Small-angle x-ray scattering of semicrystalline polymers. II. Analysis of experimental scattering curves

The small-angle x-ray scattering (SAXS) patterns of a number of linear polyethylene (PE) and polyoxymethylene (POM) samples have been measured and compared to the intensity functions of one-dimensional paracrystalline lattices. It was found that the ratio of the angular positions of the second and first scattering maxima (θ₂/θ₁) is generally less than or equal to 2.0, implying that the paracrystalline lattice statistics are symmetric or moderately skewed to larger periods. The Bragg spacing (“long period”) of such samples is within 3% of the identity period of the macrolattice. With quenched POM the ratio θ₂/θ₁ is substantially larger than 2.0, which indicates either extremely asymmetric lattice statistics or coexisting structures within the material. From consideration of the reduced widths of the first scattering maxima, it was found that some broadening is present in addition to that from the paracrystallinity. This excess broadening could result from a finite lattice length of ～1000 Å. The need for careful experimental technique for obtaining the actual position of the scattering maximum is emphasized. In addition, it is demonstrated that the scattering curve and the correlation function of the system yield essentially the same apparent structural periods.     

Small-angle x-ray scattering studies of crazed glassy polymers

A small-angle x-ray scattering (SAXS) study of the relaxed craze structure in polystyrene was performed using the Oak Ridge National Laboratory 10-m SAXS facility. Coupled with known results from transmission electron microscopy studies, the SAXS patterns can be interpreted as scattering from an open-cell foam with void spaces interspersed among the fibrils. Results have shown the scattering centers in crazed polystyrene can be modeled as cylinders the axes of symmetry of which are parallel to the tensile axes. Scattering centers are bimodal in their size distribution, with aspect ratios of 1.0 and 2.6. Crazes in lower-molecular-weight polystyrene have more and larger scattering centers than crazes in higher-molecular-weight polystyrene, while variations in strain rate and test temperature during craze formation have no effect on the relaxed craze morphology. A comparison of SAXS patterns from polystyrene and polycarbonate indicates that the morphologies of their respective crazes are significantly different.     

Molecular aggregation of solid aromatic polymers. I. Small-angle x-ray scattering from aromatic polyimide film

Molecular aggregation in a commercial polyimide film, Du Pont Kapton, was investigated by small-angle x-ray scattering (SAXS). From the analysis of the desmeared SAXS curve, it is concluded that aggregation in the Kapton film can be elucidated in terms of a two-phase structure having electron density fluctuations within the phases. For comparison with the molecular aggregation in Kapton, molecular aggregation in polyimides synthesized in our laboratory was also investigated. It was found in this case that molecular aggregation is controlled by the initial imidization temperature. Molecular aggregation of polyamic acid and polyimide cyclized at a low temperature gives amorphous structures. On the other hand, molecular aggregation of polyimide cyclized at high temperatures gives two-phase structures like that of Kapton film. The SAXS curve for a polyimide having the two-phase structure shows a peak due to interference between ordered regions. The two-phase structure of the polyimide can be explained in terms of a one-dimensional model. The more ordered phase is produced at the higher initial imidization temperature. The relative density difference between two phases is only a few percent for polyimide films cyclized at high temperatures. This result shows that the two-phase structure of aromatic polyimide differs essentially from that of ordinary crystalline polymers.     

Structure of glassy polymers. V. Small-angle x-ray scattering from polystyrene

Small-angle x-ray scattering (SAXS) from glassy atactic polystyrene has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference.The desmeared absolute intensity decreases strongly with increasing scattering angle over the range between 20 sec and 20 min. At larger angles, the intensity decreases much more slowly with increasing angle and approaches the value expected for density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 10 to 4000 Å. The present SAXS results on glassy polystyrene seem inconsistent with the presence of nodular features as representative of the bulk polymer.     

The influence of crystallinity distribution on small-angle x-ray scattering from semicrystalline polymers

Theoretical x-ray scattering curves have been developed for the lamellar structure in semicrystalline polymers in which there are present distributions of lamellar thickness and crystallinity. The models have been tested against samples of linear low-density, low-density and crosslinked polyethylenes. When variation in crystallinity is present in a material, a major effect is an increase in the magnitude of near-zero angle scattering. The Bragg maximum can appear as an ill-defined hump on an apparently high level of background scattering. The shape of the Bragg peak is influenced more by crystallinity distribution than by lamellar thickness distribution. Of the polymers we have studied so far only linear low density polyethylene shows significant crystallinity distribution effects. A “rule-of-thumb” method for rapid estimation of crystallinity distribution effects has been developed, obviating the need for lengthy simulation.     

