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

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.     

Crystal orientation in a semicrystalline polymer in relation to deformation of polymer spherulites. IV. Crystal orientation mechanism of nylon-6 under uniaxial stretching

A model relating crystal orientation to the deformation of nylon-6 spherulites under uniaxial stretching is discussed in terms of the orientation distribution functions of reciprocal lattice vectors of crystal planes, such as the (002) and (200) planes. The distribution functions calculated from the model are compared with those obtained from x-ray diffraction experiments. It is found that the crystal a axis and, consequently, the direction of hydrogen bonds within the crystal (α modification) orient parallel to the lamellar axis in the undeformed state, and that the crystal orientation behavior of nylon-6 is much different from that of low-density polyethylene, being characterized by much smaller values of the reorientation parameters of crystallites within orienting lamellae. Moreover, small-angle light scattering for H_v and V_v polarization is also calculated on the basis of the spherulite deformation model by taking the nylon-6 crystal as having orthogonal–biaxial symmetry in optical anisotropy. It is concluded that the H_v scattering can be realized in terms of the proposed model for spherulite deformation by taking into account a considerable contribution of hydrogen bonds to the molecular polarizability, so as to make the polarizability along the crystal a axis larger than that along the b axis. In other words, this conclusion suggests positively birefringent spherulites in the nylon-6 samples studied.     

Small-angle neutron and x-ray scattering study of swollen nylon-6

Results of swelling and small-angle scattering experiments on samples of nylon-6 swollen with heavy water are discussed on the basis of the lamellar and switchboard models. The small-angle neutron scattering (SANS) intensity is very sensitive to the distribution of water in swollen samples, while the small-angle x-ray scattering (SAXS) data characterize the dry samples. The observed values of the mean-square fluctuation of scattering-density can be explained by a model with assumed inhomogeneous swelling of the amorphous phase.     

Thermal behavior of α nylon-12

The thermal behavior of α nylon-12 film cast from a phenol-ethanol mixture has been studied by differential scanning calorimetry. Polymorphism has been analyzed by x-ray diffraction. The γ form exhibits a single endothermic melting peak in the thermogram, whereas the α form exhibits double peaks. Samples with mixed α and γ forms show double peaks at the same positions and the area ratio changes in accordance with the amounts of the two forms. The appearance of the γ peak, even for the α sample, is explained by recrystallization to the γ form after melting of the α form. The melting point of α nylon-12 is ca. 173°C, which is lower by 6–7° than that of the γ form. Once the α or γ sample has been melted and then cooled, its heating thermogram shows a small peak before the appearance of the main peak. The small peak seems to be due to incomplete and/or smaller crystallites formed during cooling. Heat treatment below the melting point of α nylon-12 is effective in transforming the α form to the γ form, probably via a melt-recrystallization process.     

Bulk properties of synthetic polymer-inorganic salt systems. V. Mechanical properties of oriented poly(caproamide)

Single filaments of nylon-6 and of its mixtures with KCl, LiCl, and LiBr (salt content up to 5% w/w) were prepared by extrusion at 265°C. As-spun filaments with a varying degree of orientation were obtained by altering the take-up velocity a t constant outflow velocity. These as-spun filaments were further subjected to controlled thermal and mechanical treatments. Determinations of the elastic modulus, of birefringence, of wide-angle x-ray scattering, and of shrinkage were carried out for the as-spun and for the treated filaments. While KCl caused no detectable alteration of the properties of nylon-6, lithium halides caused a considerable increase of the elastic modulus of the polymer. Under the conditions adopted, moduli up to 14 GPa were obtained. The birefringence of as-spun fibers was, however, lower when lithium salt was present. Greater shrinkage a t 170°C was exhibited by the salted than by the pure polymer. The body of results has been interpreted in terms of a more efficient orientation of the extruded polymer when lithium salt is present. The latter effect is associated with the role of these salts in reducing the crystallization rate and in increasing the melt viscosity of the polyamide as characterized in preceding papers of this series. Lithium salts also favor the α → γ transformation between the two crystalline forms of nylon-6. The transformation was, however, reversed under sufficiently high applied stress.     

