Applications of x-ray investigations of polymers under load. 1. Measurements of WAXS reflections shifts induced by elastic stretching of oriented polymer systems along their orientation axis

What information can be obtained by wide-angle x-ray scattering (WAXS) from elastic deformation of oriented polymer systems along their orientation axis? This article is a critical review and some generalization of answers for this question. Different cases are analyzed that occur in practice or that might occur in the future: (1) determination of Young's moduli E _c of crystalline lattices parallel to the polymer chains and establishment of correlations between E _c and chain conformation in crystalline lattices; (2) estimation of elastic properties of different fragments of polymer chains, especially of multiatomic complex fragments; (3) detection of conformational polymorphism in crystalline lattices; (4) determination of Poisson's coefficients of crystalline lattices; (5) estimation of potential ability of a given polymer for formation of systems with high moduli; (6) estimation of structural inhomogeneity of amorphous polymers; (7) study of interaction character of structural elements in oriented polymer blends; (8) investigations of systems with a combination of extended and folded-chain crystals; (9) study of influence of cross-linking on structure-mechanical behavior; (10) estimation of adhesive interaction of different components in polymer composites. Only Points 1 (see, e.g., Refs. 1–18) and 4 [19] have been considered in earlier literature by other authors, mainly for soft-chain polymers. Thus, similar results are considered here only briefly, and primary attention is focused on the peculiarities of investigations of rigid-chain polymers. As for the other points, they were considered earlier in our separate works [20–38] (or have not been considered at all) and up to now have not received wide acceptance. During the consideration here, both series and parallel models of interactions of different structural elements were used.     

On one supramolecular mechanism of the nonlinear viscoelasticity of oriented polymers

A phenomenological model of the viscoelasticity of highly oriented polymer systems is developed based on the results of studying the relaxation of such systems (mainly, fibers of polyethylene terephthalate, polyamide-6, polyvinyl alcohol, and other polymers) in the loaded state. The effect of an applied load on their relaxation spectra agrees qualitatively with the deformation behavior of crystal-like bandles that are present in amorphous intercrystalline layers of the fibrillar supramolecular structure.     

Yielding of glassy polymer on a microstructural level

Based on recent studies of the morphology and of shear bands and crazes in amorphous polymers it is suggested that shear is the basic mechanism of plastic deformation. Three stages are proposed for the formation of crazes, shear yielding at a defect or craze tip due to stress concentration, nodular movement resulting in fibril formation, followed by void formation between the fibrils.     

Regularly arranged superstructures on stretched high polymers

Contrary to previous assumptions, the deformation processes occurring in amorphous and partially crystalline high polymers cannot be considered as locally uniform but is anisotropic, with the formation of regularly arranged crazes. Newly developed methods of preparation allow for the first time the obtaining of direct evidence of these superlattice structures in many high polymers subjected to uniaxial, biaxial, or multiaxial stretching. The investigations have led to new concepts of the supramolecular structure of high polymers; they extend our knowledge of the relationships between the technological properties and molecular structures of polymers.     

Comments on “Translation-invariant bipolarons and the problem of high-temperature superconductivity”

We comment on the recent results of Refs. [1], [2] on the bipolaron problem derived using an approximation of Gross–Tulub. It is proved that, contrary to the claim made in Refs. [1], [2], the bipolaron ground-state energy calculated there in the strong-coupling approximation has not been shown to constitute a variational upper bound.     

An electron paramagnetic resonance study of the tetragonally distorted [Formula: see text] ion in [Formula: see text] and [Formula: see text

Chromium-doped [Formula: see text] and [Formula: see text] have been studied by both EPR and ENDOR spectroscopy. [Formula: see text] ions enter the fluorite structure in distorted substitution cation sites. In both matrices the distortion observed is tetragonal. X- and Q-band EPR measurements at temperatures between 4 and 300 K allowed us to determine the ion symmetry and the following spin-Hamiltonian parameters: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text]; and [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] for [Formula: see text]. For [Formula: see text], the weak superhyperfine interaction of [Formula: see text] with the surrounding [Formula: see text] ions has been studied by both EPR and ENDOR techniques for [Formula: see text]. No ENDOR signals were detected for [Formula: see text]. The results are tentatively explained in terms of a Jahn - Teller effect corresponding to [Formula: see text] coupling strongly stabilized by lattice stresses, although other possible origins for the distortion cannot be completely ruled out.     

