Wide-and small-angle x-ray scattering studies on the real structure of fractions of (ethylene-α-olefine)-copolymers

Heink, M.; Haberle, Klaus; Wilke, W.

doi:10.1007/bf00657404

Cited by 20 publications

(30 citation statements)

References 14 publications

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“…( 210), but not others, e.g. ( 020), has been attributed 9,49 to anisotropic mosaicity of the lamellar crystallites, often with small grain widths perpendicular to the b-direction. In some cases, 9 the lamellar crystallites have been proposed to consist of rod-shaped grains that are as narrow as the crystal is thick (see Figure 13c).…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…In addition, the crystal thickness in these analyses, assumed to be equal to the thickness along the crystalline c-axis, is usually larger than that measured by other methods. 9 With a tilt angle ϕ between the chain axis and the normal to the crystal surface, all these contradictions can be eliminated and the lamellar structure without small-scale mosaicity confirmed. As seen in Figure 13e, with chain tilt the thickness along the c-axis exceeds the crystal thickness L c while the correlation lengths for certain sets of (hk0) lattice planes are reduced to values on the order of L c /sin ϕ.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

“…The differential broadening is most pronounced in materials with small crystal thickness, e.g., controlled by branching due to comonomers. 9 Heink et al 9 studied PE with ethyl branches by WAXD (see Figure 14a) and proposed rod-like rather than lamellar crystallites. The claimed crystal thickness of nearly 10 nm was more than twice larger than that determined by SAXS and was also too large to be explained in terms of the monomer sequence distribution at a branch concentration of >4%.…”

Section: ■ Results and Discussionmentioning

confidence: 99%

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Avoidance of Density Anomalies as a Structural Principle for Semicrystalline Polymers: The Importance of Chain Ends and Chain Tilt

2017

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On the basis of sufficiently realistic chain models and simulations, it is concluded that the commonly used models of the lamellar structure of melt-crystallized semicrystalline polymers unintentionally but inevitably contain layers with a higher density than in the crystallites (density anomalies). The density excess would be particularly pronounced in polymers with planar zigzag conformations in the crystallites, such as polyethylene (PE). To avoid density anomalies, the structural models must be modified, with chain ends at the crystal surface and/or chain tilt in the crystallites. NMR and X-ray evidence for these structural features in PE is presented. Termination of chains at the crystal surface keeps dangling chain ends out of the crowded interfacial layer, reducing the density at the interface by about 17% for M n = 15 kg/mol, a common value in commercial high-density polyethylenes. NMR of PEs shows that most CH3 end groups are indeed in all-trans chains in a nearly solid-like environment. When the ends of polydisperse polymers are trapped at the crystal surface, many chain folds cannot be tight, in agreement with NMR showing fast trans–gauche isomerization even for solution crystals of PE. We propose that for polydisperse PE, interfacial chain ends are required for the formation of regular stacks of flat melt-crystallized lamellae without extreme chain tilt or density anomalies. Chain tilt in the crystallites, which decreases the area density of chains emerging from the crystal surface, is another indispensable structural adjustment in PE that reduces excess noncrystalline density; it has occasionally been reported but was usually considered as incidental. For instance, in X-ray analyses of PEs, chain tilt was ignored, and differential broadening of the (hk0) Bragg peaks was mistakenly attributed to mosaicity, in extreme cases resulting in the assumption of overly thick, rod-shaped rather than lamellar crystallites. For various oriented PE samples, including blown films and annealed fibers, published scattering patterns exhibit clear evidence of macroscopically aligned lamellar stacks with pronounced chain tilt. Literature data for PE also show examples of the increasing importance of chain tilt at high molecular weights, where the density reduction by chain ends is minor and evidence of extreme chain tilts of up to 60° has been shown. Alternatively, when chain-end concentrations are very low, the assumption of wide regularly stacked lamellae may have to be given up in favor of ribbon-shaped crystallites. The interplay of the density effects of chain ends and chain tilt can explain many molecular-weight-dependent structural features in polyethylene. On the basis of the combined effects of chain ends at the crystal surface, chain tilt in the crystallites, and adjacent reentry of ∼1/3 of chains, we can construct a lamellar model of PE without density anomalies. Chain tilt and chain ends at the crystal surface are required to “make space” for short loops, in conjunction with noncrystalline chain segments eme...

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Section: ■ Results and Discussionmentioning

confidence: 99%

Section: ■ Results and Discussionmentioning

confidence: 99%

Section: ■ Results and Discussionmentioning

confidence: 99%

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Avoidance of Density Anomalies as a Structural Principle for Semicrystalline Polymers: The Importance of Chain Ends and Chain Tilt

2017

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“…The incorporation of 1‐hexene units into the polymer chain leads to the reduction of the crystallinity, which was already investigated by X‐ray crystallography 31–33. The catalysts 6 and 8 with bulky ligands show almost complete depletion of the crystallinity at concentrations of 0.50 mol · L –1 and higher, which proves their high potential for α‐olefin insertion (Figure 6).…”

Section: Resultsmentioning

confidence: 99%

Catalytic Activity of [2]Borametallocenophanes

Braunschweig

Dörfler

Friedrich

et al. 2011

Zeitschrift anorg allge chemie

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“…To calculate the crystallinity, the diffraction curve of an investigated polymer has to be decomposed into crystalline peaks and the amorphous component. In some works (Vonk, 1973;Howard & Crist, 1989;Heink, et al, 1991;Isasi et al, 1999) the shape of the scattering from the amorphous component was approximated by the experimental curve measured for the amorphous standard (usually molten polymer). Such a curve was scaled to the diffraction curve of the investigated sample in the angular ranges where crystalline peaks were absent and then subtracted from the diffraction curve.…”

Section: Introductionmentioning

confidence: 99%

Application of immune and genetic algorithms to the identification of a polymer based on its X-ray diffraction curve

Rabiej

2013

J Appl Cryst

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This paper describes how a combination of two methods of artificial intelligence, an immune algorithm and a genetic algorithm, can be used to recognize a polymer by the shape of its X-ray diffraction curve. To this end, the hybrid algorithm uses a database which contains theoretical functions describing wideangle X-ray diffraction curves of different polymers. These curves are compared by the algorithm with the experimental diffraction curve and the most similar are chosen. Such theoretical curves are kept in the immunological memory, and their parameters can be set as the starting ones in the optimization methods used for decomposition of the experimental curve into crystalline peaks and amorphous component. Using this algorithm, the preparation of the starting parameters is much easier and faster. Decomposition is the most important step in polymer crystallinity determination.

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Wide-and small-angle x-ray scattering studies on the real structure of fractions of (ethylene-α-olefine)-copolymers

Cited by 20 publications

References 14 publications

Avoidance of Density Anomalies as a Structural Principle for Semicrystalline Polymers: The Importance of Chain Ends and Chain Tilt

Avoidance of Density Anomalies as a Structural Principle for Semicrystalline Polymers: The Importance of Chain Ends and Chain Tilt

Catalytic Activity of [2]Borametallocenophanes

Application of immune and genetic algorithms to the identification of a polymer based on its X-ray diffraction curve

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