Small-angle x-ray scattering studies of melting

The course of melting of melt-crystallized polyethylene fractions and of a poly(ethylene oxide)-polystyrene-poly(ethylene oxide) triblock copolymer has been followed by small-angle x-ray scattering (SAXS). Changes in the intensity and shape of the SAXS curves indicated that both surface melting and melting over the full crystallite thickness (full-strand melting) take place. Full strand melting is the final, irreversible process. Comparison with an analytical model indicates that in the earlier stages of the irreversible, full-strand process the crystallites melt out randomly throughout the bulk. Later stages may occur by the simultaneous melting of a larger stack of crystallites.     

On the structure of glassy polymers. IV. Small-angle x-ray scattering from rigid polyvinyl chloride

The small-angle x-ray scattering (SAXS) from quenched and annealed rigid polyvinyl chloride (PVC) has been measured using a Bonse–Hart system. After correcting for absorption, background, and beam divergence, the scattering has been placed on an absolute basis using a standard silica suspension as a reference. The scattering from annealed (6 days at 75°C) and unannealed PVC was identical within experimental error, varying with scattering angle in a manner similar to the SAXS from other amorphous polymers. The intensity decreases rapidly with increasing scattering angle over the ranges from 20 sec to 20 min. Beyond 20 min the intensity is fairly constant, decreasing only slightly with increasing angle. At the largest angles of measurement (in the range of 120 min), the measured intensity is close to the value calculated for thermal density fluctuations frozen-in at the glass transition. The angular variation of intensity is well described by the scattering from heterogeneities of various sizes and concentrations superimposed on the scattering from thermal density fluctuations. These heterogeneities range in radius from 50 to 4500 Å and, assuming the crystalline excess density, the total concentration of heterogeneities is less than 0.5%. The mean-square fluctuation in density, determined from the measured intensity invariant, is also consistent with such a distribution of heterogeneities. The present SAXS results on rigid PVC are inconsistent with the presence of nodular features as representative of the bulk polymer. Rather, it is suggested that they are associated with surface effects. It is further suggested that previously indicated volume fractions of crystallinity in rigid PVC (generally in the range of 5–12%) are incorrect, and that the model of a three-dimensional network of crystallites used to explain the rheological behavior of this material should be re-examined.     

Small-angle x-ray scattering of isotactic polystyrene

Isothermal crystallization process of isotactic polystyrene at 167°C has been studied by smallangle x-ray scattering. The observed SAXS intensities consist of the twophase lamellar structure component, the density fluctuation, and the foreign particle components. The profile of lamellar structure component remains unchanged during crystallization while its intensity increases with crystallization. The lamellar structure of isotactic polystyrene is investigated on the basis of the interface distribution function. An interface distribution function is obtained from the lamellar structure component after correcting the effect of the finite thickness of boundary regions between crystalline and amorphous phases. In order to obtain the structure parameters, the Gaussian correlation model is used, in which the correlation between the distributions of neighboring crystal and amorphous thicknesses is taken into account. Agreement is satisfactory between the experimental results and the calculations. The structure parameters of isotactic polystyrene are determined for isothermal crystallization at 167°C as follows: the average and the standard deviation of crystal thickness are 40 A and 10 A, respectively, those of amorphous thickness are 70 A and 23 A, and the standard deviation of long period is 31 A.     

On the structure of glassy polymers. III. Small-angle x-ray scattering from amorphous polyethylene terephthalate

The small-angle x-ray scattering (SAXS) from glassy polyethylene terephthalate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 15 min, decreases more gradually in the range between 15 min and 45 min, and reaches a nearly constant asymptotic value over the range between 45 min and 2 deg. The magnitude of the scattering in the constant range, about 0.4 (electrons)² Å^?3, is very close to the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass-transition temperature [0.34 (electrons)² Å^?3]. The increase in intensity at angles smaller than about 45 min cannot be described by structures on the scale and volume fraction of the nodules reported in amorphous PET (50–100 Å), but can be well represented by small concentrations of heterogeneities, ranging in size from 100 to 2000 Angstroms, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material seems well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration (<1 vol-%) of heterogeneities covering a range of sizes. The heterogeneities in the small end of the range may well be crystallites which formed on cooling.     

