Dislocation Movement Induced by Molecular Relaxations in Isotactic

Article pubs.acs.org/Macromolecules

Dislocation Movement Induced by Molecular Relaxations in Isotactic Polypropylene Florian Spieckermann,*,†,‡ Gerald Polt,‡ Harald Wilhelm,‡,∥ Michael B. Kerber,‡ Erhard Schafler,‡ Marius Reinecker,§ Viktor Soprunyuk,§ Sigrid Bernstorff,⊥ and Michael Zehetbauer‡ †

Department for Material Physics, Montanuniversität Leoben, Jahnstrasse 12, 8700 Leoben, Austria Research Group Physics of Nanostructured Materials, Faculty of Physics, and §Research Group Physics of Functional Materials, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Wien, Austria ∥ Laboratory of Polymer Engineering, LKT-TGM, Wexstrasse 19-23, 1200 Wien, Austria ⊥ Elettra − Sincrotrone Trieste, Strada Statale 14 km 163.5 in AREA Science Park, 34149 Basovizza, Trieste, Italy ‡

ABSTRACT: The thermal stability of deformation-induced dislocations was investigated in polypropylene (PP) during annealing by means of in-situ X-ray diffraction using synchrotron radiation. The samples were cold rolled to high strains (ε = 1.2) in order to introduce a high number of dislocation lattice defects and immediately stored in liquid nitrogen afterward. Then, stepwise annealing was applied from −180 °C up to above the melting temperature (165 °C) while synchrotron X-ray diffraction patterns were recorded at each step. The resulting low noise, high angular resolution diffraction patterns were evaluated using multireflection X-ray profile analysis (MXPA), revealing parameters such as the dislocation density and the thickness of the crystalline lamellae as a function of the annealing temperature. Two significant decreases of the dislocation density were found at annealing temperatures of about 10 and 85 °C. These distinct changes in the dislocation density could be identified as the mechanisms of β- and α-relaxation, respectively, by performing additional dynamic mechanical thermal analysis (DMTA). This behavior could be attributed to an increased intrinsic mobility of the macromolecules at these temperatures accompanied by thermal activation of dislocations, resulting in their mutual annihilation or their movement into the adjacent amorphous phase. The reduction of the dislocation density at the glass transition (β-relaxation) occurs because the stabilizing effect of backstresses originating from the amorphous phase is lost. At the α-relaxation the reduction in the dislocation density is attributed to defect propagations within the crystalline lamellae as well as in the amorphous phase and the recrystallization of intralamellar mosaic blocks (i.e., grains).

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INTRODUCTION

mechanisms of dislocation generation, mobilization, and annihilation in melt grown polymer crystals remain to a great extent unclear. Because of the nanometer thickness of the crystalline lamellae, the earliest models for dislocation generations such as the one proposed by Young in 197412 suggested nucleation of monolithic screw dislocations. Another mechanism related to the propagation of chain twist defects1,3 suggested that molecular relaxation mechanisms may interfere in the generation and mobility of dislocations in semicrystalline polymers. The aim of this work was to study the thermal stability and annihilation of deformation-induced dislocations in polypropylene. For this purpose in-situ X-ray diffraction studies during heating from far below the glass transition up to the melting temperature were performed on cold rolled samples. A special X-ray technique was used15,16 to determine the evolution of the

Understanding the mechanisms of plasticity in semicrystalline polymers has been one of the major research focuses in polymer science and has attracted much attention in the past decades, not only from the technological but also from the scientific point of view. In this context, the crystalline phase plays a key role since, above the glass transition temperature, the overall yield stress is primarily determined by the yield stress of the crystals rather than that of the amorphous phase. It is commonly accepted that plastic deformation of polymer crystals, among twinning, martensitic transformation, and adiabatic melting, occurs mainly via crystallographic slip mechanisms.1−7 A large amount of literature exists, which takes into account dislocations in modeling plasticity,8−10 but also their experimental verification, especially in melt-grown semicrystalline polymers, which is challenging due to the multiphase structure, attracted some attention.6,11,12 In recent investigations it was possible to show quantitatively that during crystallographic slip crystalline defects, namely dislocations, are generated facilitating the plastic flow.13,14 However, the © XXXX American Chemical Society

Received: May 10, 2017 Revised: August 7, 2017

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DOI: 10.1021/acs.macromol.7b00931 Macromolecules XXXX, XXX, XXX−XXX

