About the Lorentz correction used in interpretation of small‐angle X‐ray scattering data of semicrystalline polymers

Lorentz correction is used to correct the intensities of X‐ray scattering of single‐crystal diffractometry in order to recalculate intensities to obtain structure factors. This correction reduces the intensities to zero at zero diffraction angle. Small‐angle scattering is used to study the dimensions of heterogeneities in polymeric materials. The scattering intensities at a near to zero scattering angle originate partly from periodic systems (reciprocal lattice) and partly from dispersed particle systems. Periodic systems should result in individual Gaussian or Lorentzian peaks with the position of a peak maximum depending on the length of the periodicity. Particle scattering results in a Gaussian peak centered at zero scattering angle. The effect of the Lorentz correction on the interpretation of small‐angle X‐ray scattering data is shown for some semicrystalline polyethylenes (high‐density, linear low‐density, and low‐molecular‐weight waxy polyethylenes). The data are compared to those for amorphous block copolymers (styrene–butadiene), in which there is a periodic system with homogeneous lamellar thickness. Lorentz correction destroys the characteristics of the particle scattering and can be applied only for periodic systems. It should not be used to produce a peak on scattering data, which do not show periodicity (peaks) without correction. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 358–366, 2001     

X‐ray diffraction studies on reverse‐annealed polyethylenes

Linear low and high density polyethylene sheets were compression molded and crystallized at a 5–10°C/min cooling rate. Parts of the sheets were annealed at different temperatures up to 2°C below the melting temperature. The small angle X‐ray scattering (SAXS) and the wide angle X‐ray scattering intensities of the annealed samples were studied. SAXS intensities showed particle scattering with a bimodal size distribution. The estimated radii of gyration were 15–17 nm and 5–7 nm, respectively. The crystallinity and the radius of gyration increased slightly with increasing annealing temperature for some samples; others did not show any change. No peaks characteristic of intercorrelated lamellar crystallinity in the SAXS intensities developed during the annealing. The original broad peak of high density polyethylene disappeared from the SAXS recordings on annealing. The length of the perfect chain versus melting temperature was calculated by the Thomson‐Gibbs formula and Flory's concept of melting temperature depression where methyl groups and tertiary carbon atoms at the branches were regarded as second components (solvent). Linear relationships were found for both cases. Experimental data for a linear low density polyethylene obtained from the literature were in between the two functions. A lamellar model of crystallization corresponding to the data is proposed. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 340–349, 2001     

Study of the orientation and the degree of exfoliation of nanoparticles in poly(ethylene‐vinyl acetate) nanocomposites

Nanocomposites formed from organically modified montmorillonite and poly(ethylene‐co‐vinyl acetate) were studied by X‐ray diffraction techniques. Wide‐ and small‐angle X‐ray scattering intensities (SAXS and WAXS) were recorded by transmission mode on test bars cut from compression‐molded plaques tilted by different angles with respect to the plane of the plaque. The height of the Bragg peaks characteristic of intercalated particles reduced to the baseline at tilt angles greater than 30°. Guinier analysis of the SAXS characteristic of particle scattering showed a radius of gyration of 0.69 nm and the scattering intensity was slightly dependent on the tilt angle. Recording of WAXS in the usual (i.e., in reflective) mode enhanced the effect of the structural features of the surface area and showed much higher degree of intercalation and particle size of the scattering particles than that in transmission mode. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 3026–3031, 2003     

Peak‐fitting analysis of cotton fiber powder X‐ray diffraction spectra

The precision and accuracy of diffraction peak positions resolved from the powder X‐ray diffraction spectra of cotton fibers by means of the residuals peak‐fitting procedure of a commercial peak‐fitting software package (PeakFit®) was investigated to explore the potential of such programs in providing reliable data that are not readily apparent in diffuse X‐ray spectra. Each intensity spectrum was fitted by employing a Gaussian function as the peak profile. The precision of 15 pairs of the resolved diffraction peaks is 0.0017 mm; 9 of the 15 pairs fall into the 99% confidence interval. The precision in 2θ of four commonly identified peaks through four independent fittings is from 0.002 to 0.014°. The 2θ accuracy of the resolved peaks is good in comparison to data calculated for both the traditionally accepted and the more recently revised concepts of the cellulose I crystal structure. A peak resolved at about 15.3° may be attributed to the triclinic crystal structure component of cellulose I. Although distinct peaks are not readily apparent in the diffuse spectrum of cellulose, peak‐fitting procedures may provide additional data for structure determination. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 2019–2024, 2004     

Correlation between interlamellar amorphous structure and gas permeability in poly(lactic acid) films

We have investigated the relationship between amorphous structure and its gas permeability of poly(lactic acid) (PLA) using differential scanning calorimetry, wide‐angle X‐ray scattering, and small‐angle X‐ray scattering measurements. We focused on the hierarchical interlamellar amorphous structure of various gas‐permeable PLA films. The films crystallized just above T_g did not have any long‐spacing period peaks at the room temperature even with the existence of crystals; conversely, peaks could be observed from long spacing periods with heating. Therefore, the interlamellar amorphous density became as high as crystalline region one at the room temperature. These high‐density amorphous regions, the so‐called rigid‐amorphous phase, reduced the gas diffusion and permeation. In the case of samples crystallized above 90°C, the long spacing period peaks could be observed even at the room temperature. The amorphous region did not develop the rigid‐amorphous phase, and the gas permeability depended only on crystallinity. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40626.     