Small-angle x-ray scattering by nylon 6

Small-angle x-ray scattering (SAXS) of isotropic or uniaxially oriented nylon 6 was investigated as a function of thermal and mechanical history. In addition to the peak position and linewidth of the SAXS maximum, the integrated SAXS intensity was measured. It was found that the radial intensity distributions of isotropic or arced patterns are controlled to some extent by the small width of the semicrystalline macrolattice, rendering the conventional long period and line shape analysis inapplicable to these patterns. A two-dimensional analysis is possible with well-oriented fibers; the major structural changes which are seen in fibers after annealing above 190°C are associated with melting and recrystallization. Extensive cold drawing and subsequent annealing cause rather modest (ca. ～30%) changes in the integrated SAXS intensity. These effects are consistent with the generation of homogeneous interfibrillar regions during the latter stages of plastic deformation. On annealing a quenched film on nylon 6, the transformation of the crystals from a pseudohexagonal to a monoclinic habit occurs above 170°C.     

On the structure of glassy polymers. I. Small-angle X-ray scattering from polycarbonate

The small-angle x-ray scattering (SAXS) from glassy bisphenol-A polycarbonate has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.44 (electrons)² Å^?3, is well represented by the thermodynamic theory for fluids applied at the glass-transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in this material (50–200 Å), but can be well represented by a small concentration of heterogeneities (0.04% by volume or less), several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen in at the glass transition. It is suggested that the nodular features reported for this material are not representative of bulk material but should be associated with surface effects. The bulk structure can—as far as the SAXS is concerned—be well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

Small-angle x-ray scattering study of ionomer deformation

The small-angle x-ray scattering (SAXS) pattern from a cesium salt of a 6.1 mole % ethylenemethacrylic acid (E-MAA) copolymer is shown to become azimuthally dependent on sample elongation. SAXS was measured using the Oak Ridge National Laboratory (ORNL) spectrometer with pinhole collimation and a two-dimensional position-sensitive detector. The sample was quenched prior to deformation to avoid crystallization of the ethylene unit which would complicate the interpretation of scattering. The observed SAXS patterns are interpreted in terms of several proposed models for the structure of ionomers. A model in which ionic aggregates are arranged on a paracrystalline lattice is found to be largely in disagreement with the results for undeformed and deformed samples. Spherical and lamellar models incorporating local structure around a central ionic core are capable of predicting the observed SAXS for the undeformed sample. A model of ellipsoidal deformation of the spherical shell-core model fails to predict the correct azimuthal dependence of scattering. However, a deformation scheme involving rotation of the lamellar model is more satisfactory.     

Small-angle x-ray scattering of distorted lamellar structures

Small-angle x-ray scattering (SAXS) intensity for the lamellar structure of polymeric materials has been formulated with consideration of structural defects such as the finiteness of the lamellar stack, the lamellar bend, and the paracrystalline distortions. In particular, the effects of the lamellar bend on the SAXS profile have been elucidated on the basis of Vonk'xss formula γ₁(x) – γ(x)exp(?2x/d). Here, the scattering profile due to the lamellar bend is shown to be expressed by a Cauchy function. The integral breadth is equal to 2π/d, being independent of the order of scattering. As an example of the SAXS analysis based on the theory, the characterization of the lamellar structure in the “hard” elastic polypropylene films is reported. The long period and the lamellar thickness are evaluated from the correlation function, and the distortion length and Hosemann's g factor are estimated according to the procedure presented here. On the basis of these structural parameters, the relationship between the manufacturing process and the lamellar structure of the polypropylene films is discussed. © 1993 John Wiley & Sons, Inc.     

