Critical Strains for Lamellae Deformation and Cavitation during

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Critical Strains for Lamellae Deformation and Cavitation during Uniaxial Stretching of Annealed Isotactic Polypropylene Baobao Chang,*,†,‡ Konrad Schneider,† Fei Xiang,†,‡ Roland Vogel,† Stephan Roth,∥ and Gert Heinrich†,§ †

Leibniz-Institut für Polymerforschung Dresden, D-01069 Dresden, Germany Institut für Werkstoffwissenschaft and §Institut für Textilmaschinen und Textile Hochleistungswerkstofftechnik, Technische Universität Dresden, D-01069 Dresden, Germany ∥ Photon Science at DESY, D-22607 Hamburg, Germany Macromolecules Downloaded from pubs.acs.org by UNIV OF SUSSEX on 08/10/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: The lamellae deformation and cavitation behavior of annealed isotactic polypropylene during uniaxial stretching are comprehensively investigated by in situ synchrotron small-angle Xray scattering and wide-angle X-ray scattering. We reveal how lamellae deformation occurs in the time scales of elastic deformation, intralamellar slip, and melting−recrystallization, separated by three critical strains which are only rarely influenced by annealing. Strain I (0.1) marks the end of elastic deformation and the onset of intralamellar slip, beyond which the crystallinity decreases gradually. Strain II (0.45) signifies the start of the recrystallization process, from where the long period in the stretching direction begins to decrease from its maximum and the polymer chains in the crystal start to orient along the stretching direction. The energy required for melting arises from the friction between the fragmented lamellae produced by intralamellar slip. Strain III (0.95) denotes the end of the recrystallization process. Beyond the strain of 0.95, the long period and the crystal size remain nearly unchanged. During further stretching, the newly formed lamellae serve as the anchoring points for polymer chains in the amorphous phase. The extension of the polymer chains in between lamellae triggers the strain hardening behavior. On the other hand, annealing significantly decreases the critical strain for voids formation and increases the voids number but restricts the void size. For those samples annealed at a temperature lower than 90 °C, voids are formed between strain II and strain III, and voids are oriented in the stretching direction once they are formed. However, for those samples annealed at a temperature higher than 105 °C, voids are formed between strain I and strain II. In this case, voids are initially oriented with their longitudinal axis perpendicular to the stretching direction and then transferred along stretching direction via void coalescence. Additionally, the formation of voids influences neither the critical strains for lamellae deformation nor the final long period, the orientation of polymer chains, or the crystal size. The final long period, the orientation of polymer chains in the crystal, and the crystal size are determined only by the stretching temperature through melting−recrystallization.

1. INTRODUCTION

transformed into highly oriented structure along the loading direction.6 In the past decades, abundant works have been performed via either experimental method7 or simulation procedure8 on the plastic deformation of lamellae in various semicrystalline polymers, for instance, polyamide 6 (PA6),7,9 poly(ε-caprolactone) (PCL),10 polyethylene (PE),11,12 polybutene-1 (PB-1),13 and isotactic polypropylene (iPP).14−17 Based on the results, two distinct mechanisms have been proposed to account for the plastic deformation of lamellae.18 The first one was proposed by Peterson19 and further explored by Shadrake and Guiu20 and Yong,21 which supposed that

Owing to the increasing use of semicrystalline polymer materials in engineering structures and in our daily life, it is of utmost importance to assess their mechanical behavior with accuracy. Being composed of layered crystalline lamellae and amorphous phase between the lamellae with entangled polymer chains,1 the mechanical behavior of semicrystalline polymers correlates intimately with its structural evolution during deformation. Uniaxial stretching is one of the most frequently encountered loading modes which arises in the tensile test or fiber spinning.2 During uniaxial stretching, a macroscopic necking phenomenon of the specimen combined with a yield point on the engineering stress−strain curve is readily observed.3−5 After necking, the original lamellae will be © XXXX American Chemical Society

Received: April 2, 2018 Revised: June 29, 2018

A

DOI: 10.1021/acs.macromol.8b00642 Macromolecules XXXX, XXX, XXX−XXX

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2. EXPERIMENTAL PART

crystallographic slips are triggered by the emission of screw dislocation from the edges of lamellae. The advantage of the crystallographic slip theory is that it could describe quite well the yield stress dependency of the lamellae thickness.22 The second one is the partial melting−recrystallization theory10,23 which was supported by the evidence that the newly formed crystalline lamellae after the yield point depended only on the stretching temperature irrespective of the original structure.24,25 Except for the plastic deformation of lamellae, a stress whitening phenomenon could be observed during uniaxial stretching in most cases, indicating the formation of numerous voids inside the bulk material.9,26−31 Recent investigations about voids’ formation in semicrystalline polymers were elaborately reviewed by Pawlak, Galeski, and Rozanski.32 Generally, the voids can be induced before the yield,33 during the yield, or after the yield,34,35 depending on the crystal form,14,27,36 crystallinity,37,38 lamellae branching,39 lamellae thickness,29 and the state of the amorphous phase.40 The relationship between lamellae deformation and cavitation behavior has caught a lot of attention in the past few years. In the work of Pawlak and Galeski,26 a set of semicrystalline polymers with different lamellae thicknesses and crystallinity were used. An assumption was proposed that the cavitation or crystal plastic deformation could be activated only when the local stress σ is higher than that required for cavitation (σcav) or crystallographic slip (σsh). For a thick lamella with high plastic resistance, σcav is lower than σsh. As a consequence, the initiation of cavitation occurs first, and cavitation can be readily observed. Whereas for a thinner lamella, σsh is lower than σcav. Then the crystal slip occurs first. The assumption was further checked by Humbert;41 in his work quite simple equations were proposed to describe the relationship between the lamellae thickness and σcav or σsh. The important point about the equations is that σcav decreases with the thickness of lamellae, while σsh increases. In addition to the above-mentioned study, Hughes related the onset of both intense microvoiding and stress-induced martensitic phase transitions of PE to the yield point.42 However, Schneider found that martensitic transformation arose earlier than cavitation.43 Auriemma found that in iPP initially crystallized α and/or γ forms will be transformed into the mesomorphic form with a small fraction of nanovoids formed by the effect of stretching.44 Despite the fact that numerous studies have been performed on the relationship between lamellae deformation and the void formation, it is still an ongoing topic. The main objective of this work is to comprehensively investigate the lamellae plastic deformation and the cavitation behavior in semicrystalline polymer during uniaxial stretching, especially the critical strains for each structural evolution process. For this purpose, iPP was used as a model polymer because of its wide applications in both industrial fields and scientific studies. The microstructure including the thickness of the lamellae, the crystallinity, and the mobility of the polymer chains in the amorphous phase was controlled by an annealing process. In particular, in situ small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) measurements were performed with the synchrotron X-ray beam to monitor the complex hierarchical structural evolution including void formation, lamellae fragmentation, melting−recrystallization, polymer chains orientation, and more.