Cracks and crazes: on calculating the macroscopic fracture energy of glassy polymers from molecular simulations

We combine molecular dynamics simulations of deformation at the submicron scale with a simple continuum fracture mechanics model for the onset of crack propagation to calculate the macroscopic fracture energy of amorphous glassy polymers. Key ingredients in this multiscale approach are the elastic properties of polymer crazes and the stress at which craze fibrils fail through chain pullout or scission. Our results are in quantitative agreement with dimensionless ratios that describe experimental polymers and their variation with temperature, polymer length, and polymer rigidity.     

Gamma relaxation in nitric acid-treated polyethylene single crystals

There has recently been considerable interest in the gamma relaxation of polyethylene (PE). Determined by dynamic mechanical measurements at 1 cps, this relaxation would be located near 150°K. The gamma loss peak has been observed both in bulk PE [1-5] and in mats of solution-grown crystals [5-8] by a variety of techniques. The origin of this relaxation has variably been attributed to the amorphous component [1-6,9,10], the crystalline component [8,11], or both [12,13]. According to the last view, the gamma relaxation consists of two superposed peaks (γ_a and γ_c) attributable, respectively, to the two components.     

Excellence – energy – ethics

Dear pss readers, As the previous year approached its end, news on three excellent prize winnings and nominations of pss authors and editors reached us: Gerhard Abstreiter of TU Munich will receive the Stern–Gerlach Medal 2014, the highest prize of the German Physical Society for experimental physics, honoring his work on low‐dimensional electron systems in semiconductor hetero‐ and nanostructures. His Review@RRL on InGaAs nanowires on silicon is opening the 2014 volume of pss (RRL) [1]. It is a welcome addition to our recent successful Focus Issue on Semiconductor Nanowires [2]. Our long‐term Editorial Advisory Board member, Wiley author and Guest Editor, Rainer Waser of RWTH Aachen and Research Centre Jülich, is one of the 11 winners of the highly prestigious Leibniz Prize for his outstanding research on nanoelectronics, especially oxides, ferroelectrics and resistive switching [3, 4]. Last but not least, one of the three nominated teams for the German Future Prize has been led by Wolfgang Schnick , LMU Munich, and Peter J. Schmidt , Philips Lumileds Aachen. Their groundbreaking work on new phosphor materials in white light emitting diodes (LEDs) for solid‐state lighting [5] goes back to a highly‐cited pss (a) article from 2005 [6] (see figure). The technology is now being commercialized and expected to enable energy savings on a grand scale in the coming years. Speaking of energy, research results related to this global challenge have been important throughout the year, touching areas such as thermoelectrics [7], efficiency of organic LEDs [8] and photovoltaics [9]. The latter field is even better represented since the recent introduction of our section rrl solar, covering solar cell materials or device development and characterization (see Editorial [10]). The full‐paper sister journals pss (a) and (b) presented an unprecedented number of high‐profile special issues in 2013 [11–15]. With heartfelt gratitude we look back onto fruitful collaboration with highly engaged guest editors, who helped bring to light issues such as the “Advanced Concepts for Silicon Based Photovoltaics” [11], the “Quantum Criticality and Novel Phases” [12], the “Disorder in Order: A special issue on amorphous materials” [13], the “Substrate Interactions in Heterogeneous Catalysis” [14], and the “Quantum Transport at the Molecular Scale” [15] among other interesting topical issues and sections. Both contributors and fine articles are too numerous to do justice to all of them here. We must restrict ourselves to a general invitation to browse this content, only hinting a few possible starting points, such as topological insulators [16], molecular electronics [17] and quantum phase transitions [18].

