X-ray small-angle scattering of bulk polyethylene

Summary A previously described method for evaluating X-ray small-angle scattering curves was applied to a number of well-characterized polyethylene samples. The average thicknesses of the crystalline and amorphous layers were estimated by this method; furthermore, the mean square of the density fluctuations within the samples was determined from the integral small-angle scattering. From these data, combined with the overall densities of the samples, the densities of the crystalline and amorphous layers were calculated; these densities compare well with the figures generally assumed for a two-phase structure.The effects of molecular weight and cooling rate on the thicknesses of the crystalline and amorphous layers are noted, and the thicknesses of the crystalline layers are compared with the melting points of the samples.Finally, a discussion is given of the errors which may be involved ifBragg's law is applied to small-angle scattering curves.

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Zusammenfassung Eine bereits früher beschriebene Methode zur Bewertung von Röntgen-Kleinwinkelstreuungskurven wird auf eine Anzahl genau charakterisierter Polyäthylenproben angewandt. An Hand dieser Methode wird die mittlere Dicke der kristallinen und amorphen Schichten geschätzt; ferner wird an Hand der Integral-Kleinwinkelstreuung das mittlere Quadrat der Dichteschwankungen in den Proben bestimmt. Aus den so erhaltenen Unterlagen und Gesamtdichten der Proben werden die Dichten der kristallinen und amorphen Schichten berechnet; diese Werte entsprechen durchaus den im allgemeinen für eine Zweiphasenstruktur angenommenen Zahlen.Es wird der Einfluß von Molekulargewicht und Kühlgeschwindigkeit auf die Dicke der kristallinen und amorphen Schichten angegeben; außerdem werden die Dicken der kristallinen Schichten mit den Schmelzpunkten der Proben verglichen. Schließlich werden die Fehler erörtert, welche sich bei Anwendung desBragg-schen Gesetzes auf Kleinwinkelstreuungskurven ergeben.

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With 6 figures in 7 details and 2 tables     

Structure of some ethylene–phosphonic acid copolymers

An x-ray study has been made of the structure of a series of ethylene–phosphonic acid copolymers and the parent low-density polyethylene from which they were derived. The phosphonic acid contents (groups per 100 carbon atoms) of the copolymers were: A, 0.8; B, 1.8; C, 2.8; and D, 8.0. Small-angle x-ray scattering (SAXS) results show that the phosphonic acid substituents do not incorporate into the crystal lattice to any appreciable extent, that the substituents have the effect of decreasing the average thickness of the crystal lamellae and increasing the breadth of the size distribution of thicknesses, and that a two-phase model does not adequately account for the observed SAXS invariant. Wide-angle x-ray scattering (WAXS) results show that specimens, A, B, and C are partially crystalline with the polyethylene crystal structure and that D is amorphous. The observed broadenings of the 110 and 200 crystal reflections in the copolymers indicate that the substituents decrease the lateral dimensions of the crystalline lamellae and/or increase the deformation of the lattice due to external strain. Specimen D, completely amorphous according to the WAXS criterion, exhibits the largest value of the SAXS invariant of all the copolymers studied and must thus possess a multiphase structure consisting of small ordered regions and a disordered phase. The results of the study show the structure of the copolymers to be consistent with the fringe-micelle model but do not rule out the folded-chain model, although a regular fold surface is unlikely.     

Crystal structure of ethene-/α-olefin copolymers with various long comonomers (C8–C26)

Ethene-/α-olefin copolymers having a wide range of comonomers between 8 and 26 carbon atoms in length were characterized by wide angle X-ray diffraction (WAXD). It was found that the crystallinities for the shorter comonomers (C₈, C₁₂) matched fairly well with the crystallinities from DSC and volumetric measurements, while for the longer comonomers (C₁₈, C₂₆) distinct differences between the three methods were found. This was explained by the presence of an additional crystalline phase of the side chains slightly deforming the amorphous peak.     

Crystalline structure of polyamide 12 as revealed by solid‐state 13C NMR and synchrotron WAXS and SAXS

The crystalline structure of polyamide‐12 (PA12) was studied by solid‐state ¹³C nuclear magnetic resonance (NMR) as well as by synchrotron wide‐ and small‐angle X‐ray scattering (WAXS and SAXS). Isotropic and oriented PA12 showed different NMR spectra ascribed to γ‐ and γ′‐crystalline modifications, respectively. On the basis of the position of the first diffraction peak, the isotropic γ‐form and the oriented γ′‐form were shown to be with hexagonal crystalline lattice at room temperature. When heated, the two PA12 polymorphs demonstrated different behaviors. Above 140 °C, the isotropic γ‐PA12 partially transformed into α‐modification. No such transition was observed with the oriented γ′‐PA12 phase even after annealing at temperatures close to melting. A γ′–γ transition was observed here only after isotropization by melting point. Various structural parameters were extracted from the WAXS and SAXS patterns and analyzed as a function of temperature and orientation: the degree of crystallinity, the d‐spacings, the Bragg's long spacings, the average thicknesses of the crystalline (l_c) and amorphous (l_a) phases, and the linear crystallinity x_cl within the lamellar stacks. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3720–3733, 2005     

