General procedure for evaluating amorphous scattering and crystallinity from X-ray diffraction scans of semicrystalline polymers

Mathematical functions for the representation of chromatographic peaks.

https://soar-ir.repo.nii.ac.jp/?action=repository_uri&item_id=12732&file_id=65&file_no=1

Fabrication of aligned carbon nanotube-filled rubber composite

Crystallinity and crystallite size measurement in polyamide and polyester fibres

The use of infrared spectroscopy as a technique for characterizing the state of intercalation and exfoliation in polymer nanocomposites prepared from montmorillonite-based nanoclays was investigate...

/pdf/use-of-infrared-spectroscopy-to-characterize-clay-59r96jx4rf.pdf

Use of Infrared Spectroscopy To Characterize Clay Intercalation and Exfoliation in Polymer Nanocomposites

A wide-angle x-ray method has been developed by which quantitative structural information can be obtained on nylon-6 yarns. To this end, experimental equatorial diffractometer scans measured in transmission were fitted to a mathematical model describing the profiles as the envelopes of three bell-shaped functions. Four different models were investigated using, respectively, Gauss, Lorentz (Cauchy), Logistic, and Pearson-VII functions. The last model, which can be regarded as a generalized Lorentz function, gave the best fit. On the basis of a statistical analysis of the results of well-separated x-ray peaks, two parameters could be fixed. Another reduction of the number of parameters was achieved by interrelating the peak areas of the two outer reflections. These reductions widened the applicability of a computer program based on the aforementioned model to highly overlapping x-ray peaks. So the whole variety of x-ray scans, which can be obtained from nylon-6 yarns made under widely varying process conditions, can be well described. The fitting procedures provide unique solutions and hence objectively determined parameters.

Quantitative information from x‐ray diffraction of nylon‐6 yarns. I. Development of a model for the analytical description of equatorial x‐ray profiles

Types of nylon 6 yarn which contain large γ crystals cannot be described by a model comprising three Pearson VII curves, as we formerly proposed. Hence, a new extended computer program has been developed containing five Pearson VII lines. Two lines are related to the α phase, two to γ-phase crystals, and the fifth describes the amorphous contribution. Some physical relations between parameters could be derived and were incorporated into the computer program. This program provides extremely good fits to all equatorial diffractometer scans which can be obtained from nylon 6 yarns, including those containing large γ crystals. The parameter accuracy is quite satisfactory for diffractometer traces with well-resolved peaks from both α and γ crystals. However, if the traces are poorly resolved or the samples do not contain a sufficient amount of the γ modification, resulting in a lack of detailed information, the parameter accuracy can be rather poor. For those cases special versions of the computer program were developed which contain further empirical interrelations between parameters. With these programs crystal sizes and molecular distances within the crystals of both the α and β modifications can be determined. The method has also been applied to radial scans at various small azimuthal angles with respect to the equator. In that way the relative amounts of the α and γ crystals as well as their orientation factors could be determined. Various aspects of this investigation are illustrated by some examples.

Five‐line model for the description of radial x‐ray diffractometer scans of nylon 6 yarns

A mathematical model developed in an earlier paper describes the experimental x-ray profiles of equatorial nylon-6 reflections in terms of Pearson VII functions. The present paper deals with the physical aspects and interpretations of the interrelations of the parameters obtained and the relation between these parameters and the results of other types of measurements. It was found that the growth of the crystallites perpendicular to the chain axis is not isotropic, the strongest growth being in the direction of the hydrogen bonds. Growth and perfection of the crystallites are found to be highly correlated. Large crystals are related to short distances between the planes containing the hydrogen bonds and so to densely packed, i.e., perfect unit cells. This correlation forms the basis for the observed similarity between our quantification technique and the method of the crystal perfection index introduced by Statton. Curve resolution, however, makes the method better applicable for poorly crystallized samples. Comparison of the results with those of small-angle x-ray scattering gave a high degree of consistency with respect to the determined crystal size. In the literature mention is made of a relation between the dimensions and the melting point of the crystals; this relation is confirmed by comparing the appropriate x-ray parameters with DTA results of methoxymethylated nylon 6-yarns.

Information about the γ-phase can be obtained from equatorial and meridional reflections. The expected relationship between the relevant peak areas was established. This reported evidence shows the physical validity of the parameters obtained using the Pearson VII model for the analytical description of x-ray reflections of nylon-6 yarns.

Quantitative information from x-ray diffraction of nylon-6 yarns. II. Physical aspects of some quantitative parameters

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Quantitative information from x‐ray diffraction of nylon‐6 yarns. I. Development of a model for the analytical description of equatorial x‐ray profiles

Five‐line model for the description of radial x‐ray diffractometer scans of nylon 6 yarns

Quantitative information from x-ray diffraction of nylon-6 yarns. II. Physical aspects of some quantitative parameters