2.1. Materials and Sample Preparation. A homo-iPP, grade HD120MO from Borealis (Linz, Austria), was used in this study. The melt flow index is 8 g/10 min under ASTM D1238 conditions of 230 °C and 2.16 kg. The weight-average and number-average molecular weights are 365 kg/mol and 67.6 kg/mol, respectively. iPP plates with a thickness of 1 mm were prepared by compression molding in the following procedure: first, the plate from injection molding was kept at 210 °C for 10 min to fully erase any thermomechanical history. Afterward, the plates were cooled by water (10 °C) and kept at room temperature for 48 h. Then the plates were annealed in a vacuum oven (Thermo Scientific, USA) under 75, 90, 105, 120, and 135 °C for 6 h. For clarification, the plate without annealing was named PPna, and the plates with annealing were named PPTa with Ta referring to the annealing temperature. For instance, PP75 means that the plate was annealed at 75 °C for 6 h. 2.2. Characterization. 2.2.1. Differential Scanning Calorimetry (DSC). The melting behavior of the sample before and after uniaxial stretching was measured on a Q2000 (TA Instruments, USA). The instrument was temperature and melting enthalpy calibrated by using indium as a standard before the test. Dry nitrogen was used as a purge gas at a rate of 50 mL min−1 during the test. A 5 mg sample sealed in an aluminum pan was heated from −80 to 200 °C with a heating rate of 10 K min−1. The crystallinity (Xc‑DSC) could be calculated by Xc‐DSC =

ΔHm × 100% ΔHm*

(1)

where ΔHm and ΔH*m are the fusion enthalpy and the equilibrium * = 207 J g−1.45 melting enthalpy of samples; for iPP ΔHm 2.2.2. Dynamic Mechanical Analysis (DMA). The mechanical relaxation behavior of polymer chains was tested with an ARES G2 rheometer (TA Instruments, USA). The sample with a width of 11 mm and a free length of 10 mm was cut from the plate. Nitrogen was used as the heating gas during the measurement. Each test was started 4 min after the sample was inserted into the rheometer to ensure the attainment of thermal equilibrium. The angular frequency was 1 rad s−1, the strain amplitude was 0.05%, the temperature range was from −70 to 160 °C, and the heating rate was 5 K min−1. 2.2.3. Scanning Electron Microscopy (SEM). The morphology of the sample after stretching is observed by SEM (Zeiss Ultra Plus, Germany). Before the observation, the samples were etched in a solution of KMnO4−H2SO4−HNO3 and then sputter-coated with a layer of platinum (with a thickness of 5 nm). The measurement was operated under a voltage of 3 kV and Inlens signal mode. 2.2.4. In Situ Synchrotron X-ray Scattering Measurements. In situ synchrotron X-ray scattering measurements were performed at the MiNaXS Beamline at Deutsches Elektronen Synchrotron (DESY), in Hamburg, Germany. The wavelength of the X-ray was 0.106917 nm. An exposure time of 0.1 s and a time interval of 0.15 s were used to realize a high time resolution without burning the sample by X-rays. For small-angle X-ray scattering (SAXS), patterns were recorded by a Pilatus 1M detector (981 × 1043 pixels, pixel size 172 × 172 μm2), and the distance between the sample and the detector was 4961 mm. For wide-angle X-ray scattering (WAXS), patterns were recorded using a Pilatus 300K detector (487 × 619 pixels, pixel size 172 × 172 μm2), and the distance between the sample and the detector was 202 mm. Pattern preprocessing including masking and reconstruction of blind areas was performed by a self-written subroutine on PV-Wave from Visual Numerics. The uniaxial stretching was performed on a custom-made miniature tensile machine designed by Leibniz Institute of Polymer Research Dresden (IPF) for online studies at the synchrotron. Waist-shape specimens were CNC milled from the compression-molded plate. During the measurement, both grips moved simultaneously in opposite directions to keep the X-ray beam at a fixed position on the sample. The temperature was controlled by a heating gun. In every test, the specimen was stretched with a cross-head speed of 0.02 mm s−1. The local strain at the X-ray beam position was determined optically by monitoring a grid pattern (0.35 mm × 0.35 mm) painted B


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Figure 1. (a) 2D-SAXS and WAXS patterns of the sample with different annealing histories. (b) Lorentz-corrected 1D-SAXS curve obtained from azimuthal integration 2D-SAXS patterns of the annealed iPP. (c) 1D-WAXS curve obtained from azimuthal integration 2D-WAXS patterns of the annealed iPP. (d) The melting behavior and (e) the mechanical relaxation behavior of iPP annealed at different temperatures. For clarification, the curves in (c), (d), and (e) are vertically shifted. on the surface of the sample. The optical images were taken every 1 s during stretching. The Hencky strain εH is used as a basic quantity of the local strain, which is defined as εH = ln

ΔL + L0 L0

optical signal detection and to avoid heating the specimen during testing, the light directed onto the specimen was provided by a cold light system Dedocool (Dedo Weigert Film GmbH, Munich, Germany). One example of the DIC system is provided in Figure S1 of the Supporting Information.

