Changes of Crystal Structure and Morphology during Two-Way Shape

Article pubs.acs.org/Macromolecules

Changes of Crystal Structure and Morphology during Two-Way Shape-Memory Cycles in Cross-Linked Linear and Short-Chain Branched Polyethylenes Igor Kolesov,*,† Oleksandr Dolynchuk,† Dieter Jehnichen,‡ Uta Reuter,‡ Manfred Stamm,‡,§ and Hans-Joachim Radusch† †

Center of Engineering Sciences, Martin Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germany Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Straße 6, D-01069 Dresden, Germany § Technische Universität Dresden, 01062 Dresden, Germany ‡

ABSTRACT: The present work comprehensively describes the formation of crystal structure and morphology of crosslinked linear and short-chain branched polyethylenes during their nonisothermal crystallization under constant mechanical load. The crystalline phase of linear as well as medium branched polyethylenes with about 30 CH3/1000Cformed as a result of the crystallization process under load and accompanied by an anomalous elongationis represented by lamellae oriented perpendicular to the stretch direction with tilted folded chains. In contrast, highly branched polyethylene with about 60 CH3/1000C processed under similar conditions contains only small crystallites, whose c-axis is oriented parallel to the applied force. Experimentally determined crystallinity, type of crystalline structure as well as size and orientation of the crystallites were compared with theoretical predictions got by modeling the two-way shape-memory (SM) behavior. Qualitative and quantitative characteristics of the two-way SM effect and the experimental curves of temperature dependent strain as well as the features of generated crystalline structures are in good agreement with the theory.

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INTRODUCTION Already more than 60 years ago Flory1,2 and Mandelkern3,4 had predicted and observed the anomalous elongation of a polymer network accompanying its crystallization from the oriented “molten” state. Such an anisotropic state of “molten” polymer network, e.g., of cross-linked polyethylene, characterized by a marked orientation of the molecular chains, can be caused by the application of sufficiently high uniaxial extension.3,4 The surprising macroscopic elongation of a predeformed polymer network taking place during its crystallization under load5 (at constant force) was denoted as “anomalous” due to discrepancy between this phenomenon and the simultaneously observed logical increase of the storage modulus E′ as shown below. Recently, Mather and co-workers have reported on the socalled two-way shape-memory effect (SME) in polycyclooctene/trans-polyoctenamer (PCO/TOR) cross-linked by dicumyle peroxide as well as in a chemical/physical double-network on the basis of poly(ε-caprolactone) (PCL) and polyhedral oligosilesquioxane (POSS), respectively.6,7 This dual two-way SME is revealed as the considerable increment and decrement of strain in the course of nonisothermal crystallization and subsequent melting under load, respectively.6,7 In addition to the dual two-way SME, a two-way triple-shape memory effect, which is accompanied by the appearance of two strain steps during both nonisothermal crystallization and melting under load, has been detected and described by Lendlein and co© XXXX American Chemical Society

workers for copolymer networks prepared by cross-linking of two star-shaped precursors of poly(ω-pentadecalactone) and PCL having different melting and crystallization temperatures.8 More recently, Pandini et al. have investigated the dual two-way SME of cross-linked PCL.9,10 Both the anomalous stress-induced elongation of a polymer network initiated by the nonisothermal crystallization during cooling under load and the expected contraction of a crosslinked sample during heating under the same load triggered by melting of the oriented crystalline phase are the physical background of the two-way SME, which was observed and described in aforementioned works.5−10 The performance of SME in cross-linked crystallizable polymers strongly depends on the properties of the covalent polymer network and the crystalline structure, which has to be generated in the specimen during isometric programming or shape-memory (SM) nonisothermal creep. In particular, melting and crystallization temperatures (Tm and Tc) serve as the SM switching temperatures, whereas cross-link density and crystallinity of network are responsible for the magnitude of elastic forces produced by loading and for the ability to store these elastic forces, respectively.5−11 Received: January 16, 2015 Revised: June 19, 2015

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DOI: 10.1021/acs.macromol.5b00097 Macromolecules XXXX, XXX, XXX−XXX

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EXPERIMENTAL SECTION Materials and Processing. The PEs studied in the present work are commercially available products (Dow Chemical, Schkopau, Germany), namely, high-density polyethylene (HDPE) and two metallocene-catalyzed homogeneous ethylene-1-octene copolymers (EOC) with approximately 30 and 60 hexyl branches per 1000 C (EOC30 and EOC60, respectively). The PEs were cross-linked by 2,5-bis(tert-butylperoxy)-2,5dimethylhexane (DHBP) at 463 K. The true DHBP content in all samples determined by thermogravimetric analysis (TGA, Mettler-Toledo) points to lower true values as compared to desired ones. It should be noted that differences between true and desired values increase significantly with increasing crystallinity of polymers. Few relevant parameters of the materials used are given in Table 1. The stretched samples were prepared via crystallization during cooling under load with initial stress (σini) of 1 MPa in case of HDPE (residual strain at 273 K is about 109%), 0.6 MPa in case of EOC30 (residual strain at 273 K is about 104%), and 0.3 MPa in case of EOC60 (residual strain at 273 K is about 70%) using specific thermomechanical experiment, which is described in the section TwoWay SM Behavior. Simultaneous DMTA and SM Tests under Constant Load. Dynamic-mechanical thermal analysis (DMTA) of specimens loaded with a static force has been carried out in tensile mode using a mechanical spectrometer with measuring head Mark III (Rheometric Scientific Inc., Piscataway, NJ, USA). The miniature tensile test specimens shaped as shouldered test bars with cross-sectional area of 2.0 × 0.5 mm2 and initial clamps distance between 6 and 12 mm were tested at the frequency of 1 Hz during the thermal loops at heating and cooling rates of 2 K·min−1. The initial static stress value laid between 0.3 and 1.2 MPa. The combination of low dynamical deformation with amplitude of 0.1% along with relatively high static load enables to obtain simultaneously the temperature dependencies of dynamical storage modulus E′ and of macroscopic strain induced by static load and reached some hundred percent. Thus, the thermal loops of storage modulus E′ as well as SM creep and recovery strain in the first cooling and second heating runs, respectively, were measured simultaneously. Differential Scanning Calorimetry (DSC). Melting and crystallization behavior of PEs under study was investigated with a power compensation DSC 7 equipped with the liquid nitrogen accessory CCA-7 (PerkinElmer LAS GmbH, Rodgau, Germany) for controlled cooling at a rate of 10 K·min−1 and heating at a rate of 20 K·min−1. The DSC data were collected for two sets of samples of each cross-linked polyethylene: the first set was taken from undeformed PEs in their original permanent shapes, whereas the second set was cut from the drawn samples. Note that initial stress is also denoted according to Gedde as nominal stress (σ0N = σini).17 Each drawn sample was sealed in 20 mL aluminum pan between two thin films of polytetrafluoroethylene (PTFE) in order to ensure free mobility of a sample during recovery of its original shape at heating. The sample mass was about 8 mg. Heat-flow rate raw data were corrected for the instrumental asymmetry and converted into temperature dependencies of apparent specific heat capacity cp(T). The measured cp(T) values in conjunction with theoretical values of specific heat capacity for crystalline and amorphous polyethylene taken from the advanced thermal analysis system (ATHAS)18 was utilized for the calculation of

