Chain Deformation on the Formation of Shish Nuclei under Extension

Nov 23, 2016 - The deformation of molecular chain obtained by SANS shows that shish forms at a rather small chain deformation of about 1.3, which does...
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Chain Deformation on the Formation of Shish Nuclei under Extension Flow: An in Situ SANS and SAXS Study Haoran Yang,† Dong Liu,‡ Jianzhu Ju,† Jing Li,† Zhen Wang,† Guanyun Yan,‡ Youxin Ji,† Wenhua Zhang,† Guangai Sun,‡ and Liangbin Li*,† †

National Synchrotron Radiation Lab and CAS Key Laboratory of Soft Matter Chemistry, University of Science and Technology of China, Hefei 230026, China ‡ Key Laboratory of Neutron Physics and Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics (CAEP), Mianyang 621999, China ABSTRACT: By combining extensional rheological and in situ small-angle neutron and synchrotron X-ray scattering (SANS, SR-SAXS) techniques, the correlation between chain deformation and morphology of nucleus in a lightly cross-linked deuterated PE (D-PE)/hydrogenated PE (H-PE) blend has been studied at different draw ratios. The deformation of molecular chain obtained by SANS shows that shish forms at a rather small chain deformation of about 1.3, which does not support either coil−stretch transition or the simple stretch network model. Combining these data with the SAXS results, we speculate that the conformation ordering couples with density, instead of single chain conformation, is the key factor for shish formation. Meanwhile, due to the different alignment of the center of mass of the stretched network in samples with different draw ratios, a periodic concentration modulation of D-PE appears after crystallization of the samples stretched to the hardening zone, which, however, does not occur under the small draw ratio.

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INTRODUCTION For almost all kinds of polymer processing methods, polymer melts undergo complex flow field which dramatically influences the crystallization behavior such as crystallinity and crystalline morphology, thus the physical properties of final products.1−6 Therefore, flow-induced crystallization (FIC) of semicrystalline polymers is of vital importance for industry and always a fascinating subject in the realm of polymer physics for decades. Among various researches in FIC,1,7−11 clarifying the formation mechanism of highly oriented shish-kebab superstructure gains much attention,10,12−14 not only for the dramatic change in crystalline morphology but also due to the remarkable increase of strength and stiffness.15−17 Two possible mechanisms have been proposed for flow-induced shish, namely the concept of effective straining time,18 coil−stretch transition (CST),11 and stretched network model (SNM),19−22 and the debate between them has never been stopped up to now. Recently, SNM seems to prevail for polymer melt because more and more experimental results coincide with it instead of CST. Kornfield et al.23 illustrated that in long chain/short chain system the concentration of long chains in the system must be equal to or above the overlap concentration (c*) for the formation of shish, which implies that long chains may act as an entangled network rather than single chain under flow. Kanaya et al.24 showed that facilitating the formation of shish is due to more entanglement points formed by long chains. With in situ synchrotron radiation SAXS (SR-SAXS) measurements on extensional flow-induced crystallization of low molecular weight © XXXX American Chemical Society

(LMW)/ultrahigh molecular weight (UHMW) polyethylene (PE) bimodal blends, we found that the critical strain for shish formation decreases with increasing UHMW component, which agree pretty well with the SNM.25 Besides that, one should be aware that CST derived from solution is not suitable for polymer melt because there is no essential ingredient of CST, hydrodynamic effect, in melt. Lacking of chain dimension makes it impossible to quantitatively describe the relationship of “macroscopic deformation−chain conformation−nucleation morphology”. Though SNM is regarded as a more suitable mechanism for shish formation in polymer melt now, the description of SNM is still indistinct and qualitative in macroscopic deformation instead of molecular chain conformation. The combination of rheology and structural characterization methods in the study of FIC can only correlate macroscopic flow parameters with structural evolution, while chain conformation is not measured directly. Thus, real chain conformation in the deformed network is still unavailable in the study of FIC, which, however, is just the crux in clarifying the formation mechanism of shish in polymer melt. For the characterization of chain conformation, small-angle neutron scattering (SANS) is undoubtedly the most suitable method. Both hydrogen/deuterium labeling and hydrogen/ deuterium contrast matching techniques illuminate the targeting Received: September 2, 2016 Revised: November 7, 2016

