Analysis of small-angle X-ray scattering from fibers: Structural changes in nylon 6 upon drawing and annealing

The changes in the fibrillar and the lamellar structure in nylon 6 fibers resulting from drawing and annealing were studied by a detailed analysis of their two-dimensional small-angle scattering patterns. The scattering object that gives to rise the diffuse equatorial scattering in the angular range of Q = 0.02 to 0.3 Å⁻¹ is assumed to be a fibril. There are two distinct regimes in the equatorial diffuse scattering. The scattering at Q < 0.1 Å⁻¹ is dominated by scattering due to the longitudinal dimension of the fibril, and that at Q > 0.1 Å⁻¹ to the lateral dimensions/organization of the fibril. The interfibrillar regions, unlike the interlamellar regions that are essentially made of amorphous chain segments, may have microvoids in addition to amorphous chain segments. The intensity distribution within the lamellar reflections was used to obtain the lamellar spacings and the dimension of the lamellar stacks. The length of the fibrils is between 1000 and 3000 Å, the higher values being more prevalent at lower draw ratios. The fibril length is larger than the length of the lamellar stack, and approaches the latter at higher draw ratios. Annealing does not change the lengths of the fibrils, but the length of the lamellar stack increases. The fibrils form crystalline aggregates with a coherence length of ∼200 Å at higher draw ratios. The diameter of the fibrils (50–100 Å) determined from the lamellar reflection using both the Scherrer equation and the Guinier law are consistent with the lateral size of the crystallites derived from wide-angle x-ray diffraction. The longitudinal correlation of the lamellae between the neighboring fibrils improves upon drawing and decreases upon annealing. The degree of fibrillar and lamellar orientation is about the same as the crystalline orientation. Lamellar spacing increases upon drawing (from ∼60 to 95 Å) and annealing (from ∼85 to 100 Å). This is accompanied by an increase in the width of the amorphous domains from 30 to 50 Å in drawn fibers, and from 45 to 55 Å in annealed fibers. The diameter of the fibrils decreases slightly upon drawing and increases considerably upon annealing. © 1996 John Wiley & Sons, Inc.     

Initiation,Development and Stabilization of Cavities during Tensile Deformation of Semicrystalline Polymers

By using polybutene-1 as a typical example, we illustrate the initiation, development and stabilization of cavities in the sample during tensile deformation. Samples with the same crystallinity, long spacing and crystalline lamellar thickness but very different sizes of spherulites were prepared via changing the melt history. Dimension of cavities during stretching the samples was determined by in situ ultra small angle X-ray scattering techniques. It turned out that the size of the cavities was bigger in the sample with larger spherulites than the one with smaller spherulites. The results show clear evidence of initiating cavities within crystalline phase at the grain-boundary of crystalline blocks, growing of cavities passing through parallel stacked lamellar crystals and amorphous layers and finally stablized by tilted lamellae at both ends of the plate-like cavities within the spherulites.     

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.     

Extraordinary transport behavior of gases in isothermally annealed poly(4‐methyl‐1‐pentene) membranes

Poly(4‐methyl‐1‐pentene) (PMP) membranes were modified through isothermal annealing to investigate the change of their crystalline structure and rigid and mobile amorphous fractions (RAF and MAF), assuming a three‐phase model, affected the gas transport behavior. The crystalline structure was characterized by wide‐angle X‐ray diffraction (WAXD) and small‐angle X‐ray scattering (SAXS) techniques, and the free volume properties were analyzed by positron annihilation lifetime spectroscopy. Compared with the pristine membrane, the annealed membranes show higher crystallinity; the crystals undergo partial structural change from form III to form I. The lamellar crystal thickness, rigid amorphous fraction thickness, and long period in the lamellar stacks increase with crystallinity. The annealed PMP membranes exhibit higher permeability due to the increase in larger size free volumes in MAF and higher selectivity due to the increase in smaller size free volumes in RAF, respectively. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2368–2376     