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Plotting the full width at half-maximum gfwhm of the peaks as a function of their diffraction vector g allows for a first simple separation of the effects of size and strain broadening. Any deviation of the data from a monotonous behavior is an indication of anisotropic strains. Assuming that the anisotropic strains are caused by dislocations, the modified Williamson−Hall plot accounts for the defect-specific broadening using the average contrast factor for dislocations C̅ . Plotting the peak width as a function of g C̅ should result in a monotonic behavior if the anisotropy is correctly described by the model used for the distortions caused by dislocations.23,24 For polypropylene this has been shown by Wilhelm et al.,14 hence giving a direct evidence for the presence of dislocations. The measured intensity distribution of a Bragg reflection can be described by a convolution of the size and strain related intensity distributions known as the Warren and Averbach equation:25

deformation-induced dislocation structure as well as of other structural parameters such as the lamella size as a function of annealing temperature. Dynamic mechanical analysis was employed to characterize the molecular relaxation mechanisms17 and to correlate them with the structural information provided by the X-ray data. The α-transitionattributed to defect propagation within the crystalline lamellae also including motions in the amorphous phase18,19and the β-transition attributed to the glass transitionare of special relevance in this respect.

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EXPERIMENTAL SECTION

Sample Preparation. A simple way to introduce a large number of dislocations in the crystalline lamellae is to subject the samples to high amounts of plastic deformation.13,14,20 Polypropylene was chosen since this material shows several high-intensity X-ray diffraction peaks, and previous investigations on the α-phase of this material already showed that a dislocation based deformation mechanism is active. The material used for the present investigation has a molecular weight of Mn = 560 000 g mol−1, Mw = 60 000 g mol−1, a polydispersity of PDI = 9.3, and an isotacticity above 98% (type BE50 from Borealis). Small plates with a thickness of 10 mm were cut from a compression-molded sheet. To ensure that a large number of dislocations is introduced in the material, the samples were cold rolled using a two-high rolling mill (roll diameter of 120 mm with 31.5 s per revolution) in several steps (each step providing a strain of ε = 0.15) at 23 °C to a true strain of ε = 1.2 (ε = ln(d/d0)), where d and d0 are the actual and the original thickness of the sample, respectively. In order to avoid relaxation effects prior to the measurement and thus a possible loss in defect concentration, the deformed sample was immediately stored in liquid nitrogen after cold rolling. Synchrotron Measurement. The cold sample, still at liquid nitrogen temperature, was mounted to the sample stage of a LINKAM TMS 90 temperature controller. To prohibit a temperature gradient between sample and the instrument, the sample stage was precooled to a temperature of −180 °C. Wide-angle X-ray diffraction (WAXD) patterns were then recorded at different annealing temperatures ranging from −180 up to 165 °C, while each annealing temperature was held constant for 600 s. After the sample was heated above the melting temperature to 165 °C it was cooled to 22 °C, and an additional diffraction pattern of the recrystallized sample was recorded. The synchrotron measurements were performed at the Synchrotron Light Source ELETTRA in Trieste, Italy (SAXS-Beamline 5.2L). The photon energy of the beam was 8 keV, which corresponds to Cu Kα radiation with a wavelength of λ = 0.154 nm. The incident beam had a spot size of 100 μm × 400 μm on the sample. The sample was measured in a transmission setup using a DECTRIS Pilatus 100K detector allowing for 2-dimensional data acquisition with very low noise. The sample-to-detector distance and the tilt angle were calibrated using p-bromobenzoic acid as calibrant; the instrumental broadening was considered by measuring lanthanum hexaboride (at higher angles). X-ray Line Profile Analysis. Dislocation densities were evaluated from the recorded WAXD patterns by applying the multireflection Xray profile analysis (MXPA).15,16 In general, X-ray diffraction patterns of nanocrystalline materials show a distinctive broadening of its Bragg reflections. This broadening can be attributed to the small size of the crystals and to lattice strains as for instance those originating from dislocations. Each effect has a distinct functional dependence of the diffraction vector enabling their separation. The MXPA method makes use of this characteristic by modeling the whole diffraction pattern by ab initio physical functions. This allows the determination of parameters such as the density of dislocations and the coherently scattering domain size (CSD size). The CSD size determined from a X-ray profile is the smallest volume scattering coherently. The CSD size can be considered to be in the order of the lamella thickness.21 The effect of defect-induced broadening can be directly inspected using the Williamson and Hall method22 and its modified version.23,24

ln A(L) = ln AS (L) − 2π 2L2g 2⟨εg , L 2⟩

(1)

with AS(L) being the size coefficient, L the Fourier length, g the absolute value of the diffraction vector, and ⟨εg,L2⟩ the mean-square strain. Krivoglaz26 and Wilkens27,28 were able to derive the meansquare strain under the assumption that it is caused by the strain field of dislocations:

