Diffraction by cylindrical bodies with periodic axial structure

Bear, Richard S.; Bolduan, Orvil E. A.

doi:10.1107/s0365110x50000586

Cited by 36 publications

(16 citation statements)

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“…It was even suggested by Mandelkern and co-workers that the initial morphology was completely erased by the strain-induced melting-recrystallization [13,14]. In parallel, a few SAXS studies have been performed for characterizing the microfibril transverse dimension or width thanks to a Guinier analysis of the transverse intensity profile of the characteristic 2-streak of the one-dimensional fibrillar stacking [7,[15][16][17][18][19][20]. In this analysis framework, the transverse intensity profile is considered to be governed by the form factor of the scattering microfibrils.…”

mentioning

confidence: 99%

On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature

Xiong¹,

Lame²,

Chenal³

et al. 2016

Express Polym. Lett.

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A general feature of the morphogenesis of semicrystalline polymers is the regular stacking of chainfolded lamellar crystals alternating with amorphous layers. This stacking s characterized by an intercrystalline long period L p including the crystalline lamella and amorphous layer thicknesses. The stacking long period is in the range of a few nanometers to a few tens. When crystallization is performed from a quiescent melt, the resulting microstructure is isotropic with a spherulitic arrangement of the lamella stacks as a result of the radial growth of the crystals from a common multiple nucleus often designated as axialite [1]. The size scale of spherulites ranges from a few to several hundred microns. Upon plastic deformation at large strains, isotropic semicrystalline polymers transform into fibrillar materials that aroused a great interest from both academic and industrial standpoints owing to their remarkable mechanical performances [2-6] to be used as ropes, textile fibers for high performance tissues and fabrics, reinforcing fibers for polymer-based composites, etc. Abstract. The influence of crystalline microstructure and molecular topology on the strain-induced fibrillar transformation of semi-crystalline polyethylenes having various chemical structures including co-unit content and molecular weight and crystallized under various thermal treatments was studied by in situ SAXS at different draw temperatures. The long period of the nascent microfibrils, L pf , proved to be strongly dependent on the draw temperature but non-sensitive to the initial crystallization conditions. L pf was smaller than the initial long period. Both findings have been ascribed to the straininduced melting-recrystallization process as generally claimed in the literature. The microfibrils diameter, D f , was shown to depend on the draw temperature and initial microstructure in a different way as L pf . The evolution of D f was shown to correlate with the interfacial layer thickness that mainly depends on the chemical structure of the chains. It was concluded that, in contrast to L pf , the microfibril diameter should not be directly sensitive to the strain-induced melting-recrystallization. The proposed scenario is that after the generation of the protofibrils by fragmentation of the crystalline lamellae at yielding, the diameter of the microfibril during the course of their stabilization should be governed by the chain-unfolding and subsequent aggregation of the unfolded chains onto the lateral surface of the microfibrils. The morphogenesis of the microfibrils should therefore essentially depend on the chemical structure of the polymer that governs its crystallization ability, its chain topology and subsequently its fragmentation process at yielding. This scenario is summed up in a sketch.

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confidence: 99%

On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature

Xiong¹,

Lame²,

Chenal³

et al. 2016

Express Polym. Lett.

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“…Theoretically, the intensity distribution along the radius of a disc in reciprocal space is proportional to the square of a function of the type Jffu)/u, where Jl(U) is a first order Bessel function (Bear & Bolduan, 1950;Vainshtein, 1966). This intensity distribution is illustrated in Fig.…”

Section: Intensity Distribution On the Discsmentioning

confidence: 99%

Correlation between the light diffraction pattern and the structure of a muscle fibre realized with Ewald's construction

Zite-Ferenczy¹,

Häberle²,

Rüdel³

et al. 1986

J Muscle Res Cell Motil

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Ewald's construction of reciprocal space is used to explain the diffraction pattern obtained by illumination of a skeletal muscle fibre with laser light. The question of whether the illuminated fibre segment acts as a monocrystal or as a conglomerate of crystallites is answered by determining the longitudinal extension of the layer lines; neither the whole muscle fibre nor the single myofibril acts as the diffracting unit. The characteristic fine structure within a layer line ('streaks') is explained by Ewald's formalism as being caused by diffraction from partial volumes of the illuminated fibre segment. These partial volumes constitute the main diffracting units. Any cross-section of a 100 micron diameter fibre contains 3-6 such units. They are delineated from each other by the skew of the diffracting planes with respect to the fibre axis, and possibly by small differences in sarcomere length. Within a unit, skew angle and sarcomere length are nearly constant. Light intensity measurements along the length of a layer line at various tilt angles (omega) between fibre and beam axis provide an overview of the size and the skew angle of the various diffracting units within the illuminated fibre segment. The cross-sections of the diffracting units were measured in 'mini'-omega-scans of streaks created by them and from the maximal streak length. In general, the units had noncircular cross-section, the length of the main axis ranging between 10 micron and the fibre diameter. The axial extensions of the diffracting units determined in fibre length scans was 100-300 micron. The results of diffraction experiments reported in the literature as well as the data from light and electron microscopy are in agreement with the fibre structure suggested above. Sarcomere length determination by light diffractometry is discussed within the framework of the Ewald formalism, and recommendations for an experimental procedure are given.

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“…Thus Bear and Bolduan [2] examined the scattering by a cylindrical body having a periodic structure along the cylinder axis c which produces a reciprocal-lattice array of finite parallel disks spaced 1/c apart. The radial extent of these disks is relatable to the cylinder radius with allowance for possible variations in its shape.…”

Section: Introductionmentioning

confidence: 99%

X-ray diffraction by a nematic polybenzothiazole fiber

Adams¹,

Azároff²,

Kulshreshtha³

1979

Zeitschrift Für Kristallographie - Crystalline Materials

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The diffraction of X-rays by a nematic polybenzothiazole fiber produces an intensity distribution in reciprocal space that is a composite of what has been predicted for isolated periodic cylinders and for parallel arrays of infinite cylinders. It consists of periodically spaced disks and equatorial maxima corresponding to a hexagonal packing of cylinders. The number of parallel cylinders comprising coherently diffracting bundles can be estimated by comparing calculated intensity distributions rather than from line-breadth measurements of equatorial intensities.

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Diffraction by cylindrical bodies with periodic axial structure

Cited by 36 publications

References 0 publications

On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature

On the strain-induced fibrillar microstructure of polyethylene: Influence of chemical structure, initial morphology and draw temperature

Correlation between the light diffraction pattern and the structure of a muscle fibre realized with Ewald's construction

X-ray diffraction by a nematic polybenzothiazole fiber

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