Small-angle x-ray and light scattering studies of the morphology of blends of poly(ϵ-caprolactone) with poly(vinyl chloride)

Solvent-cast films of blends of poly(?-caprolactone) (PCL) with poly(vinyl chloride) (PVC) were examined by low-angle x-ray scattering and by small-angle light scattering. X-ray scattering from crystalline compositions were analyzed using the Tsvankin–Buchanan technique and led to values of the repeat period of the lamellar structure and the thickness of the crystalline and amorphous layers. With increasing content of PVC, the amorphous layer thickness increased sufficiently to accommodate the PVC, leading to values of the linear crystallinity consistent with macroscopic measurements by density and DSC techniques up to about 50% PVC by weight. Above this concentration, the lamellar structure no longer appeared to be volume filling. At high concentration of PCL, the polymer consisted of volume-filling spherulites containing the lamellar substructure. Spherulite sizes were measured by light scattering and absolute light scattering intensities were consistent with calculations based upon the degree of crystallinity and anisotropy of the spherulites. Compositions containing more than 60% PVC were amorphous. Low-angle x-ray scattering was interpreted in terms of the Debye–Bueche theory which leads to values for a correlation distance l_c and the mean-square electron density fluctuation 〈η²〉 (which was also obtained from the invariant). By the method of Porod, the correlation distances were resolved into persistence lengths within the two phases, which were determined as a function of composition. The fluctuation 〈η²〉 was analyzed in terms of a two-phase model to show that its value was somewhat larger than would be obtained if the phases were composed of the pure components. It was not possible to uniquely determine their compositions. The data were consistent with the existence of a transition zone of the order of 30 Å thick between phases.     

Crystallization and chain conformation of semicrystalline and amorphous polymer blends studied by wide‐angle and small‐angle scattering

We examine the crystallization and chain conformation behavior of semicrystalline poly(ethylene oxide) (PEO) and amorphous poly(vinyl acetate) (PVAc) mixtures with wide‐angle X‐ray diffraction (WAXD), small‐angle X‐ray scattering (SAXS), and small‐angle neutron scattering (SANS) experiments. For blends with PEO weight fractions (wt_PEO) greater than or equal to 0.3, below the melting point of PEO, the WAXD patterns reveal that crystalline PEO belongs to the monoclinic system. The unit‐cell parameters are independent of wt_PEO. However, the bulk crystallinity determined from WAXD decreases as wt_PEO decreases. The scattered intensities from SAXS experiments show that the systems form an ordered crystalline/amorphous lamellar structure. In a combination of WAXD and SAXS analysis, the related morphological parameters are assigned correctly. With the addition of amorphous PVAc, both the average amorphous layer thickness and long spacing increase, whereas the average crystalline layer thickness decreases. We find that a two‐phase analysis of the correlation function from SAXS, in which the scattering invariant is linearly proportional to the volume fraction of lamellar stacks, describes quantitatively the crystallization behavior of PEO in the presence of PVAc. When wt_PEO is close to 1, the samples are fully spaced‐filled with lamellar stacks. As wt_PEO decreases from 1.0 to 0.3, more PVAc chains are excluded from the interlamellar region into the interfibrillar region. The fraction outside the lamellar stacks, which is completely occupied with PVAc chains, increases from 0 to 58%. Because the radius of gyration of PVAc with a random‐coil configuration determined from SANS is smaller than the average amorphous layer thickness from SAXS, we believe that the amorphous PVAc chains still persist with a random‐coil configuration even when the blends form an ordered structure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2705–2715, 2001     

Quasi-equilibrium states of copolymers that simultaneously crystallize and interchange structural units

A quasi-equilibrium model of a step-growth copolymer that crystallizes and interchanges structural units simultaneously is presented. Equilibrium values of counit-sequence-length distribution in the amorphous phase and degree of crystallinity are calculated in a system for which crystallite thickness is determined by nucleation. When applied to calculations, the model predicts that the counits of the amorphous phase will tend to be ordered in blocks. The crystalline content of the whole polymer and the extent of ordering counits along the chain decreases with increasing temperature. The model predicts temperature ranges for some whole copolymers in which one of two similarly stable, disparate combinations of crystallinity and sequence-length distribution may prevail.     