⟨εL 2⟩ =

⎛ L ⎞ ⎛ b ⎞2 ⎜ ⎟ πρCf ⎜ ⎟ ⎝ 2π ⎠ ⎝ R e* ⎠

(2)

with the Burgers vector b, the dislocation density ρ, the contrast factor of dislocations C, and the Wilkens function f(L/R*e ). The Wilkens function depends on the Fourier length L and the outer cut off radius of dislocations R*e which determines the range of the distortion fields of the dislocations. The size coefficient is calculated under the assumption of a log-normal size distribution of the crystals.16 The contrast factor of dislocations C considers the anisotropy of lattice distortions generated by dislocations or, more generally, the influence of dislocations on the peak broadening and depends on the relative orientation of the Burgers vector, line vector, and diffraction vector. Thus, the dislocation related peak broadening also depends on the orientation of the diffraction vector and will therefore be varying for different reflections; the peak broadening is anisotropic. While in single crystals the contrast factor C can be determined experimentally, an average contrast factor C̅ is used in the case of polycrystals, by averaging over the possible slip systems.23,29 The most advanced version of MXPA fits ab initio physical functions directly to the measured data, called “Convolution Multiple Whole Profile-fitting” or “CMWP-fit”. The corresponding software package developed by Ribarik et al.16 has been used as a major tool for the evaluation of diffraction profiles throughout this work. It turned out to be very valuable to perform a modified Williamson and Hall analysis on the phase-separated diffraction pattern. This allows to check the influence of a different background fit on the result and gives a first rough estimation about crystallite size and dislocation density and also provides a first determination of the fit parameters for the average dislocation contrast factor C̅ . This fit parameters are then used as starting parameters and are refined in the following whole profile fitting approach with CMWP-fit. During the CMWP-fit evaluation a more accurate determination of microstructural parameters of the material, such as the dislocation density, median of grain size distribution, outer cutoff radius of dislocations, and grain ellipticity, is obtained. It was taken care that the outer cutoff radius of dislocations is fixed well below the thickness of the crystalline lamellae. In order to avoid local minima in the fitting procedure, the selfdeveloped program “multi-eval”, an extension to CMWP-fit, was used.30 Hereby, different starting values for the microstructural parameters are set, while each possible permutation of those parameters is used for an evaluation of CMWP-fit. The program analyses all results with respect to their residuals, by which the global minimum is obtained, followed by calculating the average and standard error for each parameter.30 B


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Figure 1. Diffraction patterns were recorded for various annealing temperatures, up to the melting temperature. The temperatures are represented from high to low in order to ensure legibility of the low intensities at high temperatures.

Figure 2. (a) A peak shift to lower 2Θ angles is observed, which is mainly caused by thermal expansion. (b) Representative diffraction pattern showing the separation into different phases (α, γ, and amorphous). Dynamic Mechanical Thermal Analysis (DMTA). The complex dynamic moduli were measured in compression and torsion mode for undeformed and deformed samples. The latter were also cold rolled to a true strain of ε = 1.2 and measured at frequencies of 0.1, 1, and 10 Hz, while the undeformed samples were measured at frequencies of 0.1, 1, 5, and 10 Hz. A temperature range of −190 to 150 °C with a heating rate of 2 °C/min was used on an ANTON PAAR MCR301 and a PerkinElmer Diamond device. Samples were carefully cut to dimensions of 3 × 2 mm2 area and about 30 mm in length. To ensure linear viscoelastic behavior, a dynamic strain of 0.05% was applied.

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RESULTS Figure 1 shows the diffraction patterns recorded at different annealing temperatures up to values close to the melting temperature. With increasing temperature the X-ray reflections shift to smaller 2Θ angles, especially for the (040) and (130) reflection (Figure 2). Comparison with literature31 yields that this relaxation is mostly a revesible effect due to thermal expansion. In Figure 2 it can be seen that a minor γ-phase content is present in the sample; however, since only the monoclinic α-phase shows dislocation mediated deformation mechanisms,14,20,32 the γ-fraction was modeled by means of Pearson 7 functions and removed from the diffraction pattern. The details of the phase separation and the pre-evaluation procedure have already been described in detail elsewhere.20 The MXPA evaluation of the data yields the CSD-size (Figure 3) and the dislocation density (Figure 4) as a function

Figure 3. Development of the domain size as a function of the annealing temperature for α-iPP. The error bars are in the order of the point size, which indicates well converging fits for the different starting parameters.

of the annealing temperature. It is noted that the error bars in Figures 3 and 4 represent a systematic error originating from the evaluation process; a small error bar indicates small statistic scatter of the resulting convergent fit as obtained from a rough scan over the starting value parameter space.30 C


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investigated samples using a single cantilever setup. For the weak δ-transition no sample showed a corresponding signal.

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DISCUSSION Small changes of the CSD-size between −180 and 95 °C (Figure 3) may be considered as being close to the experimental error of the method. However, the forthcoming drop and the following increase from 13 to 16 nm most probably originate from recrystallization and rearrangement processes: A possible mechanism is the reorganization of smallangle grain boundaries between mosaic blocks (which may be considered as intralamellar subgrains) within the lamellae or of small misorientations within the crystalline lamellae which are formed by geometrically necessary misfit dislocations upon bending of the lamellae during deformation.20 The increase in the lamella size above 100 °C is attributed to the recrystallization of mosaic blocks (subgrains) and lamellar thickening. After the sample was recrystallized from the melt, a CSD-size of 14 nm was obtained again.