(2)

3. RESULTS AND DISCUSSION 3.1. Microstructure of iPP after Annealing. Figure 1a presents the 2D-SAXS and WAXS patterns of the sample with different annealing histories. The scattering in all patterns are homogeneously distributed, suggesting a random orientation of lamellae and crystal. With increasing Ta, the radius of the scattering ring on 2D-SAXS patterns is decreased and the intensity of the ring is enhanced. In the 2D-WAXS patterns, a few scattering rings originating from (110), (040), (130), and (111)/(−131) crystal planes from the inner to outer region can be found.46 By circular integration of the 2D-SAXS and

where L0 andΔL are the initial length and displacement of the painted grid pattern during stretching, respectively. The true stress σ is given as

σ=

F ijj ΔL yzz jj1 + zz j A0 k L0 z{

(3)

where F and A0 are the instantaneous force and the initial crosssectional area. Additionally, the true stress−strain curve was also determined by a digital image correlation (DIC) system (ARAMIS; GOM GmbH, Germany), especially in the small strain region. To allow for sufficient C


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between 250 and 300 K denotes the cooperative motions of chain segments in the amorphous phase,51−55 and the αcrelaxation localized below the melting temperature correlates intimately with the mobility of polymer chains connecting the crystalline lamellae and the amorphous phase.56,57 The βrelaxation temperature decreases as Ta increases, suggesting that the higher polymer chains mobility in the amorphous phase is probably caused by the melting of imperfect lamellae and the increase of amorphous phase thickness. The situation of the αc-relaxation is more complicated than that of the βrelaxation. Only one broad αc-relaxation peak could be observed for PPna, and two αc-relaxation peaks (αc′-relaxation and αc″-relaxation in the order of decreasing temperature) arise after annealing. Both peaks shift toward a higher temperature as Ta increases. The increase of the αc-relaxation temperature means that the restriction on the polymer chains connecting the amorphous phase and the lamellae is enhanced. The higher rigidity of polymer chains between the lamellae and the amorphous phase favors a better load transmission when the sample is subjected to a mechanical load.58 Based on the microstructure (not only the thickness of lamellae but also the polymer chains mobility in the amorphous phase) of the annealed iPP, the stretching temperature in this study is chosen as 75 °C where the polymer chains mobility differs greatly with each other. 3.2. True Stress−Strain Curves of iPP Uniaxial Stretched at 75 °C. The true stress−strain curves of iPP stretched at 75 °C are recorded in Figure 2a. Figure 2b is the enlargement of the square region in Figure 2a. The increase of the true stress with strain shows a similar trend for all curves. A linear increase of the true stress can be found in small strain region. Then the slope of the curve decreases gradually and afterward reaches a constant value which continues in a quite large strain region. The onset of this region represents the maximum force on the force−displacement curve,59 which can be labeled as the yield strain (εy). Finally, a sharp increase of the true stress appears implying the appearance of the strain hardening. εy and the onset strain of the strain hardening (εh) are summarized in Figure 2c. It can be found that regardless of Ta, εy and εh are around 0.1 and 0.95, respectively. Figure 2c also shows that the yield stress (σy) increases with Ta, which could be understood by the screw dislocation theory60 ÄÅ É yzÑÑÑÑ ÅÅÅ ij 2π ΔGa(T ) K (T , ε)̇ expÅÅÅ−jjj σy = + 1zzzÑÑÑ zÑÑ ÅÅ j L K (T , ε)̇ b 2 2π v ÅÇ k c (6) {ÑÖ

WAXS patterns, 1D-SAXS and WAXS curves can be obtained, which are provided in Figure 1b,c. In 1D-SAXS curves, it can be found that with increasing Ta, the curve shifts to the lower scattering vector (s) and the peak width (full width at halfmaximum, fwhm) decreases gradually. The long period (Lp), containing one crystalline phase (Lc) and one amorphous phase (La) in the typical “two-phase” model of semicrystalline polymer, is estimated from the peak position (smax) on the 1DSAXS curve by Lp = 1/smax

(4)

where s = 2 sin θ/λ is the scattering vector, λ is the wavelength of X-rays, and θ is the scattering angle. Here the Lorentz correction (I(s) → s2I(s)) is employed because no lamellae orientation exists in compression-molded samples.47 Lc and La can be obtained from 1D-correlation function (K(z)) without resorting to any models.48 K(z) is given as follows: ∞

K (z ) =

∫0 s 2I(s) cos(sz) ds ∞

∫0 s 2I(s) ds

(5)

where z represents the length in real space with units of nanometers. The K(z) curves of the sample are provided in Figure S2. Lp, fwhm, Lc, and La as a function of Ta are given in Table 1. With the increase of Ta, Lp increases from 12.0 to 16.3 Table 1. Microstructure of iPP with Different Annealing Histories Lp (nm) fwhm (nm−1) Lc (nm) La (nm) Xc‑WAXS Xc‑DSC

PPna

PP75

PP90

PP105

PP120

PP135

12.0 0.041 6.1 6.9 0.48 0.53

12.4 0.033 6.3 6.2 0.48 0.56

12.7 0.028 6.5 6.4 0.49 0.55

13.5 0.028 7.2 6.6 0.53 0.57

14.1 0.026 7.6 7.0 0.54 0.60

16.3 0.019 8.9 8.3 0.56 0.62

nm. Meanwhile, fwhm decreases from 0.041 to 0.019 nm−1, indicating a narrower distribution of Lp. Lc increase from 6.1 to 8.9 nm and La increases from 6.9 to 8.3 nm, which result from the lamellae thickening process and imperfect lamellae melting during annealing.49 In the 1D-WAXS curves (Figure 1c), a few peaks originating from (110), (040), (130), (111), and (−131) crystal planes can be seen in the order of increasing scattering vector. The crystal planes mentioned above belong to α-iPP.50 No β- and γ-iPP or “mesophase” halo is found, indicating that the samples are composed only by α-iPP. The crystallinity (Xc‑WAXS) obtained from the 1D-WAXS curve by a standard peak fitting procedure (see Figure S3) is provided in Table 1. It can be found that Xc‑WAXS stays the same when Ta is lower than 90 °C and increases from 0.49 to 0.56 as Ta is increased from 90 to 135 °C. The DSC curves in Figure 1d show that irrespective of Ta, the main peak originated from the melting of α-iPP stays constant at 166 °C. When Ta is higher than 105 °C, a shoulder peak appears, and it moves from 120 to 149 °C. The appearance of the shoulder peak is ascribed to the melting of newly formed lamellae after annealing. For comparison, the crystallinity calculated from DSC (Xc‑DSC) is also provided in Table 1, which is slightly higher than the one calculated from 1D-WAXS due to the recrystallization process during DSC measurements. The mechanical relaxation behavior reflects the mobility of polymer chains, as shown in Figure 1e. The β-relaxation (the glass−rubber transition)