     

Dependence of solvent crazing in bisphenol–A polycarbonate on molecular weight of organic liquids

Solvent crazing has been investigated for bisphenol-A poly-carbonate exposed to the liquids of n-alcohols, di-n-alkylphthalates, and adipic acid polyesters. The critical strain at which crazes appeared was determined with a Bergen elliptical strain device. In the case of the n-alcohol and di-n-alkylphthalate liquids with a small number of carbons in the alkyl chain, crazes spread rapidly to areas of lower strain with time and ceased within 30 min at room temperature. Such a lower limiting value of critical strain can be predicted by using polar-nonpolar solubility parameter plotting representations employing the molar volume term. On the other hand, craze initiation was more delayed for two higher molecular weight liquids, di-n-octylphthalate and adipic acid polyester. Sorption studies were also conducted on polycarbonate immersed in both liquids. The values of the activation energy and diffusion coefficient estimated from the experimental data on craze initiation were found to be nearly comparable with the ones from the sorption experiments. In conclusion, the induction time-that is, the time at which crazes appear for a given strain–is controlled by the diffusion of the crazing liquid into the polymer. Thus, in the case of these liquids, which are miscible with the polymer, the crazing mechanism can be explained in terms of facilitated craze formation of a plasticized polymer.     

Morphology and properties of twisted polymeric fibers

The morphology and mechanical properties of four different fibers-polyethylene, polypropylene, nylon 66, and polyethylene terephthalate-under the influence of twisting, were investigated. It was found that a model for affine deformation of the fibers can be applied only for very low-twist levels. At high-twist levels the stress distribution and the deformation made in the fiber were very complex. A preferred radial orientation occurred in polyethylene, nylon 66, and polyethylene terephthalate giving rise to an ideal situation for chain tilting and kinking. Polymorphic transition, twinning, and yielding were also observed in the case of polyethylene. The fiber moduli decreased sharply with twist, and this was attributed to the effects of inhomogeneous stress distribution and fibril slippage.     

Investigation on Tensile Deformation Behavior of Semi-Crystalline Polymers

The strain rate, temperature, and microstructure-dependent, tensile-yielding behavior of three semi-crystalline polymers, namely high-density polyethylene (HDPE), polyamide 6 (PA6) and low-density polyethylene (LDPE), was investigated. It is found that, depending on the strain rate and temperature, the three polymers exhibit markedly different tensile deformation behavior, especially the shape of the stress-strain curves. LDPE exhibits a uniform extension and shows no obvious geometrically unstable effect, such as necking, during the overall tensile process. HDPE and PA6, on the other hand, show clear necking and cold-drawing phenomena during the uniaxial tensile process. When considering the effect of strain temperature on necking, significant differences between HDPE and PA6 emerge. For both, the heterogeneous necking disappears and homogeneous deformation occurs with increasing temperature. For HDPE, the homogeneous deformation takes place in the vicinity of the melting temperature, while for PA6, it takes place close to the glass transition temperature instead. The conventional yield point, corresponding to the force maximum in stress-strain curves, becomes less defined as the testing temperature is increased. It is applicable, to some extent, to combine the Brereton analysis and Considère construction to predict such a point quantitatively. However, this combination can only be suitable for homogeneously deformed material. In addition, it is found that the special, double yielding behavior will take place under certain deformation conditions for all three semi-crystalline polymers. With respect to judging the appearance of the double yielding of polymers, it seems that it can be estimated qualitatively by plotting the compression residual strain-applied strain curves of the samples.     

Fermions tunneling from rotating stationary Kerr black hole with electric charge and magnetic charge

In this paper, the method of semi-classical fermion tunneling is extended to explore the fermion tunneling behavior of a Kerr–Newman–Kasuya black hole. Thus, the Hamilton–Jacobi equation in Kerr–Newman–Kasuya space–time is derived by the method presented in Refs. Lin and Yang (2009) [24], [25], [26], the Hawking temperature at the horizon and the tunneling probability of spin- 1/2 fermions are finally obtained following the semi-classical quantum equation. The results indicate the common features of this black hole.     

Crazing and fracture of glassy plastics

A recently proposed mechanism of crazing in glassy plastics is reviewed and then extended to account for the observed structure of crazes, for the tensile properties of the crazed material, and for the effect of rate of loading upon the crazing process.     

EPR Spectra of Hydrazyl Biradicals

Electron paramagnetic resonance is the most effective method of studying the electron exchange in biradicals. Experimental EPR spectra for the solutions of some hydrazyl biradicals are available in the literature (see Refs. [I,2]), however, the interpretation of the spectra is not given.     

