A small angle X-ray scattering study of polyethylene fibres,using the two-dimensional correlation function

Summary By Fourier transformation of the intensity distribution in the small angle X-ray scattering diagram of a polymer fibre one obtains the corresponding two-dimensional correlation function. This is compared with correlation functions calculated on the basis of different models of the semi-crystalline morphology. Here, two steps may be distinguished: in the first, the correctness of a model may be checked with the aid of qualitative features, such as the relative positions and sizes of positive and negative areas; in the second a quatitative agreement is pursued by fixing the various parameters involved. This method was applied to cold drawn low density polyethylene before and after annealing at different temperatures. In the case of the non-annealed sample, the microparacrystalline model, discussed byHosemann andLoboda-Cackovic (J. Appl. Cryst.11, 540 (1978)) was found to give the best fit. Annealing at 80 °C or higher temperatures seems to lead to what has been indicated as a three-dimensional chess-board structure; it consists of fibrils in which crystalline and amorphous regions alternate in such a way that the crystalline regions in a fibril are adjacent to amorphous regions in neighbouring fibrils.

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Zusammenfassung Durch Fourier-Transformation der Intensitätsverteilung im Kleinwinkelstreudiagramm von Polymerfasern bekommt man die zugehörige zweidimensionale Korrelationsfunktion. Diese wird verglichen mit Korrelationsfunktionen, die für verschiedene Modelle der teilkristallinen Morphologie berechnet wurden.Hier werden zwei Schritte unterschieden. Im ersten Schritt wird die Richtigkeit eines Modells überprüft mit Hilfe von qualitativen Merkmalen, wie z. B. die relativen Lagen und Größen der positiven und negativen Bereiche. Im zweiten Schritt wird eine quantitative Übereinstimmung dadurch angestrebt, daß die unterschiedlich bezüglichen Parameter festgestellt werden. Diese Methode wurde angewandt bei kaltverstrecktem Polyäthylen niedriger Dichte, sowohl vor wie nach Temperung bei verschiedenen Temperaturen. Im Falle einer nicht getemperten Probe zeigte sich, daß das mikrokristalline Modell, vorgeschlagen von Hosemann und Loboda-Cackovic (J. Appl. Cryst.11, 540 (1978)), am besten zutrifft. Temperung bei 80°C oder bei höheren Temperaturen scheint zu einer Struktur zu führen, die als dreidimensionale Schachbrett-Struktur bezeichnet wurde. Sie besteht aus Fibrillen, in denen kristalline und amorphe Bereiche abwechseln, und zwar so, daß die kristallinen Bereiche in einer Fibrille nur von amorphen Bereichen in nächstliegenden Fibrillen umgeben sind.

     

X-ray small angle scattering of bulk polyethylene

Summary A computor method for slit-height correction is described, in which the experimental X-ray small angle scattering curve is represented by aFourier series. It is particulary applicable to curves showing broad maxima or shoulders, like those of solid polymers.

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Zusammenfassung Es wird eine Methode zur elektronischen Berechnung der Entschmierung beschrieben, bei der die Röntgen-Kleinwinkelstreuungskurve durch eineFouriersche Reihe dargestellt wird. Sie eignet sich insbesondere für Kurven mit breiten Maximalbereichen oder Schultern, wie sie bei festen Polymeren erhalten werden.

     

The determination of the lamellar thickness in semi-crystalline polymers by small-angle scattering

Three small-angle scattering methods for determining the thickness of the crystalline lamellae in polymers are described. These are based on 1. observation of the identity period, 2. determination of the specific surface of the phase boundary, and 3. analysis of the shape of the peak at the origin. The conditions for application of these methods and the types of average obtained are discussed, and some results are presented.     

An x-ray diffraction study of nonlinear polyethylene. I. Room-temperature observations