Figure 4. Comparison of the loss tangent signal and the evolution of the dislocations density as a function of annealing temperature. A significant drop in the defect concentration can be observed at the glass transition temperature Tg = 10 °C and beyond 85 °C (red curve), which correspond to the β- and α-relaxation, respectively. Loss factor tan(δ) measured by DMTA with a frequency of 1 Hz (blue curve). The error of the dislocation density of the recrystallized sample (filled red triangle) is in the order of the point size.

The CSD-size shown in Figure 3 only changes slightly between −180 °C and approximately 95 °C. A small drop at the glass transition is followed by a subsequent increase up to some 14 nm. Lamellar thickening up to about 16 nm occurs between 115 and 150 °C. The recrystallized sample (after melting) again shows a CSD-size of 14 nm. The dislocation density in Figure 4 starts at a value of ρ = 1 × 1016 m−2, decreasing slightly until a temperature of −100 °C; above that it stays relatively constant up to the glass transition temperature Tg ≅ 10 °C of PP (β-relaxation). Exceeding Tg, the density of dislocations starts to decrease significantly followed by a small plateau between 50 and 85 °C. A further increase in the annealing temperature results in a drastic decrease of the dislocation density, arriving at a value as low as ρ = 0.9 × 1015 m−2. The recrystallized sample (after melting) shows a dislocation density of 0.6 × 1015 m−2. Figure 5 shows the effect of the deformation on the loss factor curve. In the DMTA-derived tan(δ) curve of the deformed sample, shown in Figure 4 two prominent transitionsthe α- and the β-transitioncould be detected; the γ-transition could only be resolved in a few of the

Figure 6. Loss factor versus temperature of samples deformed to ε = 1.2 for three different test frequencies.

Considering the changes of the dislocation density obtained from the MXPA evaluation together with those of the loss factor (tan(δ)) obtained by DMTA at 1 Hz (Figure 4), significant changes are observed at specific transition temperatures related to characteristic molecular relaxations, as there are the glass transition (β-transition) and the α-transition. According to the literature, molecular relaxations have already been rigorously investigated for PP, and three main transitions in the order of decreasing temperature,33 α, β, and γ, could be identified. Using dielectric spectroscopy, a fourth relaxation, known as the δ-relaxation,34−36 located at a temperature below −173.15 °C (100 K), was reported. A detailed discussion of the transitions observed in comparison with literature and the results of the MXPA is done in the following. γ- and δ-Relaxation. The γ- and δ-relaxation, usually observed in PP between −120 to −50 °C and −240 to −173 °C, respectively,34,37 could not be resolved by DMTA in torsion mode in the present work. However, the MXPA reveals an initial drop in dislocation density (Figure 4) located in the same temperature range as literature states for the two transitions γ and δ below Tg. It is not evident whether these can be the reason for the decrease in defect concentration at this temperature. Especially the δ-relaxation with its low activation energy between 4.2 and 5 kJ mol−1 is usually attributed to small vibrations of CH3 groups and can therefore not account for the comparatively large rearrangements necessary for dislocation

Figure 5. Loss factor curves for the undeformed (ε = 0, black triangles) and deformed (ε = 1.2, red squares) samples at a test frequency of 1 Hz. D


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thermally whereas stresses acting from the now softened amorphous phase should only play a minor role. For the α1-process as a grain boundary sliding mechanism no grain growth is expected. The annihilation of dislocations during the α2-process would also involve the recrystallization of small-angle grains formed by dislocation structures. This is indeed reflected in the increase of the CSD-size as represented in Figure 3 at temperatures above 115 °C. Also, a limited reduction in the dislocation density above Tg and below 100 °C as shown in Figure 4 supports an intergranular mechanism rather than an intragranular one. A closer explanation of a defect based mechanism at the origin of the α2-relaxation maybe provided by a molecular model based on chain twist defects (Figure 7).3,47 The