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to plates with thickness of 1 mm by a vacuum press at 200 °C and then cooled down to room temperature by throwing it into ice water immediately after the vacuum press for the purpose of avoiding phase separation of D-PE and H-PE. The plates are annealed under vacuum at 90 °C for 24 h in order to eliminate residual stress. After that, the plates are exposed to a 60Co γ-ray radiation source (located in USTC, Hefei, China) at room temperature. The dose rate is 35 Gy/min, and the total absorbed dose is 50 kGy. In order to reduce the formation of peroxide radicals, oxygen is isolated from the sample during the radiation process. The trapped free radicals are further eliminated through annealing at 90 °C for 24 h under vacuum. The cross-linking degree of the lightly cross-linked D-PE/H-PE blend (XL-D/H-PE) sample is expressed as gel fraction. The samples are extracted in boiling xylene for 48 h with Soxhlet extractor, and then dried in a vacuum oven at 70 °C for 24 h, until the weight of residual no longer decreased. The gel fraction is calculated gravimetrically from the weight of the sample before and after extraction. The gel fraction of XL-D/H-PE is 56 wt %. To determine the distribution of D-PE in the gel and free chain part, the XL-D/H-PE is characterized by using Fourier transform infrared spectroscopy (FTIR). Here, the frequency regions of the CH2 and CD2 rocking modes33 are detected (data are not shown here), and the area ratios (CD2/CH2) of these two regions in gel and free chain are calculated to represent the relative contents of D-PE in the two different parts, respectively. The calculated area ratio in the gel is about 0.048, which is much larger than that in free chains (about 0.0072). Combined with gel fraction data, we can roughly calculate that the D-PE in gel part is nearly 8.2 times of the D-PE in free chains. Moreover, the overall content of D-PE in blend is low (5 wt %). Therefore, the signal detected by SANS mainly derives from the contrast between D-PE in gel and H-PE in gel and free chain, which just reflects the conformation of D-PE chains in the cross-linked network. This also makes the determination of the dimension of the polymer chain after deformation more precise because the relaxation of the gel during SANS experiment can be dramatically suppressed by the cross-linking points. A homemade two-drum extensional rheometer used in this work can apply well-defined thermal history and impose extensional flow field; a detailed introduction of the rheometer can be seen in our previous publications.34 Figure 1 shows how the rheometer works with SANS and SAXS.

molecular chains for investigations on the dimension, orientation, and conformation of molecular chains.26−28 Recently, SANS also be used in the field of FIC. Kimata et al.29 used three kinds of isotactic polypropylene (iPP) resins that with well-matched molar mass distributions but different chain lengths labeled with deuterium to examine whether long chain is dominant in the formation of shish. The samples prepared by blending hydrogenated and deuterated polypropylene first suffered to a shear and thermal procedure and then were quenched in cold water for ex situ SANS characterization. 2D SANS patterns of different samples showed that long chains are not overrepresented in the shish relative to their concentration in the material as a whole, and the role of longest chains is catalytic which could recruit adjacent chains to form shish. Kanaya et al.30 also used SANS to elucidate the hierarchic structure of shish kebab. By quantitatively analyzing the ex situ SANS data, they proposed a multi-core−shell cylinder model for shish kebabs formed in their experiment. These examples demonstrate that SANS is an effective characterization method in FIC. In FIC, nucleation morphology can be tuned by imposing different strain, and much attention has been paid on chain conformation in the nucleation stage rather than the following solidification process. In strain-induced crystallization of rubber, it has been proved that stress relaxation could be detected in the crystallization stage which indicates a relaxation of parts of the deformed chain segments occurs.31,32 However, chain conformation under different draw ratio/strain state during solidification is still obscure. To gain a comprehensive understanding of the whole process of FIC, evolution of chain conformation during solidification should not be ignored, which can also be followed by SANS. In this work, chain conformation and morphology of nuclei/ crystal are studied with a combination of in situ SANS, SR-SAXS, and extensional rheometer, where a lightly cross-linked deuterated PE (D-PE)/hydrogenated PE (H-PE) blend is employed to serve as a dynamic asymmetric system with crosslinked network and free chain and to avoid phase separation. With irradiation, such PE blend obtains a very long relaxation time, which allows SANS to measuring stretched chain conformation with a low time resolution. Combined with rheological and X-ray/neutron scattering results, we establish the relationship between chain conformation and shish formation. Besides, the evolution of chain conformation during crystallization under different draw ratio is also obtained by comparing the X-ray and neutron scattering data before and after crystallization.