On the structure of glassy polymers. II. Small-angle x-ray scattering from poly(methyl methacrylate)

The small-angle x-ray scattering (SAXS) from glassy poly(methyl methacrylate) has been measured using a Bonse–Hart system. The data cover the angular range (2θ) between 20 sec and 2 deg. After correcting for absorption, background, and beam divergence, the data have been placed on an absolute basis by comparison with the scattering from a standard silica suspension. The corrected absolute intensity decreases strongly with increasing angle over the range between 20 sec and 30 min, and is nearly constant between 30 min and 2 deg. The magnitude of the scattering in the constant range, 0.6 (electrons)² Å^?3, is within a factor of 1.5 of the value predicted by the thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at smaller angles cannot be described by structures on the scale of the nodules reported in highly isotactic PMMA (150–200 Å), but can be well represented by small concentrations of heterogeneities, several thousand angstrom units in size, superimposed on the thermal density fluctuations frozen-in at the glass transition. The bulk structure of this material is well described as a random amorphous solid, containing simple thermal fluctuations and a small concentration of relatively large heterogeneities.     

Hydration in semicrystalline polymers: Small-angle neutron scattering studies of the effect of drawing in nylon-6 fibers

Water absorbed by nylons appears to be partitioned into interlamellar and interfibrillar spaces. The amount of water in the interfibrillar region remains essentially unchanged with increasing draw ratio, whereas that in the interlamellar regions decreases with draw ratio; the latter accounts for the decrease in the water uptake in the drawn fibers. These results suggest that the amount of the amorphous material in the interfibrillar regions remains unchanged during drawing, and the increase in the crystallinity during drawing results from the incorporation of the amorphous chain segments in the interlamellar regions into the crystalline lamellae. Further, the interfibrillar water is more tightly bound than the interlamellar water. The length of the longitudinal channels into which water diffuses is about the same as that of the fibrils, and increases from ca. 1500 to 2000 Å upon drawing. The longitudinal channels are highly oriented even in undrawn fibers, and their misorientation increases from 5° to 15° upon drawing. These channels can be described as surface fractals of dimension 3.4–3.6. © 1994 John Wiley & Sons, Inc.     

Small-angle x-ray scattering studies of isothermally crystallized bulk polyethylene

A set of isothermally melt-crystallized polyethylene samples was examined using small-angle x-ray scattering (SAXS). Time and temperature of crystallization were the variable parameters used to create the set of samples. Following background subtraction, desmearing, and application of the Lorentz factor to the raw SAXS data it is possible to see many orders of reflection. This suggests that much higher degrees of order are present in isothermally melt-crystallized samples than had previously been thought possible. A combination of SAXS and DSC data indicates that there is no evidence for isothermal thickening in these samples. This study, coupled with data obtained from PE single crystals, produced information concerning the extrapolation of single-crystal data to fit bulk systems. In addition, the equilibrium melting point T determined is somewhat lower than previously claimed. This study also suggests that the surface energy of the mature crystals is always lower than that of the nucleated state and/or the nucleation factor Kσ_en increases with decreasing supercooling.     

Small-angle x-ray scattering studies on epoxidized butadiene-styrene block copolymers

Small-angle x-ray scattering (SAXS) and scanning electron microscopy (SEM) investigations for epoxidized butadiene-styrene (BS) block copolymers were performed. For unepoxidized copolymers, the SAXS curve exhibits a maximum which indicates that the copolymer has heterogeneity domain morphology. Using the standard theory for a two-phase system, mean distances between domains, the correlation length l _p , and the thickness of the phase boundary were calculated from the SAXS data. It was found that the epoxidation of BS copolymers decreases the ability of the copolymer to separate the individual components. As the content of the epoxide groups increases, the dimensions of the domains decrease until they disappear, the boundary between domains and the matrix becomes less and less definite, and the copolymer composes a homogeneous system. The disappearance of the two-phase structure of the BS copolymers indicates an increase in the compatibility of polystyrene and epoxidized polybutadiene. According to the method of Van Krevelen, the solubility parameters of polystyrene and epoxypolybutadiene were calculated. Small differences between these parameters support the conclusions drawn from the SAXS investigations     

Small-angle scattering of partially oriented polymers: model calculations

Three-dimensional small-angle intensity plots are calculated and discussed for a structure consisting of a linear paracrystalline lattice built up by finite lamellar or cylindrical crystallites, tilted with respect to the lattice direction. The lattice directions are distributed with respect to the fiber axis. The effects of different parameters (orientation, tilt angle, crystallite size, etc.) on the diffraction pattern are studied.