Norbert Stribeck

Extraction of domain structure information from small-angle scattering patterns of bulk materials

A method is presented that permits the extraction and visualization of topological domain structure information contained in small-angle scattering (SAS) patterns without complex pretreatment. Multi-dimensional noisy raw data can be processed. Such data are, for instance, accumulated in the field of materials research from short-exposure-time in situ small-angle X-ray scattering (SAXS) experiments with synchrotron radiation. The result is a multi-dimensional intersect or chord distribution, which is defined as the Laplacian of the correlation function. Moreover, it is equivalent to the autocorrelation of the gradient of the electron density. The procedure is, in particular, adapted to the analysis of the nanoscale structure of samples with fibre symmetry, such as polymer fibres or strained elastomers. Multi-dimensional relations among morphological components become apparent in real space and help to elucidate the nature of the processes governing formation and change of structure on the nanometre scale. Utilizing digital signal processing tools, the algorithm is based on spatial frequency filtering of the raw data. The background to be subtracted from the small-angle scattering pattern is formed from its own low spatial frequencies. Noise may be removed by suppressing high spatial frequencies. In the frequency band between these low and high spatial frequencies, the domain structure information of the studied nanocomposite appears.

Determination of the interface distribution function of lamellar two-phase systems

The concept of interface distribution functions [Ruland (1977). Colloid Polym. Sci. 255, 417–427] has been applied to the evaluation of the small-angle scattering of a series of polyethylene samples. The results indicate that the statistics of the lamellar stacking is not necessarily determined by next-neighbor interactions and that non-negligible volume fractions of amorphous domains outside the lamellar systems are observed in a number of samples.

Mapping the local nanostructure inside a specimen by tomographic small-angle x-ray scattering

Small-angle x-ray scattering is combined with scanning microtomography to reconstruct the small-angle diffraction pattern in the direction of the tomographic rotation axis at each location on a virtual section through a specimen. These data yield information about the local nanoscale structure of the sample. With rotational symmetry present in the diffraction patterns, e.g., for isotropic or fiber-textured scatterers, the full reciprocal space information in the small-angle scattering regime can be reconstructed at each location inside the specimen. The method is illustrated investigating a polymer rod made by injection molding.

Nanostructure of Nafion membrane material as a function of mechanical load studied by SAXS

The nanostructure of a perfluorinated membrane material (Nafion 117 by DuPont) is investigated as a function of strain and load by smallangle X-ray scattering (SAXS) at a synchrotron source. Two-dimensional SAXS patterns are evaluated utilizing the multi-dimensional chord distribution function (CDF). Anisotropy of the extruded material is considered. Both the ionomer domain and matrix polymer nanostructure are studied. For the neat material the classical ionomer domain model (domains as inverted micellae interconnected by channels) is confirmed and refined. Matching the plastic deformation behavior of the material, the domain structure in the relaxed and in the elongated state are found to be very similar. During elongation, ionomer channels open to form hollow ionomer layers(‘slits’) that are oriented parallel to the strain with a thickness of 1.9 nm and a long period of 3.8 nm. The slit height increases from 3 nm at elongation 1 ¼ 0:5 to 6 nm at 1 ¼ 1:25; whereas the slit width decreases to 1.5 nm. The ultimate structure is characterized by ensembles of not more than three slits that are in good lateral register. In the polymer matrix during elongation, cylindrical crystallites with a thickness of 2.5 nm and a most probable height of 7 nm are disrupted and parallelized with respect to the straining direction. The ultimate structure before sample failure is characterized by a broad domain height distribution ranging from a most probable domain height of 4 nm with a corresponding ultimate inclination of 408 to some perfectly parallelized domains of 20 nm height. q 2003 Elsevier Science Ltd. All rights reserved.

Investigation of secondary crystallization of polymers by means of microbeam X-ray scattering

Abstract The kinetics of secondary crystallization during spherulite growth of isotactic poly(propylene) (iPP) and poly(vinylidene flouride) (PVF 2 ) is studied using a novel technique that employs a micron size X-ray beam. The data are combined with separate conventional simultaneous on-line SAXS/WAXS measurements and optical microscopy studies. In our experiments, crystallization takes place at low undercooling so that slowly growing large single spherulites are obtained. The data reveal that the main mechanism of secondary crystallization is the growth of new lamellae stacks within remaining amorphous regions. It is shown that a substantial amount of crystallites form as a result of secondary crystallization while the spherulite is growing. Furthermore, secondary crystallization is strongest directly behind the boundary of the spherulite and is independent of its size or growth state. A separate, off-line microfocus study on a quenched spherulite sample confirms this observation; the crystallinity is higher in the main body of the spherulite and lower near the boundary, where crystallization progressed to a lesser degree.

Investigation of the high speed spinning process of poly(ethylene terephthalate) by means of synchrotron X-ray diffraction

Measurements of wide-angle diffraction during high speed spinning of poly(ethylene terephthalate) (PET) have been performed using synchrotron radiation. The experimental set-up has been improved so that it became possible to determine the degree of crystallinity, crystallite orientation and fiber diameter along the spin line. For take-up speeds of 3600 m/min and higher, the crystal reflections appeared at a distance of 40 cm from the spinneret, just after the necking region. The crystallization speed increases proportional to increasing take-up speed. For the take-up speeds investigated, this results in a constant crystallinity profile when measured as a function of the distance from the spinneret. The final fibers exhibited an extraordinarily high degree of crystallinity, which has been attributed to the high molecular weight of the polymer. Below 3500 m/min, no crystallization and no necking could be detected up to a distance of 90 cm from the spinneret. The results showed that necking and crystallization were closely coupled. No orientation of the amorphous matrix prior to crystallization could be detected by means of X-ray diffraction. Moreover, the orientation of the crystallites was constant along the spin line.