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EXPERIMENTAL SECTION

Figure 1. Three-dimensional view of the extensional rheometer working with the SANS and SAXS experiments.

The high-density PE (HDPE) granules used in this study is supplied by Sinopec Qilu Co. Ltd. The number-average (Mn), weight-average (Mw), and Z-average molecular weight (Mz) are about 42, 823, and 4395 kg/mol, respectively. The D-PE (Mw = 36.1 kg/mol and polydispersity index Mw/Mn of 1.7) was purchased from Polymer Source Inc. The chemical purity of deuterium is larger than 98%. Solution blending is used to ensure two components are intimately mixed at the molecular level. The blending procedure is listed as following. The mixture of D-PE and H-PE is first dissolved in xylene to form a homogeneous solution and then held at 140 °C for 120 min with continuous stirring under a nitrogen atmosphere. Then, the solvent is extracted by adding acetone with the temperature below zero, in order to prevent the phase separation of two components. After that, the extracted solid mixture is filtered and dried in a vacuum oven at 60 °C for 3 days to remove the residual acetone. The precipitates are molded

The apparatus for in situ neutron scattering study on flow-induced crystallization of polymer is tested on the SANS beamline in China Academy of Engineering Physics (CAEP).35,36 Neutron used in the experiments has a wavelength λ of 0.53 nm, with a spread Δλ/λ = 10%. The neutron flux is on the order of 100 photo/s during the whole experiments. A He-3 position-sensitive detector with a total area of 640 × 640 mm2 and a space resolution of 5 mm is installed on a movable trolley on rails to collect SANS data, and the sample-todetector distance is 11 m. The XL-D/H-PE thin plate with thickness of 1 mm is cut into rectangular shape with length and width of 50 and 40 mm, respectively. The rectangular-shaped samples are clamped on the two drums through two thin steel stripes, which are fixed with two fine screws at B

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Figure 2. Experimental procedures of the in situ (a) SANS and (b) SAXS experiments.