In this investigation on samples of high- and low-density polyethylene and ethylene-vinyl acetate copolymers, crystallinities ?_W and crystalline densities ρ_cW were obtained with the aid of wide-angle x-ray scattering (WAXS) methods. From small-angle x-ray scattering (SAXS) the following characteristics were obtained either directly or by combination with the WAXS data: values, or limiting values, of the crystallinity ?_S; crystal densities ρ_cS; thicknesses of the diffuse boundary layer; number-average thicknesses of the crystalline and amorphous layers; and both number and weight averages of the long periods. It was shown that a discrepancy between ?_S and ?_W cannot be attributed to the occurrence of large amorphous regions outside the regular stacks of lamellae; the data were reconciled by assuming that the WAXS crystallinities pertain to the cores of the crystalline lamellae, whereas part of the diffuse boundary layers is comprised in the values of ?_S. The ρ_cW and ρ_cS data of the nonlinear samples show systematic differences, which were attributed to partial incorporation of side groups in the crystalline regions at a concentration estimated to be of the order of 20–40% of the overall concentration. With increasing side-group concentration, the thickness of the core of the crystalline lamellae was found to approach the average length of the linear chain segments between side groups. On the basis of these observations a scheme for the crystallization of nonlinear polyethylene is proposed according to which a number of side groups is encapsulated by the growing crystal. The data can be explained by assuming that all chains, offered at a crystal face where growth takes place, crystallize directly, irrespective of whether the crystallizing stem carries a side group. Further crystallization would then proceed by chain folding at both ends of the first stem, until a noncrystallizable unit is met. In this scheme, allowance is made for about half the stems in the crystals to be connected by folds; this is required in view of the “overcrowding” effect. Finally, the effect of cooling rate and molecular weight on the thicknesses of the crystalline and amorphous layers is discussed, and differences between the amorphous densities of high-and low-density polyethylene are noted.     

Electrochemical Characterization of the Interaction of Multiwalled Carbon Nanotubes with Doxorubicin

It has been suggested that multiwalled carbon nanotubes (MWCNTs) interacting with pharmaceutics may be introduced into the body as nanocarriers. To deliver the anticancer drugs, covalent or noncovalent functionalization of MWCNTs is required. In this study, the influence of oxidation on MWCNTs in the interaction with chemotherapeutic drug, doxorubicin, was characterized. The binding of doxorubicin with MWCNTs decreased rapidly with the increasing oxidation period with sulfuric acid. However, with nitric acid, the interaction increased initially and slowly decreased with time. The best results were obtained for sulfuric and nitric acid following 1 and 3?h of oxidation, respectively. The results show that sulfuric acid provided more favorable interaction for MWCNTs with doxorubicin than nitric acid.     

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU–GPU parallelism are discussed.     

The Kramer–Mesner method with tactical decompositions: some new unitals on 65 points

We propose a combination of two known computational methods for the construction of designs with prescribed groups of automorphisms: the Kramer–Mesner method and the method of tactical decompositions. This combined method is used to construct new unitals with parameters 2‐(65, 5, 1). © 2011 Wiley Periodicals, Inc. J Combin Designs 19:290‐303, 2011     

Interlaboratory Study of Digital Volume Correlation Error Due to X-Ray Computed Tomography Equipment and Scan Parameters: an Update from the DVC Challenge

Experimental Mechanics - The quality of Digital Volume Correlation (DVC) full-field displacement measurements depends directly on the characteristics of the X-ray Computed Tomography (XCT)...     

X-ray small-angle scattering of bulk polyethylene

Summary On the basis of the assumption that bulk polyethylene is built up of parallel layers differing in electron density, the correlation function for the direction perpendicular to the layers is calculated from the experimental scattering curve at small angles. This function is compared with that calculated for a model consisting of alternating crystalline and amorphous layers. One scale factor and three parameters have to be adjusted to obtain good agreement. The scale factor accounts for the average periodicity in the direction perpendicular to the layers. The parameters are the crystalline fraction and the width of the distributions of the thicknesses of the crystalline and amorphous layers respectively. It is furthermore shown that especially the crystallinity thus found is not appreciably influenced by even relatively large deviations from the primary model.

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Zusammenfassung Ausgehend von der Annahme, daß aus der Schmelze erstarrtes Polyäthylen aus parallelen Schichten unterschiedlicher Elektronendichte zusammengesetzt ist, wird die Korrelationsfunktion für die Richtung, senkrecht zu den Schichten, aus der experimentellen Kleinwinkel-Streuungskurve berechnet. Diese Funktion wird mit derjenigen Funktion verglichen, welche für ein wechselweise aus kristallinen und amorphen Schichten bestehendes Modell berechnet worden ist. Es mußten zur Erreichung einer guten übereinstimmung ein Skalenfaktor und drei Parameter eingestellt werden. Im Skalenfaktor gelangt die mittlere Periodizität in der Richtung, senkrecht zu den Schichten zum Ausdruck. Die Parameter sind die Kristallinität und die Verteilungsbreite der Dicke der kristallinen, bzw. amorphen Schichten. Es wird ferner nachgewieser, daß vor allem die so ermittelte Kristallinität durch sogar relativ große Abweichungen vom primären Modell nur unwesentlich beeinflußt wird.

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With 6 figures in 7 details