Correlation between Flow-Induced Nucleation Morphologies and

Apr 24, 2013 - ... work can apply well-defined thermal history and impose extensional flow .... Increasing strain leads to an increase of period in me...
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Correlation between Flow-Induced Nucleation Morphologies and Strain in Polyethylene: From Uncorrelated Oriented Point-Nuclei, Scaffold-Network, and Microshish to Shish Dong Liu, Nan Tian, Kunpeng Cui, Weiqing Zhou, Xiangyang Li, and Liangbin Li* National Synchrotron Radiation Lab and College of Nuclear Science and Technology, CAS Key Laboratory of Soft Matter Chemistry, University of Science and Technology of China, Hefei, China ABSTRACT: Extension-induced crystallization of lightly cross-linked high density polyethylene (XL-HDPE) has been studied with a combination of extensional rheology and in situ synchrotron radiation small-angle X-ray scattering (SR-SAXS) measurements, where XL-HDPE is a dynamic asymmetric system containing both cross-linked network and free chains (23 wt % gel fraction). SR-SAXS results revealed that the nucleation morphologies can be divided into four regions in strain space, namely uncorrelated oriented point-nuclei, scaffold-network nuclei, microshish nuclei, and shish nuclei. The definition of these four regions coincides nicely with the transitions in stress−strain curves, which allows us to establish a correlation between extension-induced conformations of chains and morphologies of nuclei. Even orientation of cross-linked network and free chains leads to the formation of uncorrelated oriented point-nuclei in region I, while the emergence of dynamic asymmetric nature due to disentanglement of free chain results in scaffold-network nuclei in region II. Formation of microshish in region III requires not only orientation but also stretch of chain segments, and finally nearly full extension of chain segments corresponds to shish nuclei in region IV.

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via optical microscope (OM).41−44 These observations reveal that the shish-kebab entity consists of two structural levels, namely micro shish-kebab and macro shish-kebab. The macro shish is constructed by micro shish-kebab, while macro kebab grows on the surface of macro shish.45,46 Such a hierarchical structure of shish-kebab has been confirmed by different groups with techniques in real space like scanning electron microscope (SEM) and reciprocal space like X-ray and neutron scattering (SAXS and SANS).47−60 The static picture between microshish and shish is well established, while the dynamic process concerning the evolution from microshish to shish with strain and time is still absent, which carries the molecular mechanism of flow-induced nucleation. Though the underlying mechanism for shish formation is still an open debate,26,61,62 strain is undoubtedly a necessary condition. The idea of coil−stretch transition (CST)63 from de Gennes et al. and Keller et al. emphasizes on strain rate, where a steady flow is assumed and strain is a prerequisite for shish formation.64 The transition from “point-like” to “threadlike” precursors under flow also lists strain as a basic requirement.65−68 Recently, in situ synchrotron radiation SAXS (SR-SAXS) measurements on extensional flow induced crystallization revealed that shish forms with strain smaller than yield point for polyethylene (PE). This indicates that the necessary condition for shish formation in PE is the network stretching rather than CST.69 While for isotactic polypropylene

INTRODUCTION Flow-induced crystallization (FIC) of semicrystalline polymers is not only a fundamental nonequilibrium thermodynamic challenge, but also of vital importance in processing like spinning,1 film stretching,2,3 injection,4 etc., during which entangled polymer liquid is subjected to complex flow prior to crystallization.5,6 Flow can enhance crystallization rate in orders of magnitude and induce orientated nuclei like shish or row nuclei.7−9 By adjusting the processing conditions (temperature, strain, strain rate) and molecular parameters, different crystalline morphologies such as spherulite, row-nucleated structure, shish-kebab, and fibrous crystal, can be obtained,10−27 27 which essentially stem from flow-induced different morphologies of nuclei. Among them, shish-kebab is the most widely studied morphology, as the primary nuclei shish not only carries the molecular mechanism of FIC, but also possesses improved mechanical and thermal properties.28−30 Unveiling the mechanism of shish formation is a critical step to establish molecular theory of FIC. Since its first discovery in 1960s, Pennings et al. and Keller et al. had devoted great efforts to elucidate the structure of shishkebab from stirred solution31−34 and deformed bulk polymer melt.35,36 Early picture for shish-kebab composes of parallel extended long chains as shish or row nuclei, which serves as nucleation sites for an epitaxial growth of folded-chain crystals as kebab.37−40 Transmission electron microscope (TEM) showed a shish of ca. 10 nm in diameter and several micrometers in length,29,37−39 while long oriented objects similar to the shish structure with diameter of several micrometers aligned along flow direction are often observed © 2013 American Chemical Society

