Light scattering from tilted two-dimensional spherulites

The theory of small-angle light scattering was developed for oblique incidence of the light beam on the surface of a two-dimensional spherulite. Results of the theory were compared with previously reported results of light scattering from two-dimensional and three-dimensional spherulites for normal incidence, and with some experimental patterns. The comparisons suggest that the scattering intensity distributions of two-dimensional spherulites deviate from those of three-dimensional spherulites when the sample surface is tilted with respect to the propagation direction of the incident beam, although they are almost identical when the sample surface is normal to the incident beam. Observation of the change of scattered intensity distributions upon tilting the samples thus provides a method of distinguishing between two-dimensional and three-dimensional spherulites. Moreover, this observation makes it possible to determine the degree of planar orientation of the optic axes of optically anisotropic scattering elements within two-dimensional spherulites. The calculations were carried out for special cases of two-dimensional spherulites with the optic axis orientation confined to the two-dimensional plane and randomly or helicoidally rotated around the spherulite radii.     

Morphological studies on polybutylene terephthalate

The morphology of poly(butylene terephthalate) (PBT) crystallized from the melt at various temperatures was studied by small-angle light scattering, polarizing microscopy, and wide-angle x-ray diffraction. Spherulites with a maltese cross at 45° to the polars formed at lower temperatures while spherulites having an apparently higher melting point with a maltese cross along the polars (0°–90°) formed at higher temperatures. The spherulite size and crystallinity increased with increasing crystallization temperature. The H_v scattering patterns arising from the spherulites formed at lower temperature showed intensity maxima at azimuthal angles of 0° and 90°, while those obtained at higher temperatures showed the more common 45° intensity maxima. Microtomed samples from molded PBT bars showed spherulites with a 45° maltese cross which changed to a 0°–90° maltese cross upon heating just prior to melting. The skin-core effect due to varying thermal histories in these molded bars was clearly observed. Solvent crystallized films contained positive 0°–90° spherulites. Some changes occurring upon uniaxial stretching of PBT films are also discussed.     

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.     

聚对苯二甲酸乙二酯形态结构的光散射研究

在不同结晶条件下,聚对苯二甲酸乙二酯样品出现了三种不同的光散射图形(正常球晶、异常球晶和混合球晶散射图形)。并假定正常球晶的光轴方向与半径垂直;异常球晶的光轴方向与半径夹+45°角或-45°角;混合球晶则是正常球晶与异常球晶叠加的结果。基于这些假定,按照Clough的计算公式,用二维球晶模型分别对具有上述各种光轴取向的球晶进行了计算。结果表明,计算出的H_v、V_v散射图形与实验所得的散射图形符合得很好。偏光显微镜的观察结果也进一步证实了这些模型的假定。     

Effect of birefringence on light scattering from deformed spherulitic polymer films

Light scattering from oriented samples of crystalline polymers is affected by the birefringence of the sample. An extension of the theory for scattering from uniaxially deformed two-dimensional and three-dimensional spherulites is made so as to include the retardation of the incident and scattered beams in passing through the birefringent sample. Strain influences scattering, in that it changes the birefringence of the sample and it also changes the anisotropy and shape of the spherulites. Scattering intensities are calculated for both crossed and parallel polarizers as a function of Ω, χ, and Φ, where Ω is the angle between the stretching direction of the sample and the horizontal direction, and χ and Φ are the angles between the stretching direction and the polarization directions of the polarizer and analyzer, respectively. It is shown that for crossed polarizers with Φ = 45° and χ = 45° birefringence changes largely influence the results but that for the polarizers parallel at Φ = 0° and χ = 0° or crossed at Φ = 90° and χ = 0° the birefringence effect is minimized. The intensity distributions for crossed polarizers at Φ = 45° and χ = 45° from polyethylene films stretched to give retardations up to several wavelengths, are found to be in good agreement with the calculated results.     

