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. 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.     

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. 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.     

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.     

Structural heterogeneity and pressure-relaxation in compressed borosilicate glasses by in situ small angle X-ray scattering

We report on Brillouin and in situ small angle X-ray scattering (SAXS) analyses of topological heterogeneity in compressed sodium borosilicate glasses. SAXS intensity extrapolated to very low angular regimes, I(q = 0), is related to compressibility. From Brillouin scattering and analyses of the elastic properties of the glass, the Landau-Placzek ratio is determined and taken as a direct reflection of the amplitude of frozen-in density fluctuations. It is demonstrated that with increasing fictive pressure, topological (mid- and long-range) homogeneity of the glass increases significantly. Heating and cooling as well as isothermal scans were performed to follow the evolution of density fluctuations upon pressure recovery. For a sample with a fictive pressure p(f) of 470 MPa, complete recovery to p(f) = 0.1 MPa was observed to occur close to the glass transition temperature. The values of fictive and apparent fictive temperature, respectively, as obtained via the intersection method from plots of I(q = 0) vs. temperature were found in good agreement with previous calorimetric analyses. Isothermal scans suggest that mid- and long-range recovery govern macroscopic density relaxation.     

On the structure of glassy polymers. VI. Electron microscopy of polycarbonate,poly(ethylene terephthalate), poly(vinyl chloride), and polystyrene

High-resolution electron microscopy studies have been carried out on four glassy polymers examined in previous small-angle x-ray scattering (SAXS) investigations. The polymers include polycarbonate, poly(ethylene terephthalate), poly(vinyl chloride), and polystyrene. For all four polymers, both bright field and dark-field observations indicate the general absence of microstructural features of a size down to the resolution limit of the electron microscope. Only “pepper and salt” features on a scale ca. 5 Å are seen as characteristic of the structures. These features reflect simple interferences as the resolution limit is approached, and are seen for single crystal and oxide glasses as well as for the polymers. The present results, taken together with structural information from light scattering, SAXS, and small-angle neutron scattering, indicate that glassy polymers should be regarded as having rendom structures. The combined results are inconsistent with heterogeneous microstructures having regions of locally high order present in large volume fractions.     

Microvoid formation during deformation of high-impact polystyrene

Small-angle x-ray scattering (SAXS) has been used to study the formation of microvoids in polymers which craze or stress-whiten extensively. Specimens are subjected to a stepwise uniaxial strain, with scattering curves being obtained at each step. The increase in scattering intensity upon crazing is attributed to the formation of microvoids, and the relative size, shape, and concentration of the scattering elements are determined by a Porod analysis of the SAXS curves. The major portion of our work has been on high-impact polystyrene which shows a large increase in SAXS intensity as crazing occurs. We are able to follow the changes in void size and concentration during craze initiation and growth. Effects of temperature, molecular orientation, and matrix molecular weight have also been studied. The results add to the information on craze growth and microstructure known from electron microscopy and dilatometry. In addition, a qualitative physical model for microvoid nucleation is proposed, and the implications for toughness are discussed.     

Asymmetric diblock copolymers-phase behaviour and kinetics of structure formation

 The structure of a series of three molecular weights of diblock copolymers polystyrene/b-isoprene with 11% volume fraction of polystyrene and low polydispersity has been investigated using small angle X-ray scattering (SAXS). In between the disordered and the BCC ordered state a micellar state with liquid-like order was found. The transition between these states was investigated in a temperature-driven experiment. Whereas the micelles appear gradually with lowering temperature the formation of the BCC ordered state occurs discontinuously at a well-defined temperature. Detailed analysis of the scattering profiles provides access to the micellar size and distance in the liquid-like as well as in the BCC state. The kinetics of the ordering transition was studied using time-resolved SAXS after temperature jumps from the liquid-like to the BCC state. The growth of the micelles and their ordering on the periodic lattice were found to occur on clearly separated time scales. Received: 12 September 1996 Accepted: 2 December 1996     