Received: January 5, 2013 Revised: April 12, 2013 Published: April 24, 2013 3435

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Figure 1. Frequency dependence of G′, G″, and η* at 200 °C for (a) original HDPE and (b) XL-HDPE with total absorbed dose of 50 kGy. samples were 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 was calculated gravimetrically from the weight of the sample before and after extraction. The gel fraction of original HDPE sample is 0 wt %, while the value of XL-HDPE is 23 wt %. The XL-HDPE sample irradiated with 50 kGy in this study can be treated as a dynamic asymmetric system with cross-linked network (long chains) and free short chains. The samples are further characterized through small amplitude oscillation shear (SAOS) measurements, using the rheometer AR2000EX equipped with parallel plates with a diameter of 25 mm at frequency ranging from 100 to 0.1 and 2% strain. The results of SAOS at 200 °C for original HDPE and XL-HDPE are depicted in Figure 1, parts a and b, respectively. ω, G′, G″, and η* represent angular frequency, storage modulus, loss modulus and complex viscosity (η* = [(G′2 + G″2)1/2/ω]), respectively. It can be seen from Figure 1a that the original HDPE has typical viscoelastic liquid response when ω < 1.56 rad/s and viscoelastic solid like when ω > 1.56 ras/s. The terminal relaxation time (τd) was determined as 0.64 s at 200 °C. The shape change of the G′, G″ of XL-HDPE at the same temperature (200 °C) indicates the existence of structural change. And the fact that G′ > G″over the whole range of frequencies for XLHDPE, as shown in Figure 1b, implies viscoelatic solid response like elastomer. This further proves the existence of cross-linked network. The XL-HDPE samples for extensional flow test were cut into rectangular shapes with length, width and thickness of 30, 18, and 1 mm, respectively. A homemade two-drum extensional rheometer used in this work can apply well-defined thermal history and impose extensional flow field. The details of this apparatus have already been described elsewhere.76 Its design is similar to the commercial Sentmanat extensional rheometer, as schematically shown in Figure 2. The ends of samples are secured to geared drums by means of

(iPP), the formation of shish requires strains exceeding fracture. Different from PE, the iPP shish is induced along the tails left by the displacement of initial point nuclei.70 With ultrahigh molecular weight polyethylene (UHMWPE) having long relaxation times, Hsiao et al. investigated the effect of strain through shear-induced shish formation in UHMWPE/HDPE blends with different fractions.71 Focusing on strain-induced crystallization of rubbers, Toki et al. and Tosaka et al. investigated the molecular mechanism of strained and nonstrained molecules, and proposed the strained network acts as nuclei (shish-kebab) and coiled chain surrounding the nuclei partake in the epitaxial growth (lamella).72−75 Evidently all these observations point to that strain is a prerequired condition for shish formation. What will happen with strains smaller than the critical strain for shish formation? Comparing with the efforts on shish-kebab, this question has attracted less attention, which, however, may hold the key to knock out the mechanism of shish formation. The spatial distribution of “point-like” nuclei and the formation of microshish are the cornerstone to unveil the physics of shish formation and FIC. In this work, the effects of strain on chain conformation and the morphology of nuclei are studied with a combination of in situ SR-SAXS and extensional rheometer, where a lightly crosslinked PE network is employed to serve as a dynamic asymmetric system with cross-linked network (long chain) and free short chain. With the preprocedure of irradiation, such semicrystalline polyolefin system gains a very large relaxation time. SAXS results reveal that the morphologies of nuclei can be divided into four regions in strain space, namely (I) “uncorrelated oriented point-nuclei”, (II) “scaffold-network nuclei”, (III) “micro-shish nuclei”, and (IV) “shish nuclei” regions. The transition points in stress−strain curve coincides well with the division of four nucleation morphology, which allow us to constructs a one-to-one correlation between conformation of chains and morphology of nuclei.