Orientation-independent charge transport in single spherulites from solution-processed organic semiconductors

Due to the rapidity of morphological development during deposition, solution-processed organic semiconductor thin films exist in semicrystalline or polycrystalline states, incorporating a high degree of local variations in molecular orientation compared to their single-crystal counterparts. Spherulites, a common crystalline superstructure found in these systems, for example, incorporate a large distribution of molecular orientations about the radial axis to maintain their space-filling growth habit. Here, we aim to determine how this distribution of molecular orientations influences charge transport by fabricating arrays of devices on single spherulites. Given that the orientation distribution that is present about the radial axis mandates the presence of low-angle grain boundaries within single spherulites, we find intraspherulitic charge transport to be independent of the general direction of π-stacking; organic field-effect transistors exhibit comparable mobilities regardless of how their channels are oriented with respect to the general π-stacking direction.     

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.     

Scattering of light by disordered spherulites

The scattering of light by a two-dimensional spherulite of radius R is calculated when there is disorder of optic axis orientation with respect to the radius. Special cases are considered when (1) the disorder occurs in the radial direction only, (2) the disorder occurs in the angular direction only, (3) there is combined radial and angular disorder, and (4) the optic axis makes a constant angle with the radius but there is disorder in the twist angle about the axis. In all of these calculations, a correlation function for disorder is defined and the scattering pattern depends on the ratio of the associated correlation distance to the size of the spherulite. With decreasing correlation distance, the azimuthal dependence of the scattering becomes less and there is a change in the variation of scattered intensity with scattering angles in a manner dependent upon the type of disorder.     

Scattering of light by disordered spherulites. II. Effect of disorder in the magnitude of the anisotropy

The contribution to the disorder scattering by imperfect spherulites resulting from fluctuations in the magnitude of the anisotropy is analyzed for two-dimensional spherulites. The fluctuations are described in terms of a parameter characterizing the meansquare amplitude of the fluctuation and a correlation function describing the distance over which the correlation occurs. Cases considered are those where the correlation depends on either the radial or the angular separation of the scattering volume elements. As with the case of disorder in orientation, one finds that disorder in anisotropy may result in a nonzero value of intensity at μ = 0° and 90°, a decrease in the higher-order variation of scattered intensity with θ, and an increase in the intensity of scattering at higher values of θ over that for a perfect spherulite. In addition, disorder in the angular direction leads to an increase in the scattered intensity at small values of θ as compared with the zero intensity of scattering from a perfect spherulite at θ = 0°.     

Electron microscopy study of the structure of normal and abnormal poly(butylene terephthalate) spherulites

Normal and abnormal spherulites of polybutylene terephthalate cast from solution in HFIP were investigated by electron microscopy (CTEM and STEM). Both spherulite types crystallize in the α form. The crystallite is biaxial with its greatest polarizability directions Z and Y oriented along the molecular chain and perpendicular to it in the plane of the terephthalate residue. In the normal spherulites, the [2 10]^* direction is parallel to the radius direction, so that both Z and Y directions are oriented tangentially (negative spherulites). In the abnormal spherulites, the [1 11]^* direction is parallel to the radius, and this explains the observed abnormal light scattering pattern.     

Morphological studies of deformed polybutylene terephthalate (PBT)

PBT is a semi-crystalline thermoplastic polymer whose deformation behavior highly depends on processing parameters. This makes it a model polymer for investigating morphological changes caused by deformation on the spherulitic and lamellar level. In the neck region all states of deformation of the spherulites are observed. Even in the fibrillar phase the borders of the spherulites remain visible. The spherulitic structure is not totally destructed in the neck. The lamellar structure of the fibrillar phase significantly differs from that of the spherulitic region. The lamellae are orientated with respect to the direction of deformation and the lamellae heights are reduced distinctly. Scanning electron microscopy of fracture surfaces reveals for some samples a sharp frontier between spherulitic and fibrillar region. This leads to the conclusion that the necking process may be a phase transition between an isotropic and a highly orientated phase, as predicted for a Van der Waals network.     