Structure of polypropylene crystallized in confined nanolayers

Films with a thousand alternating layers of isotactic polypropylene (PP) and polystyrene (PS) were prepared by layer‐multiplying coextrusion. The crystal structure of extremely thin PP layers confined between PS layers was studied by optical light microscopy (OM), atomic force microscopy (AFM), differential scanning calorimetry (DSC), small‐angle X‐ray scattering (SAXS), and wide‐angle X‐ray scattering (WAXS). Changes in structure were observed as the PP layer thickness decreased to the nanoscale. The thin PP discoids were largely composed of edge‐on lamellae with (040) planes lying flat on the interface. In layers 65 and 10‐nm thick, compressed d‐spacings in the directions perpendicular to the chains and loss of registry along the chain axis were suggestive of smectic packing of conformationally distorted chains. Even so, crystalline lamellae were distinguishable in the AFM images. In addition to the crystal population with (040) planes parallel to the interface, the WAXS from layers 65‐nm thick revealed another crystal fraction with (110) planes parallel to the interface and (040) planes perpendicular to the interface. This fraction was more evident in layers 10‐nm thick, where it accounted for approximately 10–20% of the crystallinity. Decreasing layer thickness resulted in a change of the crystal growth plane from the usual (110) to the more rare (010). The new crystal structure possibly served to fill‐in the radial structure of the dendritic discoids when a limitation to the thickness of the layer left only a little space for secondary nucleation of the crosshatched lamella. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3380–3396, 2004     

Side-chain crystallinity. II. Heats of fusion and melting transitions on selected copolymers incorporating n-octadecyl acrylate or vinyl stearate

The heats of fusion and the melting transitions of the crystallinity present in the side chains were determined for selected copolymers incorporating n-octadecyl acrylate or vinyl stearate. A major purpose of this investigation was to ascertain the effect of interrupting the long ordered 18-carbon side chains by randomly interspersed amorphous side chains of various lengths. For this purpose the lower acrylate homologs (C₁ through C₈ and including oleyl, C₈) were copolymerized over the composition range with n-octadecyl acrylate. It was found that simple dilution of the crystalline component (from comonomer b) by the amorphous component (from comonomer a) governed the decline in the heats of fusion and the fraction of crystallinity present. High crystallization rates were encountered because equilibrium crystallinity was nearly achieved for most of the copolymers. Melting point depression was less than theory in copolymers having short amorphous comonomer side chain lengths, but approached the theoretical depression as these side chains became very long. Thus the outer methylene sequences (the crystalline sequences) of the fatty co-units could bridge the smaller amorphous a units, giving rise to larger crystal sizes than theory specified. Main-chain stiffness, when present in the melt, had a small effect on the distribution of crystallite sizes but exhibited a much larger influence in preventing the attainment of equilibrium crystallinity, especially at high amorphous comonomer compositions. However, crystallinity was still high compared with that of copolymers described in the literature crystallizing through their main-chain units. When long blocks of crystalline segments were present (as in compositionally heterogeneous vinyl stearate copolymers), melting point depression was small and followed the theoretical probability sequence function.     

Preparation of Oriented Liquid‐Crystalline/Isotropic Block Copolymer Films with Parallel or Perpendicular Arrangement of Smectic Layers and Lamellar Microdomains

Films of a symmetric liquid‐crystalline/isotropic block copolymer consisting of a smectic LC side‐chain polymer and polystyrene were prepared by solvent casting from solution and from the isotropic melt. By annealing the solvent‐cast film in the S_A phase an oriented microphase‐separated film of lamellar morphology was obtained in which both the lamellae of the block copolymer and the smectic layers of the LC block were oriented parallel to the film surface. A lamellar morphology with perpendicular orientation of lamellae and smectic layers was generated by cooling the block copolymer from the melt.     