In contrast to the irreversible one-way SME, the invertible two-way SME can be reproduced as long as a sample is loaded and the temperature change is sufficient to cause the subsequent crystallization and melting of a sample. Although some specific investigation has been performed in that field already, there is still a lack in experimental study of the physical background of the two-way SME. A novel theoretical approach, which is able to explain and describe the two-way SME in cross-linked crystallizable polymers, has been derived recently by Dolynchuk et al.12,13 The proposed theory was developed on the basis of a threeelement mechanical model taking into consideration the viscoelastic deformation of entangled slipping macromolecules and crystallization/melting of a covalent polymer network as two basic mechanisms involved in SM performance.12,13 It is postulated that crystallizing/melting of the covalent network plays a key role in the two-way SME and is responsible for the anomalous stress-induced elongation of a sample during nonisothermal crystallization at cooling. On the basis, partly, of the theory of stress-induced crystallization of polymer networks under isometric and isothermal conditions proposed by Gaylord,14,15 a thermodynamic description of the behavior of covalent networks has been performed, which allows calculating the free energy change of the network deformed under constant load (force) and cooled down below the crystallization temperature at a constant cooling rate, i.e., under nonisometric and nonisothermal conditions, respectively. The theoretical approach enables the prediction of crystalline structure and orientation of the crystals in case of different number of chain links. It has been determined that the anomalous elongation is possible when the orientation of crystal chains formed at cooling is parallel to the direction of external load or makes a relatively small angle with it. The conclusions of the developed theory were successfully confirmed by means of fitting the temperature dependent strain in the course of two-way SME in high-density polyethylene (HDPE) experimentally obtained for the first time.12,13 However, the theoretical predictions about the type of crystalline structure, crystal thickness, and crystal orientation are still needed to be experimentally verified. In this context, the aim of present work is to test three different polyethylenes (PEs), namely, HDPE and two shortchain branched low density PEs, characterized by different crystallization/melting temperatures and crystallinities for twoway SME in order to observe and describe the influence of the above-mentioned characteristics on the SM performance. Furthermore, a comprehensive investigation and description of the crystal structure and morphology formed during the nonisothermal crystallization of loaded cross-linked PEs is intended, namely, the determination of crystallinity, type of supermolecular and crystalline structure, its size and orientation by means of differential scanning calorimetry, transmission electron microscopy as well as wide- and small-angle X-ray scattering. This investigation aims for the experimental elucidation of the structural-physical background of the aforementioned anomalous elongation. The modeling of twoway SM behavior in case of short-chain branched PEs on the basis of the recently presented theoretical approach as well as the comparison between the experimentally obtained characteristics of crystal morphology and their theoretical prediction shall be performed as well. B


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measured by means of test apparatus MI 21,6 (Göttfert). bobtained by means of DSC11,16 cobtained by means of swelling and tensile tests11,16

enthalpy-based crystallinity as a function of temperature χc(T) on the basis of the two-phase model as described by Mathot et al.19 Transmission Electron Microscopy (TEM). The highresolution TEM images of two sets of samplesslowly crystallized undeformed samples and drawn samples crystallized after cooling under load during two-way SME (see section Two-Way SM Behavior)were obtained on a LIBRA200 MC (Carl Zeiss Microscopy GmbH, Oberkochen, Germany). Sample preparation was carried out at ultramicrotome EM UC6/FC6 (Leica Microsystems GmbH, Wetzlar, Germany). First step for sample preparation was the manufacture of cross sections of the undeformed and drawn specimens at 123 K under dry nitrogen atmosphere. Afterward cross sections were stained in RuO4 vapor for 24 h and then degassed for further 24 h. Finally, the ultrathin sections were sliced at 123 K under dry nitrogen atmosphere and transferred for image acquisition onto copper grids coated with carbon film. The place of sampling of drawn PE samples is shown in Figure 1.

Figure 1. Schematic representation of the exposure of the drawn specimens to X-ray beam during WAXS and SAXS as well as the preparation of drawn specimens for TEM investigation.

Wide- and Small-Angle X-ray Scattering (WAXS and SAXS). WAXS and SAXS investigation of two sets of samplesslowly crystallized undeformed samples and stretched samples crystallized after cooling under load during two-way SME (see section Two-Way SM Behavior)were carried out at a 3-fold pinhole system (self-construction) with rotating anode (Rigaku Corporation, Tokyo, Japan) using Cu Kα radiation (λ = 0.15418 nm), monochromatized by primary confocal multilayer optic (Max-Flux Optics, now: Rigaku Corporation, Tokyo, Japan) and area detection system MarCCD (now: Rayonix, L.L.C., Evanston, IL, USA). The samples were exposed to X-rays as shown in Figure 1. The results will be discussed (see section Results and Discussion) based on 2D scattering patterns. Intensity plots I(q) were created by means of sectorial integration over ±5° to the orientation on equator in case of WAXS and 360°-integration in case of SAXS (orientation-averaged). The scattering curves of SAXS are displayed as I(q)·q2 data vs scattering vector q = 2π/d without background subtraction and I(χ) vs azimuthal angle χ, respectively. Two-Way SM Behavior. SM investigations were carried out in tensile mode using a mechanical spectrometer measuring head Mark III (Rheometric Scientific Inc., Piscataway, NJ, USA). The samples of cross-linked HDPE, EOC30, and EOC60 shaped as shouldered test bars with cross-sectional area 2.0 × 1.0 mm2 were tested during the specific thermomechanical experiment at an initial clamps distance of 10 mm. The HDPE samples were loaded by the initial/nominal stress (σini/σ0N) of 1 MPa, EOC30 and EOC60 specimens were loaded by applying the σini stress of 0.6 and 0.3 MPa,

a

110 140, 270 150, 190 ∼0 ∼30 ∼60 4.3 2.3 2.5 3.0 5.0 4.4 HDPE EOC30 EOC60

10.1 17.7 15.9

2.5 4.2 3.4

405 369 332

955 900 870

99 64 87

cross-link density vc̅ c (mol·m−3) degree of branching (CH3/1000C) polydispersity M̅ w/M̅ n mass-average molecular mass M̅ w (kg·mol−1) Tmb (K) density (kg·m−3) 403 K/5.0 kg 463 K/5.0 kg 463 K/2.16 kg designation

melt-flow index (MFI)a (dg·min−1)