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the two ends. During the SANS experiments, blend samples are first heated up to 200 °C and held at this temperature for 10 min to eliminate thermal and mechanical memory. Then it is cooled to the temperature of 170 °C at which crystallization does not set in before stretching. The temperature procedure is shown in Figure 2a. To avoid temperature overshoot to temperature under 170 °C, the latter cooling rate of 5 °C/min is slower than the former one of 10 °C/min. The shape of sample is checked after this temperature cycle, which does not show observable predeformation. As soon as the temperature reaches the preset 170 °C, a step extension is imposed on blend sample with a draw ratio rate of 0.1 s−1. As for the collecting of SANS pattern, it should be noted that due to the limit of the flux of neutron, it takes nearly 1 h to obtain one 2D pattern. Therefore, to accurately correlate the chain dimension with nucleation morphology, the relaxation during SANS characterization must be taken into account. In preceding research on the stretch of XL-D/H-PE sample at 170 °C, we find that when extension stops, the stress first shows a dramatic decrease, and then it tends to be stable and changes little for a rather long time which is sufficient for SANS characterization. This indicates that some orientation or stretching of molecular chains or chain segments can be retained at 170 °C, and they are stable during SANS characterization. Therefore, a sufficient relaxation after the cessation of extension is performed before the start of each SANS characterization at 170 °C. And the data collected just reflect the conformation of the survival oriented or stretched chains and chain segments which is stable during the characterization of SANS. After collecting one pattern, the sample is cooled down to 120 °C and isothermally crystallized under that circumstance. After the isothermal crystallization, a second 2D SANS pattern is collected. To learn about the crystalline and nuclei morphology, the stretched samples at solid and melting state are characterized by SAXS at the beamline BL19U2 of the Shanghai Synchrotron Radiation Facility (SSRF). The experimental procedure is shown in Figure 2b. The stretched sample is fixed on two drums to prevent the relaxation during heating. Then the sample is heated from room temperature to 200 °C with a heating rate of 30 °C/min. When temperature reaches 100 °C, the shutter is opened and characterization begins. Data are collected during heating until the 2D pattern turn to totally isotropic. The X-ray wavelength is 0.103 nm, and a PILATUS-1M detector is employed to collect time-resolved 2D SAXS patterns. The exposure time is 90 ms with an additional 10 ms for reading and cleaning (i.e., patterns are acquired at a rate of 100 ms/frame). The sample-todetector distance is calibrated to be 5848 mm by beef tendon. Fit2D software from the European Synchrotron Radiation Facility is used to analyze the SAXS data, which are corrected for background scattering through subtracting contributions from the extensional rheometer and air. The 2D SAXS pattern is integrated azimuthally to obtain one-dimensional (1D) scattering profile as a function of q = 4π(sin θ)/λ, where q is the module of scattering vector, 2θ the scattering angle, and λ the X-ray wavelength. In order to verify the shish can form when the deformation exceeds hardening zone, an extension experiment also has been done with the same procedure as SANS experiment at beamline BL19U2 in SSRF. The SAXS patterns are acquired at a rate of 1 s/frame.

RESULTS The XL-D/H-PE samples are first stretched at 170 °C. The relationship between nucleation morphologies and the draw ratio is studied by using the in situ SAXS technique. Engineering stress−draw ratio plots of XL-D/H-PE and 2D SAXS patterns of samples with different draw ratio are presented in Figure 3. The extension direction is equatorial as indicated by

Figure 3. Stress−draw ratio curve and the selected in situ 2D SAXS patterns of XL-D/H-PE with different draw ratio at 170 °C.

the double-headed arrow in the upper left corner of Figure 3. Hereinafter, meridional and equatorial are also used as the representative of the direction parallel and perpendicular to the extension direction, respectively. As shown in Figure 3, the engineering stress−draw ratio curve can be roughly divided into two zones, namely nonhardening zone and hardening zone. With the applying of extension, the 2D SAXS pattern of XL-D/H-PE gradually changes from isotropic to anisotropic. When extension reaches the hardening zone, the scattering signal of a combination of a pair of lobule-shaped pattern and the streak pattern appear.9 Further increasing draw ratio, both of them become more intensive. According to our previous work,9,37 this kind of signal can be assigned as the combination features of shish and microshish superstructure induced by extension which confirms that the widely accepted superstructure of shish with microshish as its subunit can generate in this XL-D/H-PE system. Since this work mainly focuses on the formation of shish nuclei and the shish structure cannot form in the early stage of the nonhardening zone,37 the SANS experiment starts from λ = 1.82. The step extension which is the same as that in SXAS experiment is applied to the XL-D/H-PE at 170 °C, and the chain conformation is characterized by SANS. C

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obtained after deducting the intensity of empty cell with Kapton window. Chain dimension Rg can be deduced by fitting the absolute intensity with the equation28 I = v−1NϕHϕD(bH − bD)2 P(q)

(1)

where bD and bH are the neutron scattering lengths of hydrogenated and deuterated monomers, ϕ is the fraction of one component, ν−1 is the molar volume of the monomer, and P(q) is the structure factor of a single chain. For polymer chain of sufficient length, P(q) is approximately given by the Debye equation: 2 [λ − 1 + e−λ] λ2

P(q) =

Figure 4. Stress−draw ratio curve and the in situ 2D SANS patterns of XL-D/H-PE with different draw ratio of the extension processes at 170 °C. The numbers in the upper left corner of each pattern represent experimental draw ratio.