Structure investigations of PE-g-LCP copolymers

 Transesterification products – copolymers of semiflexible liquid crystalline polymer SBH 112 grafted to functionalized low molecular mass polyethylene (PEox) obtained by melt polycondensation or reactive blending procedures have been investigated by wide-angle x-ray scattering (WAXS) and scanning electron microscopy (SEM). The x-ray diffraction patterns of PE-g-LCP copolymers obtained via both procedures consist of reflections typical for the orthorhombic crystalline lattice of PE and the single reflection of the solid LCP. The lack of d _hkl variations with respect to those of neat PEox and SBH indicates the absence of interactions in the crystalline phase or that of cocrystallization phenomena between the components of the PE-g-SBH copolymers. The analysis of the crystallinity degree and normalized amorphous and crystalline contributions to the diffraction patterns of the products suggests that both copolymer components are partly miscible in the amorphous phase. The extent of miscibility depends on the copolymer structure, namely on the length of PE segments and SBH grafts. PE segments in PE-g-SBH copolymers obtained by the reactive blending are longer and exhibit a higher crystallizability than those obtained via melt polycondensation. SBH grafts of the copolymers obtained by the reactive blending are also longer than those in the products obtained via melt polycondensation. The morphology of the samples has been interpreted as determined by the different structure of the copolymers obtained by both procedures. Received: 3 April 1996 Accepted: 15 August 1996     

Characterization of selectively degraded poly(ethylene terephthalate)

To investigate the morphology of unoriented poly(ethylene terephthalate) (PET) films and the selective character of the aminolysis of PET, 67% crystalline polymer samples were degraded with 40% aqueous methylamine at room temperature. The aminolyzed PET samples were subjected to gel permeation chromatography (GPC), viscometry, electron microscopy, and small-angle x-ray diffraction (SAXD). Weight loss and density crystallinity measurements were also made. After 24 hr of aminolysis, the amorphous regions and chain folds were completely removed. The long molecular chains in the semi-crystalline polymer were reduced to monodisperse rods having a molecular weight of 1,800. The corresponding lamellar thickness was calculated to be 101 Å, consistent with the x-ray diffraction and electron microscope (EM) measurements. The EM photographs of “stripped” crystals show the lamellar structure previously found for other selectively degraded polymeric materials. The weight of crystalline debris remaining was consistent with the initial crystallinity. After degradation the crystallinity as determined by density was 96%.     

Investigations of tin (II/IV) phosphates prepared by various methods,Mössbauer study and X-ray diffraction characterization

Using various methods different tin phosphate samples were prepared. One of them was amorphous, while the others were crystalline with monoclinic structure, having unit cell parameters as follows: a=4.586 Å, b=13.618 Å, c=5.818 Å, β=99.61° [Sn (H₂PO₄)₂] and a=8.612 Å, b=4.964 Å, c=15.860 Å, β=98.87° [Sn(HPO₄)₂], respectively. The crystal water content and the method of thermal decomposition of the samples were determined. The chemical composition of the end products of preparations was determined by promt-gamma activation analysis and was found to be Sn:P=1:2 for all samples independent of their preparation method. The oxidation state of tin atoms in samples as determined by Mossbauer spectroscopy was mainly +2 in sample no. 2, while in some other samples it was +4.     

Preparation and Properties of Polyallenes. II. Phase Transitions of Polyallene

Polyallenes prepared with the aid of organoaluminum-VOCl₃ catalysts appear to exist in three distinct phases: two crystalline phases (I and II) and an amorphous phase. Phase I shows two strong X-ray diffraction peaks at d = 5.62 Å and d = 4.04 Å; phase II has three strong peaks at d = 6.28 Å, d = 5.03 Å, and d = 4.21 Å. The band of the amorphous phase has its maximum at about d = 5.6 Å.     

