out as a function of the apex angle of the sector. It is found that while for a complete spherulite the H_v scattered intensity is zero at zero scattering angle, there is an increasing intensity of scattering at 0° as the sector angle narrows. For very small values of the sector angle, the scattering becomes similar to that of a rod, with the exception that a scattering maximum is still seen at an angle close to that at which the spherulite scattering maximum occurs. The predictions of the model compare favorably with the scattering patterns observed for polymers in early stages of spherulitic growth.     

Small-angle light scattering by random assemblies of incomplete spherulites. Systems with partial degree of volume filling

A theory is presented to account for the effect of the impingement of growing spherulites on their H_v small-angle light scattering patterns. The theory is developed on the basis of results of computer-simulated two-dimensional spherulite growth and calculated scattered intensities. The impingement produces a lowering of the intensity of the scattering maximum and the diminishing of the overall sharpness of the scattering peak. The extent of these effects increases with area fraction of spherulites. A procedure is suggested for determining correction factors that may be applied to intensity data obtained during the course of spherulite crystallization. An interpretation is made of the type of average spherulite size determined from the scattering angle of maximum intensity.     

Supramolecular structure investigation of poly(γ-benzyl, α-l-glutamate)-benzyl alcohol system by static light scattering

The cholesteric mesophase of the PBLG-BA system in concentrated solutions and in the gel phase has been investigated by static laser light scattering. The observed ‘distortion’ of the patterns in terms of their dependence on the azimuthal angle was studied. Effect of form-optical rotation on the pattern is discussed. The manner of distortion in the H_v pattern determines the sense of cholesteric twisting. The observed scattering patterns are analogous to those obtained by previous investigators in other solvents. Quantitative measurements of the intensity as a function of scattering vector provide information on the sense and pitch of the cholesteric twisting, as a function of temperature and concentration. Optical microscopy studies reveal onset and build-up of the cholesteric structure. Optical rotation and differential scanning calorimetry (DSC) studies support the conclusions obtained from light-scattering experiments.     

Optical studies of the deformation of model filled rubbers

The strain pattern about a spherical glass bead imbedded in a stretched rubber has been calculated and used to predict the birefringence and light scattering. This is compared with experimental measurements of the retardation pattern observed using a polarization microscope and deduced from the low-angle laser H_v light scattering pattern. The agreement with theory is favorable. The light scattering is suggestive of similar origins of light scattering from crystallizing rubbers and from inhomogeneously crosslinked rubbers.