(2)

with λ = q Rg , where Rg is the radius of gyration of the tracer molecule. Particularly, for anisotropic samples, the dimensions of the tracer chains along and perpendicular to the flow direction, namely Rg∥ and Rg⊥, can be derived from the scattering intensity distribution parallel and perpendicular to extension direction, respectively.42,46−50 And the real deformation of molecular chains can be determined by comparing Rg∥ and Rg⊥. Therefore, we pick a rectangular area in meridian and equator passing through the beam center from the 2D SANS patterns for fitting Rg∥ and Rg⊥, respectively49−51 (two masked patterns in the right column of Figure 5a are listed as representative). The scattering intensity of both meridional and equatorial directions (hollow symbols) is displayed in Figure 5b−f. Each of the 1D SANS curve is fitted (the solid line) by using the Debye equation to obtain Rg∥ and Rg⊥. The fitted results are listed in Table 1. The microscopic chain deformation λ*∥ = Rg∥/Rg0∥ is far smaller than the macroscopic deformation λ, indicating a nonaffine deformation of polymer network. Unexpectedly, the microscopic chain deformation λ*∥ is only 1.24 and 1.39 for B3 and B4, respectively, at which SAXS results confirm the formation of shish. In another word, a rather small chain deformation can induce shish! Additionally, B2 has a larger λ*∥ than that of B3, which may also be a hint for the formation of shish. Though our samples are cross-linked network, shish formation with such a small chain deformation suggests that CST is certainly not required. 2

Figure 4 shows 2D SANS patterns under different drawing ratios λ at 170 °C. Sample B0 with λ = 1 gives an almost isotropic scattering patterns. At λ = 1.82 (B1), the anisotropic scattering feature appears and the 2D SANS pattern of the deformed sample becomes slightly lozenge with its long axis perpendicular to stretch direction, indicating that weak chain stretch happened during extension.38 By stretching the sample to large λ, the 2D SANS patterns become more anisotropic and regular lozenge pattern emerges in all the three samples with draw ratio of 2.72 (B2), 3.32 (B3), and 4.06 (B4), respectively, which suggests that chain stretching becomes dominant at the end of end of nonhardening zone and at hardening zone.39 Besides, a streak signal appears perpendicular to the extension direction in the 2D SANS patterns of B3 and B4, indicating the formation of rod or cylindrical structure. According to the SAXS results, shish forms in this draw ratio region, suggesting that the streak signal in SANS patterns derives from shish structure. With above SAXS and SANS experimental results, we correlate the formation of shish with chain conformation, namely radius of gyration Rg in parallel Rg∥ and perpendicular Rg⊥ to extension direction. Rg is defined as the root-mean-square distance of all scattering elements from the center of gravity, which represents the overall size of a polymer chain.40−45 In this work, the absolute neutron scattering intensity can be

2

Figure 5. Integrated 1D SANS curves (hollow symbol) and the nonlinear fit (solid line) curves of sample B0 (b), B1 (c), B2 (d), B3 (e), and B4 (f) in both meridian and equator of 170 °C. 2D SANS patterns in the right side of (a) show the mask protocol used for integration. D

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Macromolecules Table 1. Fitted Results Based on SANS Dataa at 170 °C

a

sample

λ

B0 B1 B2 B3 B4

1.00 1.82 2.72 3.32 4.06

Rg∥ (Å) 425 451 536 525 589

± ± ± ± ±

3.9 4.2 3.3 3.1 3.0

Rg⊥ (Å)