where K(T,ε̇) is the crystalline shear modulus of the slip planes (which depends on the stretching temperature and strain rate), ΔGa is the Gibbs free energy for dislocation nucleation (assumed to be proportional to the absolute temperature), bv is the magnitude of the Burgers vector, and Lc can be regarded as the lamellae thickness. For the sample stretched at a constant temperature (namely 75 °C in this case), σy is controlled only by Lc. As has been demonstrated in section 3.1, annealing will perfect the lamellae and increase the thickness of the lamellae, which results in a larger Lc in eq 6, consequently leading to a larger σy. 3.3. In Situ SAXS and WAXS Results. In Figure 3, some representative 2D-SAXS patterns during stretching are provided. The specified strain for each pattern is provided. The stretching temperature is 75 °C, and the stretching direction is horizontal. Upon stretching, the evolution of the pattern is quite different with varying annealing temperatures. D


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Figure 2. (a) True stress (σ)−strain (εH) curves of iPP with different annealing histories uniaxial stretched at 75 °C. (b) Enlargement of the square region in (a) obtained by the DIC system. (c) Plots of the critical strains at the end of elastic deformation (εy) and the onset of strain hardening (εh) and the yield stress (σy) as a function of Ta.

For PPna, at the εH of 0.05 the homogeneous ring changes into “two arcs” shape concentrated on the equator, indicating the slight lamellae orientation along the loading direction. The slight orientation is caused by the rotation of lamellae.61 As εH increases to 0.53, the “two arcs” pattern is replaced by a “four arcs” elliptical pattern with the intensity focused at oblique angles. The “four arcs” elliptical pattern originates from the tilting of the lamellae.61 With a strain of 0.76 the lamellar scattering becomes very blurry, indicating the melting of the lamellae, and the diffusing scattering focuses mostly on the equator. As εH increases further to 1.22, the “two lobes” shape scattering can be found at the equator, suggesting the formation of new lamellae with their normal direction aligned along the loading direction, and in the center region of the pattern, a diamond shape scattering could be found. Generally, the appearance of the diamond shape scattering means the formation of elongated structure, such as fibrillary structure or void. Because no obvious stress whitening is observed at this strain value, thus no certain cause can be ascribed to the streak signal immediately. To figure out the origin of the weak diamond scattering, the morphology of PPna after stretching is investigated by SEM measurement. The result is provided in Figure S4. In the SEM image, the lamellae are roughly oriented with their normal along the stretching direction. And a few voids, rather than fibrillary structure, indicated by the arrow can be found, verifying that the diamond scattering in the center region of the 2D-SAXS pattern originates from voids. For PP105, the “two arcs” pattern shows up at the strain of 0.05. And the “four arcs” elliptical pattern can be found at the strain of 0.40, which is similar to that of PPna. Furthermore, the scattering in the center region starts to grow along the horizontal direction, which is greatly different from that of

PPna. The scattering on the equator provides evidence for the formation of the elongated structure, and the elongated structure is arranged with its longitude axis perpendicular to the stretching direction. With the increase of εH, the “four arcs” scattering diminishes gradually, suggesting the disappearance of the lamellae. Additionally, the scattering in the center region grows in the vertical direction, implying the direction transition of the elongated structure. At the εH of 1.22, the lamellae scattering shows up again in the form of “two lobes” at the equator, and the diamond scattering is oriented in the meridian. For PP135, the typical “two-arc” pattern existed in PPna and PP105 can be found again at the εH of 0.05. With the increase of εH, the intensity in the center region of the pattern starts to grow noticeably at the equator without the formation of the “four arcs” pattern. The disappearance of the “four arcs” pattern indicates that no lamellar tilting occurs here. The evolution of the scattering at the equator changes in a similar way as that of PP105. When εH is further increased, the direction of the scattering transfers from the equator to the meridian, and the scattering undergoes a significant thinning process. In addition, lamellae scattering can also be found at the equator. The 2D-WAXS patterns during stretching are presented in Figure 4. With the increasing of εH, the scattering of crystal planes changes in a similar trend for all samples regardless of the annealing histories. As the strain is increased, the scattering of crystal planes containing the axis of polymer chains ((110), (040), and (130) crystal planes) tends to focus their intensity on the meridian. Meanwhile, the scattering of the external two crystal planes with the index of (hk1) transforms into a fourpoint pattern, indicating the presence of two populations of lamellae in the material.16 As εH is further increased, the E


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Figure 3. Representative 2D-SAXS patterns of iPP with different annealing histories during uniaxial stretching at 75 °C. The color scale is linear and identical for all patterns. The size of the pattern is 600 × 600 pixels. The stretching direction is horizontal.

Ta as a result of imperfect lamellae melting and lamellar thickening. Upon stretching, the evolution of Lp shows a similar trend for all samples. First, Lp increases gradually due to the separation of lamellae since that amorphous phase in between has a lower modulus.7 Then Lp reaches a maximum at the εH of 0.45. As expected, the maximum Lp increases with Ta. With the further increase of εH, Lp starts to decrease which was also found by other researchers in the system of iPP,15,64,65 PCL,10 and PE.66,67 At an even larger εH, Lp reaches a plateau value, and all samples show a same Lp as εH is larger than 0.95. The decrease of Lp at moderate εH is caused by the melting− recrystallization process, which inserts newly formed lamellae into the old one. The DSC results in Figure 5b verify that Lc of the stretched samples is also the same, which confirms the occurrence of the melting−recrystallization process during stretching. After yielding, the massive fragmentation of lamellae via interlamellar slip happens and continues during the following stretching. The friction between the fragmented

scattering width of the crystal planes is broadened noticeably due to the formation of defective crystals.16,62 3.3.1. Lamellae Deformation. 3.3.1.1. Evolution of Lp. In this section, the evolution of Lp along the stretching direction is studied, reflecting the deformation of the lamellae aligned with their normal direction along the stretching direction and therefore suffer a tensile stress during stretching. It should be pointed out that some 2D-SAXS patterns exhibit elliptical “four arcs” scattering due to lamellae tilting.63 The scattering maximum is located off to the equator. By plotting the 1DSAXS curve at different azimuthal angle (see Figure S6), it is found that the intensity difference between the scattering on the equator and on the arc is only 2 au, suggesting that a large group of lamellae are still oriented with their normal direction along the stretching direction. So the definition of Lp along the stretching direction is valid during the whole stretching process. The evolution of Lp as a function of εH is summarized in Figure 5a. Without stretching, Lp increases with increasing F