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EXPERIMENT

The raw high density PE (HDPE) granules used in this study were supplied by Sinopec Qilu Co. Ltd.. The number-average (Mn), weightaverage (Mw), and Z-average molecular weight (Mz) are about 42 kg/ mol, 823 kg/mol, and 4395 kg/mol, respectively. The granules were first molded to plates with a thickness of 1 mm by a vulcanizing press at 180 °C and then cooled down to room temperature. The plates were annealed under vacuum at 90 °C for 24 h in order to eliminate residual stress. After that the plates were 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 was isolated from the sample during the radiation process. The trapped free radicals were further eliminated through annealing at 90 °C for 24 h under vacuum. The cross-linking degree of the lightly cross-linked high density polyethylene (XL-HDPE) sample is expressed as gel fraction. The

Figure 2. Schematic drawing of the homemade extensional rheometer for in situ SAXS measurement. clamps. The length of samples (L0) subjected to stretching equals the distance between the axes of two drums, where L0 is kept at a constant value of 20 mm during test. With a constant angular velocity ω of drums, the extensional strain rate is constant as ε̇ = ΔL/tL0 = ωd/L0, where d is the diameter of drums. With this uniaxial extensional rheometer, strain rate as well as Hencky strain ε can be varied independently. Each sample was first heated up to 200 °C and held for 10 min in order to erase thermal and mechanical histories. Then it was cooled to 3436

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Figure 3. Stress−strain curves for XL-HDPE melt under strain rate of 10 s−1. (a) Engineering stress−Hencky strain curve. (b) True stress−Hencky strain curve (black open rectangle). In order to show the evolution of true stress in regions I, II, and III, an operation of zoom-in is applied in the strain range from 0 to 2.0 (blue open cycle). (c) Selected initial 2D SAXS patterns immediately after step extension with different strains, which are indicated with the numbers at right-down corners of the patterns. (d) Corresponding 2D SAXS patterns after completion of crystallization of each sample. The extensional flow direction (FD) is horizontal, as indicated by the double-headed arrow. (Black arrows indicate the boundaries among rheological zones in stress−strain curve, black dash line are the boundaries among four regions divided according to the morphologies.). 132 °C with a rate of 2 °C/min. A nitrogen gas flow was used to homogenize temperature and prevent samples from degradation. The temperature fluctuation was within ±0.5 °C. Immediately after reaching 132 °C, step extensions with constant strain rate of 10 s−1 and different strains from 0.5 to 3.0 were imposed on the supercooled melt to induce crystallization. Torque was recorded continuously during and after step extensions with the torque sensor. Subsequent isothermal crystallization process on 132 °C was monitored by in situ two-dimensional (2D) SAXS measurement at the beamline BL16B of the Shanghai Synchrotron Radiation Facility (SSRF). The X-ray wavelength was 0.124 nm and a Mar165 CCD detector (2048 × 2048 pixels with pixel size of 80 μm) was employed to collect time-resolved 2D SAXS patterns. The exposure time was 10 s with an additional 5 s for reading and cleaning (i.e., patterns were acquired at a rate of 15 s/ frame). The sample-to-detector distance was calibrated to be 5300 mm by beef tendon. Fit2D software from the European Synchrotron Radiation Facility was used to analyze the SAXS data, which were corrected for background scattering through subtracting contributions from the extensional rheometer, air, and the XL-HDPE melt under quiescent conditions. The 2D SAXS pattern was 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.

zone in true stress−Hencky strain curve is the same as that in the engineering stress−Hencky strain curve, which locates at strain larger than 2.0. Figures 3c presents selected 2D SAXS patterns immediately after step extensions with different strains. The extensional flow direction is horizontal, as indicated by the double-headed arrow. The 2D SAXS patterns collected immediately after the step extension show clearly different features with different strains, which can be defined into four regions versus strain. The boundaries are indicated as black dash line in Figure 3. Region I coincides with the linear deformation zone in the engineering stress−Hencky strain curve (0 < ε < 0.8), where no extra scattering signal is detected comparing to scattering from the initial melt. It indicates that neither crystallization nor any other density fluctuation is induced immediately after extensional flow in this region. For the convenience of description, region I is defined as “un-correlated oriented point-nuclei” region, as nuclei formed later are well separated from one another in space. After strain exceeds linear deformation region, strong lozenge-shaped scattering signal appears immediately after step extension, which we propose caused by stretched network of nuclei. Note here that stretched network represents the spatial distribution of density fluctuation or nuclei rather than molecular chain network, as the latter could not give notable electronic density contrast. Thus, we define region II as “scaffold-network nuclei” region to represent the spatial distribution of flow-induced nuclei. Interestingly, region II covers a strain range approximately from 0.8 to 1.25 (0.8 < ε < 1.25), which coincides with the strain window between the ends of linear deformation zone in engineering stress−Hencky strain and true stress−Hencky strain curves. Further increasing strain, the scattering patterns transform from the lozengeshaped to a pair of lobule-shaped maxima in equator (where the fiber axis is with the stretching direction in horizontal). This transformation of scattering patterns represents a transition of spatial distribution of nuclei from deformed scaffold to parallel alignment with defined lateral periodicity. It should be noted that the periodicity follows the direction perpendicular to the

