Small‐angle X‐ray scattering and polymer melting: A model study

Small‐angle X‐ray scattering (SAXS) gives information on lamellar stacks in semicrystalline polymers. SAXS experiments have been used to follow the melting transition that occurs over a temperature range of 10 °C or more. One common feature is the increase in the average period by 50–100% during the melting process, a change that is often attributed to sequential melting of crystals in the lamellar stack. A quantitative treatment shows that the scattering experiment indicates only the original period, not the average period that increases throughout sequential melting. With this model, I discuss the relation between structural parameters of the melting structure and quantities derived from the SAXS intensity, the correlation function, and the interface distribution function. Uncertainties persist in our understanding of polymer melting. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2454–2460, 2001     

Time‐resolved crystallization study of absorbable polymers by synchrotron small‐angle X‐ray scattering

Changes in the lamellar morphology that occurred during the quiescent isothermal crystallization of absorbable poly(p‐dioxanone) (PDS) and PDS/poly(glycolide) block copolymer were studied by synchrotron small‐angle X‐ray scattering. Important morphological parameters such as the lamellar long period, the thicknesses of the crystal and amorphous phases, and the scattering invariant were estimated as a function of time, and trends observed over a wide range of experimental conditions are discussed. Thicker but more perfect lamellae were detected at higher crystallization temperatures. The breadth of the normalized semilog Lorentz‐corrected intensity peak systematically decreased with increasing temperature. In addition, the values of the crystallization half‐time and the Avrami exponent (n = 2.5), determined from the real‐time changes in the lamellar development, showed superb agreement with the bulk crystallinity data generated from other experimental techniques, such as calorimetry and dielectric relaxation spectroscopy. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 153–167, 2001     

Crystallization and chain conformation of semicrystalline and amorphous polymer blends studied by wide‐angle and small‐angle scattering

We examine the crystallization and chain conformation behavior of semicrystalline poly(ethylene oxide) (PEO) and amorphous poly(vinyl acetate) (PVAc) mixtures with wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and small‐angle neutron scattering (SANS) experiments. For blends with PEO weight fractions (wt_PEO) greater than or equal to 0.3, below the melting point of PEO, the WAXD patterns reveal that crystalline PEO belongs to the monoclinic system. The unit‐cell parameters are independent of wt_PEO. However, the bulk crystallinity determined from WAXD decreases as wt_PEO decreases. The scattered intensities from SAXS experiments show that the systems form an ordered crystalline/amorphous lamellar structure. In a combination of WAXD and SAXS analysis, the related morphological parameters are assigned correctly. With the addition of amorphous PVAc, both the average amorphous layer thickness and long spacing increase, whereas the average crystalline layer thickness decreases. We find that a two‐phase analysis of the correlation function from SAXS, in which the scattering invariant is linearly proportional to the volume fraction of lamellar stacks, describes quantitatively the crystallization behavior of PEO in the presence of PVAc. When wt_PEO is close to 1, the samples are fully spaced‐filled with lamellar stacks. As wt_PEO decreases from 1.0 to 0.3, more PVAc chains are excluded from the interlamellar region into the interfibrillar region. The fraction outside the lamellar stacks, which is completely occupied with PVAc chains, increases from 0 to 58%. Because the radius of gyration of PVAc with a random‐coil configuration determined from SANS is smaller than the average amorphous layer thickness from SAXS, we believe that the amorphous PVAc chains still persist with a random‐coil configuration even when the blends form an ordered structure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2705–2715, 2001     

Probing multiple melting behaviors in poly(ethylene naphthalene 2,6‐dicarboxylate) with different thermal histories by simultaneous wide‐angle and small‐angle X‐ray scattering

A simultaneous wide‐angle and small‐angle X‐ray scattering study of two poly(ethylene naphthalene 2,6‐dicarboxylate) samples crystallized from the glassy state at different annealing temperatures for different annealing times was carried out with synchrotron radiation. Either single or dual melting was induced in the samples, as confirmed by differential scanning calorimetry (DSC). The correlation function and interface distribution function were calculated to evaluate microstructural parameters such as the long spacing, the thickness of the amorphous and crystalline phases, and the width of the size distributions. The sample with dual melting behavior exhibited an abrupt increase of all microstructural parameters at temperatures above the melting of the lowest endotherm, whereas the sample revealing a single melting endotherm did not show such a sudden change. This finding agrees with the concept that the appearance of two melting peaks in DSC traces can be explained by the dual lamellar stacking model. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 881–894, 2001     

Morphology of polyanhydride copolymers: Time‐resolved small‐angle X‐ray scattering studies of crystallization