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Figure 4. Selected 2D-WAXS patterns of iPP with different annealing histories during uniaxial stretching at 75 °C. The color scale is linear and identical for all patterns. The size of the pattern is 600 × 600 pixels. The stretching direction is horizontal.

Figure 5. (a) Evolution of Lp along the stretching direction as a function of εh. (b) Melting behavior of the uniaxial stretched sample.

stretching temperature is provided in Figure S7, coinciding with the proposal by Men24,68 that the recrystallization process during stretching is mediated by the formation of a

lamellae leads to an increase of the temperature of the sample,64 providing the energy for the melting. The dependence of the reciprocal of the lamellae thickness (1/Lc) on the G


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pointed out that the critical strains existing in Figure 6 coincide with the εy and εH in Figure 2. As shown in eq 8, the crystal size is determined by the peak position and the peak width of the crystal plane. The evolution of the peak position and peak width of (040) crystal plane during stretching is provided in Figure S8a,b to provide a deep insight into the structural cause of the decrease of the crystal size. 3.3.1.3. Orientation of the c-Axis of the Crystal. The orientation of the crystal can be evaluated by the Herman’s orientation factor ( f H)72

mesomorphic phase. The transition strain of 0.95, which is the same with the onset of strain hardening (see Figure 2c), indicates the end of the recrystallization process. By lamellae fragmentation and melting−recrystallization, abundant lamellae blocks are formed in the sample. The structural element inside the stretched sample can be regards as a “lamella− amorphous phase” two-phase model, where fragmented or newly formed lamellae severing as physical cross-linking points are connected by polymer chains in the amorphous phase. With the further increase of εH the polymer chains connecting the lamellae blocks are stretched, triggering the appearance of strain hardening. It should be pointed out that due to the heterogeneous distribution of tie chain/trapped entanglement in interlamellar amorphous nanolayers,69−71 the stretching of polymer chains in the amorphous phase may lead to microphase separation as proved by Lin.70 3.3.1.2. Evolution of the Crystal Size. In addition to Lp, the evolution of the crystal size from (110) and (040) crystal planes are calculated based on the Scherrer equation17 τ(hkl) =

0.9λ β cos θ

fH = 2

⟨3 cos φ 2⟩ − 1 2

⟨cos φ⟩ =

∫0

π /2

(8)

I(ψ , φ)cos 2(ψ , φ) sin(ψ , φ) dψ

∫0

π /2

I(ψ , φ) sin(ψ , φ) dψ

(9)

φ is the angle between stretching direction and the normal of the crystal, and ψ is the azimuthal angle ranging from 0 to 360°. f H = 1 means that the crystal is perfectly oriented along the stretching direction, f H = 0 means that the crystal is oriented randomly, and f H = −0.5 means that the crystal is oriented perpendicular to the stretching direction. The normal of the crystal can be estimated by the azimuthal intensity distribution of the (00l) crystal plane. However, no (00l) crystal plane can be employed directly from the 2D-WAXS pattern of iPP. For α-iPP, which belongs to the monoclinic system, Wilchinsky proposed that73

(7)

where τ(hkl) is the crystalline size determined in the direction perpendicular to the (hkl) crystal plane, λ is the X-ray wavelength, β is the full width at half-maximum of (hkl) diffraction peak, and 2θ is the peak position of the (hkl) crystal

( s ×2 λ ). In this study, a vertical cut is

plane with θ = arcsin

performed to get the peak position and peak width of (110) and (040) crystal planes. The change of the τ(hkl) as a function of εH is given in Figure 6. Interestingly, annealing has only a

⟨cos2 φa⟩ + ⟨cos2 φb⟩ + ⟨cos2 φc⟩ = 1

(10)

where ⟨cos2 φb⟩ = ⟨cos2 φ040⟩, ⟨cos2φ110⟩ = e2⟨cos2φa⟩ + f 2⟨cos2 φb⟩, e2 + f 2 = 1, and e = 0.9537; therefore ⟨cos2 φc⟩ = 1 − 0.90054⟨cos2 φ040⟩ − 1.09945⟨cos2 φ110⟩ (11)

⟨cos φ110⟩ and ⟨cos φ040⟩ could be assessed from the azimuthal intensity distribution of (110) and (040) crystal planes. The orientation of the c-axis of the crystal is given in Figure 7. In the meantime, b-axis orientation obtained from ⟨cos2 φ040⟩ is also provided. As it appears, annealing has a very weak influence on the orientation of the b-axis and c-axis. Before stretching, the orientation factor is nearly 0, which suggests the random orientation of the crystal. As the strain is increased, a transition strain of 0.45 can be found for both baxis and c-axis orientation. Beyond the strain of 0.45, the 2

Figure 6. Plots of the τ(hkl) from (110) and (040) crystal planes as a function of εH during stretching of the sample with different annealing histories.

small influence on the crystal size. The initial τ(110) is around 19.5 nm for all samples. Obviously, the evolution of the τ(110) with εH can be divided into three regions. Region I covers a strain range from 0−0.1. In this region the τ(110) decreases drastically from 19.5 to 16.2 nm. Region II starts at a strain of 0.1 and ends at 0.95, and the τ(110) decreases further to 9.0 nm. Region III covers the last part of the plot, and the τ(110) levels off to a plateau with only small variation. The τ(040) is larger than the τ(110). But its evolution trend takes place in a similar way as the latter one. Two distinct transition strains (0.1 and 0.95) can be also found. Before stretching, the τ(040) is 40 nm, and it decreases to 32 nm at a strain of 0.1. Further increase of the strain results in a further decrease of the τ(040) to 21 nm. In the last region, the τ(040) is changed only slightly. It should be