λ*∥

± ± ± ± ±

1.00 1.06 1.26 1.24 1.39

356 355 292 307 275

3.6 3.8 2.9 3.5 3.6

Besides that after crystallized at 120 °C, the relatively concentrated D-PE domains formed only in the samples stretched to the hardening zone and the periodicity (LD) of D-PE concentration modulation does not change when the samples are cooled down to room temperature. Take sample B4 as an example. At both 120 °C and room temperature, LD is around 48.0 nm (Figure 6c, 1D SANS curves). However, for the long period (L) of lamellar crystals, it changes from 41.8 nm at 120 °C to 29.1 nm at room temperature (Figure 6c, 1D SAXS curves). This phenomenon indicates that the relatively concentrated D-PE domains formed at the beginning of crystallization is not influenced by the insertion of lamellar crystal during cooling which can just reflect the motion of molecular chains at the early stage of the crystallization after stretch. Taking the same method for analysis Rg at 170 °C, we obtain Rg⊥ of B3 and B4 to be 33.7 and 30.7 nm at 120 °C after crystallization, respectively, which are larger than their corresponding Rg⊥ at 170 °C in melt, while at 120 °C LD obtained by SANS is smaller than the corresponding Rg∥ in melt at 170 °C. This indicates that in samples B3 and B4 crystallization results in shrinkage and expansion of Rg∥ and Rg⊥, respectively.

λ*∥ = Rg∥/Rg0∥.

After being stretched at 170 °C, samples are cooled down to 120 °C for isothermal crystallization. SANS patterns of different samples after crystallization show great distinctions. As shown in the inset of Figure 6a, strong equatorial scattering exists

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DISCUSSION In this work, in situ SANS and SAXS measurements have been used to detect the chain conformation and nucleation/ crystalline morphology in extension-induced crystallization of XL-D/H-PE sample. According to the results of extension rheological and the in situ small-angle scattering measurement, some interesting findings are obtained. (i) Chain deformation is unexpectedly small for shish formation. (ii) Accompanied with the formation of shish in B3 and B4, periodical D-PE concentration modulation along flow direction occurs after crystallization, as observed in 2D SANS patterns. Combining these findings, we will attempt to correlate chain conformation with shish formation and provide our view of point on the motions of chain segments when they crystallize under different draw ratio states. As mentioned above, B3 and B4 are stretched to the hardening zone; the stretch of chain segments in B3 and B4 should be more intensive which makes the conformation of the whole molecular chain deviates from Gaussian chain. Actually, the Debye function we used for fitting can only be applied to Gaussian chain.28 Although the fitting results of B3 and B4 cannot reflect the real dimension of the deformed chains, we believe that the deviation should not be dramatic. Because in this experiment, the deformation of the sample is continuous and the deformation of molecular chains is significantly affected by the constraint brought by the entanglement/cross-linking points, there should not be a sudden increase of the length of molecular chain along extension direction compared with that of sample B2, which is just stretched to the end of nonhardening zone. According to this, using the fitted parameter of B2 to correlate the deformation of molecular chain or chain segments with shish structure should be acceptable. In polymer entanglement or cross-linked network the end-toend distance of chain segments between two adjacent entanglement points in equilibrium Gaussian configuration is25

Figure 6. (a) 2D SANS patterns of four samples at 120 °C after crystallization and corresponding 1D SANS scattering profiles in meridian of 2D SANS patterns of XL-D/H-PE after crystallization at 120 °C. (b) 2D SAXS patterns of four samples after stretch and crystallization in SANS experiment; the patterns are taken at room temperature and 120 °C during melting. (c) 1D SANS and SAXS curves of B4 sample at room temperature and 120 °C.

evidently near the beamstop for all samples. The SANS patterns of B1 and B2 after crystallization show no obvious scattering intensity along extension direction, and no intensity maximum can be observed in the 1D SANS profile either. The only change compared with that at 170 °C is a slightly broadening of scattering intensity along extension direction. As for the other two samples in hardening zone, lobes of intensity in the meridional direction are evident in both of their 2D SANS patterns. Meanwhile, an intensity maximum appears in both of their 1D SANS curves as shown in Figure 6a. Different from their 2D SANS patterns at 120 °C, a pair of meridional two point pattern exists in 2D SAXS patterns for all samples at room temperature and 120 °C (as shown in Figure 6b), which indicates that the periodically stacked lamellar crystals form in all samples regardless of the draw ratio. The difference between SAXS and SANS pattern along extension direction must be due to the fact that the signals detected by SANS come from the contrast between D-PE and H-PE chain, instead of electronic density contrast between crystalline and amorphous regions. The meridian scattering peaks in B3 and B4 represent the periodicity of the relatively concentrated D-PE domain. The existence of these domains, on the other hand, supplies some information about the different motions of molecular chains when they crystallize under different draw ratio states.