SAXS data analysis of a lamellar two-phase system. Layer statistics and compansion

An analysis of small angle x-ray scattering (SAXS) data from three injection molded poly(ethylene terephthalate) (PET) samples is carried out. Two of the samples are annealed at different temperatures. The chosen concept of data analysis is that of Rulands interface distribution function (IDF) of lamellar two-phase systems. The IDF can be expanded into a series of distance distributions, containing the information on the topological properties of the ensemble of lamellar stacks in the semicrystalline sample.The paper describes the stepwise refinement of a topological model. The final model is described by only few parameters of physical meaning. It unifies the well-known concepts of an ensemble of non-uniform stacks, finite stack size and one-dimensional paracrystalline disorder in an analytical expression. In order to deduce this expression, the concept of inhomogeneity (imagine a variation of the long period from stack to stack) is generally treated in terms of “compansion”, a suggested superposition principle. Its mathematical equivalent in one dimension is the Mellin convolution.

Small-angle X-ray scattering investigations of styrene-butadiene-styrene block copolymers during stretching

Abstract A small-angle X-ray scattering study on styrene-butadiene-styrene block copolymers during stretching is reported. Measurements have been performed at the Hamburg Synchrotron Radiation Laboratory at DESY using a two-dimensional position-sensitive detector. A pattern of layer lines perpendicular to the stretching direction with ellipsoidal envelope is obtained. This indicates a good orientation of cylindrical polystyrene domains along the stretching direction. The diameter-to-length ratio of the cylinders was found to be 0.6, the length being approximately 39 nm. The long period of the undrawn sample is about 47 nm. Upon stretching, initially this value increases almost affinely, while for γ >3 it tends to reach a constant value. The extension at which the curve bends coincides with the inflection point in the stress-strain curve; at higher values of extension, most of the polybutadiene chains are probably completely stretched and further extension is achieved partly by disruption of the polybutadiene matrix.

Nanostructure Evolution of Oriented High-Pressure Injection-Molded Poly(ethylene) During Heating

Abstract High-pressure injection-molded polyethylene (PE) rods are studied by ultra small-angle X-ray scattering from synchrotron during the heating of the polymer. Injection of a cool melt into a cold mold yields highly oriented PE rods with a core–shell structure. Samples from both the core and the shell material are studied. The two-dimensional scattering patterns are evaluated utilizing the multi-dimensional chord distribution function (CDF) analysis. From the obvious evolution of the nanostructure during successive crystallite melting, the sequence of processes occurring during crystallization is elucidated. First, nuclei form one-dimensional lattices with short-range order along the fiber axis. From this row structure, lamellae grow with wide lateral extension. An indication of an intermediate block structure is observed. Finally two steps of insertion crystallization result in two long period halvings. Increase of the mold pressure increases the lateral extension of the inserted lamellae in the shell material. In the core material a uniform row structure is absent. Extended primary lamellae form stacks with decreasing long periods before insertion crystallization takes over. But crystallites inserted in the core material do not form extended lamellae. Each of these steps leaves its footprint in the nanostructure and the corresponding scattering pattern. After CDF interpretation of the heating series, the room temperature pattern can be explained. The strong two-point pattern is associated with the primary lamellae and the intensity ridge extending along the meridian results from irregular insertion of lamellae. When the row structure is observed in the CDF, the fiber pattern exhibits equatorial scattering. Domain roughness generates a strong background scattering, which cannot be separated in one step. For the presented material it is shown that iterative background subtraction eliminates the scattering effects of the imperfect (i.e. inserted) lamellae.

The Equatorial Small-Angle Scattering during the Straining of Poly(ether ester) and Its Analysis

A method for the quantitative analysis of two-dimensional (2D) small-angle X-ray scattering (SAXS) patterns with fiber symmetry by successive information filter- ing is proposed and applied to a series of images recorded during a straining experiment of a two-phase polymer sample at a synchrotron beamline. The studied equatorial scattering is similar to the frequently discussed void scattering, but originates from an ensemble of rodlike soft domains (needles) in the sample, orientated in the direction of strain. The intensity is extracted and projected onto the equatorial plane, the ideal two-phase structure is extracted, and the 2D chord distribution is computed. This curve describes a 2D two-phase morphology made from needle cross-sections embedded in matrix material. Because interparticular correlation is found to be weak in the chord distribution, pure particle scattering is assumed. Modeling the needle cross-sections by circular disks leads to a simple theory, which allows the deconvolution of a disk diameter distribution from the chord distribution. It is shown how parameters of the disk diameter distribution can be computed without deconvolution. For the selected poly(ether ester) thermoplastic elastomer the study of the soft domain needles indicates strain-induced hardening. While for low elongation e the soft needles are more com- pressible than the microfibrillar matrix, saturation is observed for e . 2.5.