Structure and characterization of poly[(vinylidene fluoride)‐co‐hexafluoropropene]–(dibutyl phthalate) blends

Blends of poly[(vinylidene fluoride)‐co‐hexafluoropropene] with dibutyl phthalate were examined by wide‐ and small‐angle X‐ray scattering, differential scanning calorimetry and dynamic mechanical spectroscopy, in order to study the influence of amount of plasticizer and the crystallization rate on the crystallinity and lamellar morphology of the copolymer. The dibutyl phthalate seems, at least for the cooling and heating rates used, simply to dilute the crystalline phase without affecting the amount of polymer that is able to crystallize. Furthermore, the small‐angle X‐ray scattering technique points out that the plasticizer mostly enters the amorphous phase either outside or inside the lamellar stacks. © 2001 Society of Chemical Industry     

Small‐angle X‐ray scattering investigation of the deformation processes in the amorphous phase of high density polyethylene

In situ small‐angle X‐ray scattering of high density polyethylene under uni‐axial tensile test was used for investigating the deformation at the scale of the periodic crystalline–amorphous nano‐structure. The more or less uniform elastic straining of the rubbery amorphous layers is discussed in terms of mechanically active intercrystalline tie chains. Correlation is made with the long‐term use properties. It is concluded that this approach is a powerful means to assess the mechanical efficiency of tie molecules. Copyright © 2004 Society of Chemical Industry     

Recent developments in polymer applications of synchrotron small‐angle X‐ray scattering

Synchrotron radiation facilities have been established and become very familiar in the polymer community not only from academic but also industrial viewpoints. It is not so unusual now to conduct simultaneous measurements of small‐angle X‐ray scattering (SAXS) with other techniques such as wide‐angle X‐ray scattering, stress–strain, light scattering, and so forth. New techniques have also been established and have become more familiar in recent years. In this review, recent developments in polymer applications of synchrotron SAXS are summarized. Instrumental developments and progress in data analyses are reviewed from the following aspects: ultra‐small‐angle X‐ray scattering, anomalous SAXS, X‐ray photon correlation spectroscopy, new types of simultaneous measurements, grazing‐incidence SAXS, new trends in nanoparticle analyses and industrial applications. © 2016 Society of Chemical Industry     

Morphology of Poly(1‐olefin)s from Poly(1‐octene) to Poly(1‐eicosene)

Poly(1‐olefin)s from poly(1‐octene) to poly(1‐eicosene) synthesized by isospecific metallocene catalysts are investigated by wide and small angle X‐ray scattering (WAXS and SAXS) and by atomic force microscopy. The crystal structure of poly(1‐eicosene) is determined and the scattering peaks are assigned. Additionally, 1‐dodecene is polymerized using a constrained geometry catalyst and the obtained atactic polymer is compared with the isotactic species. Using this sample it is possible to determine the amorphous halo in the small angle regime at room temperature. For poly(1‐decene), poly(1‐dodecene), and poly(1‐hexadecene) a long period can be measured by small angle X‐ray scattering which coincides with the results from AFM measurements.     

Thermal and dynamic mechanical behavior of ethylene/norbornene copolymers with medium norbornene contents

A range of ethylene/norbornene copolymers were synthesized using the commercially available rac‐Et(Ind)₂ZrCl₂ metallocene catalyst. A large window of norbornene contents, between 30 and 55 mol % was used to facilitate the interpretation of the results. The polymers were characterized by means of wide‐angle X‐ray scattering, differential scanning calorimetry, and dynamic mechanical thermal analysis. The X‐ray diffractograms showed two amorphous halos, the low‐angle one increasing in the intensity with norbornene content. Calorimetric and dynamic mechanical results led to a linear relation between the glass transition temperature and the norbornene content. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 2159–2165, 2001     

Relation of chain constitution with phase structure in blends: compatibility of two phases in blends of polyamide with low‐density polyethylene and its ionomers