Table 1. Designations as well as some physical and molecular parameters of used PEs

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C


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Figure 2. Simultaneously measured temperature dependencies of corrected storage modulus E′cor as well as of thermally induced creep/recovery strain ε of unconstrained and loaded samples of nearly linear (a) and short-chain branched PEs (b−d) with different degree of branching and crosslink density νc.

respectively, at the highest temperature of Thigh of 438 K in case of HDPE, 413 and 393 K in case of EOC30 and EOC60, correspondingly. The samples under constant load were cooled down to the lowest temperature Tlow of 273 K at an average cooling rate of 2 K·min−1, thermally equilibrated for 5 min, and then heated to the temperature Thigh at heating rate of 2 K· min−1. The strain as a cyclic function of temperature was measured during the thermo-mechanical experiment. It is well-known that some differences exist between the measured temperature of specimen and its true value in each cooling/heating tensile experiment using a mechanical spectrometer. In order to correct this undesired effect, a special calibration sample of polyamide 6 with embedded thermocouple was prepared. The sample was tested during conventional DMTA experiment under thermal conditions described above. Thereby, two temperature sets were registered and their difference versus measured temperature was approximated by a polynomial function. The received correction function was used to calculate the true temperature of specimens on the basis of sensor temperature values collected in the course of two-way SM tests.

(ε) and storage modulus (E′) of cross-linked linear HDPE, medium- and high-branched EOC30 and EOC60, respectively, performed under constant load, exhibit (Figure 2) the distinct occurrence of the anomalous macroscopic elongation (thermally induced SM creep) along with the stepwise increase in E′ during nonisothermal crystallization at cooling and the pronounced contraction (thermally induced SM recovery) along with the stepwise decrease in E′ during subsequent melting at heating. In contrast, the same unconstrained polymer networks reveal a weak decrease and increase in strain during nonisothermal crystallization at cooling and melting at heating, respectively. The values of E′ were corrected taking into consideration the change of sample length and correspondingly of the crosssectional area. Assuming that polymer networks in the first approximation are incompressible, i.e., the sample volume calculated as the product of its length and cross-sectional area is constant, the corrected E′ value (E′cor) can be obtained by means of simple transformation of measured E′ values (E′meas): E′cor = E′meas × (l0 + Δl)/l0, where l0 and Δl are initial length and absolute elongation/contraction of a sample, respectively. As well seen from Figure 2, the stepwise elongation and E′ increase at cooling of cross-linked PEs occur at the same temperatures lying in the range of crystallization. Such behavior depicts directly that just crystallization under load causes the anomalous elongation of polyethylene networks. The comparison of corrected temperature dependencies of E′ obtained for loaded and unconstrained samples allows concluding that all cross-linked PEs under load demonstrate higher values of crystallization and melting temperatures (Tc and Tm), higher E′ values in entire temperature range, as well as higher E′

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RESULTS AND DISCUSSION Simultaneous DMTA and SM Test under Constant Load. The clear manifestation of invertible two-way SME can be observed obviously in each crystallizable covalent polymer network if suitable values of cross-link density (νc) and load (σini) are employed.5−10 The results demonstrated in Figure 2 prove that the linear and short-chain branched PEs cross-linked by peroxide are not an exception to this statement. The simultaneously measured temperature dependencies of strain D


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Figure 3. Apparent specific heat capacity (a, b) and enthalpy-based crystallinity as functions of temperature (c, d) at heating and cooling (cooling runs preceded the second heating) of undeformed samples of cross-linked HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3) and their stretched samples crystallized during cooling under load.

Table 2. DSC Peak Temperatures of Melting and Crystallization as Well as Enthalpy-Based Crystallinity of Undeformed or Stretched Samples of Cross-Linked HDPE, EOC30, and EOC60 Crystallized under Load during Cooling Stage of Two-Way SME Cycle crystallinity χc at 298 K (%)

melting temperature Tm (K) samples

type

1st heating run

2nd heating run

crystallization temperature Tc (K)

1st heating run

cooling run

2nd heating run

HDPE

undeformed drawn undeformed drawn undeformed drawn

− 397.2 − 361.7 − 332.1

391.4 395.1 360.5 360.6 329.7 330

378.3 379.2 343 343.2 311.1 310.8

− 54.3 − 30.8 − 13.7

49.7 50.9 27.8 27.9 9.9 9.7

50.4 51.8 29.6 29.3 12.4 12.3

EOC30 EOC60

crystallization behavior of stretched samples of cross-linked PEs prepared by crystallization during cooling under load in comparison with undeformed samples as reference objects. Enthalpy-based crystallinity as a function of temperature calculated on the basis of DSC curves is depicted in Figure 3, parts c and d. Table 2 lists the melting and crystallization temperatures obtained as peak temperatures of corresponding DSC traces as well as values of crystallinity at room temperature (298 K). Note that the endothermic melting process measured in the first heating run reflects the preceding mechanical treatment and thermal history of specimens, whereas in the second heating run the shape of DSC melting trace is affected only by conditions of nonisothermal crystallization in previous cooling run.23−26 The first heating runs of drawn cross-linked EOC30 and EOC60 samples exhibit a minimum followed by a maximum arising in the temperature range between approximately 280 and 325 K and caused by annealing at room temperature during storage of prepared samples, as it was

increment and decrement during nonisothermal crystallization and melting, respectively. The described behavior can be explained as a result of the reduction of entropy of polymer chains in the course of uniaxial extension after application of a constant load during two-way SME and,20 consequently, as a result of the initial ordering of network chains already in the amorphous phase that contributes to a formation of crystal precursors and leads to the crystallization at higher temperature similarly to quiescent flow-induced crystallization of entangled polymer melt (see also next section).21 It is well-known that the crystalline phase, which is crystallized at higher Tc, will melt at higher Tm as well.22 Moreover, the lamellar orientation and the formation of crystalline texture results in significant increase in E′ (see next sections Melting and Crystallization Behavior as well as Crystal Morphology).17 Melting and Crystallization Behavior. Temperature dependencies of apparent specific heat capacity cp(T) shown in Figure 3, parts a and b, allow discussing the melting and E


