Molecular aggregation of solid aromatic polymers. III. Small-angle X-ray scattering from aromatic polyamideimide film

Molecular aggregation in polytrimellitamideimide (PAI) was investigated by small-angle x-ray scattering (SAXS). PAI films annealed above the glass transition temperature show a scattering peak characteristic of two-phase structure. A one-dimensional model was used to analyze these SAXS curves. The more ordered phases are produced at higher annealing temperature. The average thickness of the ordered lamellae is comparable with the repeating length of the main chain. The relative difference of electron density between two phases is only a few percent, which shows that the two-phase structure of PAI, like that of aromatic polyimide, differs essentially from that of ordinary crystalline polymers.     

Molecular aggregation of solid aromatic polymers. II. Mechanical properties of aromatic polyimide film

Molecular aggregation of the aromatic polyimide poly(4,4′-oxydiphenylene-pyromellitimide) is influenced by the initial imidization temperature and by cold drawing. The effect of molecular aggregation in polyimides on their mechanical properties has been investigated. The density of a polyimide in which molecular aggregation gives an amorphous state is increased slightly by cold drawing. On the other hand, if molecular aggregation leads to a heterogeneous two-phase structure, the density is decreased by cold drawing. With increasing initial imidization temperature, the α absorption peak in dynamic tensile measurements becomes broader and smaller, and shifts to a higher temperature. From analysis of correlations between molecular aggregation and mechanical properties, it is concluded that the mode of molecular motion corresponding to the α dispersion in polyimide is a long-range cooperative motion of the main chain which is associated with the glass transition.     

Small-angle x-ray scattering of semicrystalline polymers. I. Review of existing models

The effect of previously proposed distributions of particle size and interparticle “gap” lengths on the small-angle x-ray scattering of a paracrystalline one-dimensional macrolattice has been examined. It was concluded that the general paracrystalline model, in which the fluctuations of crystalline and amorphous thickness both contribute to the destruction of long-range order, best describes the structure of lamellar aggregates in semicrystalline polymers. By using this model, the influence of symmetric and asymmetric lattice statistics on the positions of the scattering maxima were investigated. It was found that positively skewed thickness distributions result in the second-order maximum occurring at an angle greater than twice that of the first-order maximum (sx?₂/sx?₁ > 2.0); the position of the first-order maximum is generally greater than the Bragg angle of the structure. With negatively skewed distributions, the ratio of the scattering angles, sx?₂/sx?₁, is less than 2.0, and the first maximum is displaced below the Bragg angle. Qualitatively similar behavior is found with lattices characterized by symmetric lattice statistics, though these deviations from the Bragg conditions are smaller than in the case of negatively skewed distributions. The ratio of the scattering angles of the second and first maxima best reflects the general shape of the lattice statistics in a paracrystalline lattice. The effect of a transition zone, having properties intermediate between those of the crystalline and amorphous regions, was also considered. While the intensity of the higher-order maxima is decreased, no significant shift of the scattering angles results from the incorporation of such a transition zone.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Structure of glassy polymers. VII. Small-angle X-ray scattering from epoxy resins

The small-angle x-ray scattering (SAXS) from an Epon 812 and two Epon 828 (one amine-cured and one anhydride-cured) epoxy resins has been measured using a Bonse-Hart system. The data cover the angular range (2θ) between 20 sec and 60 min. After correction for absorption, background and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a previously studied polycarbonate sample. The corrected absolute intensity decreases strongly with increasing angle between 20 sec and 2 min, decreases more gradually between 2 and 20–30 min, and reaches a nearly constant asymptotic value at larger angles. The magnitude of the intensity in the constant-intensity region is close to the value predicted by thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at angles smaller than 20–30 min is associated with heterogeneities in the cured resins. These heterogeneities cover a range of sizes in all samples, from less than 100 Å to more than 1000 Å, with the most frequently occurring size in the range 100–200 Å.     

Dynamic small-angle x-ray scattering from crystalline polymers

The variation in small-angle x-ray scattering (SAXS) for samples of crystalline polymers subjected to oscillatory strains has been observed employing the 10-m SAXS apparatus with a two-dimensional position-sensitive detector at the National Center for Small-Angle Scattering Research at Oak Ridge National Laboratory. Signal averaging has been carried out in accordance with the π/2-sector technique by gating the detection of scattered intensity in synchronism with the sample strain. In-phase and out-of-phase intensity changes have been observed for a high-density polyethylene at various frequencies (0.05–3.2 Hz) and temperatures (0–70°C). Changes are greatest at small scattering angles. Frequency dependence is greatest at lower temperatures, indicating a time-dependent response of the structural changes leading to scattering at these temperatures. The behavior is not pronounced at elevated temperatures. The similarity of the scattering at both azimuthal angles of 0° and 90° suggests the existence of an additional mechanism, perhaps microvoid formation. To evaluate void contribution, the dynamic invariant function is determined as a function of frequency and temperature. It appears that the microvoid formation lags behind the applied strain. The static and swelling SAXS studies present further evidence of void generation during elongation.     

Small-angle x-ray scattering from solution of rodlike particles with length distribution

The scattering function of rods with a constant radius, 8 Å, and a length distribution of the Schulz–Zimm type was calculated on a computer as a model of helical synthetic polypeptide. The influence of length and length distribution on the scattered intensity of small-angle x-ray scattering was clarified. As length grows and length distribution broadens it is difficult to obtain reliable values of molecular weight and radius of gyration from a Zimm plot. The influence of length distribution on the mass per unit length, M_q, and the radius of gyration of the cross section, 〈S〉^1/2, from the Guinier plot of the cross-sectional factor decreases as the length increases, and reliable values of M_q and 〈S〉^1/2 can be obtained even for rods with wide distribution for rods more than 600 Å long. In particular, it is pointed out that the value of 〈S〉^1/2 is little influenced by length and length distribution.