Studies of short-range order in amorphous polymers by radial distribution functions derived from X-ray diffraction

Interatomic and intermolecular ordering in amorphous polymers can be characterized by radial distribution functions (RDF) derived from radiation scattering measurements (X-rays, neutrons, etc.). The type of information which may be derived from RDF data in monatomic systems is illustrated by measurements on a sample of vitreous carbon, which is shown to consist of graphite-like sheets of hexagonally packed carbon atoms with no true graphitic registration between the sheets. As an example of the type of information available in polyatomic systems, an RDF study of aluminum phosphate is given to show that the basic atomic arrangement is very similar to vitreous silica with aluminum and phosphorous stoms occupying positions in aluminum phosphate similar to silicon atoms in silica.

RDF methods have been applied to investigate short-range ordering in amorphous bisphenol A polycarbonate which has been reported to exhibit a grainy or nodular structure under electron microscopy. Two samples with different thermal histories were examined. Both had been rapidly quenched from the melt, and subsequently one was annealed below Tg to produce a marked change in impact properties. Most of the intramolecular distances in the polymer repeat unit were successfully resolved in the RDF patterns in the region 1< r< 6 Å. However, there were only suggestions of broad peaks at r < 5.5 Å and r < 10 Å, attributable to inter-molecular ordering, indicating that little intermolecular ordering had occurred in either sample. The RDF patterns were virtually identical, indicating that the short-range order (0 to 10 Å) in the samples has been essentially unaffected by the annealing procedures. In order to assess the sensitivity of the RDF method to short-range intermolecular ordering, a more highly annealed sample was examined. In addition to the intramolecular distances which were very similar to those resolved in the previous samples, the RDF plot showed a marked periodicity peaking at intervals of ～ 5.5 Å which was attributable to intermolecular ordering, thus confirming the sensitivity of the RDF technique to intermolecular ordering in amorphous polymers.

Similar studies have been made on polyethylene terephthalate films, both “quenched amorphous” and one annealed near Tg (100 hr at 65[ddot]C) to provide complementary structural information on structures reported in electron micrographs under similar conditions. Again, all intramolecular peaks of the polymer repeat unit were resolved in the RDF's for both samples for r < 6 Å. However, there were only suggestions of broad peaks at ～5 and ～8 Å which might be attributed to intermolecular ordering, and there was no detectable increase in intermolecular ordering on annealing.

It is not necessary to assume intermolecular ordering over much greater than ～ 10 Å to explain the RDF data for either polycarbonate or polyethylene terephthalate, and the relevance of this finding to proposed models of polymer structure is discussed.     

Crystallization Kinetics for the Split Dual Phase Model of the Amorphous State of Polymers

We analyze constant rate cooling and heating crystallization kinetics of PET samples by DSC. The samples have various degrees of disentanglement, obtained by Rheo-Fluidification. According to the interactive Split Dual Phase model, the amorphous state is made up of two coupled and interactive amorphous phases. These two phases have distinct viscoelastic and thermodynamic characteristics (T_g, free volume, G′ and G^″, etc.), which are determined by the potential energy of the conformers and by the state of entanglement of the macromolecular coils. Semi-crystalline polymers, such as polyethylene terephthalate (PET), are amorphous in the molten state and should have Dual Phase behavior. The phase duality should manifest itself during crystallization from the melt during cooling, or during cold crystallization while heating quenched samples. The purpose of this communication is to quantitatively describe the kinetics of crystallization of PET samples with a dual phase kinetics formulation, and determine the respective influence of molecular weight and degree of entanglement on the kinetics parameters, rate of crystallization and percentage of crystallinity.     