movement such as a chain twist. Still, the mobility in the amorphous fraction is already increasedpossibly allowing for a first stress relaxation: The stress applied on the crystallites would decrease and depin a few dislocations. β-Relaxation. So far the β-transition is related to relaxations in the amorphous component solely.38 The assignment of the β-relaxation to the glass transition in PP was also confirmed by its higher activation energy when compared to that of the αrelaxation. The decrease of the dislocation density around the glass transition temperature observed in the present investigation (Figure 4) can be explained by the reduction in backstresses acting on the crystalline phase as follows:39 Below Tg, the material remains highly strained from the rolling procedure. Quenching the sample to liquid nitrogen temperature immediatly after deformation prohibited any intermittent sample relaxation; thus, a large amount of stresses was “frozen” within the material. It appears that a significant part of these stresses in the amorphous phase is transmitted to the neighboring crystallites, thus stabilizing the dislocations therein. Increasing the temperature above Tg, however, results in an increase of the mobility of chains and of free volumes in the amorphous phase, which is indicated by a decrease in its modulus E′.The relaxing back-stresses increase the dislocation mobility as well, which leads to a reduction in the density of dislocations by their propagation into the adjacent amorphous phase, resulting in a deformation step on the crystal surface. The activation energy for the mobilization of dislocations can be considered as being provided by both thermal energy and back-stresses. α-Relaxation. Compared to polyethylene (PE),40−48 the mechanical α-transition in PP was less investigated. However, it is commonly agreed that the origin of this transition can be attributed to relaxations of both the amorphous and the crystalline phase. The α-transition can further be divided into an α1 and an α2 transition being located at a lower and higher temperature, respectively.17 Alberola et al.49 proposed that both relaxations result from the same origin, i.e., a consequence of defect diffusion within crystalline lamellae of different thicknesses. However, later investigations on highly oriented PE films explicitly demonstrated a different relaxation behavior of the same sample, independent of the lamella thickness distribution; the only dependence observed was on the direction of the dynamic oscillation with respect to the sample orientation.40 As a consequence, the α1- and α2-transitions can be related to specific intralamellar motions (such as mobility of mosaic blocs) and intracrystalline processes (such as motion of chain twist defects or chain diffusion) due to the anisotropy of the crystal lattice potential.40 The α-transition in general was attributed to an exchange of isotactic chain segments between the crystalline and the amorphous phase, depending on the final crystallite size and its distribution which is influenced by the molar mass, microstructure, and the processing conditions.50 Up to today the exact origins of both the α1- and the α2-transition are still under debate. The lower temperature α1peak was assigned to friction between the (sub)grain boundaries or intralamellar mosaic blocks17 (intergranular process), while the higher temperature α2-peak was attributed to chain diffusion through the crystallites51 (intragranular process). In general, based on the data available in the literature in contrast to the reduction of the dislocation density during the β-relaxation, in the case of the α-relaxation the main part of the activation energy to annihilate dislocations is provided

Figure 7. Under the application of a shear stress τ, crystal slip with a Burgers vector b = c/2 occurs due to propagation of a 180° chain twist defect.3,47

operation of this molecular relaxation mechanism within the crystalline phase would cause a strong reduction of the dislocation density when the defect propagates along the chain axis into the adjacent amorphous phase. As a consequence, there occurs a translation of the chain stems by the distance of a Burgers vector, resulting in a surface modification consisting of shortening of the chain loops (Figure 8). This in further consequence allows for an extension

Figure 8. Reorganization of the crystal interface occurs by (a) shortening of chain loops (CL), which permits (b) lengthening of tie chains (TC) permitting additional deformation of the amorphous phase (modified from ref 47).

of tie chains permitting additional deformation of the amorphous phase resulting in an increase in the tan(δ) signal.47,52,53 In this context the concept of the rigid amorphous phase should be discussed.54,55 Ejection of chain segments from the crystalline to the amorphous areas may soften the rigid crystal−amorphous interface by affecting the confinement of non folded chain segments. Also, in this scenario a further E


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be tuned to a certain extent. On a longer term it may be possible to contol properties such as the yield strength,57 the thermal conductivity,58 the gas permeability,59 or even electronic transport in conductive/conjugated semicrystalline polymers60 by controlling the dislocation density.

reduction of crystalline defects may be triggered because they are not stabilized any more by the interface. This explanation is supported by the DMTA results presented in Figure 5, which shows a comparison of the tan(δ) signal for an undeformed and deformed sample. It is apparent that the intensity of the signal is strongly increased in the case of the deformed sample. Considering that the mechanical αprocess can be related to inter- and intralamellar shear processes which stimulate the transfer of chain segments from the crystalline to the amorphous phase, it is plausible that the peak broadening and/or increase in intensity occurs for one or both of the corresponding α1- and α2-relaxations in the mechanical loss spectra.40 The higher the initial dislocation density is in the deformed sample, the more chain segments are being transported to the amorphous phase via propagating twist defects. However, the stronger α-relaxation signal may also be caused by the higher initial fraction of the amorphous phase since it is well-known that crystallinity decreases with increasing deformation. Differentiation between them in the DMTA loss factor curves is difficult as both signals strongly overlap. Careful inspection of the curves in Figure 5 reveals that particularly the signal attributed to the α2 transition and located at about 100− 110 °C increases with deformation. It has to be considered that the chain twist mechanism only operates in chain direction along the c-axis. Yet, previous investigations show that with increasing deformation also dislocations with screw and edge character operating in transverse direction are activated.56 Consequently, and according to Figure 4, it is possible that not only the reduction in dislocation density but also the intensity of this α-transition is caused by both dislocations with chain character and dislocations with transverse character.