Small-angle x-ray scattering by crystalline polymer fibers 2. Investigation of the linear paracrystalline model using various materials

The linear position-sensitive detector is well-suited to measure quantitatively the distribution parallel to the fibre axis of the intensity of small-angle x-ray scattering (SAXS) by polymer fibres, except that in the case of four-point patterns their width is greater than that of the detector window. A method is described which overcomes this problem, and which has high angular resolution. Using this method, the variation of scattered intensity with angles from 0.3° to 2.5° has been measured for fibres of poly(ethylene terephthalate), nylon, and low density poly(ethylene) (LDPE), and compared with that predicted by the linear paracrystalline model. In all cases except LDPE, when the distribution of phase lengths was given by the Reinhold function, there was no significant disagreement between the measured and predicted scattering except for a very small range of angles on the low angle side of the peak intensity. With LDPE small but significant discrepancies were found at other angles as well, and these were worse if the symmetrical Gaussian distribution function was used. The method enabled quantitative parameters describing the morphology to be obtained. It is concluded that the morphology of the linear paracrystalline stack is consistent with the SAXS intensity distribution, and that the Reinhold function is a reasonable approximation to the distribution of phase lengths. A small modification so that this decays more rapidly at long lengths might be necessary to explain the scattering for all materials over the entire angular range and other small changes might be needed with LDPE, although the asymmetrical nature of the distribution must be retained.On leave from Department of Physics, University of Technology Malaysia, 81300 Sekudai, Malaysia.     

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.     

Lamellar morphology and equilibrium melting temperature of syndiotactic polystyrene in β‐crystalline form

Lamellar morphology and thickness of syndiotactic polystyrene (sPS) samples melt‐crystallized at various temperatures were probed using transmission electron microscopy (TEM) and small‐angle X‐ray scattering (SAXS). In addition, the melting temperature and enthalpy of the crystallized samples were characterized with differential scanning calorimetry. Under appropriate thermal treatments, all the samples investigated in this study were crystallized into β′ crystal modification, as revealed by wide‐angle X‐ray diffraction. From the SAXS intensity profiles, a scattering peak (or shoulder) associated with lamellar features as well as the presence of anomalous scattering at the zero‐scattering vector were evidently observed. The peculiar zero‐angle scattering was successfully described by the Debye–Bueche model, and subtraction of its contribution from the raw intensity profiles was carried out to deduce the intensity profile merely associated with the lamellar feature. The lamellar thickness obtained from Lorentz‐corrected intensity profiles in this manner agrees with that measured from the TEM images, provided that the two‐phase model is applied. On the basis of the Gibbs–Thomson equation, the modest estimations of equilibrium melting temperature and the surface free energy of the fold lamellar surface are 292.7 ± 2.7 °C and 20.2 ± 2.6 erg/cm², respectively, when lamellar thicknesses measured by TEM are applied. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1626–1636, 2002     

Negative thermal expansion of water in hydrophobic nanospaces

The density and intermolecular structure of water in carbon micropores (w = 1.36 nm) are investigated by small-angle X-ray scattering (SAXS) and X-ray diffraction (XRD) measurements between 20 K and 298 K. The SAXS results suggest that the density of the water in the micropores increased with increasing temperature over a wide temperature range (20-277 K). The density changed by 10%, which is comparable to the density change of 7% between bulk ice (I(c)) at 20 K and water at 277 K. The results of XRD at low temperatures (less than 200 K) show that the water forms the cubic ice (I(c)) structure, although its peak shape and radial distribution functions changed continuously to those of a liquid-like structure with increasing temperature. The SAXS and XRD results both showed that the water in the hydrophobic nanospaces had no phase transition point. The continuous structural change from ice I(c) to liquid with increasing temperature suggests that water shows negative thermal expansion over a wide temperature range in hydrophobic nanospaces. The combination of XRD and SAXS measurements makes it possible to describe confined systems in nanospaces with intermolecular structure and density of adsorbed molecular assemblies.     