Dynamics of plastic deformation: Waves of localized plastic deformation in solids

Conclusions It has been shown here that a localized plastic deformation in structurally inhomogeneous media can be of a wave nature and can propagate in the form of nonlinear plastic waves, not only at the microscopic level but also at the mesoscopic level. It has been established that there is an interrelationship between this new effect and grain-boundary slippage (an effect which has been under study for a long time) and also with certain types of quasiviscous fracture in plastically deformable materials.We have discussed certain specific practical problems in the mechanics of plastic deformation, and for certain types of fracture. In the future, these problems will be discussed at a more profound level and in greater detail, because of experimental studies which are presently being carried out on the dynamics of deformation for various types of loading and fracture [17, 18, 31]. We hope that the approach proposed here for a theoretical study of the localization of deformation and fracture can be taken to study such effects as splitting off [31], the influence of defect fluxes on grain-boundary slippage [22], superplasticity [23], the behavior of tectonic faults and boundaries of various types [32], electroplastic and magnetoplastic effects, and high-temperature localization of deformation [25].The general nature of the approach proposed here results from the circumstance that a localization of deformation is present explicitly or implicitly during plastic deformation, and the behavior of this deformation plays a role of fundamental importance in the propagation of plastic deformation through a material.The author wishes to thank V. E. Panin for a constant discussion of this problem and I. O. Nedavnii for carrying out the numerical calculations.V. V. Kuibyshev Tomsk State University. Institute of Strength Physics and Materials Science. Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 19–41, April, 1992.     

Structure of polyethylene sulfide

The structure of the polyether series expressed by the general formula [─(CH₂)_m─O─]_n with m = 1-4, 6, 8-10, and 12 was previously determined [l]. The molecular structure of polyoxymethylene (m = 1) is a sequence of nearly gauche forms (9/5 o r 29/16 helix [a]). On the other hand, the conformation of polythiomethylene, the first member of the polythioether series [─(CH₂)_m ─S─]_n, was found to also be a nearly gauche sequence (l7/9 helix) by Carrazzolo and Valle [3]. Both of these polymers have the highest melting point of each series (polyoxymethylene, 180°C; polythiomethylene, 245°C). Polyethylene oxide (m = 2) is a 7/2 helix consisting of nearly trans, trans, and gauche forms and has rather a low melting point (66°C). Polyethylene sulfide has a very high melting point (210°C) compared with polyethylene oxide. In this respect it is thus of much interest to investigate the structure of polyethylene sulfide. Boileau et al. [4] synthesized high molecular weight polyethylene sulfide and reported its unit-cell dimensions, but they did not determine its structure. In this note, the molecular and crystal structure of polyethylene sulfide is briefly reported.     

Colossal dielectric constant in high entropy oxides

Entropic contributions to the stability of solids are very well understood and the mixing entropy has been used for forming various solids, for instance such as inverse spinels, see Nawrotsky et al., J. Inorg. Nucl. Chem. 29 , 2701 (1967) [1]. A particular development was related to high entropy alloys by Yeh et al., Adv. Eng. Mater. 6 , 299 (2004) [2] and Cantor et al., Mater. Sci. Eng. A 375–377 , 213 (2004) [3] (for recent reviews see Zhang et al., Prog. Mater. Sci. 61 , 1 (2014) [4] and Tsai et al., Mater. Res. Lett. 2 , 107 (2014) [5]) in which the configurational disorder is responsible for forming simple solid solutions and which are thoroughly studied for various applications especially due to their mechanical properties, e.g. Gludovatz et al., Science 345 , 1153 (2014) [6] and Lu et al., Sci. Rep. 4 , 6200 (2014) [7], but also electrical properties, Kozelj et al., Phys. Rev. Lett. 113 , 107001 (2014) [8], hydrogen storage, Kao et al., Int. J. Hydrogen Energy 35 , 9046 (2010) [9], magnetic properties, Zhang et al., Sci. Rep. 3 , 1455 (2013) [10]. Many unexplored compositions and properties still remain for this class of materials due to their large phase space. In a recent report it has been shown that the configurational disorder can be used for stabilizing simple solid solutions of oxides, which should normally not form solid solutions, see Rost et al., Nature Commun. 6 , 8485 (2015) [11] these new materials were called ”entropy‐stabilized oxides”. In this pioneering report, it was shown that mixing five equimolar binary oxides yielded, after heating at high temperature and quenching, an unexpected rock salt structure compound with statistical distribution of the cations in a face centered cubic lattice. Following this seminal study, we show here that these high entropy oxides (named HEOx hereafter) can be substituted by aliovalent elements with a charge compensation mechanism. This possibility largely increases the potential development of new materials by widening their (already complex) phase space. As a first example, we report here that at least one HEOx composition exhibits colossal dielectric constants, which could make it very promising for applications as large‐k dielectric materials. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)