Use of SAXS and linear correlation functions for the determination of the crystallinity and morphology of semi‐crystalline polymers. Application to linear polyethylene

The use of correlation functions to obtain the morphological parameters of crystalline‐amorphous two‐phase lamellar systems is critically reviewed and extended. It is shown that processing of the experimental SAXS‐patterns only significantly affects the curvature of the autocorrelation triangle and that the parameters of the corresponding ideal two‐phase structure can be determined independently of the data processing procedure. The methods to be used depend on the normalization of the correlation function. The validity of the formulation is illustrated for a sample of linear polyethylene, cooled and heated at 10°C per min. Crystallite thickening during crystallization and surface melting during heating are observed. The overall crystallinity and the fraction of semi‐crystalline stacks during crystallization and melting are determined quantitatively as a function of temperature using the total scattering power of the corresponding ideal two‐phase structure, correlation functions, and a scaling procedure. Absolute intensities are not required. The SAXS results are confirmed by independent techniques (DSC, WAXD, and SALLS). During crystallization, amorphous regions are present outside the semi‐crystalline regions because growing spherulites do not fill space completely. During melting, larger amorphous regions develop in the spherulites because of the complete melting of stacks. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1715–1738, 1999     

Thermal properties and the structure of amorphous Sb2Se3 thin film

The amorphous Sb₂Se₃ film with a thickness ~0.9 µm was prepared by thermal evaporation and its composition was confirmed using an energy-dispersive X-ray analysis. The amorphous state was checked by an X-ray diffraction analysis. The optical gap E _g ^opt was determined to be 1.32 eV. The glass transition temperature could not be found by either a differential scanning calorimetry or a thermomechanical analysis. The film was crystallized and characterized using the quasi-isothermal method. The temperature dependence of the isobaric heat capacity was raised monotonously and no drop over the course of the crystallization was observed. The temperature-modulated thermomechanical analysis determined a temperature T = 133 °C which can be assumed to be the temperature of the structural reorganization beginning. Raman spectra of amorphous Sb₂Se₃ revealed that the vibrations of both the amorphous and crystalline phase are close to one other. Raman scattering revealed that both the short and the medium-range order of amorphous and crystalline phases are similar.     

Small-angle scattering studies of nafion membranes

The physical structure of Nafion membranes has been investigated by small-angle neutron scattering (SANS) and small-angle x-ray scattering (SAXS). Samples in the acid form may exhibit two scattering peaks. The first, observed by SANS at an angle corresponding to a Bragg spacing of 180 Å, is shown to arise from structures in crystalline regions. A second peak at larger scattering angles is shown to arise from ion-containing regions which may be swollen with water. Salt-form samples made by soaking the acid form in an aqueous salt solution can also exhibit the same two scattering signals. But in amorphous salt-form samples produced by quenching from the melt the first peak is absent. This permits a more accurate study of the second peak by SAXS, which shows that the second scattering component is present as a maximum over a wide range of water contents but is absent in a sample dried at 200°C. The position of the peak shifts to lower scattering angles (or larger spacings) at higher water contents. Possible structural models that might give rise to the maximum are discussed. A calculation of the SAX invariant is made and results are consistent with a phase separation of a large fraction of the water.     

