The effect of spherulitic truncation on small-angle light scattering

The effects of spherulitic truncation on the H_v small-angle light-scattering (SALS) patterns are determined by computer simulation of spherulite nucleation and growth. The simulation is carried out for simultaneous and sporadic nucleation of two-dimensional spherulites and simultaneous nucleation of three-dimensional spherulites. The scattered intensity differences between truncated spherulites and round spherulites are determined as functions of the type of growth and the volume (or area) fraction of spherulites. Methods for the determination of certain geometrical characteristics of spherulites systems by SALS are developed. These characteristics include the volume (or area). fraction of spherulites, the average spherulite radius, and the average spherulite volume (or area). The results of this study are essential in the quantitative analysis of H_v SALS from spherulitic systems. The simulation process is readily extendable to the examination of other morphological phenomena by SALS.     

Scattering from truncated spherulites

A general two-dimensional theory is derived to explain the light scattering from truncated spherulites. The severity of the truncation is expressed by a statistical parameter σ²/ā² which is the ratio of the variance σ² of the size of the spherulite to the square of its average size ā. The H_v light-scattering patterns are calculated for different values of the truncation parameter. It is observed that the truncation decreases the position of maximum scattering intensity of the pattern. It also increases the scattering intensity at small and large angles, but reduces it at intermediate angles. For a spherulitic polyethylene sample, the truncation parameter is found to equal 0.100 ± 0.030 as measured microscopically. The theory can also be used to calculate light-scattering patterns from row-nucleated spherulites. If it is assumed that the interference effect averages out to zero when a large number of spherulites is involved, a single “sliced” spherulite model can be used. Then, the scattering intensity per unit area decreases as the “slice” becomes very thin.     

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.     

Crystal and amorphous orientation behavior of poly(chlorotrifluoroethylene) films in relation to crystalline superstructure

The relationship between the crystalline superstructure of polymer films and molecular orientation was studied in cold-drawn poly(chlorotrifluoroethylene) films by wide-angle x-ray diffraction, birefringence, and depolarized light scattering. By changing crystallization conditions, specimens with almost identical crystallinity but different crystalline superstructures were obtained; i.e., (1) a structure having a random array of crystallites, (2) a superstructure having a rod-like orientation correlation of the chains (a prespherulitic and sheaf-like superstructure), and (3) spherulitic superstructure. Upon stretching of specimens, crystallites initially randomly arranged orient with their chain axes along the stretching direction in accord with simple affine deformation. The amorphous chains also orient along the stretching direction. The orientation behavior of the specimens having the rod-like superstructure is similar to that of the specimens with a random array of crystallites, indicating that the interaction between the crystallites in the superstructure is relatively weak. The molecular orientation behavior of the spherulitic specimens, however, strongly deviates from simple affine deformation owing to strong interaction of the crystallites in the spherulites. The deviation can be interpreted in terms of spherulite deformation and of internal reorientation of chains within deformed spherulites.     

Quantitative characterization of deformation in drawn polypropylene films

The submicroscopic morphology of uniaxially deformed isotactic polypropylene films has been examined by small-angle light scattering (SALS), electron microscopy, optical microscopy, small-angle x-ray scattering (SAXS), wide-angle x-ray diffraction, birefringence, sonic modulus, and density methods. Several new interpretations and extensions of existing theories are developed and verified experimentally as follows. (1) The V_v SALS pattern is shown to be a new tool for the identification of the sign of the birefringence of spherulites too small to be seen in the optical microscope. The theoretical dependence of the V_v SALS pattern is developed and verified experimentally with patterns from isotactic polypropylene, polyethylene, Penton, nylon 6,6, poly(ethylene terephthalate), and nylon 6,10. (2) Intraspherulitic lamellar behavior during deformation can be identified from the SAXS pattern. This includes quantitative evaluation of the long spacing between lamellae and their average orientation. (3) The two-phase sonic modulus theory is valid over the wide range of deformations, crystallinities, processing temperatures, and molecular weights used in this study. The deformation of isotactic polypropylene films drawn at 110 and 135°C. has been characterized quantitatively in terms of an integrated picture of mass movement on all morphological levels: the molecular, the interlamellar, and the spherulitic. At both temperatures, the spherulites deform affinely with extension, whereas the deformation mechanisms within the spherulite depend on the location of the radii with respect to the applied load. During spherulite deformation, lamellar orientation and separation processes predominate, whereas at high extensions, fibrillation occurs and crystal cleavage processes predominate. The noncrystalline region orients throughout the draw region. At 135°C. non-orienting relaxation processes appear in the noncrystalline region which retard the rate of molecular orientation with extension.     

Quantitative small-angle light scattering studies of the melting of poly(ethylene terephthalate)

Quantitative H_v small-angle light-scattering (SALS) studies of the melting of poly(ethylene terephthalate) (PET) have been performed. The results are compared with those from differential scanning calorimetry (DSC). It is found that fully grown spherulites melt over a temperature range of about 20°C without change in spherulite size, number, or internal disorder. The decrease in H_v SALS intensity is due to a decrease in spherulitic crystallinity over the melting range. The corrected experimental intensities are lower than, but in reasonable agreement with, the theoretically predicted intensities based on the DSC results. Procedures are presented for the quantitative analysis of H_v SALS intensities from spherulitic systems, including the corrections for the experimental, external disorder, and internal disorder effects.     

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.     

Effect of optical rotation on low-angle light-scattering patterns

The effect of optical rotation of the environment is calculated for the H_v and V_v low-angle light-scattering patterns of two-dimensional spherulites. As with the effect or birefringence, the change in the H_v pattern is greater than that of the V_v pattern. With increasing optical rotation, the patterns lose their characteristic shape and become more circular.     

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.     