Microstructure rearrangement during the heat-treatment of melt-drawn poly(ethylene terephthalate) fibers

Melt-spun poly(ethylene terephthalate) fibers were isothermally heat-treated at constant length. Microstructural changes occurring during the heat-treatment were monitored using specific gravity, wide-angle x-ray scattering (WAXS), small-angle x-ray scattering (SAXS), optical birefringence, and static mechanical testing. Major changes in the density of the most highly oriented fiber examined occurred in times below 100 ms. For less oriented fibers, the time scale for significant density change increases to the 1–10 s range. The course of birefringence increase approximates that of the density. WAXS measurements show that crystallinity develops at essentially constant crystal perfection, but that the orientation of the crystallites first decreases and then increases with time. SAXS results show development of a four-point pattern, the azimuthal angle of the lobes decreasing with initial orientation, with temperature, and with time. A streak transverse to the fiber axis develops more rapidly than do the lobes. A two-stage transformation process is envisaged, the first stage being the formation of defective crystal fibrils and the second being internal rearrangement of the fibrils to form more perfect crystallites, separated by more amorphous zones. Changes in the crystallite orientation are related to constraints of the noncrystalline material on the crystallites.     

Investigation of heterogeneities in solid polyethylene by small angle neutron scattering

Small angle neutron scattering was applied to the investigation of heterogeneities in solid poly-ethylene. The heterogeneities arise from the contrast between amorphous and crystalline regions and also from the presence of a small fraction of voids. The method is easily put on an absolute basis by calibration with an incoherent scatterer, in this case, cyclohexane.     

Investigation of Voids in Polyacrylonitrile Fibers by USAXS and SAXS

The void structure of polyacrylonitrile(PAN) fibers was investigated using ultra-small angle X-ray scattering(USAXS) and small angle X-ray scattering(SAXS). A quantitative method was developed to analyze connected USAXS/SAXS data and thus determine the void parameters of PAN fibers. The results showed that voids affected the mechanical performance of PAN fibers and were present throughout the entire wet-spinning process. When the absolute quantity and size of voids decreased, the tensile strength and modulus of PAN fibers increased. The void parameters were optimized by controlling the production process, and thus the tensile strength and modulus of PAN fibers were increased. The method for analyzing the void structure developed in this study is useful for analyzing voids over with larger size range, as well as the effect of the void structure on the mechanical performance of fibers.     

Crystallization and structure formation of block copolymers containing a glassy amorphous component

Formation of higher‐order structure in crystallization from microphase‐separated melts was studied for polystyrene–polyethylene (PS–PE) diblock copolymers and PS–PE–PS triblock copolymers with time‐resolved synchrotron small‐angle X‐ray scattering (SR–SAXS) techniques. The PE block was crystallized at temperatures when the PS block was in the glassy state. In both crystallization and melting processes, only the peak intensity in the SR–SAXS curve changed, however, the peak positions including higher‐order peaks did not change. This means that the microphase‐structure in the crystalline state was completely the same as that in the molten state. These behaviors were observed regardless of any melt microphase structure. Also, once a stable microphase structure was formed in the molten state, the structure was not changed even if crystallization and melting were repeated. Behavior of crystallization from such microphase‐separated melts was also studied. Apparent activation energies of crystallization were high for all block copolymers, compared with that for the PE homopolymer. In particular, the triblock copolymers showed higher apparent activation energies than the diblock copolymers. Both degrees of crystallinity and Avrami indices were greatly suppressed in crystallization from the cylindrical domain. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4199–4206, 2004     

Kinetics of microstructure rearrangement during annealing of cold-drawn isotactic polypropylene