SAXS determination of the amorphous surface layer thickness of polymer single crystals

Polyethylene single crystals were grown from 0.1% solutions in xylene at 80 and 87°C. Oriented mats were made from each preparation and the small-angle x-ray scattering (SAXS) profiles obtained. Following treatment of the raw data for main-beam position and width, background scatter, and the Lorentz factor, five Bragg reflections were resolved. A one-dimensional lattice was used as a model for the oriented mats of single crystals. This model contains three parameters. An additional parameter G_x was also introduced to demonstrate the general effect of a broadening factor on the model. The effect of each parameter on the calculated diffraction pattern was examined. From this examination it was found that by assuming that the broadening functions are zero we can determine directly from the number of observable peaks the maximum possible thickness of the amorphous surface. Further, we find that the thickness of the amorphous layer must be less than the maximum value calculated if G_x is assigned values greater than zero. A “best-fit” diffraction pattern was generated in order to estimate how much smaller the surface thickness can be such that one can still resolve five diffraction maxima. The range of amorphous surface thicknesses found from the calculated diffraction profile is 12–20 Å. This is in good agreement with complementary studies performed on the same crystal preparations.     

The microstructure of poly(vinyl chloride) as revealed by x-ray and light scattering

Small-angle x-ray scattering (SAXS) and wide-angle x-ray scattering (WAXS) as well as small-angle light-scattering (SALS) techniques have been applied to investigate the microstructure of a number of commercial poly(vinyl chloride) (PVC) samples. From the wide-angle x-ray scattering, crystallinity and crystal size parameters have been determined. The crystallinity of the samples investigated range from 5% to 10%. Superstructure parameters such as crystallite thickness, distribution functions of crystallite and amorphous thicknesses, and size of ordered regions have been obtained by an analysis of the SAXS curves using the cluster model. The crystallinity agrees well with the WAXS crystallinities indicating that most of the crystals are lamellar shaped, though some rodlike entities are present in the sample as is shown by the small-angle light scattering. From the SAXS analysis, the microstructure is described as clusters of lamella stacks which are identical with the subprimary particles. Their size is determined to be 220–240 Å. Emulsion type PVC also contains lamellar-shaped crystals. The superstructure, however, of this type of PVC is different from that of mass or suspension-polymerized material. The SAXS curve does not reveal any correlation between the crystals.     

An anomalous x-ray diffraction study of the hydration structures of Cs+ and I- in concentrated solutions

Anomalous x-ray diffraction experiments were carried out on concentrated aqueous solutions of sodium iodide (6 molal) and cesium iodide (3 molal). Data were gathered at two energies below the absorption edges of the Cs+ and I- ions in order to avoid contributions from fluorescence. The statistics and quality of the raw data were improved by the use of a focusing analyzer crystal. Differences were taken between the data sets and used to calculate the hydration structures of Cs+ and I-. The structures found are more complex than anticipated for such large ions with relatively low charge densities and show evidence of ion-pair formation in both solutions. A two-Gaussian fit to the Cs+ data gives information about the Cs+-O and Cs+-I- correlations. The central position of the Gaussian representing the Cs+-O was fixed at 3.00 A, that is, the maximum of this contribution. The other parameters were allowed to vary freely, giving a Cs+-I- distance of 3.84+/-0.05 A and coordination numbers of 7.9 and 2.7, respectively, for the Cs+-O and Cs+-I- correlations. The results on the structure of I- in the 6 molal NaI aqueous solution were also fitted to a model based on Gaussians; this gives correlations for I- -O and I- -Na+ at 3.17+/-0.06 and 3.76+/-0.06 A with respective coordination numbers of 8.8 and 1.6. The structure of I- in the 3 molal CsI solution shows overlapping contributions due to I- -H, I- -O, and I- -Cs+. The best Gaussian fit gives two peaks centered at 3.00+/-0.08 and 3.82+/-0.04 A and shows that the latter two correlations are unresolved. The hydration structures are compared with those of other alkali and halide ions. The results are also found to be in good agreement with those obtained from standard x-ray diffraction and computer simulation.     