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RESULTS Step extensions with different strains from 0 to 3.0 and a constant strain rate of 10 s−1 were imposed on XL-HDPE samples to induce crystallization at temperature of 132 °C. Figure 3 presents the stress−strain curves and the selected 2D SAXS patterns. Engineering stress−Hencky strain curve and true stress−Hencky strain curve are depicted in Figure 3, parts a and b, respectively. The engineering stress−Hencky strain curve can be roughly defined into three zones, namely linear elastic, stress plateau and strain hardening zones, whose boundaries are located at strains of around 0.8 and 2.0 (as indicated by the black arrow). The true stress−Hencky strain curve can also be defined into three zones, which, however, are different from those of engineering one. The linear elastic zone covers strain up to 1.25, which is followed by the second zone with continuously increasing of modulus. The strain hardening 3437

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flow direction. Thus, we assign the lobule-shaped maxima in equator to the lateral correlation of microshish rather than the periodicity of lamellar crystals. The lobule-shaped scattering patterns appear in a strain region from about 1.25 to 2.0 (region III, 1.25 < ε < 2.0), which coincides with the second zone in the true stress−Hencky strain curve with true stress slightly deviated from linear deformation. Region III is defined as “micro-shish nuclei” region. The final region (IV) is located in the strain hardening zone in stress−strain curves (ε > 2.0), where the scattering patterns show typical feature of shish with two streaks in equatorial direction. Thus, we define region IV as “shish nuclei” region. Moreover, the identifications of the four regions are clearly shown in the corresponding patterns of Figure 3c at the end of isothermal crystallization, as Figure 3d indicated. Region I shows a pair of meridianal two point pattern. Region II shows a pair of angular two point pattern. Regions III and IV have a meridianal pattern along with equatorial streak. However, the ones in region III are more diffusive. The different morphologies of nuclei and the final crystal, as well as their transformation with strain and time are further analyzed in the following sections, which confirm the assignment of these four regions. Figure 4a gives selected 2D SAXS patterns during crystallization of sample stretched with a strain of 0.6 (a

point-nuclei”. Long period of lamellar stacks (LLS), which is the distance between the adjacent oriented lamellas statistically, was estimated from the position of the intensity maxima along the meridian in the SAXS patterns. LLS keeps as a constant of about 67 nm in early stage of crystallization and then decreases sharply into a plateau of about 45.5 nm. Decrease of LLS in later stage of crystallization is generally attributed to the insertion of lamella,77 which suggests that the interlamellar amorphous part is sufficiently large and here chain segments can still enjoy their freedom to crystallize. As a representative for region II, Figure 5a depicts several 2D SAXS patterns of the XL-HDPE sample collected at the early

Figure 4. (a) Selected 2D SAXS patterns of the XL-HDPE sample during isothermal crystallization after extension with strain of 0.6 (representative of region I). (b) Integrated 1D SAXS curves during the early stage of crystallization. (c) Time evolution of normalized scattering intensity (black open rectangle) and long period of lamellar stacks (LLS, blue open cycle) during crystallization, respectively.