Salt-catalyzed addition reaction of monoepoxides with philosamia cynthia ricini and bombyx mori silk fibroins

The heterogeneous addition reaction of various monoepoxides with silk fibroins of Philosamia cynthia ricini and Bombyx mori was investigated at 45–75°C by use of aqueous solutions of various salts as padding catalysts. The effects of salt on the epoxide–silk fibroin reactions were attributed mainly to the nucleophilicity of the anions and also to the acidity or the electronegativity of the cations. The effect of the substituent of the epoxide on the add-ons was elucidated by the modified Taft equation, (log W ? log W₀)/σ* = ρ_p + ρ_sE_s/σ*, where W₀ and W are the add-ons for the reaction of a given compound and of its substituted derivatives, σ* and E_s are the polar and the steric substituent constants, ρ_p and ρ_s are the polar and the steric reaction constants, respectively. Histidine, lysine, arginine, tyrosine, serine, and acidic amino acids were found to react. The reactivity difference between Philosamia cynthia ricini and Bombyx mori fibroins towards the epoxide was discussed in the light of the observed phenomena.     

Effects of Branch Content and Branch Length on Polyethylene Crystallization: Molecular Dynamics Simulation

Influences of branch content (BC) and branch length (BL) on isothermal crystallization of precisely branched polyethylene are studied by molecular dynamics simulation. Branch acts as a defect both in nucleation and crystal growth process. BC affects not only crystallization kinetics but also final morphologies. Crystallization rate and crystallinity decrease as BC increases. Morphology Regimes change from lamellae crystal to bundle crystal at critical BC (20/1000 C) because of different folding pattern. 50 CH₂ is the critical methyl sequence length to form lamellae crystal. Lamellae thicknesses of final morphologies decrease in gradient corresponding to Morphologies Regimes. BL has no influence on the crystallization kinetics, and only affects the final morphologies when more branches inclusion happens with BL increasing. Trans‐rich phenomenon in pre‐crystalline state is observed. Crystallization process begins at the end of induction stage when trans state population reaches a critical value, and this value is independent of BC and BL.     

Plastic deformation of poly(tetramethylene oxide). II. Molecular orientation as measured by x-ray diffraction and NMR measurements

The orientation of the crystalline and amorphous phases in uniaxially drawn samples of polytetramethylene oxide has been studied by x-ray and NMR methods. Pole figure measurements give the orientation of the crystalline phase. Its dependence on the draw ratio does not obey the pseudoaffine model. The crystalline fraction is derived from NMR measurements at temperatures between T_g and T_m, where the free induction decay (FID) of the unoriented sample can be analyzed in terms of a rigid (crystalline), a constrained, and an amorphous phase. Low temperature (T < T_g) measurements of the NMR second-moment anisotropy in protonated and deuterated samples give a mean orientation of the chains higher than that corresponding to the crystalline phase. The lack of anisotropy in the tail of the FID at temperatures between T_g and T_m indicates no appreciable anisotropy in the truly amorphous interlamellar phase. From this and from the ratio of the P₄/P₂ orientations, factors which obey the “most probable distribution,” it is concluded that the amorphous orientation is due to the layer of constrained chains at the surface of the lamellae.     

Rotating frame proton spin-lattice relaxation measurements of poly (ethylene oxides)

Measurements of T_lρ as a function of temperature have been made on two polyethylene oxides (PEO) with molecular masses of 5,000 and 30,000. The T_1ρ measurements show biexponential behavior of the relaxation function in the temperature range from 170 K to 350 K. The intensities of the components of the relaxation function are constant over this temperature range in agreement with the crystallinities of the samples. The two relaxation times can be associated with the crystalline and amorphous component; the relaxation time minima describe the α relaxation in the crystalline regions of PEO and the glass transition in amorphous PEO.     

Differential scanning calorimetry,small‐angle X‐ray scattering,and wide‐angle X‐ray scattering on homogeneous and heterogeneous ethylene‐α‐copolymers

The objective of this work was to use both X‐ray and differential scanning calorimetry techniques in a comparative study of the lamellar and crystalline structures of heterogeneous and homogeneous ethylene‐α‐copolymers. The samples differed in the comonomer type (1‐butene, 1‐hexene, 1‐octene, and hexadecene), comonomer content, and catalyst used in the polymerizations. Step crystallizations were performed with differential scanning calorimetry, and the crystallinity and lamellar thicknesses of the different crystal populations were determined. Wide‐angle X‐ray scattering was used to determine crystallinities, average sizes of the crystallites, and dimensions of the orthorhombic unit cell. The average thickness, separation of the lamellae, and volume fractions of the crystalline phase were determined by small‐angle X‐ray scattering (SAXS). The results revealed that at densities below 900 kg/m³, polymers were organized as poorly organized crystal bundles. The lamellar distances were smaller and the lamellar thickness distributions were narrower for the homogeneous ethylene copolymers than for the heterogeneous ones. Step‐crystallization experiments by SAXS demonstrated that the long period increased after annealing. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1860–1875, 2001     