⟨R2⟩1/2 =

Nl

(3)

where N is the number of Kuhn segments between two adjacent entanglements (N = Me/Mkuhn) and l is the Kuhn length. E

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Figure 7. Schematic of molecular chain crystallizes under different draw ratio state.

precursors or nuclei compose of intrachain and interchain orderings, where the latter, in fact, are more commonly detected with experimental techniques like streak signal in SAXS and crystalline diffractions in WAXS. Ironically, we mostly observe interchain ordering but attribute our observations mainly to intrachain conformation. Moreover, chain conformation in FIC is generally deduced from rheological concept rather than experimental data like SANS directly. In fact, stretching chain to fully extended is extremely hard, while interchain ordering like crystallization can realize chain segment extension spontaneously, as chain segments inside PE orthorhombic crystals always adopt extended the all-trans conformation.56,57 This suggests that interchain interaction may play more important role in FIC than that of intrachain conformation although flow indeed initiates conformational ordering at the early stage of FIC. Our recent work on extension-induced crystallization of PE shows that shish precursor can be a thermodynamic phase in stress−temperature space,58 where we denote this noncrystalline shish as a new δ phase. The phase zone of the δ phase in stress−temperature space defines a temperature−stress equivalence for its thermodynamic stability. At different temperature, different strain or stress is required to induce shish formation, indicating that shish can form at different oriented or stretched chain conformations. Evidently, chain conformation is not the only factor for shish formation, which can occur at small chain deformation as observed by SANS in this work. The shish signal observed by SAXS stems from density contrast, indicating that density, originated from interchain packing, is one key factor in FIC. The above analysis supports that coupling between intrachain conformation and interchain density is the molecular mechanism for FIC instead of intrachain conformation alone. During crystallization, the periodical domains with modulated concentration of D-PE form in samples stretched into hardening zone (B3 and B4). In these samples parts of stretched segments in the network participate in the formation of shish, while the rest remains as stretched amorphous network chains. Although these stretched amorphous network chains does not form shish bundles yet, their center of mass should arrange into a train aligning in extension direction, as evidenced by lozenge patterns of SANS. A schematic illustration is presented in Figure 7 (row I), where only D-PE is drawn and H-PE is omitted for a better view. Upon cooling to

For a chain in the fully extended configuration, the end-to-end distance is25 R max = Nl

(4)

Therefore, the extension ratio needed to switch the Gaussian configuration to fully extended configuration is25 λmax = R max /⟨R2⟩1/2 =

N

(5)

According to the fitting results listed above, the λreal of molecular chain in B2 is Rg2∥/Rg0∥ = 1.26; thus, the molecular weight of the chain segments that can be fully stretched is 239 g/mol. Compared with the molecular weight between two adjacent entanglements (Me) of PE melt (about 900 g/mol),52 the stretch of the molecular chains is relatively weak, suggesting that the segments between entanglements in PE network do not need to be fully extended for shish formation, let alone the fully extension of whole chain. This also coincides with our recent experiment results of LMW-PE/UHMWPE blend under extension.25 It should be noted that for pristine sample Rg∥ differs from Rg⊥. The only possible reason for this is that the flow field imposed to molecular chain may be inhomogeneous. However, the present analysis and the corresponding conclusion in our article are still reasonable and valid for two reasons. First, shish structures do not appear at small draw ratio region until the sample is stretched to the hardening zone, which indicates that the initially existing chain deformation does not show huge influence on the flow-induced shish structure. Second, according to the values of Rg∥ (425 Å) and Rg⊥ (356 Å), the Rg of the totally isotropic sample is estimated to be around 390 Å. Based on this value, the λreal of molecular chain calculated is 1.37, which is a little larger than 1.26. However, it is still rather small and does not affect the validity of the conclusion. Since the real deformation of the molecular chain is small, how does shish form under this circumstance? Many research results have proposed that highly stretch of chain or chain segment is necessary for the formation of shish nuclei. On the basis of our results, we speculate that the conformation ordering couples with density is the key factor for shish formation53−55 rather than intrachain conformation alone. Indeed, interchain interaction is an obvious overlooked point in the study of FIC. Both CST and SNM emphasize only on intrachain conformation. However, either shish F