A three-phase microstructural model to explain the mechanical relaxations of branched polyethylene: a DSC,WAXD and DMTA combined study

The thermal transitions of well-characterised single-site catalysed polyethylenes having various degrees of short chain branching have been studied by differential scanning calorimetry, X-ray diffraction and dynamic mechanical thermal analysis. A critical discussion based on the results obtained by means of the different techniques is presented. The results suggest that the γ transition is independent of the branching content and degree of crystallinity, pointing towards a sub-glass local relaxation mechanism related to both amorphous and crystalline fractions. The temperature of the β transition, T _β from dynamic mechanical measurements, is in agreement with the glass transition temperature obtained by calorimetry, T _g. Moreover, T _γ, and also T _β are directly related to a change in the thermal expansion coefficient of the amorphous phase observed by X-ray scattering. It is found that the corresponding scattering distance of the amorphous halo depends on crystallinity. In addition, the calorimetric heat capacity values at T _β do not account for the total amorphous fraction determined for each material. The relaxation motions assigned to the amorphous phase glass transition seems to parallel the subsequent melting of the crystalline structure, suggesting a hierarchical motion of different structures as temperature increases. Dynamic mechanical thermal analysis supports these observations, showing a broad transition in the phase angle involving first the relaxation of amorphous phase, then the (presumable) more rigid intermediate phase, and finally the crystalline phase, as the temperature increases.     

Cellulose I crystallinity determination using FT–Raman spectroscopy: univariate and multivariate methods

Two new methods based on FT–Raman spectroscopy, one simple, based on band intensity ratio, and the other using a partial least squares (PLS) regression model, are proposed to determine cellulose I crystallinity. In the simple method, crystallinity in cellulose I samples was determined based on univariate regression that was first developed using the Raman band intensity ratio of the 380 and 1,096 cm^?1 bands. For calibration purposes, 80.5% crystalline and 120-min milled (0% crystalline) Whatman CC31 and six cellulose mixtures produced with crystallinities in the range 10.9–64% were used. When intensity ratios were plotted against crystallinities of the calibration set samples, the plot showed a linear correlation (coefficient of determination R ² = 0.992). Average standard error calculated from replicate Raman acquisitions indicated that the cellulose Raman crystallinity model was reliable. Crystallinities of the cellulose mixtures samples were also calculated from X-ray diffractograms using the amorphous contribution subtraction (Segal) method and it was found that the Raman model was better. Additionally, using both Raman and X-ray techniques, sample crystallinities were determined from partially crystalline cellulose samples that were generated by grinding Whatman CC31 in a vibratory mill. The two techniques showed significant differences. In the second approach, successful Raman PLS regression models for crystallinity, covering the 0–80.5% range, were generated from the ten calibration set Raman spectra. Both univariate-Raman and WAXS determined crystallinities were used as references. The calibration models had strong relationships between determined and predicted crystallinity values (R ² = 0.998 and 0.984, for univariate-Raman and WAXS referenced models, respectively). Compared to WAXS, univariate-Raman referenced model was found to be better (root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) values of 6.1 and 7.9% vs. 1.8 and 3.3%, respectively). It was concluded that either of the two Raman methods could be used for cellulose I crystallinity determination in cellulose samples.     

Powder diffraction data and mesomorphic properties of 4-butyloxyphenyl 4′-decyloxybenzoate

Unit cell parameters calculated from X-ray powder diffraction data are presented for the crystalline phase of a liquid crystal 4-butyloxyphenyl 4′-decyloxybenzoate: a = 23.098 (4) Å, b = 5.974 (6) Å, c = 12.357 (10) Å, β = 121.5283 (788)°, unit-cell volume V = 1453.56 ų. Temperature dependent X-ray diffraction data confirmed the existence of smectic A and smectic C mesophases and a more ordered, tilted crystalline smectic phase. Possibility of existence of previously reported smectic B phase as well as another crystalline phase was refuted.     