Synchrotron small‐angle X‐ray scattering (SAXS) was used to study the isothermal crystallization kinetics of a family of polyanhydride copolymers consisting of 1,6‐bis(p‐carboxyphenoxy)hexane and sebacic acid monomers. In situ SAXS experiments permitted the direct observation of the crystallization kinetics. The structural parameters (the long period, lamellar thickness, and degree of crystallinity) were obtained from Lorentz‐corrected intensity profiles, one‐dimensional correlation functions, and interface distribution functions to form a comprehensive picture of the crystal morphology. The combination of these three analyses provided information not only on the lamellar dimensions but also on the polydispersity (nonuniformity) of these dimensions. Where possible, the crystallization kinetics were interpreted with a modified version of the Avrami equation. The results can be used to perform the rational design of controlled‐drug‐release formulations because crystallinity affects drug‐release kinetics. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 463–477, 2005     

Investigation of the deformation of homogeneous poly(ethylene‐co‐1‐octene) by wide‐ and small‐angle X‐ray scattering using synchrotron radiation

The deformation behavior of homogeneous ethylene‐1‐octene copolymers was investigated as a function of the crystallinity and the crystal size and perfection, respectively, by wide‐ and small‐angle X‐ray scattering using synchrotron radiation. The crystallinity and the crystal size and perfection, respectively, are controlled by the copolymer composition and the condition of melt crystallization. The deformation includes rotation of crystals, followed by plastic deformation and complete melting of the initial crystal population, and final formation of microfibrils. The process of rotation, plastic deformation, and melting of crystals of the initial structure is completed at lower strain if the size and perfection of the crystals, respectively, decrease, that is, if crystals thermally melt at lower temperature. The kinetics of the fibrillation of the initial structure seems independent of the crystal symmetry, that is, rotation and melting of pseudohexagonal and orthorhombic polyethylene crystals (as evident in low‐crystalline specimens) are similar. The structure of the microfibrils, before and after stress release, is almost independent of the condition of prior melt crystallization, which supports the notion of complete melting of the initial crystal population. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1919–1930, 2002     

Effect of the initial matrix material on the structure of radiation‐grafted ion‐exchange membranes: Wide‐angle and small‐angle X‐ray scattering studies

Seven different fluoropolymer films were used as matrix materials for radiation‐grafted ion‐exchange membranes. The crystallinity and preferred orientation of these membranes were studied with wide‐angle X‐ray scattering, and the lamellar structure of the membranes was examined with small‐angle X‐ray scattering. The crystallinity of poly(vinylidene fluoride) (PVDF)‐based matrix materials varied between 57 and 40%, and the crystallinity of the sulfonated samples varied between 34 and 23%. The lamellar periods of PVDF‐based matrix materials were about 115 Å, and the lamellar periods of poly(ethylene‐alt‐tetrafluoroethylene) and poly(tetrafluoroethylene‐co‐hexafluoropropylene) were 250 and 212 Å, respectively. When the samples were grafted, the lamellar periods increased. Correlation function analysis showed very clearly that the long‐range order decreased because of grafting and sulfonation processes. For those samples that showed good proton conductivity, the lamellar period also increased because of sulfonation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1539–1555, 2002     

Online wide‐angle X‐ray diffraction/small‐angle X‐ray scattering measurements for the CO2‐laser‐heated drawing of poly(ethylene terephthalate) fiber

Fiber‐structure‐development in the poly(ethylene terephthalate) fiber drawing process was investigated with online measurements of wide‐angle and small‐angle X‐ray scattering with both a high‐luminance X‐ray source and a CO₂‐laser‐heated drawing system. The intensity profile of the transmitted X‐ray confirmed the location of the neck‐drawing point. The diffraction images had a time resolution of several milliseconds, and this still left much room for improvement. Crystal diffraction appeared in the wide‐angle X‐ray images almost instantaneously about 20 ms after necking, whereas a four‐point small‐angle X‐ray scattering pattern appeared immediately after necking. With the elapse of time after necking, the four‐point scattering pattern changed into a meridional two‐point shape. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1090–1099, 2005     

Oriented lamellar structures in uniaxially drawn films of poly(vinylidene fluoride) and poly(3‐hydroxybutyrate) blends studied by small‐angle X‐ray scattering measurements