Figure 5. (a) 2D SAXS patterns of the XL-HDPE sample at early stage of crystallization after extension, with a strain of 0.9 as a representative for region II. (b) Highlight of the first pattern (0 s), the dash lines demonstrate the integration sector of meridian (M) and equator (E) at −15° ∼15° and 75°∼105°, respectively, and (c) the corresponding 1D SAXS scattering profiles. (d) Results of Bragg period in both directions as a function of Hencky strain. (e) Time evolution of the equatorial scattering profiles in the early stage of crystallization.

representative for region I). It shows that no extra scattering signal is detected immediately after the step extension comparing to scattering from the initial melt. It takes about 450 s for a pair of blob-shaped two-point pattern in meridian to show up. It should be mentioned here that no intensity change is observed within 2 h for the quiescent condition at 132 °C. Figure 4b presents integrated 1D SAXS curves during the early stage of crystallization, as the nucleation is emphasized in this work. The normalized scattering intensity and the evolution of lamellar periodicity are plotted versus time in Figure 4c. The level-up of intensity, indicating the onset of crystallization or the end of induction period, corresponds to the appearance of the scattering peak due to lamellar periodicity, which manifests that the scattering signal is dominantly from lamellar stacks rather than from primary nuclei. This assignment leads to a conclusion that nuclei formed during induction period are well separated from one another, which give undetectable signal from our current SR-SAXS. Thus, in respect to nucleation morphology, we denote region I as “un-correlated oriented

stage of crystallization after extension with a strain of 0.9. Figure 5b is a highlight of the first lozenge-shaped pattern with red dash lines indicating the azimuthal angle range for integrations in both meridianal (M) and equatorial (E) directions. The integrated 1D SAXS curves in both directions are plotted in Figure 5c, where a shoulder peak appears in each curve. The existence of scattering peaks indicates that extension-induced precursors or nuclei disperse periodically rather than completely random in both directions, though the periodicities are still rather weak with diffusive scattering peaks. The coexistence of periodicities in meridian and equator describes a scaffold-network spatial distribution of nuclei, which allows us to assign this region as “scaffold-network nuclei” region. The q value at the peak maximum in equator is larger than that in meridian, which matches with the anisotropic feature of the lozenge-shaped pattern. Figure 5d plots the Bragg period in both directions as a function of Hencky strain, which are calculated with L = 2π/q. Increasing strain leads to an increase of period in meridian (LM) and a decrease in equator 3438

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periods increase from initial 38.1, 32.6, 28.8, 26.7 nm to 75.7, 70.6, 66.1, 65.4 nm with strains of 1.3, 1.4, 1.6 and 1.8, respectively, which falls roughly into a rule of doubling and suggests a possible merging between two neighbor microshish. According to the data above, it can be seen that the initial lateral periodicity of microshish in region III decreases with the increase of strain. This seems reasonable, as increasing strain may pull microshish close to each other or equivalently increase the number density of microshish, which ultimately leads the microshish to form shish. In region IV, intense equatorial streaks appear immediately after extension, which is generally assigned as the scattering of fibril shish. Selected initial 2D SAXS patterns in region IV with different strains are highlighted in Figure 7a. Interestingly, the

(LE), which enlarges the gap between the periodicities in two directions. Eventually the meridianal scattering peak disappears, marking the transition from scaffold-network nuclei to microshish. The morphology of scaffold-network nuclei not only evolves with strain, but also changes with crystallization time, as observed from Figure 5a. Along with crystallization time, on top of the initial lozenge-shaped pattern, weak two scattering streaks appear in equator, indicated by red arrows in the third pattern (30 s after the extension), which is generally assigned as the characteristic feature of shish in FIC. Figure 5e presents the time evolution of 1D SAXS curves in equatorial direction, showing that the appearance of the streaks overshadows the initial shoulder peak along with crystallization time. This suggests that the initial scaffold-network nuclei may partially transform into shish like structure through growth or merging among adjacent nuclei along with crystallization time. Figure 6a exhibits several representative 2D SAXS patterns during crystallization. The sample is extended with a strain of

Figure 7. (a) Selected initial 2D SAXS patterns in region IV. The numbers in each pattern represent the corresponding imposed Hencky strain. The last two patterns are the results after an operation of subtraction. (b) Corresponding 1D SAXS scattering profiles with strains indicated with the curves.