Quiescent and strain-induced crystallization of poly(p-phenylene terephthalamide) from sulfuric acid solution

Quiescent and strain-induced crystallization of poly(p-phenylene terephthalamide) (PPTA) from sulfuric acid solution has been studied. Negative spherulites (SA-PPTA spherulites) are formed from hot concentrated solutions by cooling. The spherulite consists of radiating fibrous lamellae several hundred angstroms wide. The electron diffraction pattern indicates that PPTA molecules are oriented perpendicular to the long axes of the fibrous lamellae and that the [010] or [110] direction of the modification I crystal and [010] direction of the modification II crystal are parallel to the long axes of the fibrous lamellae. The width of the lamellae is much smaller than the chain length of the starting PPTA. It appears that hydrolysis of PPTA during melting crystallization determines the chain length, i.e., the width of the fibrous lamella. Stacked, lamellar structures like “row structures” are formed under shear. The longer axes of the fibrous lamellae are oriented perpendicular to the shear direction. It is confirmed by electron diffraction studies that the PPTA molecules are oriented parallel to the shear direction. Well-developed fibrils with the PPTA molecules oriented to the fibril axis, are formed by adding the SA-PPTA spherulites to water with vigorous stirring.     

Nonisothermal crystallization behavior, and morphology of poly(trimethylene terephthalate)/polyethylene glycol copolymers

Poly(trimethylene terephthalate)/polyethylene glycol (PTT/PEG) copolymers, with PEG content ranging from 27.2 to 47.4 wt%, were synthesized by melt copolycondensation. Wide-Angle X-ray diffractometer revealed that all copolymers had the same crystal structure of homo-PTT at room temperature. All copolymers could form ring-banded spherulites, and band spacing increased with increasing PEG content at a given crystallization temperature. Nonisothermal crystallization morphology of copolymers was greatly influenced by cooling rate. When the cooling rate was 2.5 °C/min or lower, banded patterns were absent, whereas when the cooling rate was 20 °C/min or higher, a novel crystal morphology composed of non-banded spherulites (central part) and ring-banded spherulites with decreasing band spacing along the radial growth direction was observed. Moreover, the size of the non-banded spherulitic part decreased with increasing cooling rate. Finally, the nonisothermal crystallization kinetics of copolymers were analyzed and only the Mo method was satisfactory to accurately describe this system.     

A light-scattering study of deformation of liquid-crystalline spherulites of poly(γ-benzyl-L-glutamate) in an electric field

The deformation of liquid-crystalline spherulites of poly(γ-benzyl-L -glutamate) (PBLG) in an electric field was investigated by light scattering, polarized-light microscopy, and birefringence measurements. Under the polarizing microscope, the deformation was found to be dependent upon the field strength. The spherulites deformed perpendicular to the field. Above 75 V/cm in N,N-dimethylformamide or 120 V/cm in 1,1,2-trichloroethane, the deformed spherulites were transformed to rodlike textures. With increasing voltage, the rods gradually oriented parallel to the electric field. On the basis of the experimental results, models for affine deformation are proposed. With these models, light-scattering patterns are calculated. The calculated and experimental patterns agree semiquantitatively.     

Scattering of light from oriented polymer films. II

A statistical theory for the scattering of light from oriented polymer films is developed in terms of angularly dependent generalized correlation functions. Numerical calculations of scattering patterns are carried out for special cases. The scattering depends upon two types of distributions describing (1) the orientation distribution of optical axes of scattering elements and (2) the angular dependence of correlation in orientation between pairs of optic axes. These distributions are expanded in Fourier series (in a two-dimensional treatment), the coefficients of which are functions of elongation and describe the elongation dependence of the scattering patterns.     

The structure and physical properties of in situ composites based on semiflexible thermotropic liquid crystalline copolyesteramide and poly(butylene terephthalate)

Liquid crystalline polymer–poly(butylene terephthalate) (LCP/PBT) blends were prepared by melt mixing. The LCP employed was a thermotropic copolyesteramide based on 30 mol % of p‐amino benzoic acid (ABA) and 70 mol % of poly(ethylene terephthalate) (PET). The thermal, dynamic mechanical and rheological properties, morphology, and crystal structure of LCP/PBT blends were studied. The results showed that the semiflexible ABA30/PET LCP is miscible in the melt state with PBT, and they are partial miscible in the solid state. Differential scanning calorimetric measurements showed that the introduction of the semiflexible LCP into LCP/PBT blends retards the crystallization rate of PBT. However, the LCP dispersed phase acted as the sites for the nucleation of spherulites and enhance the degree of crystallinity of PBT. Hot‐stage optical microscopy examination revealed that the LCP microfibers with random orientation are dispersed in the PBT matrix of compression molded LCP/PBT blends. Under the application of a shearing force, the LCP domains in the PBT matrix tended to deform into microfibers, and to orient themselves along the flow direction. The formation of microfibers resulted in an increase of the storage modulus. The torque measurements indicated that the melting viscosity of the LCP/PBT blends is much lower than that of the pure PBT. Finally, the wide‐angle X‐ray diffraction patterns indicated that PBT shows no structural change with the incorporation of LCP, but the apparent crystal sizes of several diffraction planes change significantly. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 403–414, 2000     