The lamellar structures in uniaxially drawn films of miscible crystalline/crystalline polymer blends of poly(vinylidene fluoride) (PVDF) and poly(3‐hydroxybutyrate) (PHB) were investigated by static and time‐resolved measurements of small‐angle X‐ray scattering (SAXS). Intense SAXS in the low angle range of the meridian was interpreted as originating from the interlamellar inclusion structure, in which the PHB chains were included between the lamellae of PVDF. The interlamellar inclusion was induced for the uniaxially drawn films of PVDF/PHB = 30/70 blend with a draw ratio (DR) of 2.8–4.5, whereas the lamellae of the PVDF and PHB components were mutually excluded from each other forming their own lamellar stacks (interlamellar exclusion) in the blend with a higher DR (5.0–5.7). When the highly drawn film with the interlamellar exclusion structure was heat treated at 154–165 °C, the interlamellar inclusion structure was partially induced by the heat treatment. The time‐resolved SAXS measurements indicated that the interlamellar inclusion structure was developed by melting and recrystallization of PVDF during the heat treatment. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 381–392, 2009     

Application of SSA thermal fractionation and X‐ray diffraction to elucidate comonomer inclusion or exclusion from the crystalline phases in poly(butylene succinate‐ran‐butylene azelate) random copolymers

Poly(butylene succinate‐ran‐butylene azelate) random copolyesters were thermally fractionated by successive self‐nucleation and annealing (SSA). The samples before and after SSA were analyzed by differential scanning calorimetry (DSC) and X‐ray diffraction (WAXS and SAXS). WAXS results indicate that a small degree of comonomer inclusion is present in the crystalline phases that are formed in the copolymers depending on composition: a PBS‐like unit cell or/and a PBAz‐like unit cell, thus confirming the isodimorphic behavior of the samples. SSA on the other hand demonstrated that the degree of comonomer exclusion during crystallization is far larger than comonomer inclusion, as judged by the increase in fractionation degree with compositions leading to the pseudo‐eutectic point. Furthermore, WAXS, SAXS, and SSA results show that the isodimorphic behavior is not highly dependent on kinetic factors, as the degree of comonomer inclusion or exclusion in the samples was not significantly altered by SSA thermal fractionation, a thermal treatment that promotes annealing and molecular segregation of defects to the amorphous regions of the material. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2346–2358     

Morphological changes during heating in poly(L‐lactic acid)/poly(butylene succinate) blend systems as studied by synchrotron X‐ray scattering

Blends of poly(L ‐lactic acid) (PLA) and poly(butylene succinate) (PBS) were prepared in various compositions via melt mixing, and the morphological changes were investigated with differential scanning calorimetry and synchrotron wide‐angle and small‐angle X‐ray scattering techniques at a heating rate of 10 °C/min. Differential scanning calorimetry thermograms of PLA/PBS blends showed two distinct melting peaks over the entire composition range. The exothermal peak for PLA shifted significantly to a lower temperature and overlapped with that of PBS around 100 °C. A depression of the melting point of the PLA component via blending was observed. The synchrotron wide‐angle X‐ray scattering during heating revealed that there was no cocrystallization or crystal modification via blending. The synchrotron small‐angle X‐ray scattering data showed that well‐defined double‐scattering peaks (or peaks with a clear scattering shoulder) appeared during crystallization, indicating that this system possessed dual lamellar stacks. These peaks were deconvoluted into two components with a peak separation computer program, and then the morphological parameters of each component were obtained by means of the correlation function. The long period and average lamellar thickness of the two components before melting decreased with an increasing content of the other polymer component. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1931–1939, 2002     

Synchrotron SAXS and WAXS Studies on Changes in Structural and Thermal Properties of Poly[(R)‐3‐hydroxybutyrate] Single Crystals during Heating

Summary: The annealing and melting behavior of poly[(R)‐3‐hydroxybutyrate] (P(3HB)) single crystals were followed in real time by synchrotron small‐ (SAXS) and wide‐angle X‐ray scattering (WAXS) measurements. The real‐time SAXS measurements revealed that the P(3HB) single crystal exhibits a discontinuous increase of lamellar thickness during heating. The structural changes as observed by SAXS and WAXS were in response to the thermal properties of single crystals characterized by differential scanning calorimetry.

A series of two‐dimensional small‐angle X‐ray scattering patterns of P(3HB) single crystal mats during the lamellar thickening process.     