Annealing experiments on drawn nylon 66 fibers

Drawn, nylon 66 yarns have been annealed in oil under relaxed conditions. Shrinkage and tensile modulus were measured and the yarns were examined by wide- and small- angle x-ray diffraction. The results are similar to those obtained by Dismore and Statton, but there are significant differences. The data indicate a model for a drawn nylon 66 fiber in which substantial amounts of folds remain.     

An stable approach to a kind of problems involving the inversion of a Volterra integral equation of the first kind: application to x-ray fluorescence analysis

In some physical problems it is necessary to obtain a function coming from the inversion of an unstable problem, and use it to calculate some global quantities by integrating it weighted by the appropriate weighting functions. When the desired function comes from a first kind Volterra integral equation, the explicit inversion can be avoided by integrating by parts in the integrals in which the above mentioned function appears. That is the case of the fundamental parameters method of x-ray fluorescence analysis. To obtain the concentrations of chemical elements in the sample which is analyzed it is necessary to calculate some integrals of the spectral distribution of the fluorescence exciting x-ray beam multiplied by a weighting function which depends on the concrete analysis to be done. The spectral distribution of the fluorescence exciting beam is related to the experimental measurements of the fluorescence excited on a set of targets made up of pure elements by a Volterra integral equation of the first kind, and it can be obtained by inverting the Volterra equation. By integrating by parts in the integrals in which the spectral distribution appears we avoid the unstable reconstruction of the spectrum of the fluorescence exciting x-ray beam and the concentrations can be calculated in a stable fashion.     

Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

General analysis of the measurements of the lateral crystal lattice moduli of semicrystalline polymers by x-ray diffraction and the application to nylon 6

A mathematical representation based on a linear elastic theory is proposed by which one may investigate the dependences of molecular orientation and crystallinity on the crystal lattice moduli and linear thermal expansion coefficients in the direction perpendicular to the chain axis as commonly measured by x-ray diffraction. In the theoretical calculation, a previously introduced model was employed in which oriented crystalline phase is surrounded by oriented amorphous phase and the strains of the two phases at the boundary are identical. The mathematical analysis indicated that the lateral crystal lattice moduli and linear thermal coefficients as measured by x-ray diffraction may be different from the intrinsic crystal moduli and linear thermal coefficients of a crystal unit cell, depending on the structure of the polymer solid. The numerical calculation was applied to nylon 6. As a result, it may be confirmed that the lateral crystal lattice moduli measured by x-ray diffraction are sensitive to the morphology of the bulk speciments and close to the intrinsic crystal moduli if the morphology of the test specimen can be represented by a parallel model with respect to the original stretching longitudinal direction.     

Effect of casting conditions on polymorphism of nylon-12

Polymorphism in nylon-12 film, which appears on casting from a phenol-ethanol solution, has been investigated by x-ray diffraction and infrared absorption. The casting temperature was varied from 30 to 130°C and the ambient atmospheric pressure from 50 to 760 Torr. Casting at 30°C gives only the α form, while casting above 90°C yields only the γ form. At intermediate temperatures, both α and γ forms are obtained, with the γ content increasing as the casting temperature and/or the rate of evaporation of solvent are increased. The ethanol component of the casting solvent appears to act only as a melting-point depressant for phenol. In contrast, nylon-6 film cast from the same solvent system between 30 and 160°C gives only the α form. It is proposed that the difference in polymorphism of nylons-12 and -6 is caused by differences in molecular flexibility due to the length of the methylene chain.     