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Figure 4. High-resolution TEM images of undeformed cross-linked HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3) (a−c) and of their samples uniaxially stretched during nonisothermal crystallization under load (d−f). Residual strain amounts about 100% for HDPE and EOC30 and about 70% for EOC60. White arrows in images (d−f) indicate the stretch direction.

crystallization under load in the course of SM creep are depicted in Figure 4. As shown, the crystalline phase of crosslinked HDPE and EOC30 is represented by lamellae, which are well distinct in HDPE and thin, short, and substantially distorted in EOC30. These lamellae are randomly oriented in undeformed samples (Figure 4a,b) and oriented nearly perpendicular to the loading force direction in stretched specimens having residual strain of about 100% (Figure 4d,e). The received TEM images allow estimating the lamellae thickness that amounts roughly 12 nm for both undeformed and drawn cross-linked HDPE. At the same time, drawn and undeformed samples of cross-linked EOC60 (Figure 4c,f) contain small crystallites, whose size and orientation cannot be evaluated on the basis of obtained TEM images. In this connection, it should be noted that supermolecular structure/ morphology of uncross-linked and undeformed short-chain branched PEs has been investigated earlier as a function of degree of branching by means of TEM and atomic force microscopy (AFM).25,27−29 The results of these investigations have revealed that in the case of linear, slightly branched, and partly medium-branched PEs especially if samples were slowly crystallized or well annealed, well organized and laterally extended lamellae (folded-chain crystals) can be seen clearly with a tendency to formation of lamellae stacks. With increasing degree of branching and crystallization rate the described supermolecular lamellar structure is more and more replaced with smaller, poor-faceted, and randomly oriented lamellae as well as by so-called bundle-like crystals or fringed-micelles structure containing extended-chain crystals.27−29 In the light of these results, it can be assumed that the changes of crystal morphology with increasing degree of branching in crosslinked PEs reveal the trend similar to that was demonstrated for

already shown for uncross-linked EOCs and other random copolymers of ethylene with α-olefins especially with high degree of branching.19,23−26 As seen from Table 2 and Figure 3, melting temperatures Tm and crystallinity in entire temperature range of preliminarily drawn cross-linked HDPE, EOC30, and EOC60 in the first heating run are higher as compared to their values for undeformed samples. That is a result of the initial ordering of network chains in the amorphous phase as it was explained in the previous section. As is well-known, the crystalline phase, which is crystallized at higher Tc, will melt at higher Tm as well.22 Such an explanation is supported by the crystallization behavior at cooling (Figure 3b) of previously melted samples during the first heating run. In spite of the fact that stretched samples were placed between two thin films of PTFE as described in the Experimental Section in order to ensure free recovery of their permanent shapes during the first heating run, crystallization temperatures Tc of previously melted samples are higher than Tc of undeformed specimens, especially for HDPE. This is apparently caused by the incomplete recovery of the initial shape after processing. The second heating runs following the cooling of these samples are also characterized by higher melting temperatures Tm. As it is seen from Table 2, the enthalpy-based crystallinity of PEs under study is sufficiently different. Furthermore, the deformation of samples results in higher crystallinity values as shown in Figure 3, parts c and d, as well as in Table 2 that evidence the higher ordering of the stretched samples and is more distinct for HDPE. Crystal Morphology. The TEM images of cross-linked HDPE, EOC30, and EOC60 samples prepared both during slowly nonquiescent crystallization and during nonisothermal F


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Macromolecules uncross-linked PEs, i.e., the substitution of folded-chain crystals by extended-chain crystals with increasing degree of branching (e.g., in cross-linked EOC60). At the same time, the additional constraints of nucleation and crystal growth in cross-linked PEs caused by net-points molecular orientation during crystallization of loaded network should be taken into account. WAXS. In order to determine the orientation of the crystals, WAXS images depicted in Figure 5 were recorded for slowly

reflections from (110), (200), and (020) crystallographic planes (in case they were resolved) were used to calculate the parameters a and b of the unit cell on the basis of Bragg’s law.30 In order to determine the positions of peaks precisely, the experimental findings in 1D plots were approximated by the Gaussians functions corresponding to the amorphous halo and crystallographic peaks as shown in Figure 6. Both reflections (110) and (200) in drawn EOC60 are oriented perpendicular to the stretch direction (Figure 5f), therefore it can be concluded that the axes a and b of unit cell are normal to the stretch direction, whereas the c-axis, i.e., axis of crystal stems (molecular chains inside of lamellae), coincides with the direction of draw. Thus, the orientation of unit cell of drawn EOC60 was already obtained and no further calculation is needed. It should be also noted that crystalline structure of EOC60 possesses disordered pseudohexagonal symmetry according to the statement of some authors.23,31 At the same time, the determination of crystal orientation in drawn HDPE and EOC30 requires additional treatment. Since the crystal morphology of these samples is represented by lamellae as shown and discussed above (Figure 4d,e) and crystal symmetry is orthorhombic,32 the orientation of unit cell is calculated on the basis of the following equations:30

Figure 5. WAXS images of undeformed (a−c) and drawn due to crystallization under load (d−f) foils of HDPE, EOC30 (νc = 270 mol· m−3), and EOC60 (νc = 190 mol·m−3). Yellow arrows in parts d−f indicate the stretch direction.

cos2φhk 0, Z = ea 2 ·cos2φh00, Z + eb 2 ·cos2φ0k 0, Z

(1a)

cos2φh00, Z + cos2φ0k 0, Z + cos2φ00l , Z = 1

(1b)

where φhk0,Z is the angle between unit vector normal to (hk0)plane and the stretch direction Z, φh00,Z is the angle between unit vector normal to (h00)-plane, i.e. a-axis, and the stretch direction Z, ea is the cosine of the angle between unit vector normal to (hk0)-plane and a-axis, and eb is the cosine of the angle between unit vector normal to (hk0)-plane and b-axis. The consecutive substitution of the angles values φ110,Z and φ200,Z determined from WAXS images in Figure 5d,e into the left part of eq 1a and the solution of received systems of eq 1 allows calculating the orientation of unit cell related to the stretch direction for drawn HDPE and EOC30. It should be also noted that reflections in Figure 5d,e are represented by the relatively wide arcs that have to be accounted in the calculation. Parameters a and b of unit cell as well as its orientation for all

crystallized undeformed and drawn foils of PEs under study. WAXS images of undeformed specimens exhibit continuous concentric circles of reflections (Figure 5a−c) that evidence the random orientation of crystals. On the contrary, arcs of reflections in WAXS patterns of drawn PEs foils prepared under conditions typical for two-way SM test (Figure 5d−f) point to the preferred orientation of crystals chains. So, (020) reflection is only found in equatorial direction of the WAXS images of all drawn PEs, while reflections (110) and (200) appear in the quadrants for HDPE and EOC30 (Figure 5d,e) and on equator for EOC60 (Figure 5f). Equatorial scattering plots shown in Figure 6 were obtained by means of sectorial integration over ±5° related to the orientation on equator of WAXS images. The peak positions of

