Orientation distribution of crystallites in polyethylene terephthalate fibers (original) (raw)
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Applied Spectroscopy, 1998
Polarized confocal Raman microscopy has been used to m easure molecular orientation in uniaxially drawn poly(ethylene terephthalate) (PET) ® lm s, prep ared with draw ratios from 1 to 3.5. The P 200 values obtained agreed well with those m easured with the use of refractiv e index and infrared dichroism, provided that the numerical aperture (NA) of the microscope objective was not too high. For example, a 0.75 NA objective gave good agreement with IR and refractiv e index results, but a 0.95 NA objective signi® cantly reduced the measured P 200. Corrections for the in¯uence of sample birefringence on the m easured Raman intensities were m ade and found to have a sm all (; 5%) effect on P 200. This resu lt is fortunate, because such corrections demand knowledge of the principal refractive indices of the sample, which m ay be unavailable. It was also shown that the presence of signi® cant biaxial orientation in these samples did not signi® cantly affect the P 200 values com puted under the assumption of uniaxial orientation. O rientation m easurements were also com pared with crystallinity data obtained by confocal Raman mapping through the thickness of a PET ® lm. Significant gradients in both crystallinity and orientation were found through the thickness of the ® lm. Surprisingly, these gradients were in the opposite sense, so regions of high crystallinity correlated with low orientation and vice versa. These results illustrate the extra insight obtained by combining m ultiple m orphological m easurements on the same sample.
Study of crystalline orientation in drawn ultra-high–molecular weight polyethylene films
Journal of Polymer Science Part B: Polymer Physics, 1993
Centre de recherches en sciences et ingbnierie des macromolbcules, Dkparternent de chimie, Universith Laval, Qubbec (Canada), G1 K 7P4 SYNOPSIS A wide-angle x-ray diffraction (WAXD) study of the development of molecular orientation in the crystalline phase of ultra-high-molecular weight polyethylene films prepared by the gelation-crystallization method is presented. 'WAXD scans of the undrawn films show that the lamellae are oriented in the plane of the films. Upon drawing at 130°C, the orientation of the molecular chains changes from the direction normal to the film surface (ND) to the elongation direction. The decrease of the 200/020 intensity ratio a t low draw ratio (A < 10) indicates that double orientation develops during the transformation from the lamellar to the fibrillar morphology, with the a-axis oriented parallel to ND. The orientation distributions of the 110,200,020, and 002 planes of the orthorhombic unit cell of polyethylene were studied and characterized by the coefficients of a Legendre polynomial series. At a draw ratio of 4.5, the second-order coefficient, (P2(cos x), already gets close to its limiting value, but it is shown that higher order coefficients of the polynomial series can be used to describe the evolution of the orientation, event up to X = 50. The coefficients relative to the molecular chain orientation, (P , (cos x))~, can be calculated from different crystalline reflections. Curve-fitting calculations were made in order to improve the correlation between the results obtained from the orientation distribution of the 110, 020, and 002 planes. A Pearson VII function was found to give a better fit of the experimental curves than Gaussian or Lorentzian equations.
Optical diffraction technique for determination of crystal orientations
Applied Optics, 1981
An optical technique for determination of crystal orientations is described. This technique uses texture etching to generate pseudoperiodic surface structures whose groove shape is characteristic of the surface orientation. When such a textured surface is illuminated with monochromatic light, a far-field diffraction pattern characteristic of the surface orientation is observed. A procedure for analysis of diffraction patterns to determine crystal orientations is discussed. Results obtained by this technique agree very well with those using the x-ray Laue technique.
Orientations and Crystallinities of Drawn Fibers Using Two Beam Interferometry
Egyptian Journal of Physics
I N this work, the Pluta interference microscope was used to study the effect of drawing process on the optical, structural, and mechanical properties of polyethylene terephthalate (PET) fibers. The orientational behavior of drawn PET fibers to different draw ratios was investigated using the calculated values of the refractive indices and the double refraction. Changing the draw ratio resulted in changes in optical parameters, which were used to determine the mechanical factors of orientation. Different orientation functions, such as f 2 (θ), f 4 (θ), f 6 (θ), f a , f c , and f av , were calculated. Molecular reorientation during the cold drawing process can be considered the main reason for the major variations in the properties of PET fibers. It can be concluded that double refraction related to the total overall orientation of the crystalline and amorphous phases. The different crystallinities parameters were measured. Microinterferograms were utilized to illustrate these variations.
A diffractometer technique for precise orientation of single crystals
Journal of Applied Crystallography, 1978
A diffractometer technique for determining the orientation of single crystals is described. The technique is well suited for small spherical or nonabsorbing crystals, as well as for large, extended-face crystals and boules. Since the orientation is determined in a plane perpendicular to the plane of incidence of the diffractometer, the technique does not require an accurate knowledge of the lattice parameter for cubic crystals. The c/a ratio or all cell parameters must, however, be known accurately for crystals of lesser symmetry. It is shown that the orientation can be determined to within 0.005 ° . Factors affecting the precision of the technique are discussed.
Journal of Elasticity, 2019
The present work continues the investigation first started by Lobos et al. (J. Elast. 128(1):17-60, 2017) concerning the orientation average of tensorial quantities connected to single-crystal physical quantities distributed in polycrystals. In Lobos et al. (J. Elast. 128(1):17-60, 2017), central orientation density functions were considered in the orientation average for fourth-order tensors with certain index symmetries belonging to single-crystal quantities. The present work generalizes the results of Lobos et al. (J. Elast. 128(1):17-60, 2017) for the orientation average of tensors of arbitrary order by presenting a clear connection to the Fourier expansion of central orientation density functions and of the general orientation density function in terms of tensorial texture coefficients. The closed form of the orientation average based on a central orientation density function is represented in terms of the Fourier coefficients (referred to as texture eigenvalues) and the central orientation of the central orientation density function. The given representation requires the computation of specific isotropic tensors. A pragmatic algorithm for the automated generation of a basis of isotropic tensors is given. Applications and examples are presented to show that the representation of the orientation average offers a low-dimensional parametrization with major benefits for optimization problems in materials science. A simple implementation in Python 3 for the reproduction of all examples is offered through the GitHub repository https://github.com/mauricio-fernandez-l/centralODF-average. Mathematics Subject Classification 74A40 • 74A60 • 74Q15 • 42C10 • 82D25 • 15A69 Keywords Orientation average • Polycrystals • Central functions • ODF • Isotropic tensors 1 Introduction Polycrystalline materials exhibit, in general, a complex distribution of crystallographic orientations. Models for the computation of approximations or bounds of physical properties B M. Fernández
New insights on single-crystal orientation by the diffractometer method
Materials Characterization, 1991
Applications of the diffractometer method are found in the identification of the stereographic triangle where the tensile (or compressive) axis of a single crystal is positioned after deformation. Also, the method is used in the determination of the shear planes responsible for fracture, when shear band formation and fracture occurs along specific crystalline planes of the single crystal. A computer algorithm, based on spherical trigonometric equations, which eliminates the use of the Wulff net, is also presented. The algorithm calculates the position of specific directions of the crystal on the standard <ereographic triangle using direct information obtained from the diffractometer.