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AUTHOR INFORMATION

Corresponding Author

*E-mail fl[email protected]; Ph +43 (0) 3842-804-325 (F.S.). ORCID

Florian Spieckermann: 0000-0003-4836-3284 Sigrid Bernstorff: 0000-0001-6451-5159 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The present work was supported by the Austrian Science Foundation FWF project Nr P 22913 and FWF Project Nr. P 28672-N36.

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REFERENCES

(1) Séguéla, R. Dislocation Approach of the plastic Deformation of Semicrystalline Polymers: Kinetic Aspects for Polyethylene and Polypropylene. J. Polym. Sci., Part B: Polym. Phys. 2002, 40, 593−601. (2) Peterson, J. Peierls Stress for Screw Dislocations in Polyethylene. J. Appl. Phys. 1968, 39, 4920−4928. (3) Nikolov, S.; Raabe, D. Yielding of polyethylene through propagation of chain twist defects: Temperature, stem length and strain-rate dependence. Polymer 2006, 47, 1696−1703. (4) Lin, L.; Argon, A. S. Rate Mechanism of Plasticity in the Crystalline Component of Semicrystalline Nylon 6. Macromolecules 1994, 27, 6903−6914. (5) Galeski, A. Strength and toughness of crystalline polymer systems. Prog. Polym. Sci. 2003, 28, 1643−1699. (6) Gleiter, H.; Argon, A. S. Plastic deformation of polyethylene crystals. Philos. Mag. 1971, 24, 71−80. (7) Séguéla, R. On the Natural Draw Ratio of Semi-Crystalline Polymers: Review of the Mechanical, Physical and Molecular Aspects. Macromol. Mater. Eng. 2007, 292, 235−244. (8) Argon, A.; Galeski, A.; Kazmierczak, T. Rate mechanisms of plasticity in semi-crystalline polyethylene. Polymer 2005, 46, 11798− 11805. (9) Kazmierczak, T.; Galeski, A.; Argon, A. Plastic deformation of polyethylene crystals as a function of crystal thickness and compression rate. Polymer 2005, 46, 8926−8936. (10) Xiong, B.; Lame, O.; Chenal, J.-M.; Men, Y.; Seguela, R.; Vigier, G. Critical stress and thermal activation of crystal plasticity in polyethylene: Influence of crystal microstructure and chain topology. Polymer 2017, 118, 192−200. (11) Galeski, A.; Bartczak, Z.; Kazmierczak, T.; Slouf, M. Morphology of undeformed and deformed polyethylene lamellar crystals. Polymer 2010, 51, 5780−5787. (12) Young, R. J. A dislocation model for yield in polyethylene. Philos. Mag. 1974, 30, 85−94. (13) Spieckermann, F.; Polt, G.; Wilhelm, H.; Kerber, M.; Schafler, E.; Zehetbauer, M. J. The role of dislocations for the plastic deformation of semicrystalline polymers as investigated by multireflection X-ray line profile analysis. J. Appl. Polym. Sci. 2012, 125, 4150−4154. (14) Wilhelm, H.; Paris, A.; Schafler, E.; Bernstorff, S.; Bonarski, J.; Ungar, T.; Zehetbauer, M. Evidence of dislocations in melt-crystallised and plastically deformed polypropylene. Mater. Sci. Eng., A 2004, 387− 389, 1018−1022. (15) Ungár, T. Characterization of nanocrystalline materials by X-ray line profile analysis. J. Mater. Sci. 2007, 42, 1584−1593.

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SUMMARY AND CONCLUSIONS For the first time the evolution of the density of deformationinduced dislocations as a function of the annealing temperature was studied in highly deformed α-phase polypropylene. Two distinct reductions in the dislocation density at T ≃ 10 °C and T ≃ 85 °C were observed which could be correlated to the well-known relaxation mechanisms in PP, β, and α, respectively, by means of DMTA measurements. The drop at the β-transition temperature (glass transition temperature Tg ≃ 10 °C) can be related to an increased mobility of the macromolecules in general, especially the increased temperature leads to a thermal activation of mobile dislocations, which then move to the amorphous phase or annihilate. The stronger decrease of the dislocation density during the α-relaxation as compared to the β-relaxation results from the fact that the α-transition is not restricted to the amorphous phase. Instead, intralamellar processes and exchanges of isotactic sequences between the crystalline and amorphous phases occur by dislocations moving out of the crystal. This results in an increase of the tan(δ) signal from the DMTA measurements at the α-transition for the deformed samples. Additional extension of tie molecules which occurs concomitantly with chain loop shortening (caused by an increasing number of dislocations running through the crystals) permits more deformation of the amorphous phase. It can be concluded that by annealing of deformationinduced dislocations their density and hence the crystallographic order and subsequently also the physical properties may F