Figure 6. Equatorial scattering curves of undeformed (a) and stretched, i.e. crystallized under load during SM creep, samples of cross-linked HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3) (b) received by means of sectorial integration over ±5° related to the equator direction of WAXS patterns. Gray points represent experimental findings; green lines represent simulation curves. G


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Macromolecules drawn PEs under study are listed in Table 3. Also, angles φ200,Z and φa,Z are the same, therefore only values φa,Z are shown in

Assuming that all crystalline and amorphous regions are arranged as sublayers in lamellar stacks, the crystals thickness Lc for all samples of PEs can be calculated by multiplying the long period L determined as the peak position of curves in Figure 8a by the corresponding crystallinity values obtained on the basis of DSC and listed in Table 2. Calculated values of crystal thickness Lc, the values of full width at half-maximum (fwhm) of scattering curves presented in Figure 8b, and relative orientation degree Θrel = (180° − fwhm)/180° are listed in Table 4. The values of calculated crystal thickness of PEs are in satisfactory agreement with the rough estimations obtained on the basis of TEM. In addition, crystals in drawn EOC30 and EOC60 are slightly thicker as compared with undeformed samples that is logical consequence of stretching. On the basis of the results on orientation of unit cell received from WAXS images of drawn HDPE and EOC30 as well as on the data on orientation determined from SAXS and TEM of these samples it can be concluded that alternating crystalline and amorphous regions are arranged perpendicularly to the stretch direction Z. The basal surfaces of lamellae are orthogonal to Z, however, the crystalline structure of HDPE and EOC30 inside the lamellae owns a tilted arrangement so that the chain axis makes an acute angle with Z. According to the WAXS results, the axis b of unit cell is perpendicular to Z, whereas axes a, c make acute angles with Z and lie in one plane with Z. The sketch presented in Figure 9 shows one possible arrangement of lamellae stacks, unit cell axes, and stretch direction Z relatively to the X-ray beamline. In the entire sample volume rotated versions of lamellae stacks around Z have to be taken into account as well. Thus, the angles between cell axes and stretch direction remain unchanged. The rotating arrow in Figure 9 exemplifies this circumstance. Note that the tilted arrangement of crystal stems is wellknown for melt-crystallized linear PEs.33−36 The theoretical estimation of crystal stems inclination relative to the lamellar normal in the light of overcrowding problem within the interface between crystalline and amorphous phases, which was made by Sir Charles Frank, points to a decisive role of backfolding (adjacent re-entering) of molecular chains: (1st) if 70%

Table 3. Structural Parameters a and b of the Unit Cell and Its Orientation Related to the Stretch Direction (Designated as Z) As Determined for Stretched Samples of HDPE, EOC30, and EOC60 Crystallized under Load during the Cooling Stage of the Two-Way SM Cycle samples

a (Å)

b (Å)

φ110,Z (deg)

φa,Z (deg)

φb,Z (deg)

φc,Z (deg)

HDPE EOC30 EOC60

7.51 7.45 7.43

4.99 4.98 4.97

66 ± 13 70 ± 11 90 ± 8

41 ± 11 57 ± 7 90 ± 7

90 ± 3 90 ± 4 90 ± 7

45 ± 10 33 ± 7 0±7

Table 3. As it is seen, though crystal chains of drawn HDPE are oriented, but make sufficiently large angle with the stretch direction and exhibit wide distribution of orientation. In addition, the crystal unit cell of drawn EOC30 exhibits stronger orientation with narrower distribution as compared to the HDPE sample. SAXS. SAXS images of slowly crystallized undeformed and drawn samples of HDPE, EOC30, and EOC60 crystallized under load during two-way SME are presented in Figure 7. Continuous reflections in Figure 7a−c indicate that alternating crystalline and amorphous regions are randomly oriented. However, the long period (repeating unit) of this layered structure L can be determined as L = Lc + La (2) where Lc is thickness of crystalline sublayer and La is thickness of amorphous sublayer. Additionally, 2D images of drawn PEs under study in Figure 7d−f evidence that periodic crystalline structure is ordered normal to the stretch direction. Note that Figure 7c has an only low contrast due to the low crystallinity of EOC60. The plots of SAXS intensity I·q2 as a function of scattering vector q = 2π/d, where d is the interplanar spacing, received by means of 360°-integration and curves of intensity I vs azimuthal angle χ obtained at the maximum of the I·q2-curves by means of integration over a small Δq interval are shown in Figure 8.

Figure 7. SAXS images of undeformed (a−c) and drawn crystallized under load during cooling stage of two-way SM cycle (d−f) samples of HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3). White arrows in parts d−f indicate the stretch direction. H


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Macromolecules

Figure 8. SAXS intensity I·q2 vs scattering vector (a) obtained by means of 360°-integration of SAXS images of crystallized unconstrained and crystallized under load samples of HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3) as well as intensity I vs azimuthal angle (b) of drawn PEs under study.

Table 4. Crystal Thickness of Undeformed and Stretched Samples of HDPE, EOC30, and EOC60 As Determined by Means of SAXS as Well as Relative Orientation Degree Θrel of Crystalline Structure of Drawn PEs Crystallized under Load during the Cooling Stage of the Two-Way SM Cycle samples

type

long period L (nm)

crystallinity at 298 K (DSC) χc (%)

crystal thickness Lc (nm)

full width at half-maximum (deg)

Θrel (−)

HDPE

undeformed drawn undeformed drawn undeformed drawn

23.2 21.7 11.7 12.6 11.3 13.6

50.4 54.3 29.6 30.8 12.4 13.7

11.7 11.8 3.5 3.9 1.4 1.9

− 18.6 − 25.6 − 43.9

− 0.9 − 0.86 − 0.76

EOC30 EOC60

free energy of transferring links from the amorphous region to the crystal; the free energy of the interface between amorphous and crystalline regions as well as the surface free energy of a crystal with f folds; the entropy change in the remaining amorphous links. A schematic illustration of crystallizing network chain is depicted in Figure 10. Figure 9. Sketch illustrating the orientation of lamellae determined on the basis of WAXS and SAXS investigation in stretched samples of HDPE and EOC30 crystallized under load during the cooling stage of the two-way SM cycle. Red points represent cross-link points.

