Effect of crystallite shape on low-angle x-ray scattering

Gerasimov, V. I.; Tsvankin, D.Ya.

doi:10.1016/0032-3950(69)90074-4

Cited by 39 publications

(3 citation statements)

References 10 publications

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“…On the other hand, the structure model by Shimizu et al was not constructed on the basis of the concept of stacked-lamellar structure. They explained the X-shaped pattern and other scattering in the SAXS patterns by inclined arrays of crystallites according to the Tsvankin theory, [19,20] because of the small crystallite sizes, of nanometer order, in the direction perpendicular to the (010) and (100) planes. Furthermore, the structure model should also be based on the following characteristic of polyesters; the molecular weight of polyesters decreases readily in the molten state, especially due to the transesterification reaction, and the resultant molecular weight is considered to be too small to form well-developed lamellar crystals.…”

Section: Resultsmentioning

confidence: 99%

Stacked-Lamellar Structure in High-Speed Spun PET Fibers as Revealed by TEM

Yoshioka

Kawahara

Kikutani

et al. 2010

Journal of Macromolecular Science, Part B

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Morphological study of high-speed spun poly(ethylene terephthalate) (HSS-PET) fibers spun at 6 km/min was performed by a combination of alkaline etching, surface replica method, and transmission electron microscopy. In the two-stage replica of the alkalineetched fiber, the stacked-lamella-like structure was observed, in which lamella-like striations were stacked in a direction leaning at about 40 • away from the fiber axis. The spacing between the adjacent striations, namely the lamellar periodicity, was measured to be 10-30 nm. We have proposed that the stacked-lamellar structure, which is mainly composed of mosaic lamellar crystals and has the extended-chain crystals connecting the adjacently stacked lamellae, is an appropriate model for the fiber structure of HSS-PET fibers.

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Section: Resultsmentioning

confidence: 99%

Stacked-Lamellar Structure in High-Speed Spun PET Fibers as Revealed by TEM

Yoshioka

Kawahara

Kikutani

et al. 2010

Journal of Macromolecular Science, Part B

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“…The positions of the fibrils in neighbouring fibrils may be assumed to be uncorrelated. Calculations and interpretations based on this model, to which we will refer as the model of inclined lamellar fibrils, were given by Gerasimov and coworkers (13,14). (In a recent paper Gerasimov et al (15) furthermore considered the possibility of the lamellae in neighbouring fibrils being correlated.…”

Section: The Calculation and Comparison Of Correlation Functions Basementioning

confidence: 97%

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

Vonk

1979

Colloid Polymer Sci

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From the general principles of diffraction theory it follows that Fourier transformation of the function describing the distribution of the diffracted X:ray intensity in reciprocal space leads to a function in direct space representing the autoconvolution of the electron density variations in the diffracting object. As on the one hand this function contains all the information that is hidden in the diffraction pattern, and on the other hand can be more readily interpreted in terms of structural details than the intensity function itself, it is often used in the solution of structures from X-ray diffraction data. In small angle X-ray scattering (SAXS) it is usually scaled to have the value 1 in the origin; it is then called the correlation function. Its general properties have been discussed by Porod (1) and by Debye, Anderson and Brumberger (2); the application of a onedimensional correlation function to the lamellar structures occurring in isotropic semicrystalline polymers was recommended by Vonk and Kortleve (3).In this paper the use of two-dimensional correlation functions in the study of SAXS from fibres of uni-axial symmetry is discussed. Here the situation differs from the one encountered in isotropic polymers in that the basic structure in the isotropic polymers (stacks of alternating crystalline and amorphous layers) might be taken for granted, whereas there is no general agreement on the basic structure occurring in polymer fibres.Many of these substances show a four-point SAXS pattern, which has been explained in different ways, as is to be discussed below. Therefore in the present case the correlation function should in the first place serve in asserting the most appropriate model, and secondly in finding the correct values of the various parameters involved. The potentiality of the correlation function in these respects will be demonstrated in the analysis of the diffraction pattern from a cold drawn and subsequently annealed fibre of low density polyethylene. The approach followed is to compare the 'observed' correlation function, obtained by Fourier transformation of the observed intensity function, with 'calculated' correlation functions, based on the different models that have or can be proposed. Furthermore, also calculated intensity functions were obtained by Fourier transforming the calculated correlation functions; the comparison of these with the original observed intensity functions was however made in a qualitative way only. Experimental and computational detailsThis was a commercial low density polyethylen of the type Stamylan 2800, manufactured by DSM. Its density after compression molding (cooling rate 40 °C/min.), as determined according to method ISO 1183 D, was 0.920; the melt flow index, determined according to method ISO R 292, amounted to 0.30 gr/10 min. From a compression molded sheet dumbbell shaped specimens were made that were drawn at room temperature at a rate of 2.5 cm/min, to fracture at an extension of 700%. Annealing was achieved in conditions where the samples were free...

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“…This procedure, however, requires thoroughly measured curves and the model seems to be relatively insensitive towards parameter variation. Tsvankin [3][4][5][6] developed a structure model basing on the concept of the linear paracrystalline lattice. Buchanan [7] modified this theory and described an evaluation method that has been widely applied in the literature.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

Brämer

Gerdes

Wenig

1983

Colloid & Polymer Sci

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Three paracrystalline lattice models for the interpretation of the small angle scattering of polyethylene are discussed: The "lattice model", the "stapel model, (often referred to as the lamellar stack model) and the "proportional model". While the applicability of the first model is restricted, the latter models differ in the statistical assumptions of lamellar and interlamellar thickness distributions. The principal advantage of the proportional model over the stapel model is its applicability through the adjustment of only three parameters : long period, crystallinity and one statistical parameter. Small angle X-ray curves of linear polyethylene are interpreted by the proportional model. The results are in good agreement with stapel model calculations.

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Effect of crystallite shape on low-angle x-ray scattering

Cited by 39 publications

References 10 publications

Stacked-Lamellar Structure in High-Speed Spun PET Fibers as Revealed by TEM

Stacked-Lamellar Structure in High-Speed Spun PET Fibers as Revealed by TEM

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

Analysis of the small-angle X-ray scattering of linear polyethylene by a paracrystalline lattice model

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