The microstructure of polypropylene, annealed after cold drawing to an oriented state, was examined using density measurements and small- and wide-angle x-ray scattering (SAXS and WAXS) techniques. SAXS patterns were obtained after annealing (in an oil bath), and during annealing (of samples annealed in a furnace placed directly in the x-ray beam). Data, for isothermal annealing, showed an increase in SAXS intensity, in crystal perfection, and in density over the observed time range, but no change in long spacing during the same period. Long spacing, SAXS intensity, and density were all strongly dependent upon annealing temperature, increasing at higher temperatures. Upon annealing the elastic modulus and yield strength dropped below the as-drawn values in an immeasurably short time, and did not appear to change thereafter during the time range examined. The decrease was more marked for higher-temperature annealing. The kinetics of the micro-structural changes are compared qualitatively to the predictions of nucleation and growth theory and of spinodal decomposition. The defects in the microstructure are considered as the “solute molecules” of the spinodal model. The experimental results do not agree neatly with either model. However, a nonequilibrium thermodynamic approach appears to be the more promising. It is suggested that the kinetics of mechanical property change may be due to different rates of migration for different defect species.     

Density dependences of long-range fluctuations and short-range correlation lengths of CHF3 and CH2F2 in supercritical states

Small-angle x-ray scattering (SAXS) measurements are carried out for supercritical polar fluorocarbons, CHF3 and CH2F2, along the isotherm of 1.04 in reduced temperatures with the density range from 0.3 to 1.5 in reduced units. A novel apparatus for determination of absorption factors of the sample fluids is used in the present measurements. The apparatus enables us to detect simultaneously the accurate factors during the observation of the SAXS signals. Long-range fluctuations such as density fluctuations and correlation lengths are evaluated from the obtained SAXS data. The reduced correlation lengths are obtained by normalization by each molecular size, in order to discuss the fluctuations independent of the difference of the individual molecular size. The density fluctuations and the reduced correlation lengths of CHF3 and CH2F2 are compared with those of CO2 and H2O. The results are as follows: H2O>CH2F2>CHF3 approximately CO2 in the order of magnitude. The fluctuations of CH2F2 are significantly distinguishable from those of CHF3 and show intermediate aspect between H2O and a group of CO2 and CHF3. In addition, the short-range correlation lengths, i.e., the Ornstein-Zernike direct correlation lengths, are firstly discussed from both viewpoints of density and substance dependences. The reduced short-range correlation lengths normalized by individual molecular size are found to trace a universal curve as a function of the reduced density.     

Confined crystallization in lamellae forming poly(3-(2′-ethyl)hexylthiophene) (P3EHT) block copolymers

Charge transport in poly(3-alkylthiophene)s (P3AT)s is closely linked to the nanoscale organization of crystallites. Block copolymer morphologies provide an ideal platform to study crystallization as the chain ends are tethered at a known interface in a well-defined geometry. The impact of soft versus hard confinement on P3EHT crystallization was studied using poly(3-(2′-ethyl)hexylthiophene) (P3EHT) containing diblocks with both rubbery poly(methyl acrylate) (PMA) and glassy polystyrene (PS) blocks. Here, P3EHT's lower melting point relative to the commonly studied poly(3-hexylthiophene) (P3HT) facilitated its confined crystallization and makes it an ideal model system. While transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) revealed well-ordered lamellar morphologies both in the melt and post-crystallization for both sets of diblocks, the glassy blocks inhibit confined crystallization of P3EHT relative to rubbery matrix blocks. Analysis of aligned diblocks by both SAXS and wide angle X-ray scattering (WAXS) revealed that the P3EHT chain axis aligns perpendicular to domain interfaces, allowing preferential growth of the alkyl-chain and π–π stacking directions parallel to lamellae. Finally, it was shown that following diblock self-assembly in the melt, crystallite growth drives expansion of microdomains to match the P3EHT contour length. It was concluded that P3EHT chains adopted an extended conformation within confined crystallites due to the rigid nature of polythiophenes relative to flexible chain crystalline polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 205–215