or more chains re-enter adjacently immediately or before passing the interface then the perpendicular arrangement of crystal stems can be observed (inclination equals zero); (2nd) in the case of total absence of back-folding the inclination can reach the maximum value of 72.5°.33 The careful TEM investigations of very well crystallized linear PE performed by the group of Basset and Hodge,34,35 which was also supported by the results of electron and X-ray diffractions,37,38 enabled the identification of crystallographic plane (201) as the most probable basal surface of lamellae with corresponding crystal stems inclination of about 35°. An irrefutable experimental evidence of crystal stems obliquity in melt-crystallized linear PEs was obtained independently from Basset and Hodge by Dlugosz et al. on the basis of the comparison between crystal stems length Lst estimated using low frequency Raman spectroscopy and long period L determined by SAXS.36 The fact that Lst is larger than L can most likely be explained by the tilted arrangement of crystal stems. Modeling the SM Behavior. The description of the behavior of semicrystalline covalent network during crystallization at cooling is based on the analysis of the free energy change, which is assumed to consist of the following terms: the

Figure 10. Sketch of crystallized chain linking two neighboring crosslink points (red points) of semicrystalline covalent network; white imagined point divides the chain into amorphous and crystallized subchains.

Thus, the free energy change as a function of temperature T and draw ratio λ is represented as follows:12,13 ⎛ T ⎞ ΔFf (T , λ) = −Nχc ΔHμ⎜1 − 0 ⎟ + Uem + fUe Tm ⎠ ⎝ ⎛ RT ⎡ 1 ⎤⎡ 2 1 ⎟⎞ 2 3ϕ2 ⎜1 + 1 2 − λ − ϕδ λ + + ⎢ ⎢ ⎥ ⎝ 2θ ⎣ Nθ ⎦⎣ 20N ⎠ λ N ⎤ 3ϕ4 3RT ⎡ 4 4 8 1 6ϕ2 2 − 3θ ⎥ + + + + + λ λ λ ⎢ 3 3 λ2 N ⎦ 20Nθ 3 ⎣ N2 +

+

⎛ 4ϕ2 1 8 4 2 ⎞⎟⎤ − ϕδ(λ 3 + 1) − ϕ3δλ − θ 2⎜5 − ⎥ ⎝ N λ N Nθ ⎠⎦ 3 (3)

I


Article

Macromolecules

Figure 11. Comparison of free energies of crystallization ΔFf(T, λ) as a function of temperature and draw ratio calculated for HDPE (a), EOC30 (b), and EOC60 (c) in case of different numbers of crystal folds f. Blue dotted arrows in parts a and b indicate the crystallization path at cooling and serve as an example of common tangent lines.

where N is number of chain links between two neighboring cross-link points, χc is crystallinity, ΔHμ is the enthalpy of fusion per link, T0m is the equilibrium melting temperature, Uem is the free energy of the interface between amorphous and crystalline regions, f Ue is the surface free energy of a crystal with f folds, each with ψ links and surface energy Ue, δ = (6/ (πN))1/2, and Nθ = (N − Nχc − ψf) is number of remaining amorphous chain links. The parameter ϕ in eq 3 is defined as l = [f 2 a0 2 + βζ 2b0 2]1/2 = ϕb0

not be taken into further consideration. At the same time, in case of HDPE and EOC30 (Figure 11a,b) the extended-chain morphology ( f = 0) has a lower free energy at the onset of crystallization, whereas further cooling results in formation of the folded-chain crystals (f = 2 or 4) oriented in the stretch direction but not parallel. The lowest specific free energy of crystallization of the network is defined as12,13 νc ·ΔFtot (T , λ) = νc ·(G0 ·ΔF0(T , λ) + Gf ·ΔFf (T , λ))

(4)

where a0 is a chain thickness; ζ is the number of links traversing the crystallite, ζ = Nχc/(f + 1); b0 is the length of a chain link; β is the parameter equals 1 for even number of folds and 0 for odd number of folds in the crystallite. Equation 4 discloses the important assumption about parallelism of the applied force and the crystal vector l shown in Figure 10, namely, number of folds f and parameter β control the orientation of the crystallite relative to the applied force. The odd number of folds results in perpendicular orientation of chains in the crystal to the external force, whereas even number of folds corresponds to the case when the orientation of chains in crystal is parallel to or makes an acute angle with the stretch direction. The free energy of crystallization ΔFf (T,λ) as a function of temperature and draw ratio was calculated for cross-linked HDPE, EOC30, and EOC60 in case of different number of folds f using the appropriate values for the parameters in eqs 3 and 4: Uem = 13791.3 J·mol−1, Ue = 13238.7 J·mol−1, b0 = 1.54 Å, a0 = 4.25 Å, ψ = 4, T0m = 419 K, and ΔHμ = 4140 J· mol−1.14,31 Results are presented in Figure 11. Numbers of chain links N were chosen so that they nearly correspond to the cross-link density of each polyethylene listed in Table 1, namely, N = 630 for HDPE (νc = 110 mol·m−3), N = 200 for EOC30 (νc = 270 mol·m−3), and N = 240 for EOC60 (νc = 190 mol·m−3). ΔFf (T,λ) values corresponding to numbers of folds f = 2,3 and f > 4 for HDPE, f > 2 for EOC30 as well as f > 1 for EOC60 are greater and so they are not shown. The results indicate that the lowest free energy for EOC60 (Figure 11c) corresponds to the extended-chain morphology oriented parallel to the direction of draw. Though the free energy of crystals with f = 1 in case of EOC60 has lower values when T < 310 K, it does not reach a minimum over the whole temperature range and reflects a nonequilibrium thermodynamic process that does not satisfy the initial assumptions, on which the theory is based, and therefore is not realized and will

G0 =

χcf − χc χcf − χc 0

,

Gf =

(5a)

χc − χc 0 χcf − χc 0

(5b)

where the values χc0 and χcf are obtained as the crystallinity corresponding to the intercepts of the common tangent line (arrows in Figure 11a,b) with the free energy curves, Gf is the fraction of network chains having crystallinity χcf, f folds in the crystal ( f = 2 and 4 for EOC30 and HDPE, respectively) and the free energy of crystallization ΔFf (T,λ). Crystallinity χc in eq 5b is considered as a function of temperature and is defined by modified Ozawa equation.12,13,39,40 In addition, it is assumed that the crystallization proceeds along the lowest free energy path (arrows in Figure 11a,b) and ceases when the network reaches a minimum free energy of crystallization value. The applied stress is calculated as a first derivative of the total free energy with respect to the draw ratio:12,13 ⎛ ∂ΔF0(T , λ) ∂ΔFtot (T , λ) = νc ⎜G0 ⎝ ∂λ ∂λ ⎞ ∂ΔFf (T , λ) ⎟⎟ +Gf ∂λ ⎠