Extraordinary transport behavior of gases in isothermally annealed poly(4‐methyl‐1‐pentene) membranes

Poly(4‐methyl‐1‐pentene) (PMP) membranes were modified through isothermal annealing to investigate the change of their crystalline structure and rigid and mobile amorphous fractions (RAF and MAF), assuming a three‐phase model, affected the gas transport behavior. The crystalline structure was characterized by wide‐angle X‐ray diffraction (WAXD) and small‐angle X‐ray scattering (SAXS) techniques, and the free volume properties were analyzed by positron annihilation lifetime spectroscopy. Compared with the pristine membrane, the annealed membranes show higher crystallinity; the crystals undergo partial structural change from form III to form I. The lamellar crystal thickness, rigid amorphous fraction thickness, and long period in the lamellar stacks increase with crystallinity. The annealed PMP membranes exhibit higher permeability due to the increase in larger size free volumes in MAF and higher selectivity due to the increase in smaller size free volumes in RAF, respectively. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2368–2376     

Multiaxial deformation of polyethylene and polyethylene/clay nanocomposites: in situ synchrotron small angle and wide angle X‐ray scattering study

A unique in situ multiaxial deformation device has been designed and built specifically for simultaneous synchrotron small angle X‐ray scattering (SAXS) and wide angle X‐ray scattering (WAXS) measurements. SAXS and WAXS patterns of high‐density polyethylene (HDPE) and HDPE/clay nanocomposites were measured in real time during in situ multiaxial deformation at room temperature and at 55 °C. It was observed that the morphological evolution of polyethylene is affected by the existence of clay platelets as well as the deformation temperature and strain rate. Martensitic transformation of orthorhombic into monoclinic crystal phases was observed under strain in HDPE, which is delayed and hindered in the presence of clay nanoplatelets. From the SAXS measurements, it was observed that the thickness of the interlamellar amorphous region increased with increasing strain, which is due to elongation of the amorphous chains. The increase in amorphous layer thickness is slightly higher for the nanocomposites compared to the neat polymer. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Small‐angle X‐ray scattering investigation of carbon nanotube‐reinforced polyacrylonitrile fibers during deformation

Structural changes during deformation in solution‐ and gel‐spun polyacrylonitrile (PAN) fibers with multi‐ and single‐wall carbon nanotubes (CNTs), and vapor‐grown carbon nanofibers were investigated using synchrotron X‐ray scattering. Previously published wide‐angle X‐ray scattering (WAXS) results showed that CNTs deform under load, alter the response of the PAN matrix to stress, and thus enhance the performance of the composite. In this article, we find that the elongated scattering entities that give rise to the small‐angle X‐ray scattering (SAXS) in solution‐spun fibers are the diffuse matrix‐void interfaces that follow the Porod's law, and in gel‐spun fibers these are similar to fractals. The observed smaller fraction of voids in the gel‐spun fibers accounts for the significant increase in the strength of this fiber. The degree of orientation of the surfaces of the voids is in complete agreement with those of the crystalline domains observed in WAXS, and increases reversibly upon stretching in the same way as those of the crystalline domains indicating that the voids are integral parts of the polymer matrix and are surrounded by the crystalline domains in the fibrils. The solution‐spun composite fibers have a larger fraction of the smaller (<10 nm) voids than the corresponding control PAN fibers. Furthermore, the size distribution of the voids during elongation changes greatly in the solution spun PAN fiber, but not so in its composites. The scattered intensity, and therefore the volume fraction of the voids, decreases considerably above the glass transition temperature (T_g) of polymer. Implications of these observations on the interactions between the nanotubes and the polymer are discussed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2394–2409, 2009     

Layer structure estimation of three‐dimensional crystal and two‐dimensional molecular film for fluorinated comb copolymers

Comb copolymers containing both hydrogenated and fluorinated side‐chains were prepared by copolymerization using acrylic or methacrylic monomers in several ratios. The crystal structures of these copolymers and layer structures of their organized molecular films were investigated by wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and out‐of plane X‐ray diffraction. Further, to selectively estimate the regularity of shorter fluorocarbon side‐chains, organized molecular films of copolymers were investigated by polarized near‐edge X‐ray adsorption fine structure (NEXAFS) spectroscopy. From the results of these measurements, it was inferred that these copolymers formed highly ordered layer structures, and a long spacing was predominantly determined by the arrangement of hydrogenated side‐chains, except in copolymers having extremely high fluorocarbon contents. In the case of the organized molecular films, the fluorinated side‐chains of methacrylate copolymers cannot form a highly ordered arrangement, whereas those of acrylate copolymers were oriented on monolayers. However, in both cases, the hydrogenated side‐chains predominantly formed layer structures in the organized films, and the fluorinated side‐chains did not contribute to the formation of the layer structures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 534–546, 2008     

Wide‐angle X‐ray diffraction and differential scanning calorimetry study of the crystallization of poly(ethylene naphthalate), poly(butylene naphthalate), and their copolymers