Light scattering from assemblies of spherulites

A general equation describing the small-angle H_v light-scattering intensity for a system of N undeformed spherulites located at random within the sample and taking into account the truncation and interference effects is given. Scattering contour plots or radial scans are reported for various arrangements of the N spherulites. The results show that the interference effect may explain the speckled appearance of the experimental patterns. Moreover, the interference and truncation effects (for the special cases where truncation is considered here) do not seem to shift the position of the maximum scattering angle of the cloverleaf pattern as calculated from the single spherulite theory. Finally, the calculations show that the truncation effect increases the relative intensity of the pattern at large and low scattering angles and at azimuthal angles 0 and 90°C, as compared with the intensity at the position of maximum scattering angle.     

Small-angle light scattering and crystallization processes in solid polymer films

Information, not previously measurable, about the internal crystallization processes occurring within spherulitic films can now be obtained by combining refractive index, birefringence, and small-angle light-scattering measurements. The surroundings of a spherulite in a solid film are composed of both the adjacent spherulites and their interstices (boundaries), and it is shown that different crystallization processes can occur in each of these regions. Upon annealing a quenched isotactic polypropylene film, the rate of crystallization within the interstices of the space-filling spherulites is observed to be greater than the rate of crystallization within the spherulites themselves.     

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.     

Crystal orientation in a semicrystalline polymer in relation to deformation of polymer spherulites. IV. Crystal orientation mechanism of nylon-6 under uniaxial stretching

A model relating crystal orientation to the deformation of nylon-6 spherulites under uniaxial stretching is discussed in terms of the orientation distribution functions of reciprocal lattice vectors of crystal planes, such as the (002) and (200) planes. The distribution functions calculated from the model are compared with those obtained from x-ray diffraction experiments. It is found that the crystal a axis and, consequently, the direction of hydrogen bonds within the crystal (α modification) orient parallel to the lamellar axis in the undeformed state, and that the crystal orientation behavior of nylon-6 is much different from that of low-density polyethylene, being characterized by much smaller values of the reorientation parameters of crystallites within orienting lamellae. Moreover, small-angle light scattering for H_v and V_v polarization is also calculated on the basis of the spherulite deformation model by taking the nylon-6 crystal as having orthogonal–biaxial symmetry in optical anisotropy. It is concluded that the H_v scattering can be realized in terms of the proposed model for spherulite deformation by taking into account a considerable contribution of hydrogen bonds to the molecular polarizability, so as to make the polarizability along the crystal a axis larger than that along the b axis. In other words, this conclusion suggests positively birefringent spherulites in the nylon-6 samples studied.     

Small-angle polarized light scattering by spherulites

The light-scattering matrix for a three-dimensional spherulite is derived within the Ray-leigh-Gans-Debye light-scattering approximation. New expressions for the polarized, small-angle light-scattering intensities I_VV and I_VH are derived from the scattering matrix. These expressions are compared with the I_VV and I_VH expressions derived for a spherulite by Stein and Rhodes. For the case of a weakly anisotropic spherulite having an average refractive index mismatch with its surroundings, the two sets of expressions predict different I_VV and I_VH intensities. In particular, our expressions show that the I_VVand I_VH patterns usually attributed to the spherulitic anisotropy and crystallinity are also predicted for an isotropic sphere. This is in accord with recent experiments.     

Effect of poly(butylene succinate) crystals on spherulitic growth of poly(ethylene oxide) in binary blends of the two substances

The effects of the lamellar growth direction, extinction rings, and spherulitic boundaries of poly(butylene succinate) (PBSU) on the spherulitic growth of poly(ethylene oxide) (PEO) were investigated in miscible blends of the two crystalline polymers. In the crystallization process from a homogeneous melt, PBSU first developed volume‐filling spherulites, and then PEO spherulites nucleated and grew inside the PBSU spherulites. The lamellar growth direction of PEO was identical with that of PBSU even when the PBSU content was about 5 wt %. PEO, which intrinsically does not exhibit banded spherulites, showed apparent extinction rings inside the banded spherulites of PBSU. The growth rate of a PEO spherulite, G_PEO, was influenced not only by the blend composition and the crystallization temperature of PEO, but also by the growth direction with respect to PBSU lamellae, the boundaries of PBSU spherulites, and the crystallization temperature of PBSU, T_PBSU. The value of G_PEO first increased with decreasing T_PBSU when a PEO spherulite grew inside a single PBSU spherulite. Then, G_PEO decreased when T_PBSU was further decreased and a PEO spherulite grew through many tiny PBSU spherulites. This behavior was discussed based on the aforementioned factors affecting G_PEO. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 539–547, 2009     

Small-angle light scattering by random assemblies of incomplete spherulites. II. Truncated spherulites

Previous theoretical calculations of the scattering from spherulites are for isolated complete spheres, whereas most spherulitic polymer samples contain truncated spherulites as a result of impingement by other spherulites. The effect of such truncations on the scattering patterns for two-dimensional spherulites is explored as a function of the size, number and location of the truncations. The scattering of severely truncated spherulites is modified, particularly with regard to the enhancement of the H_V scattering at small angles. However, reasonable amounts of truncation corresponding to experimentally observed structures do not produce appreciable modification of the pattern so that the neglect of truncation will not lead to appreciable error in the estimated spherulite size from light scattering.     

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.     

Kinetics of growth of developing spherulites

A model containing two rate constants is presented for the development of spherulites from sheaves. One, G_R, is a radial spherulite growth constant while the other, G_S, describes the rate of increase of apex angle of the sheaf. On the basis of this model, Avrami kinetics are developed which predict a change in the Avrami constant n from 5 to 3 as the sheaf develops into a spherulite. H_V light-scattering patterns are calculated according to this model and are found to compare favorably with those found during the early stages of the crystallization of poly(ethylene terephthalate).