Pressed films of binary blends (polyamide with low‐density polyethylene or Surlyn) and ternary (polyamide with low‐density polyethylene and Surlyn or a graft‐copolymer of acrylic acid onto low‐density polyethylene) were examined by dynamic mechanical analysis, thermally stimulated current, and small‐angle X‐ray scattering. The variation of the glass transition temperature for two phases in the blends was studied by dynamic mechanical analysis and thermally stimulated current. X‐ray scattering from the relation of the phases was analyzed using Porod's law and led to values of the interface layer in the blends. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 488–494, 2000     

Real‐time crystalline orientation measurements during low‐density polyethylene blown film extrusion using wide‐angle X‐ray diffraction

Real‐time wide‐angle X‐ray diffraction studies were successfully used to investigate the effect of film blowing process parameter on the crystalline orientation development during the blown film extrusion of low‐density polyethylene. Azimuthal distribution scans showed the evolution of crystalline orientation in the bubble from an isotropic state to an oriented state as inferred from (110) and (200) planes. These real‐time X‐ray diffraction measurements in a blown film line are consistent with prior observations using polarized Raman spectroscopy (Gururajan and Ogale, J. Raman Spectrosc., 40 , 212 (2009)) and small‐angle light scattering (Bullwinkel et al., Int. Polym. Proc., 16 , 41 (2001)) that significant molecular orientation takes place past the frost‐line height, even after the blown film diameter is locked into place. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

Thermal and wide angle X‐ray analysis of chemically and radiation‐crosslinked low and high density polyethylenes

Low and high density polyethylenes (PE) were crosslinked by two methods, namely, chemically by use of different amounts of tert‐butyl cumyl peroxide (BCUP) and by irradiation with different doses of electron beam. A comparison between the effects of these two types of crosslinking on crystalline structure, crystallinity, crystallization, and melting behaviors of PE was made by wide angle X‐ray diffraction and DSC techniques. Analysis of the DSC first heating cycle revealed that the chemically induced crosslinking, which took place at melt state, hindered the crystallization process and decreased the degree of crystallinity, as well as the size of crystals. Although the radiation‐induced crosslinking, which took place at solid state, had no significant influence on crystalline region, rather, it only increased the melting temperature to some extent. However, during DSC cooling cycle, the crystallization temperature showed a prominent decrease with increasing irradiation dose. The wide angle X‐ray scattering analysis supported these findings. The crystallinity and crystallite size of chemically crosslinked PE decreased with increasing peroxide content, whereas the irradiation‐crosslinked PE did not show any change in these parameters. As compared with HDPE, LDPE was more prone to crosslinking (more gel content) owing to the presence of tertiary carbon atoms and branching as well as owing to its being more amorphous in nature. HDPE, with its higher crystalline content, showed relatively less tendency toward crosslinking especially by way of irradiation at solid state. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 3264–3271, 2006     

Phase behavior and morphology in blends of poly(L‐lactic acid) and poly(butylene succinate)

Blends of poly(L ‐lactic acid) (PLA) and poly(butylene succinate) (PBS) were prepared with various compositions by a melt‐mixing method and the phase behavior, miscibility, and morphology were investigated using differential scanning calorimetry, wide‐angle X‐ray diffraction, small‐angle X‐ray scattering techniques, and polarized optical microscopy. The blend system exhibited a single glass transition over the entire composition range and its temperature decreased with an increasing weight fraction of the PBS component, but this depression was not significantly large. The DSC thermograms showed two distinct melting peaks over the entire composition range, indicating that these materials was classified as semicrystalline/semicrystalline blends. A depression of the equilibrium melting point of the PLA component was observed and the interaction parameter between PLA and PBS showed a negative value of ?0.15, which was derived using the Flory–Huggins equation. Small‐angle X‐ray scattering revealed that, in the blend system, the PBS component was expelled out of the interlamellar regions of PLA, which led to a significant decrease of a long‐period, amorphous layer thickness of PLA. For more than a 40% PBS content, significant crystallization‐induced phase separation was observed by polarized optical microscopy. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 647–655, 2002     

Crystalline structure and mechanical properties of poly(ethylene terephthalate) filament embedded with nanosize clay particles

The properties of poly(ethylene terephthalate) (PET) filaments embedded with nanosize clay powder were evaluated. The moisture management function and thermal properties of the textile were found to be improved; however, the strength of the filament was lowered with a little increase in elongation. In situ analysis of the crystalline structure with small‐angle X‐ray scattering and wide‐angle X‐ray diffraction during the tensile testing showed an unstable change in intensities during the elongation. This phenomenon is related to the earlier rearrangement and breaks down the microstructure in local regions with an increase in strain. This is expected to be due to the low adhesion strength between the matrix and the embedded nanosize clay particles. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 46321.     