The crystallization behavior of a series of poly(ethylene‐co‐butylene naphthalate) (PEBN) random copolymers was studied. Wide‐angle X‐ray diffraction (WAXD) patterns showed that the crystallization of these copolymers could occur over the entire range of compositions. This resulted in the formation of poly(ethylene naphthalate) or poly(butylene naphthalate) crystals, depending on the composition of the copolymers. Sharp diffraction peaks were observed, except for 50/50 PEBN. Eutectic behavior was also observed. This showed isodimorphic cocrystallization of the PEBN copolymers. The variation of the enthalpy of fusion of the copolymers with the composition was estimated. The isothermal and nonisothermal crystallization kinetics were studied. The crystallization rates were found to decrease as the comonomer unit content increased. The tensile properties were also measured and were found to decrease as the butylene naphthalate content of the copolymers increased. For initially amorphous specimens, orientation was proved by WAXD patterns after drawing, but no crystalline reflections were observed. However, the fast crystallization of drawn specimens occurred when they were heated above the glass‐transition temperature. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 843–860, 2004     

Lamellar structural changes in miscible crystalline polymer blends during melting and crystallization processes,as studied by real‐time small‐angle X‐ray scattering measurements

Real‐time small‐angle X‐ray scattering (SAXS) measurement using synchrotron radiation was applied to study the lamellar structural changes in miscible crystalline polymer blends of poly(1,4‐butylene succinate) (PBSU) and poly(vinylidene fluoride) (PVDF) during melting and crystallization processes. The lamella of PBSU is either included in the interlamellar region of PVDF (interlamellar inclusion structure), or rejected from the interlamellar region of PVDF (interlamellar exclusion structure). The two lamellar structures coexists in the melt‐quenched samples of the PBSU/PVDF = 30/70 blend. Only the interlamellar exclusion structure exists in the drawn films of the PBSU/PVDF = 30/70 blend. The real‐time SAXS results show that the interlamellar exclusion structure in these samples is irreversibly transformed into the interlamellar inclusion structure by heating the sample above the melting temperature of PBSU and that the PBSU chains are crystallized between the lamellae of PVDF during the cooling process. The factors controlling the lamellar structural changes are possibly a balance of the miscibility and the chain exclusion by tie‐molecules and/or the chain diffusion under confinement by the lamellae of PVDF with higher melting temperature. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1959–1969, 2007     

Salt‐induced microphase separation of amorphous dendritic poly(ethylene oxide)‐block‐linear polystyrene copolymers

We prepared two block copolymers 1 and 2 consisting of a third‐generation dendron with poly(ethylene oxide) (PEO) peripheries and a linear polystyrene (PS) coil. The PS molecular weights were 2000 g/mol and 8000 g/mol for 1 and 2 , respectively. The differential scanning calorimetry (DSC) data indicated that neither of the block copolymers showed glass transition, implying that there was no microphase separation between the PEO and PS blocks. However, upon doping the block copolymers with lithium triflate (lithium concentration per ethylene oxide unit = 0.2), two distinct glass transitions were seen, corresponding to the salt‐doped PEO and PS blocks, respectively. The morphological analysis using small angle X‐ray scattering (SAXS) and transmission electron microscopy (TEM) demonstrated that a hexagonal columnar morphology was induced in salt‐doped sample 1‐Li⁺ , whereas the other sample ( 2‐Li⁺ ) with a longer PS coil revealed a lamellar structure. In particular, in the SAXS data of 2‐Li⁺ , an abrupt reduction in the lamellar thickness was observed near the PS glass transition temperature (T_g), in contrast to the SAXS data for 1‐Li⁺ . This reduction implies that there is a lateral expansion of the molecular section in the lamellar structure, which can be interpreted by the conformational energy stabilization of the long PS coil above T_g. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2372–2376, 2010     

Spatially inhomogeneous crystallinity in heterogeneous ethylene‐α‐olefin copolymers

The crystallinity development in heterogeneous ethylene‐1‐butene copolymers is compared with that in ethylene copolymers, with more bulky 1‐heptene as a comonomer. The thermal transitions of the 1‐heptene based copolymers persistently occur at higher temperatures than of the corresponding 1‐butene copolymers. The earlier crystallization onset is reflected in thicker primary crystals, which in turn are associated with the presence of longer ethylene sequences because of the inaccessibility of 1‐heptene to sterically shielded catalytic sites. In addition, the 1‐heptene based copolymers are characterized by a higher degree of primary crystallinity, whereas the 1‐butene copolymers exhibit more prominent secondary crystallization. The 1‐butene based copolymers thus have a less heterogeneous chemical composition distribution. At high comonomer contents, the highly heterogeneous nature of the 1‐heptene copolymers is emphasized by a more pronounced presence of low crystalline spherulite inclusions accomplished by the liquid–liquid phase separation of dissimilar polymeric chains before crystallization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3000–3018, 2005