2

Figure 7. Change of the Herman’s orientation factor (f H) of b-axis and c-axis of the crystal during stretching. H


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Macromolecules orientation of the b-axis starts to decrease and the orientation of c-axis increases gradually, meaning that the c-axis of the iPP crystal starts to orient along stretching direction while the baxis orients perpendicular to the stretching direction. The critical strain for b-axis and c-axis orientation here coincides with the one observed in Figure 5a, where the long period starts to decrease from its maximum. The results here further prove the recrystallization process. Otherwise, the c-axis orientation will start to increase at a strain of 0.1 if the lamellae deformation proceeds only by intralamellar slip. 3.3.1.4. Evolution of the Crystallinity. The evolution of the crystallinity during stretching can be found in Figure 8. It is

obvious that after annealing, a higher crystallinity can be found. The evolution trend is similar for all samples with different annealing histories. Before the strain of 0.1, the crystallinity stays nearly the same, suggesting that mainly elastic deformation happens. Beyond the yield strain, a continue decrease of the crystallinity sustains until the end of stretching. The crystallinity is higher for the sample with a higher annealing temperature at any strain during stretching. The slope of the decreasing trend of the crystallinity for the samples does not change much during the whole stretching process, which is similar to the result by Lin74 when a stretching temperature between 40 and 90 °C is chosen. The critical strains for the melting−recrystallization and the strain hardening do not show up in the plot due to that the crystallinity of semicrystalline polymers is influenced by many factors including intralamellae slip, melting−recrystallization, phase transition, and pulling out of polymer chains from crystals.15,17,74,75 Combining the results from macroscopic true stress−strain curve with microscopic long period, crystal size, polymer chains orientation, and crystallinity development during stretching, a few critical strains rarely influenced by annealing are found. According to the critical strains, the lamellae deformation during stretching could be divided into four regions. Region I covers a strain range from 0 to 0.1. In this region, elastic deformation is the dominant process resulting in a steep increase of true stress. In the meantime, the long period along the stretching direction is slightly increased, which is mainly caused by the elastic elongation of the amorphous phase.7 In addition, the crystal size suffers a steep decrease, but the crystallinity stays with negligible variation. Region II starts

Figure 8. Evolution of the crystallinity as a function of the Hencky strain.

Figure 9. Logarithm of the corrected scattering intensity as a function of s2 at different strains of PP120: (a) covers Hencky strains from 0.16 to 0.62 (formation of type II voids) and (b) covers Hencky strains from 0.62 to 1.16 (direction transition for type II voids). For clarification, the plots are vertically shifted. (c) Radius of gyration (R) as a function of the Hencky strain via the slope of (a) and (b). (d) Critical Hencky strain for the void formation and void direction transition of iPP with different annealing history during uniaxial stretching at 75 °C. I


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Figure 10. Center fitting and modeling of a scattering pattern by the sum of the voids signal and the matrix signal according to Guinier’s approximation. s12 is the stretching direction.

PP120 as a function of εH. Once the void is formed, R should be larger than 0 if the intensity correction is performed in the streak direction, and R will be increased during the growth of voids; see the plot of the black squares in Figure 9. Therefore, the εH where R > 0 is used as the critical strain for void formation. As the direction of voids is changed, R should be larger than 0 in the direction transversal to the initial direction; see the plot of the red circles in Figure 9c. The critical strains for voids formation and voids direction transition are summarized in Figure 9d. In Figure 9d, two types of void formation can be confirmed. Type I exists in the sample with Ta lower than 90 °C, of which the critical strain for void formation is 0.73, 0.75, and 0.68 for PPna, PP75, and PP90. The longitudinal size of the voids is along the stretching direction once the voids is formed. Type II can be found in the sample with Ta higher than 105 °C, of which the longitudinal direction of the voids is perpendicular to the stretching direction once voids are formed and transfers toward the stretching direction at a larger strain. The critical strain of type II void formation decreases slightly from 0.31 to 0.23 as Ta is increased from 105 to 135 °C. Meanwhile, the critical strain of the voids direction transition is around 0.66. 3.3.2.2. Evolution of the Voids Size. To calculate the size of the void, the scattering intensity in the blanked region of 2DSAXS pattern is extrapolated and fitted by a sum of two 2DGaussian cup functions

at 0.1 and ends at 0.45. In this region, the deformation of lamellae occurs mainly by intralamellar slip. The lamellae are fragmented into blocks without orientation. The friction between the fragmented lamellae during intralamellar slip provides the energy of lamellae melting. Region III has a strain range from 0.45 to 0.95. In this region, recrystallization happens, and the distinct polymer chains orientation appears because the newly formed lamellae are aligned with their c-axis along the stretching direction. The recrystallization process is mediated by the formation of a mesomorphic phase.24 The long period of newly formed lamellae depends only on the stretching temperature. Region IV covers all the strain above 0.95. The long period and the crystal size stay nearly unchanged, suggesting that the recrystallization process is terminated. The newly formed lamellae serve as the anchoring point for the polymer chains in the amorphous phase. The tightening of the polymer chains in the amorphous phase in between the lamellae blocks gives rise to the strain hardening behavior. 3.3.2. Cavitation Behavior. 3.3.2.1. Onset Strain of the Voids Formation and the Voids Direction Transition. The evidence of the void formation as shown in Figure 3 is the appearance of a streak or elongated elliptical scattering depending on the annealing temperature. In both cases, the scattering of voids is quite weak at the very beginning. In fact, the scattering in the center region of the 2D-SAXS patterns is made up of two parts: the heterogeneous elongated one from the voids and the homogeneous one from the matrix. Therefore, to extract the void scattering out from the pattern, the intensity correction of Ihv(s) = Ih(s) − Iv(s) or Ivh(s) = Iv(s) − Ih(s) is employed, depending on the direction of the void. Ih(s) and Iv(s) represent the plot of the scattering intensity as a function of the scattering vector in horizontal and vertical cut, respectively. Meanwhile, at the small-angle region of the 2DSAXS pattern, the scattering intensity as a function of scattering vector should obey Guinier’s law, which is given by 2