Solid-state coextrusion of poly(ethylene terephthalate). II. Drawing of semicrystalline PET

The drawing of semicrystalline (33 and 50%) poly(ethylene terephthalate) (PET) films has been studied by solid-state coextrusion. Because of its brittleness and opacity, isotropic and semicrystalline PET film is of little practical use. Early attempts to cold-draw crystalline films led to fracture in contrast to deformation of amorphous PET. However, we have succeeded in systematically preparing films with extrusion draw ratios ≤4.4 from semicrystalline PET. In many cases, the properties of the drawn extrudates, as a function of extrusion temperature T_ext and extrusion draw ratio EDR, were similar to those prepared from amorphous PET. However, some remarkable differences have also been found. In the case of coextrudates prepared from isotropic 50% crystalline PET, we found that the larger the deformation, the lower the apparent resulting crystallinity. In the extreme, a 34% reduction in crystallinity after deformation was observed. For the coextrudates drawn from initially 33% crystalline PET, slightly different behavior occurred. For T_ext ≤ 90°C, all extrudates showed crystallinities lower than the original isotropic film, with a minimum at EDR = 3; for T_ext ≥ 110°C, crystallinities were slightly greater than in the original film and increased with EDR. Qualitative measurements of heats of fusion were in agreement with density gradient results for PET crystallinity. In contrast is our previous finding that extrudates from initially amorphous PET always increase in crystallinity with EDR, because of stress-induced crystallization. The results now suggest that in the T_ext range investigated, the initial spherulitic structure is at least in part destroyed on drawing. In addition, the percent crystallinity is revealed to be dependent on T_ext, with lower values at lower temperatures. Mechanical tests show that the extrudates are similar or sometimes higher in tensile modulus when compared to amorphous PET drawn under the same conditions.     

Nuclear magnetic relaxation and molecular motion in poly(vinylidine fluoride)

Pulsed NMR T₁, T₂, and T_1ρ measurements are reported for poly(vinylidine fluoride) (PVF₂). The results demonstrate clearly the presence of four relaxation processes, three amorphous and one crystalline. The α relaxation is undoubtedly a crystalline one, while β and γ are both amorphous, in agreement with earlier conclusions from dielectric and dynamic mechanical measurements. The fourth relaxation (β′) observed initially in the mechanical measurements of Kakutani, but undetected in dielectric experiments, has been confirmed in our results and the process is described by an activation energy of 15.1 kcl/mole. Motion of folds on the surface of crystal lamellae is deemed to be the responsible mechanism for the β′ relaxation. Two models have been considered in the interpretation of the α process; rotation of crystalline chains in the vicinity of defects and rotational oscillation of restricted amplitude of all crystalline chains about the main chain axes. Rotation of amorphous chains is a possible mechanism for the γ process while motions of a general nature are responsible for the β relaxation. Our experimental results again indicate that spin diffusion plays an important role in the overall NMR response of the polymer.     

Gamma irradiation effect on chain segment motion and charge detrapping in polyamide 610

Gamma irradiation effect on the chain segment motion and charge detrapping in polyamide 610 was investigated by means of thermally stimulated depolarization current (TSDC), wide-angle X-ray diffraction (WAXD), differential scanning calorimetry (DSC) and gel fraction. There are four current peaks (named α, ρ₁, ρ₂ and ρ₃ peak, respectively) in TSDC spectra of polyamide 610. The α peak corresponds to the glass transition, the ρ₁ peak is attributed to space charge trapped in the amorphous phase, the ρ₂ peak is originated from space charge trapped in the interphase between crystalline and amorphous regions and the ρ₃ peak is originated from space charge trapped in crystalline phase. With the increase of irradiation dose from 1.5 to 2 MGy, ρ₁ and ρ₂ peaks gradually merge into one single peak. With the increase of irradiation dose the degree of crosslinking in amorphous phase is more than that in interphase and then the trap depth of interphase is gradually close to that of amorphous phase. By analyzing the characteristic parameters of these peaks, it is found that gamma irradiation can reduce the mobility of chain segments and increase structural defects in polyamide 610. In addition, irradiation increases the stability of trapped charge in both amorphous phase and interphase, but not affecting the stability of trapped charge in crystalline phase.     