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crystallization, the stretched amorphous network chains tend to form lamellar crystals oriented in extension direction. Inside lamella, chain segments extend with all-trans conformation, while segments in interlamellar amorphous region shrink, which is commonly accompanied by sharp stress dropdown during crystallization.59−61 After crystallization, the periodicity (LD) of concentration modulation of D-PE at 120 °C is smaller than Rg∥ at 170 °C, which can be attributed to the shrinkage of interlamellar amorphous chains. On the other hand, stress relaxation corresponds to retraction of stretched network. Thus, this can explain crystallization induced shrinkage and expansion of Rg∥ and Rg⊥, respectively. Although the periodicities of lamellar crystals and concentration modulation of D-PE are not completely the same at 120 °C, we speculate that crystallization does play a role to fix the center of mass of D-PE and result in periodic concentration modulation of D-PE. After D-PE chains fixed by crystallization at 120 °C, LD is not affected by crystallization during cooling to room temperature. Thus, though lamellar periodicity (L) varies largely with temperature, while LD keeps nearly constant during cooling. For network chains under small deformation before entering hardening zone, no D-PE concentration modulation is observed in SANS patterns before and after crystallization. This may be simply due to the center of D-PE mass (stretched amorphous network) is not aligned in a train but still disperses randomly in three space (as shown in Figure 7, row II). Although crystallization can still fix their position, no periodicity of D-PE concentration modulation is generated in extension direction as the modulation is not aligned in one direction.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Julie Kornfield (Caltech) for valuable discussions and suggestions on quantifying D-PE concentrations in gel and free chain parts of the sample. This work is supported by the National Natural Science Foundation of China (51633009, 51325301, and 51227801), Key research and development tasks of MOST (2016YFB0302501), and the Project 2013BB05 supported by NPL, CAEP. The experiment is partially carried out in National Synchrotron Radiation Lab (NSRL) and Shanghai Synchrotron Radiation Facility (SSRF).

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CONCLUSION The present work is aiming to establish the correlation among macroscopic draw ratio, real chain conformations, and shish nuclei in flow-induced crystallization of polymer. The combination of extensional rheological, in situ SANS and SR-SAXS allows us to link morphologies of flow-induced nuclei with rheological property (stress−draw ratio curve) and chain conformation from SANS. According to the quantitative data, the formation of shish requires rather small chain deformation, indicating that chain conformation is not the only factor for shish formation. On the basis of this result, we propose that coupling between intrachain conformation and interchain density is the molecular mechanism for FIC. Additionally, we find that the motion of molecular chains in the following solidification step after stretch is different if they crystallize from different draw ratio states. For samples stretched into hardening zone, the center of mass of the stretched amorphous network chains arranges into a train aligning in extension direction. The center of mass of D-PE will be fixed by the crystallization and the segments in interlamellar amorphous region shrink, resulting in periodic concentration modulation of D-PE. On the contrary, if the center of D-PE mass (stretched amorphous network) is still disperses randomly in three space (for samples are not stretched to the hardening zone), the concentration modulation of D-PE will not appear.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (L.L.). ORCID

Liangbin Li: 0000-0002-1887-9856 G

DOI: 10.1021/acs.macromol.6b01945 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.6b01945 Macromolecules XXXX, XXX, XXX−XXX