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Macromolecules (16) Ribárik, G.; Ungár, T.; Gubicza, J. MWP-fit: a program for multiple whole-profile fitting of diffraction peak profiles by ab initio theoretical functions. J. Appl. Crystallogr. 2001, 34, 669−676. (17) Saitô, N.; Okano, K.; Iwayanagi, S.; Hideshima, T. Molecular Motion in Solid State Polymers. Solid State Phys. 1963, 14, 343−502. (18) Djoković, V.; Kostoski, D.; Dramićanin, M. D. Viscoelastic behavior of semicrystalline polymers at elevated temperatures on the basis of a two-process model for stress relaxation. J. Polym. Sci., Part B: Polym. Phys. 2000, 38, 3239−3246. (19) Jourdan, C.; Cavaille, J. Y.; Perez, J. Mechanical relaxations in polypropylene: A new experimental and theoretical approach. J. Polym. Sci., Part B: Polym. Phys. 1989, 27, 2361−2384. (20) Polt, G.; Spieckermann, F.; Wilhelm, H.; Kerber, M.; Schafler, E.; Bernstorff, S.; Zehetbauer, M. The role of dislocations in γ-iPP under plastic deformation investigated by X-ray line profile analysis. Mech. Mater. 2013, 67, 126−132. (21) Spieckermann, F.; Wilhelm, H.; Kerber, M.; Schafler, E.; Polt, G.; Bernstorff, S.; Addiego, F.; Zehetbauer, M. Determination of lamella thickness distributions in isotactic polypropylene by X-ray line profile analysis. Polymer 2010, 51, 4195−4199. (22) Williamson, G. K.; Hall, W. H. X-ray line broadening from filed aluminium and wolfram. Acta Metall. 1953, 1, 22−31. (23) Ungár, T.; Borbély, A. The effect of dislocation contrast on x-ray line broadening: A new approach to line profile analysis. Appl. Phys. Lett. 1996, 69, 3173−3175. (24) Kerber, M.; Schafler, E.; Zehetbauer, M. Processing and Evaluation of X-ray Line Profiles Measured from Nanostructured Material s Produced by Severe Plastic Deformation. Rev. Adv. Mater. Sci. 2005, 10, 427−433. (25) Warren, B. E.; Averbach, B. L. The Effect of Cold-Work Distortion on X-Ray Patterns. J. Appl. Phys. 1950, 21, 595−599. (26) Krivoglaz, M. Theory of X-Ray and Thermal Neutron Scattering by Real Crystals; Plenum Press: 1969. (27) Wilkens, M. The determination of density and distribution of dislocations in deformed single crystals from broadened X-ray diffraction profiles. Phys. Status Solidi A 1970, 2, 359−370. (28) Wilkens, M. X-ray line broadening and mean square strains of straight dislocations in elastically anisotropic crystals of cubic symmetry. Phys. Status Solidi A 1987, 104, K1−K6. (29) Ungár, T.; Tichy, G. The Effect of Dislocation Contrast on XRay Line Profiles in Untextured Polycrystals. Phys. Status Solidi A 1999, 171, 425−434. (30) Kerber, M. X-ray Line Profile Analysis in Theory and Experiment. Ph.D. Thesis, University of Vienna, 2012. (31) Isasi, J. R.; Alamo, R. G.; Mandelkern, L. The thermal expansion of the monoclinic unit cell of isotactic polypropylene. J. Polym. Sci., Part B: Polym. Phys. 1997, 35, 2945−2949. (32) Polt, G. Mechanisms of Plastic Deformation in γ-Isotactic Polypropylene. M.Sc. Thesis, Universtiy of Vienna, 2011. (33) Read, B. Mechanical relaxation in isotactic polypropylene. Polymer 1989, 30, 1439−1445. (34) Suljovrujic, E.; Trifunovic, S.; Milicevic, D. The influence of gamma radiation on the dielectric relaxation behaviour of isotactic polypropylene: The α relaxation. Polym. Degrad. Stab. 2010, 95, 164− 171. (35) Starkweather, H. W.; Avakian, P.; Matheson, R. R.; Fontanella, J. J.; Wintersgill, M. C. Ultralow temperature dielectric relaxations in polyolefins. Macromolecules 1992, 25, 6871−6875. (36) Brandrup, J.; Immergut, E. Polymer Handbook; Wiley: New York, 1975. (37) Roy, S. K.; Kyu, T.; Manley, R. S. J. Physical and dynamic mechanical properties of ultradrawn polypropylene films. Macromolecules 1988, 21, 499−504. (38) Jawad, S. A.; Alhaj-Mohammad, M. H. β-relaxation of drawn isotactic polypropylene in terms of a simplified two phase model. Polym. Int. 1994, 35, 395−398. (39) Polt, G.; Spieckermann, F.; Wilhelm, H.; Fischer, C.; Schafler, E.; Bernstorff, S.; Zehetbauer, M. Crystalline plasticity in isotactic