σ0N = νc

(6)

where νc is the cross-link density of covalent network. As mentioned above (in the Introduction), SM behavior of cross-linked semicrystalline polymers is also affected by the viscoelastic deformation of entangled macromolecules, which is represented as follows:12,13 ⎛ ⎞ σ0N σ0N + ⎜ε01 + ⎟ σ0N + 3νeU /4 σ0N + 3νeU /4 ⎠ ⎝ ⎡ 2V 2 σ + 3ν U /4 ⎛ U ⎞⎤ e ⎟⎥ T ·exp⎜ − ·exp⎢ − h · 0N ⎝ RT ⎠⎦ γh ⎣ Vm

ε1 = −

J

(7)


Article

Macromolecules where ε01 is the part of total strain stored by entangled slipped molecules, νe is the density of entangled slipped macromolecules, Vh is the volume of the hole swept out by the motion or activation volume,41 Vm is the volume of the flowing molecule, U is the activation energy of the viscous flow, γ is the constant cooling rate, h is the Planck constant. Theoretically derived temperature dependent strain at cooling below Tc under constant load, which will be used for fitting, is as follows:12,13 εT = εTC + ε1 + ε2 (8)

where ζ·b0 = N·b0·χcf/( f + 1) = Lst is the length of crystal stems (see Figure 10). Factor cos φc,Z takes into consideration the inclination of crystal stems. Note that eq 9a can be reliably used only for linear and medium branched PEs like HDPE and EOC30. The value Lc estimated for highly branched EOC60 basing on eq 9a exceeds the chain length between two neighboring branches. Since it is assumed that short branches cannot enter the crystals, crystal thickness Lc for EOC60 in Table 5 is calculated by the eq (10b). Constants Tcsw and Thsw in Table 5 determine the switching temperatures at cooling and heating, respectively. Received values of crystal folds f (Table 5) indicate that according to the aforementioned basic theoretical assumptions the chain axis of folded-chain crystals in HDPE (f = 4) makes acute but larger angle with the stretch direction than that in EOC30 ( f = 2), whereas the extended-chain crystals in EOC60 are oriented parallel to the applied force. These results well correlate with the orientation of chain axis calculated on the basis of WAXS images of PEs under study (Table 3). In addition, this supports the statement that the anomalous elongation of cross-linked semicrystalline polymers under constant load during nonisothermal crystallization is possible only when c-axis of crystals is oriented parallel to the applied external force or makes a relatively small angle with it. Besides, the values of switching temperatures Tcsw and Thsw are almost the same as the crystallization and melting temperatures of drawn samples of all PEs received from DSC and listed in Table 2. This additionally proves the hypothesis that exactly the crystallization of preliminarily drawn covalent network is responsible for two-way SM phenomenon. Moreover, the magnitudes of crystallinity χcf, at which covalent network reaches the state with the lowest free energy (Table 5), surprisingly well correspond to the enthalpy-based crystallinity values determined from the first heating run of drawn samples in DSC (Table 2). The crystal thickness Lcal c calculated on the basis of fitting parameters (Table 5) satisfactory accords to a first approximation with the values Lc calculated from SAXS, which are listed in Table 4. Fitting results show that the contribution of entangled slipped molecular chains (parameter ε01 in Table 5) to the total strain during two-way SME is relatively small for all PEs under study. The consideration of this contribution provides more accurate modeling the experimental data, especially in the temperature range before the anomalous elongation at cooling and after SM recovery at heating. The values of material parameters of viscoelastic deformation of entangled macromolecules, such as the density of entangled slipped molecules νe, the activation volume Vh, and the volume of flowing molecular chains Vh are higher for EOC30 and EOC60 as compared for HDPE that is expected because of the existence of short-chain branches.

where εTC is the thermal contraction of a sample during cooling, the strain of entangled slipped molecules ε1 is given by eq 7, and ε2 = ε2(T) is temperature dependent strain of crystallizing covalent network, which is not shown here but it can be expressed from eqs 5 and 6. Modeling the two-way SME as well as determination of material parameters were carried out using experimental findings for HDPE, EOC30, and EOC60 obtained and corrected as described in the section Two-Way SM Behavior. Fitting was performed by means of the Levenberg−Marquardt algorithm. The results are presented in Figure 12. As it follows

Figure 12. Experimental and fitting curves of two-way SME obtained for cross-linked HDPE, EOC30 (νc = 270 mol·m−3), and EOC60 (νc = 190 mol·m−3) loaded by σ0N = 1 MPa, σ0N = 0.6 MPa, and σ0N = 0.3 MPa, respectively. Blue and red arrows indicate cooling and heating runs, correspondingly.

from Figure 12, the current theoretical description of two-way SME demonstrates very good coincidence with the experimental data. Values of fitting parameters are listed in Table 5 along with the crystals thickness Lcal c calculated on the basis of obtained fitting parameters and experimental results of WAXS as follows: Lccal = ζ ·b0 ·cos φc , Z = Lccal =

N ·χcf (f + 1)

·b0 ·cos φc , Z

(9a)

1000 b0 number of branches per 1000C

(9b)

Table 5. Relevant Fitting and Material Parameters as Well as Those Calculated on the Basis of Crystal Thickness Lcal c for HDPE, EOC30, and EOC60 samples

ε01 (%)

νe (mol·m−3)

Vh (nm3)

Vm (103·nm3)

U (kJ·mol−1)

N (−)

νc (mol·m−3)

f (−)

χcf (%)

Tcsw (K)

Thsw (K)

Lcal c (nm)