Biaxially self‐reinforced high‐density polyethylene prepared by dynamic packing injection molding. II. Microstructure investigation

Differential scanning calorimetry, wide‐angle X‐ray diffraction, small‐angle X‐ray scattering, and transmission electron microscope are employed to study the microstructure of biaxially self‐reinforced high‐density polyethylene (HDPE) prepared in uniaxial oscillating stress field by dynamic packing injection molding. The results indicate that the biaxial self‐reinforcement of HDPE is mainly due to the existence of interlocking shish‐kebab morphology (i.e., zip fastener structure), along with the orientation of lamellae and molecular chains and the enhanced crystallinity. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1591–1596, 2004     

Structure development in amorphous starch as revealed by X‐ray scattering: Influence of the network structure and water content

The evolution of the amorphous structure of starch was characterized during the drying process by real‐time X‐ray wide‐angle scattering. The X‐ray diffractograms of injection‐molded starch show two superposed, rather broad, scattering maxima indicative of noncrystalline structures. The location of the two peaks has been associated to disordered starch single helices. A third maximum that arises upon drying the material in vacuum is associated to the scattering emerging from regions containing double helices. A model for the starch network is proposed, assuming a primary and a secondary component. The wider, temperature stable component appearing first, is correlated to the entanglement network of the melt. The narrower network component, which is created later, at lower temperature (secondary network), is explained by the formation of double helix regions that densify the wider primary network. The secondary network is increased strongly by the drying process. X‐ray experiments performed during the penetration of water, provoking a higher molecular mobility, reveal a better‐packed helical structure that becomes the precursor of a double helix crystalline formation. When temperature increases, the secondary network is dissolved and water molecules arrange themselves in better‐organized crystals as strongly bound crystal water. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 1880–1886, 2006     

Effect of clay addition on the morphology and thermal behavior of polyamide 6

The nanostructure, morphology, and thermal properties of polyamide 6 (PA6)/clay nanocomposites were studied with X‐ray scattering, differential scanning calorimetry (DSC), and transmission electron microscopy (TEM). The wide‐angle X‐ray diffraction (WAXD) and TEM results indicate that the nanoclay platelets were exfoliated throughout the PA6 matrix. The crystallization behavior of PA6 was significantly influenced by the addition of clay to the polymer matrix. A clay‐induced crystal transformation from the α phase to the γ phase for PA6 was confirmed by WAXD and DSC; that is, the formation of γ‐form crystals was strongly enhanced by the presence of clay. With various clay concentrations, the degree of crystallinity and crystalline morphology (e.g., spherulite size, lamellar thickness, and long period) of PA6 and the nanocomposites changed dramatically, as evidenced by TEM and small‐angle X‐ray scattering results. The thermal behavior of the nanocomposites was investigated with DSC and compared with that of neat PA6. The possible origins of a new clay‐induced endothermic peak at high temperature are discussed, and a model is proposed to explain the complex melting behavior of the PA6/clay nanocomposites. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1191–1199, 2007     

On the determination of platinum particle size in carbon-supported platinum electrocatalysts for fuel cell applications

Using a conventional laboratory diffractometer, small angle X-ray scattering (SAXS) was used to determine the average platinum particle size in samples of carbon with a range of platinum loadings. The results obtained were compared with those obtained from wide-angle X-ray diffraction (WAXS) studies. SAXS was more effective than WAXS for determining the average platinum particle size in samples where the grains were so small that the resultant diffraction peaks in the WAXS profiles were too broad to accurately determine the peak width for use in the Scherrer equation.     

Thermal fractionation and crystallization enhancement of silane‐grafted water‐crosslinked low‐density polyethylene

Thermal fractionations performed using differential scanning calorimetry (DSC) to characterize the heterogeneities in molecular structures of low‐density polyethylene (LDPE), silane‐grafted LDPE (G‐LDPE), and silane‐grafted water‐crosslinked LDPE with gel fractions of 30 and 70 wt % are reported. In regular DSC analyses, LDPE, G‐LDPE, and the low gel fraction of crosslinked samples (30 wt %) give one broad endothermic peak at ～110 °C, whereas the high gel fraction of crosslinked samples (70 wt %) give overlapped multiple endothermic peaks in a much broader temperature range. After thermally fractionated in the range 60–145 °C, LDPE, G‐LDPE, and the low gel fraction samples give five to six endothermic peaks in the low‐temperature range, whereas the high gel fraction samples give nine peaks, with three additional peaks appearing in the high‐temperature range. These multiple peaks correspond to fractions of different molecular structures, with the additional peaks for the high gel fraction samples corresponding to the fraction of molecular segments with low or no branching. This fraction of molecular segments is increasingly extruded out of the gel region with increasing gel fraction by crosslinking and leads to an enhancement of crystallization of the sample. This crystallization enhancement behavior is also demonstrated by the X‐ray diffraction data and polarized optical micrographs. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 591–599, 2001