2

2 2 2

Ic(s) = I0ρ V exp( −4π s R /3)

I(s) = pv0 exp( −pv1 s 2 − pv2 cos(2ψ )s 2 − ... − pvn cos(2ψ (n − 1))s 2) + pm0 exp( −pm1 s 2 − pm2 cos(2ψ )s 2 − ... − pmn cos(2ψ (n − 1))s 2)

ψ = arctan

i j

(13)

(14)

i and j define the pixel position in 2D-SAXS patterns with respect to the beam center. The first Gaussian cup describes the voids and the second Gaussian cup describes the scattering of the matrix with slight anisotropy. p with subscript is the fitting parameter. The extrapolation and fitting process are realized by a self-written subroutine on PV wave.63 The fitting procedure is illustrated in Figure 10 and can be also found in

(12)

where Ic(s) is the corrected scattering intensity, I0 is the scattering intensity at the scattering vector of 0, ρ is the electron density difference, V is the volume of scattering, and R is the gyration radius.76 Figures 9a,b show the evolution of the corrected intensity in horizontal and vertical directions of J


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0.8 to 1.6. PP75 and PP 90 show a similar trend, but the slope decreases from 187 nm/1 (PPna) to 121 nm/1 (PP90). For PP105, PP120, and PP135, S∥ increases from 35 to 82 nm and S⊥ is around 198 nm in the small strain range. During the void direction transition, the extrapolation and fitting process does not work because no obvious streak signal could be recognized in the 2D-SAXS pattern. So no information about the void size is provided in the strain region of 0.4−0.8. As the void direction is totally transferred, S∥ grows from 116 to 216 nm for PP105, from 111 to 195 nm for PP120, and from 99 to 157 nm for PP135. The slope of the plot decreases from 111 nm/1 to 105 nm/1 and then further to 98. In addition, in the large strain range, S⊥ is nearly the same for all samples, and it decreases slightly from 68 to 55 nm. From Figure 11 it can be found that S∥ decreases with the increasing of annealing temperature, which is also found by Men.79 In addition, the slope of S∥ as a function of the strain decreases continually from 187 to 98, suggesting that a larger energy barrier needs to be overcome as the annealing temperature is increased. The possible reason for this lies in the difference of the number of voids per volume, which will be explored in the following part. 3.3.2.3. Scattering Invariant of the Voids. The integrated scattering intensity, as a measure of the scattering invariant (Q) of the system, is related to the volume fraction of the dispersed phase (namely the void in this work) and the electron density contrast between the heterogeneities and the surrounding matrix. In this work, the void can be regarded as the dispersed phase. Q is given as

ref 77. Via this procedure, the scattering of the void can be extracted from the initial 2D-SAXS pattern. According to Ruland’s streak method,47,78 the integral width of the azimuthal profile (Bobs) from the void at specified scattering vector should be Bobs (s12) =

1 I(s12 , 0)

∞

∫−∞ I(s12 , s3) ds3

(15)

when the voids are perfectly oriented. s12 and s3 are the scattering vector in the stretching direction and perpendicular to the stretching direction, respectively. The size of the void (Sv) should be 1 Sv = Bobs (s) (16) From eq 13, we know for the perfectly oriented voids I(s , ψ ) = pv0 exp( −pv1 s 2 − pv2 cos(2ψ )s 2)

(17)

Therefore, the void size along the stretching direction (S∥) and the void size perpendicular to the stretching direction (S⊥) should be S = S⊥ =

pv1 + pv2 π

(18)

pv1 − pv2 π

(19)

The evolution of the void size is shown in Figure 11. For PPna, S∥ increases from 190 to 339 nm as the strain increases from

Q = 2π 2VmVv(ρm − ρv )2 Q=

1 2

∞

∫−∞ ∫0

(20)

∞

I(s12 , s3)s3 ds12 ds3

(21)

where Vm and Vv are the volume ratio of the matrix and the void and ρm and ρv are the electron density of the matrix and the void. Because ρv = 0, eq 20 is rewritten into Q = 2π 2(1 − Vv)Vvρm 2

(22)

Figure 12 plots the change of Q as a function of εH. Apparently, with the increase of Ta Q is greatly enhanced, especially for PP105, PP120, and PP135, which means that the volume fraction of voids is greatly increasing. Because of that the size of the voids is decreased as shown in Figure 11, it can be inferred that the number of voids per volume is increased

Figure 11. Evolution of (a) the void size along the stretching direction (S∥) and (b) the void size perpendicular to the stretching direction (S⊥) of iPP with different annealing histories during uniaxial stretching at 75 °C.

Figure 12. Evolution of scattering invariant (Q) of iPP with different annealing histories during uniaxial stretching at 75 °C. K


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Figure 13. Morphology of PPna with εH of 1.5 and PP135 with εH of 0.25 and 1.5. The yellow arrows are referred to the void. Figures inserted in the left corner showing the sample geometry could provide the information about the stretching direction (indicated by the red arrow). The images in the second row are the enlargement of the square region in the images in the first row.

with annealing. As εH is larger than 1.35, a slight decrease shows up for PP105 which is caused by the thinning of voids. For PP135, the decrease of Q as εH exceeds 1.25 is probably caused partly by the void coalescence80 and partly by the fact that the size of the void exceeds the detection resolution of SAXS. 3.3.2.4. Morphology of Voids. The morphology of PPna with εH of 1.5 and PP135 with εH of 0.25 and 1.5 are provided in Figure 13. Two types of voids can be clearly seen. For PPna with εH of 1.5, a few voids with their longitude direction along the stretching direction can be found. For PP135 with εH of 0.25, the number of voids is much larger than that in PPna with εH of 1.5. In addition, the longitude direction of the void is mainly perpendicular to the stretching direction. The average sizes in the long axis and short axis direction are 280 and 80 nm, which fits the result in Figure 11. For PP135 with εH of 1.5, abundant crazes consisting of voids and fibrillary links separating voids can be found. The direction of the longitude of the voids is transferred to the stretching direction. The SEM images in Figure 13 coincide well with the results obtained from SAXS measurement where a smaller voids size and larger voids number exist in PP135 compared with PPna. 3.4. Discussion. On the basis of SAXS and WAXS results, the critical strains for lamellae deformation as well as void formation and growth of iPP with various annealing histories are summarized in Figure 14. The relationship between lamellae deformation and voids formation is also discussed here. First, the lamellae deformation is revealed to proceed on the time scales of inter- and intralamellar slip, fragmentation, and melting−recrystallization separated by three critical strains which were rarely influenced by annealing. Strain I (0.1) marks the end of elastic deformation and the onset of intralamellar slip. Strain II (0.45) signifies the start of the recrystallization process, where the long period in the stretching direction begins to decrease from its maximum and the polymer chains in the crystal start to orient along stretching direction. The energy for the melting arises from the friction between the fragmented lamellae produced by interlamellar slip. Strain III (0.95) denotes the end of the recrystallization process. Beyond the strain of 0.95, the long period of the lamellae and the crystal size remain nearly unchanged. The newly formed