用X-射线衍射法测定聚对苯二甲酸乙二醇酯/聚对苯二甲酸丁二醇酯共混体系的结晶度

Based on Hermans and Weidinger postulate that the crystalline fraction is proportional to crystalline intensity Ic and that the amorphous fraction is proportional to amorphous intensity Ia, it is. Suggseteet that for PBT/PET blends we assume that the intensity at 18. 2° is completely originated from amorphous scattering. The separation between the peaks at 17. 2° and 20. 8° is 3. 6°m, which is regarded as large enough to justify this assumption. Thus , it is possible to draw an acceptable demaraction line between the crystalline and amorphous scattering. The degree of crystallinity Xc is given by X_c-I_c/(I_c+KI_a),coefficient K is available by the values of Ic plotted against the values of Ia.For PBT/PET blends,we obtain that K is 0.95 and that correlation coefficient is 0.92 According to the method revieved above,we investi-gated the crystallinity of PBT/PET blends prepared by different ways.     

Study on degrees of mesomorphic zone of polymerII. Determination of the degree of mesomorphic zone of eucommia ulmoides gum and natural rubber by dynamic mechanical thermal analysis and differential scanning calorimetry

In a foregoing article, a new method based on dynamic mechanical thermal analysis(DMTA)for determining the degrees of crystallinity of the natural rubber (NR) and the eucommia ulmoides (EU) gum, with different crosslink densities, has been established. In order to verify the effectiveness of this method, in the present paper, the degrees of crystallinity of NR and EU gum with different crosslink densities will be determined by differential scanning calorimetry (DSC). The results indicate that the degrees of crystallinity determined by DMTA are much higher than those of DSC. This is because the degree of crystallinity determined by DMTA involves not only the ratio of the crystalline zone, but also the ratio of the mesomorphic zone, while the degree of crystallinity tested by DSC includes only the ratio of the crystalline zone. So, the degree of crystallinity, the degree of mesomorphic zone and the degree of amorphous zone of NR and EU gums with different crosslink densities can be quantitatively determined by the combination of DMTA and DSC. The results show that the degree of crystallinity, the degree of mesomorphic zone and the degree of amorphous zone of NR (crystallized at −25 °C for 12 h) and EU gum are 33%, 53%, 14% and 34%, 54%, 13%, respectively. For NR, increasing the crosslink density or decreasing the induced time will decrease the degree of crystallinity and the degree of mesomorphic zone simultaneously, but will increase the degree of amorphous zones. For EU gum, increasing the crosslink density will decrease the degree of crystallinity and increase the degree of amorphous zone, but keep the degree of mesomorphic zone invariably consistent within the critical crystallization point, which is approximately 55%. At the end of the paper, the impact of crystallization on the mechanical properties of EU gum and NR is discussed as well.     

Primary and secondary dielectric relaxations in semi-crystalline and amorphous starch

The thermally stimulated depolarization current technique, TSDC, has been used to study the dielectric relaxations in cassava starch on semi-crystalline and amorphous samples. The A-type structure was observed by WAXS experiments and the variation of the crystallinity as a function of the moisture content, h, was followed on native starch. Retrogradation of the amorphous sample occurred at room temperature after 4 weeks in a closed vessel with a water activity 97.3%. In these conditions the humidity content reached a value of 28.5 wt% dry base and the crystallinity degree was comparable to that of the native starch. Three secondary relaxation modes were detected and attributed to short range orientations of polar groups and to main chain restricted motion. The influence of the moisture plasticization effect on the relaxation parameters of the local modes, was determined by decomposing the global TSDC curve in elementary Debye peaks with Arrhenius relaxation times. The main relaxation, α, which is proposed to be the dielectric manifestation of the dynamic glass transition, sweeps a wide temperature interval around room temperature as the sample dries, shifting to higher temperatures as a result of the plasticization of the polysaccharide by water molecules. The α peak deconvolution lead to the 2D relaxation time distribution and Vogel-Tammann-Fulcher parameters were obtained confirming the cooperative character of this mode. The transformed sample showed a bimodal distribution of segmental relaxation times that is interpreted as the existence of a heterogeneous amorphous phase: the mobile one which is similar to the original disordered phase present in semi-crystalline native starch and a more restricted one originated by the disruption of the crystalline lamellae during the pre-gelatinization process.