Determination of degree of crystallinity of drawn polymers by means of density measurements

The well known procedure of determining the degree of crystallinity by means of measuring the density presupposes the knowledge of both the densities ρ_c and ρ_a of the crystalline and of the noncrystalline regions. By combination of small-angle and wide-angle x-ray scattering and of density measurements it can be shown that this method is not justified in the case of drawn polyethylene if the values of ρ_c and ρ_a known from isotropic material are used. Both ρ_c and ρ_a depend considerably on annealing and drawing conditions. In addition the effective density ρ_c^* of the more densely packed phase in a two-phase structure is much lower than the value ρ_c calculated from the positions of the x-ray reflections due to a large number of lattice defects. This conclusion is based on the results of three independent sets of experiments: determination of the mean-square fluctuation of density 〈η²〉 by means of x-ray small-angle scattering; x-ray wide-angle measurements of the positions of the crystal reflections and of the halo arising from the noncrystalline regions; and comparison of densities and long periods of samples treated at various annealing temperatures.     

New zirconium kappa phases

The compounds Zr₉W₄S, Zr₉Mo₄S, and Zr₉W₄S_1?xNi_xO₃ have been prepared by high temperature techniques. They belong to the general group of K phases. Single crystal x-ray diffraction analysis of the mixed nickel/sulfide (Zr_9.2W_3.8S_0.7Ni_0.3O_3.0, R = 2.6%) reveals nickel substitution for sulfur, and confirms oxygen occupancy of interstitial sites.     

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.     

Polymerization of β-cyanopropionaldehyde. II. Crystalline poly(cyanoethyl)oxymethylene

Additional investigation was made on the polymerization of β-cyanopropionaldehyde at ?78°C. with triethylaluminum and triethylaluminum—titanium tetrachloride complexes as initiators. The complexes give a higher polymer yield than triethylaluminum alone. The yield—Ti/Al plot also has a maximum at a Ti/Al mole ratio of about 0.2 at constant Al(C₂H₅)₃ concentration. The rate of polymerization seems to be increased in the following order: toluene < methylene chloride < tetrahydrofuran. This order is reversed with regard to the content of DMF-insoluble fraction mentioned below. The polymer obtained consists of two fractions: one is soluble in dimethylformamide (DMF) and the other is not. The former consists of an amorphous polymer and the latter of crystalline polymer. It was found that the infrared absorption bands at 790, 1258, and 1375 cm.^-1 were characteristic of crystalline polymer and were assigned to crystalline bands. Those at 1270 and 1345 cm.^-1 are characteristic of amorphous bands. The crystalline bands and C? O? C bands show very intense infrared dichroism, whereas the nitrile band does not. The crystal data obtained from the analysis of the x-ray diffraction pattern, including the fiber repeat distance of 4.95 A. and other unit cell dimensions in a triclinic system, were compared with those reported for various aldehyde polymers. The unit cell dimension a′ or the maximum interplanar distance is somewhat smaller, suggesting that the molecules are more tightly packed than poly(n-butyraldehyde), in which the side chain has the same carbon number as that of poly-(cyanoethyl)oxymethylene. Internal rotation angles and a radius of helix were calculated for an isotactic fourfold helical model of the polymer. Some other characterizations of the polymer were also made.     

Nanostructure and crystallization phenomena in multilayered films of alternating iPP and PA6 semicrystalline polymers

The present work is concerned with the study of the crystalline morphology and the nanostructure of a multilayered system of two alternating immiscible semicrystalline polymers: isotactic polypropylene (iPP) and polyamide 6 (PA6). Films with a volume ratio of 70/30 were prepared by means of layer multiplying coextrusion. Contrary to previous experiments, performed with semicrystalline/amorphous and amorphous/amorphous nanolayered systems, the studied iPP/PA6 film does not exhibit a well defined maximum in the USAXS patterns. This result accounts for an irregular layered structure, as further confirmed by means of TEM images. Nevertheless, such a layered assembly still influences the crystallization behaviour of both constituent polymers. On the one hand, the crystallization of PA6 within the multilayered material is substantially hindered as evidenced by its weak scattering intensity. Real time studies as a function of temperature undoubtedly detect the presence of a WAXS peak and a SAXS maximum associated to PA6 above the melting temperature of iPP. Room temperature AFM studies also confirm the occurrence of crystalline structures within the PA6 layers. On the other hand, SAXS and WAXS measurements at room temperature reveal the occurrence of an oriented lamellar morphology within the iPP layers bearing uniaxial symmetry around an axis perpendicular to the layers surface. Results show that the crystalline molecular chains are placed mainly parallel to the layer surfaces forming edge-on lamellae. Moreover, X-ray scattering results are in agreement with the occurrence of two populations of lamellae, both edge-on and perpendicular to each other, in agreement with the crosshatched morphology observed by AFM.