Crystallization and thermoreversible gelation of poly(butylene terephthalate)–epoxy mixtures

The thermoreversible gelation of solutions of poly(butylene terephthalate) (PBT) and a liquid diglycidyl ether of bisphenol-A epoxy has been investigated. The morphology of the gels and the conditions under which they form have been characterized by optical microscopy, thermal analysis, and x-ray scattering. Gels were found to form under two different conditions and with different morphologies. Gels formed after a considerable delay when homogenous PBT-epoxy solutions were cooled to slightly below the dissolution temperature of crystalline PBT. These gels contained large, irregular PBT spherulites and smaller birefringent interspherulitic matter. The melting of these gels and the onset of macroscopic flow coincided with the melting of the interspherulitic matter, and occurred before the melting of the large spherulites. Thermoreversible gels formed very quickly when PBT-epoxy solutions were self-nucleated by heating a dispersion of crystalline PBT in epoxy slightly and briefly above the dissolution temperature and then cooling. These gels displayed only a weak background birefringence and were molten when the weak birefringence disappeared. In both cases, gelation occurred by the formation of a three-dimensional PBT network in the epoxy liquid, and the nodes of the network were crystalline PBT particles. $ 1994 John Wiley & Sons, Inc.     

Crystalline texture of injection-molded nylon 6

Injection-molded specimens of nylon 6 were examined by x-ray diffraction as a function of depth in three characteristic directions. A skin and a core were always found to be present which differed in the degree of crystalline perfection and crystal modification. While the core of pure nylon 6 was found to be not oriented, the core of specimens containing nucleating agents was found to contain a typical texture of the monoclinic modification of nylon 6 in which the distribution probability of the a^* and c^* axes resembles ellipsoids with three unequal axes. A model explaining this texture as due to degenerated (deformed) spherulites is proposed. With a transcrystalline nylon 6 specimen the direction of the fastest growth in the unit cell (which forms the radius of spherulites) is found to be close to the a axis.     

Effect of disorder in the twist angle on light scattering by a three-dimensional spherulite

Light scattering patterns are calculated for imperfect three-dimensional spherulites with fluctuations in the twist angle. The fluctuations are described in terms of a parameter characterizing the distance correlation function. Cases are considered in which (i) the principal axis of the scattering element makes a constant angle with the radius but there is disorder in the twist angle about the axis, and (ii) there is combined twist disorder and orientation disorder of the scattering elements. Calculations suggest that the disorder in the twist angle may lead to a decrease in the higher-order variation of scattered intensity with scattering angle and deviation from the four-leaf-clover-type scattering characteristic of a perfect spherulite at lower scattering angles. On the other hand, disorder in orientation has little effect on the scattering pattern.     

THE MORPHOLOGY AND STRUCTURE OF POLYETHYLENE TEREPHTHALATE SPHERULITES

The morphology and structure of three types of normal and abnormal spherulites of polyethylene terephthalate cast from solution in dimethylphthalate were studied by polarizing microscopy, transmission electron microscopy and electron diffraction techniques. In the normal negative spherulites the [0]~* direction is parallel to the radius direction. In the normal positive spherulites the radius direction is parallel to the [6]~*. In the abnormal PET spherulites the Maltese cross extinction pattern in the polarizing microscope under crossed polars is oriented at 45°to the polars and there are concentric extinction rings around the center of the spherulite. Electron diffraction pattern indicates that [2]~* is parallel to the radius of the spherulite and this explains the observed extinction pattern, in the abnormal spherulite.