Figure 14. Critical strains for lamellae deformation as well as voids formation and growth for iPP with various annealing histories during uniaxial stretching at 75 °C.

lamellae serve as anchoring points for polymer chains in the amorphous phase during further stretching. The extension of the polymer chains between the lamellae triggers the strain hardening behavior. Second, annealing significantly intensifies the formation of cavities by advancing the critical strain of voids formation and increasing the number of voids. For those samples annealed at a temperature lower than 90 °C, voids are formed between strain II and strain III. The voids are oriented in the stretching direction once they are formed. For samples annealed at a temperature higher than 105 °C, voids are formed between strain I and strain II. In this case the voids are initially oriented with their longitude axis perpendicular to stretching direction and then transferred along the stretching direction via small void coalescence. The existence of two types of voids might be related to very different local stresses in the amorphous phase. For the sample with an annealing temperature lower than 90 °C, voids are formed between strain II and strain III. During void formation the dominant lamellae deformation process is lamellae melting−recrystallization. Therefore, the critical strain for void formation shows no obvious dependence on lamellae thickness because most of the lamellae have been fragmented via intralamellar slip. In addition, as evidenced in Figure 7, the L


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hand, lamellae deformation was revealed to occur on the time scale of elastic deformation, intralamellar slip, and melting− recrystallization separated by three critical strains which were rarely influenced by annealing. On the other hand, annealing significantly intensified the cavitation behavior by decreasing the critical strain for void formation and increasing the number of voids. Additionally, void formation influences neither the critical strain values for lamellae deformation nor the final long period, polymer chains orientation, or the crystal size. The final long period, polymer chains orientation in the crystal, and the crystal size were determined only by the stretching temperature through the melting−recrystallization process. Because the recrystallization process is controlled mainly by stretching temperature, further work on the influence of stretching temperature on lamellae deformation and cavitation behavior is in progress. The work will be helpful to understand the relationship between the microstructure evolution and the mechanical properties of semicrystalline polymers during stretching.

polymer chains in the crystal are oriented along the stretching direction. So the voids are induced in an oriented network in which the crystals serve as the skeleton and the polymer chains in amorphous phase connect the crystals together. The amorphous phase is subjected to a strong constraint force in the direction perpendicular to the stretching direction; that is why the voids are oriented along the stretching direction once the voids are formed. For the samples with an annealing temperature higher than 105 °C, the critical strain for type II void formation is located between 0.1 and 0.45. By annealing the lamellae are thicker and have a higher interlamellar slip resistance. In addition, the higher αc-relaxation temperature shown in Figure 1 indicates a higher rigidity of polymer chains connecting the lamellae and an amorphous phase. Therefore, the connection between the amorphous phase and the lamellae is stronger. The extension stress is better transmitted to the amorphous phase. Because of the restriction of the lamellae, type II voids are formed initially transversal to the stretching direction. As the strain increases, the voids come in contact with other ones nearby during the growth and then coalesce with each other into larger voids, which were verified by Selles with the help of the magnified holotomography technique.9 With the further increase of the strain, the lamellae are fragmented into blocks and oriented fibrillary structures are formed; hence, the constraint force in the direction perpendicular to the stretching direction is enlarged. Therefore, the voids direction transfers finally to the stretching direction. During the further stretching process, the voids grow in the stretching direction and become thinner in the transverse direction. Third, the advancing of the voids formation by annealing influences neither the critical strains for lamellae deformation nor the final long period, the orientation of polymer chains, or the crystal size. This is different from the results of the group of Rozanski.16,40,81,82 By controlling the state of the amorphous phase, a cavitation/noncavitation iPP model system with an identical lamellae structure was obtained by Rozanski. They demonstrated that the reduction of the crystallites of cavitating iPP was approximately 5%−10% greater than in the case of the noncavitating system, suggesting that the presence of cavities clearly facilitates generating instability and increases the intensity of the lamellae fragmentation process. The orientation degree of polymer chains (at the identical value of the local strain) is significantly higher in the case of cavitating iPP because smaller crystallites present in the cavitating material will easily undergo tensile-induced rotation around the deformation direction, in contrast to the case of a noncavitating material. Therefore, the key point is the question about factors contributing to the increase of the orientation of polymer chains in the crystal: rotation of fragmented crystallites or newly formed crystals by recrystallization with the polymer chains aligned along stretching direction. In our case, the recrystallization process is verified to take place in the strain range of 0.45−0.95. Consequently, the final long period, the orientation of polymer chains in the crystal, and the crystal size were controlled by the recrystallization process, which is scarcely influenced by void formation.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00642.

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Figures S1−S9 (PDF)

AUTHOR INFORMATION

Corresponding Author

*(B.C.) E-mail: [email protected]; [email protected]. ORCID

Baobao Chang: 0000-0003-0886-325X Stephan Roth: 0000-0002-6940-6012 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to DESY for beam time within the project II-20150042. B. Chang is grateful for the Grant by China Scholarship Council.

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REFERENCES

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4. CONCLUSION In this work, the lamellae deformation and cavitation behavior of annealed isotactic polypropylene during uniaxial stretching were comprehensively investigated by in situ synchrotron small-angle X-ray and wide-angle X-ray scattering. On one M


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