HDPE EOC30 EOC60

5.2 5.1 4.9

89.5 123.9 144.4

2.1 4.3 4.5

4.2 38.4 68.3

105.7 95.8 77.8

630 200 240

110 270 190

4 2 0

57.4 34.7 18.5

375.8 342.9 310.1

396.6 362.6 333.5

7.9 3.0 2.6

K


Article

Macromolecules

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(4) Mandelkern, L.; Roberts, D. E.; Diorio, A. F.; Posner, A. S. Dimensional Changes in Systems of Fibrous Macromolecules: Polyethylene. J. Am. Chem. Soc. 1959, 81 (16), 4148−4157. (5) Kolesov, I.; Dolynchuk, O.; Borreck, S.; Radusch, H.-J. Morphology-controlled multiple one- and two-way shape-memory behavior of cross-linked polyethylene/poly(ε-caprolactone) blends. Polym. Adv. Technol. 2014, 25 (11), 1315−1322. (6) Chung, T.; Romo-Uribe, A.; Mather, P. T. Two-way reversible shape-memory in a semicrystalline network. Macromolecules 2008, 41 (1), 184−192. (7) Lee, K. M.; Knight, P. T.; Chung, T.; Mather, P. T. Polycaprolactone−POSS chemical/physical double networks. Macromolecules 2008, 41 (13), 4730−4738. (8) Zotzmann, J.; Behl, M.; Hofmann, D.; Lendlein, A. Reversible triple-shape effect of polymer networks containing polypentadecalactone- and poly(ε-caprolactone)-segments. Adv. Mater. 2010, 22 (31), 3424−3429. (9) Pandini, S.; Passera, S.; Messori, M.; Paderni, K.; Toselli, M.; Gianoncelli, A.; Bontempi, E.; Riccó, T. Two-way reversible shape memory behaviour of crosslinked poly(ε-caprolactone). Polymer 2012, 53 (9), 1915−1924. (10) Pandini, S.; Baldi, F.; Paderni, K.; Messori, M.; Toselli, M.; Pilati, F.; Gianoncelli, A.; Brisotto, M.; Bontempi, E.; Riccó, T. Oneway and two-way shape memory behaviour of semi-crystalline network based on sol-gel cross-linked poly(ε-caprolactone). Polymer 2013, 54 (16), 4253−4265. (11) Kolesov, I. S.; Kratz, K.; Lendlein, A.; Radusch, H.-J. Kinetics and dynamics of thermally-induced shape-memory behavior of crosslinked short-chain branched polyethylenes. Polymer 2009, 50 (23), 5490−5498. (12) Dolynchuk, O.; Kolesov, I.; Radusch, H.-J. Thermodynamic description and modeling of two-way shape-memory effect in crosslinked semicrystalline polymers. Polym. Adv. Technol. 2014, 25 (11), 1307−1314. (13) Dolynchuk, O.; Kolesov, I.; Radusch, H.-J. Theoretical description of an anomalous elongation during two-way shapememory effect in crosslinked semicrystalline polymers. Macromol. Symp. 2014, 346 (1), 48−58. (14) Gaylord, R. J.; Lohse, D. J. Morphological changes during oriented polymer crystallization. Polym. Eng. Sci. 1976, 16 (3), 163− 167. (15) Gaylord, R. J. A theory of the stress-induced crystallization of crosslinked polymeric networks. J. Polym. Sci., Polym. Phys. Ed. 1976, 14 (10), 1827−1837. (16) Kolesov, I.; Radusch, H.-J. Multiple shape-memory behavior and thermal-mechanical properties of peroxide cross-linked blends of linear and short-chain branched polyethylenes. eXPRESS Polym. Lett. 2008, 2 (7), 461−473. (17) Gedde, U. W. Polymer Physics; Chapman & Hall: London, 1995; pp 49, 211−214, 200. (18) ATHAS Database. Springer Materials Release 2013. Database ID athas0016 http://www.springermaterials.com/docs/content/ athaspreface.html. (19) Mathot, V. B. F.; Scherenberg, R. L.; Pijperrs, M. F. J.; Bras, W. Dynamic DSC, SAXS and WAXS on homogeneous ethylenepropylene and ethylene-octene copolymers with high comonomer contents. J. Therm. Anal. 1996, 46 (3−4), 681−718. (20) Treloar, L. R. G. The Physics of Rubber Elasticity, 3rd ed.; Clarendon Press: Oxford, 1975; pp 37, 63. (21) Hsiao, B. S. Role of chain entanglement network on formation of flow-induced crystallization precursor structure. In Progress in Understanding of Polymer Crystallization, Reiter, G., Strobl, G. R., Eds.; Lecture Notes in Physics 714, Springer: Berlin and Heidelberg, Germany, 2007; pp 133−149. (22) Wunderlich, B. Macromolecular physics; Academic Press: New York, 1976; Vol. 2 (Crystal Nucleation, Growth, Annealing), pp 149, 16.

CONCLUSIONS AND OUTLOOK Two-way SME in cross-linked linear (HDPE) and short-chain branched polyethylenes (ethylene-1-octene copolymers) with different degree of branching (EOC30 and EOC60) has been systematically investigated with the special accent on crystallization/melting behavior, morphology, size, and orientation of crystals formed during nonisothermal crystallization of constantly loaded samples. TEM study has shown that drawn samples of HDPE and medium branched EOC30 crystallized under load during cooling stage of two-way SM cycle including the anomalous elongation contain lamellae with basal surface oriented nearly perpendicular to the stretch direction, whereas the crystalline phase of highly branched EOC60 consists of small crystallites. Based on WAXS results, it was determined that the chain axis c of crystals in EOC60 is oriented parallel to the stretch direction, whereas axis c makes an angle of about 45° in HDPE and 33° in EOC30 with the direction of draw. SAXS findings of long period accompanied by enthalpy-based crystallinity values determined from DSC enabled calculating the crystals thickness in drawn PEs. Thus, the results of X-ray scattering and TEM study of drawn HDPE and EOC30 samples disclosed the specific crystalline texture comprising lamellae, whose folded chains are tilted to the basal surface of lamellae. The mechanism of lamellae formation, which consist of tilted crystal stems and are oriented perpendicular to stretch direction can be evidently explained on the basis of in situ WAXS and SAXS investigations performed using synchrotron radiation during nonisothermal crystallization of polymer network under load. Recently developed theory of two-way SME has been successfully confirmed for all PEs under study. The modeling of two-way SME performed for HDPE and EOCs revealed excellent coincidence between fitted curves and experimental findings. The material parameters obtained from the fitting procedure allowed calculating the thickness of crystals, which well correspond to those received from SAXS. The theoretical conclusions on crystal morphology and orientation of crosslinked linear and short-chain branched PEs were also qualitatively confirmed on the basis of experimental results received from TEM, SAXS, and WAXS.

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AUTHOR INFORMATION

Corresponding Author

*(I.K.) E-mail: [email protected] and igor.kolesov@ iw.uni-halle.de. Telephone: +49 3461 46-2737. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to Dr. P. Formanek, Leibniz Institut für Polymerforschung Dresden, for helpful discussion of the results and valuable recommendations.

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REFERENCES

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Changes of Crystal Structure and Morphology during Two-Way Shape

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