Dynamic x-ray diffraction studies of liquid-crystalline polyesters

Mesophase transitions in liquid-crystalline (LC) polyesters were studied by dynamic x-ray diffraction using a synchrotron radiation source. Powder and fiber samples were examined by continuous heating from 50°C to 270°C in a hot stage. The polymer systems consisted of two types of thermotropic polyesters with mesogenic cores composed of combinations of substituted terephthalate, oxybenzoate and hydroquinone units combined with aliphatic spacers placed in the main chain. One of these samples was a chemically homogeneous LC polyester (HTH12) while the other LC polyester possessed chemical heterogeneity (BP6). BP6 could also be processed to form fibers which showed thermal transition behavior by x-ray diffraction and no detectable melting or clearing transition by thermal measurements. LC textures were observed using polarized light microscopy. Results of the dynamic x-ray diffraction studies of these two LC polymers are described.     

An investigation of the smectic-isotropic transition in a side-chain liquid crystal polymer by synchrotron radiation x-ray diffraction

In this work we have used synchrotron x-radiation diffraction to follow in real-time the isotropic-smoetic phase transition of a side-chain liquid crystalline polymer. The analysis of the x-ray data indicated that the transition occurs within a very narrow biphasic region. As the transition takes place, the size of the smectic regions, as indicated by the width of the diffraction peaks, changed only very slightly before impingement, suggesting a two-dimensional growth pattern. A thermal investigation of the polymer paralleling the x-ray experiments was undertaken and a kinetic analysis applied to the resulting data. Qualitative agreement with a disk-like growth of the smectic regions was found. We have shown that the overall kinetics of the isotropic-smectic transition of a side-chain polymer can be studied by x-ray diffraction permitting the evaluation of several structural parameters. © 1993 John Wiley & Sons, Inc.     

Communication: X-ray scattering from ionic liquids with pyrrolidinium cations

We report the structure functions obtained from x-ray scattering experiments on a series of four homologous ionic liquids. The ionic liquids are 1-alkyl-1-methylpyrrolidinium cations paired with the bis(trifluoromethylsulfonyl)amide anion, with alkyl chain lengths of n = 4, 6, 8, and 10. The structure functions display two intense diffraction peaks for values of the scattering vector q in the range from 0.6 to 1.5 ?(-1) for all samples. Both diffraction peaks shift to lower values of q for increasing temperature. First sharp diffraction peaks are observed in the structure functions for q < 0.5 ?(-1) for liquids with n = 6, 8, and 10.     

Thickening of crystals during rapid heating. I. Linear polyethylene and nylon-6

The change of long spacing in polyethylene and nylon-6 during heating at 18°C/min. was measured with an apparatus devised for rapid measurement of the small-angle x-ray diffraction. The apparatus made it possible to obtain a diffraction profile in 1.8 sec. Long spacings increased notably at high temperatures near the melting point, as has been observed during low-rate heating. However, the increase in long spacing during heating was very small in a methoxymethylated nylon-6 sample. This suggests that the increase in the long spacing at high temperature is due to the thickening of crystals. The long spacing in polyethylene samples in the vicinity of the melting point is apparently independent of thermal history.     

A novel apparatus combining polymer extrusion processing and x-ray scattering

A novel apparatus was designed and constructed combining polymer extrusion processing and x-ray scattering. It allows direct, real time monitoring of structure and temperature development in polymer material during extrusion. The apparatus involves a vertical industrial extruder equipped with a four-roll stretching device to mimic the processing environments of uni-axially oriented films or sheets, a simultaneous small and wide angle x-ray scattering system and an infrared thermometer as detection unit. The charging barrel of the extruder and the stretching device can be moved upward and downward precisely. By moving the sample along the center line, structure and temperature development as a function of position can be obtained. The performance of the apparatus was verified by a test experiment, which allows us to establish the relationship between processing parameters and evolution of structure with different length scales, and may lead to a better understanding of the physics in polymer processing.