polypropylene below and above the glass transition temperature. eXPRESS Polym. Lett. 2015, 9, 894−900. (40) Zhou, H.; Wilkes, G. L. Orientation Anisotropy of the Mechanical α Relaxation of High-Density Polyethylene Films Having a Well-Defined Stacked Lamellar Morphology. Macromolecules 1997, 30, 2412−2421. (41) Chmutin, I.; Ryvkina, N.; Zubova, E.; Manevich, L. Chain diffusion in semicrystalline polyethylene: Dielectric relaxation. Polym. Sci. Ser. A 2008, 50, 181−189. (42) Matsuo, M.; Bin, Y.; Xu, C.; Ma, L.; Nakaoki, T.; Suzuki, T. Relaxation mechanism in several kinds of polyethylene estimated by dynamic mechanical measurements, positron annihilation, X-ray and 13C solid-state {NMR}. Polymer 2003, 44, 4325−4340. (43) Mano, J. F. Cooperativity in the Crystalline α-Relaxation of Polyethylene. Macromolecules 2001, 34, 8825−8828. (44) Men, Y.; Rieger, J.; Endeler, H.-F.; Lilge, D. Mechanical αProcess in Polyethylene. Macromolecules 2003, 36, 4689−4691. (45) Reneker, D.; Mazur, J. Dispirations, disclinations, dislocations, and chain twist in polyethylene crystals. Polymer 1983, 24, 1387−1400. (46) Reneker, D. H.; Mazur, J. Small defects in crystalline polyethylene. Polymer 1988, 29, 3−13. (47) Boyd, R. H. Relaxation processes in crystalline polymers: molecular interpretation − − a review. Polymer 1985, 26, 1123−1133. (48) Zubova, E.; Balabaev, N.; Manevitch, L. Molecular mechanisms of the chain diffusion between crystalline and amorphous fractions in polyethylene. Polymer 2007, 48, 1802−1813. (49) Alberola, N.; Cavaille, J. Y.; Perez, J. Mechanical spectrometry of alpha relaxations of high-density polyethylene. J. Polym. Sci., Part B: Polym. Phys. 1990, 28, 569−586. (50) Hoyos, M.; Tiemblo, P.; Gómez-Elvira, J. M. The role of microstructure, molar mass and morphology on local relaxations in isotactic polypropylene. The α relaxation. Polymer 2007, 48, 183−194. (51) Kawai, H.; Hashimoto, T.; Suehiro, S.; Fujita, K.-I. Dynamic Xray diffraction studies of spherulitic poly-alpha-olefins in relation to the assignments of alpha and beta mechanical dispersions. Polym. Eng. Sci. 1984, 24, 361−372. (52) Meier, D., Ed.; Molecular Basis of Transitions and Relaxations; Midland Macromolecular Monographs; Gordon and Breach Science Publishers: 1978. (53) Read, B.; Dean, G.; Tomlins, P. Effects of physical ageing on creep in polypropylene. Polymer 1988, 29, 2159−2169. (54) Wunderlich, B. Reversible crystallization and the rigid− amorphous phase in semicrystalline macromolecules. Prog. Polym. Sci. 2003, 28, 383−450. (55) Zia, Q.; Mileva, D.; Androsch, R. Rigid Amorphous Fraction in Isotactic Polypropylene. Macromolecules 2008, 41, 8095−8102. (56) Spieckermann, F.; Wilhelm, H.; Schafler, E.; Kerber, M.; Bernstorff, S.; Zehetbauer, M. Plasticity and X-ray Line Profile Analysis of the semicrystalline polymer poly(3-hydroxybutyrate). Journal of Physics: Conference Series 2010, 240, 012146. (57) Spieckermann, F.; Wilhelm, H.; Polt, G.; Ahzi, S.; Zehetbauer, M. Rate mechanism and dislocation generation in high density polyethylene and other semicrystalline polymers. Polymer 2014, 55, 1217−1222. (58) Shen, S.; Henry, A.; Tong, J.; Zheng, R.; Chen, G. Polyethylene nanofibres with very high thermal conductivities. Nat. Nanotechnol. 2010, 5, 251−255. (59) Wang, H.; Keum, J. K.; Hiltner, A.; Baer, E.; Freeman, B.; Rozanski, A.; Galeski, A. Confined Crystallization of Polyethylene Oxide in Nanolayer Assemblies. Science 2009, 323, 757−760. (60) Noriega, R.; Rivnay, J.; Vandewal, K.; Koch, F. P. V.; Stingelin, N.; Smith, P.; Toney, M. F.; Salleo, A. A general relationship between disorder, aggregation and charge transport in conjugated polymers. Nat. Mater. 2013, 12, 1038−1044.

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Dislocation Movement Induced by Molecular Relaxations in Isotactic

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