lobule-shaped scattering signal from microshish seems to still remain in region IV, where the tails of the streaks spray in relatively large azimuthal angle range. A strain of 2.0 locates the transition from microshish to shish, which corresponds to the onset of strain hardening in stress−strain curve. Taking the scattering pattern at strain of 2.0 to represent the contribution from microshish, a subtraction of the microshish signal makes a much clearer streak signals out off the initial patterns taken at larger strains (see Figure 7a). The corresponding 1D SAXS profiles are shown in Figure 7b. A shoulder peak at q of about 0.3 nm−1 can be easily indentified in the 1D SAXS curve at strain of 2.0, while the strong scattering from shish shadows the shoulder peaks at strains of 2.3 and 3.0 though their 2D patterns clearly show the existence of scattering due to the periodic arrangement of microshish. The combined features from both shish and microshish in region IV confirm the widely accepted superstructure of shish with microshish as its subunit. After the detailed analysis above, an overall prospect of Bragg period of flow induced nuclei as a function of strain can be obtained, which is calculated based on the first scattering patterns after stretch and summarized in Figure 8a. Distinctive features of Bragg periodicities are observed in different regions. In region I, no correlation among nuclei is observed. As soon as strain enters into region II, nuclei arrange in a diffusive periodic fashion in both meridianal (LM) and equatorial (LE) directions. The period LM in meridianal direction disappears in region III, while the lateral period LE in equator follows a continuous decrease from region II to III, reaching a plateau in region IV. Different initial morphologies of nuclei are expected to result in different final lamellar morphologies as the latter are grown from those nuclei. Figure 8b plots the orientation parameter of lamellar crystals in the final crystallized samples versus strain, which are calculated based on the full width at half-maximum (fwhm) of the azimuthal intensity distribution of scattering

Figure 6. (a) Selected 2D SAXS patterns of the XL-HDPE sample after extension with a strain of 1.4, as a representative for region III. (b) 1D SAXS scattering profiles in equatorial direction as a function of time. (c) Lateral Bragg period (LE) of microshish as a function of time, with four different strain in region III. Log scale is adopted to signify the evolution of LE in the early stage, where data of 0 s are pointed out with a break in time axis.

1.4, as an example for region III. The most featured scattering signal is a pair of lobule-shaped pattern with equatorial maxima, which is assigned as periodicity of microshish superstructure induced by extension. Comparing to region II with scattering maxima in both meridian and equator, the initial pattern (0 s) of region III only has a sharp equatorial scattering maximum, while the meridianal one seems to be completely disappeared. This difference provides a clear-cut between region II and III. The lobule-shaped maxima shift to low q side with crystallization time and transform into streaks characterizing the formation of shish-like structure. This transformation indicates that the initial microshish merge or/and grow into shish, similar to that which occurs in region II. Figure 6b depicts 1D SAXS profiles integrated in equatorial direction during early stage of crystallization, which represent the time evolution of microshish. It can be seen that the scattering maximum shifts to low q side along with time, suggesting an increase of lateral periodicity with time. The evolution of lateral periodicity of microshish superstructure is plotted versus crystallization time in Figure 6c, where data collected under four different strains in region III are summarized together. The 3439

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(1/λ1/2) if affine deformation and uncompressible condition are still held in these two regions, whereλ = eε. Figure 9 plots LE

Figure 9. Plot of LE versus inverse of square root of extension ratio (1/ λ1/2) in regions II and III. The black open cycles are experimental data, and the red line is the linear fitting. Figure 8. (a) Overall prospect of Bragg period of extension induced nuclei. (b) Orientation parameter extracted from 2D SAXS patterns of final crystallized samples after imposed by step extensions with different strains. (c) Time evolutions of long periods LLS of samples with strain of 0.6, 0.9, 1.4 and 2.3, representing four regions, respectively. (d) LLS in the final crystallized samples as a function of strain.

versus1/λ1/2, which shows a nicely linear relation except the point near the transition from region III to IV. This confirms the deformation in regions II and III following the rule of affine, while deformation with large strain near and in region IV deviates from affine. The linear fitting result (red line in Figure 9) is LE=−66.8 + 208.0(1/λ1/2) so the function can be transformed as LE = −66.8 + 208.0(1/eε/2). Note that the scope of application should restrict to ε ≤ 1.6. According to this function, the idealized theoretical requirement to induce macroshish is ε = 2.27 if LE = 0. While the experimental observation withε = 2, which is located between 1.6 and 2.27, where decreasing LE already deviates from affine but does not reach zero, due to the chain extension reach the up limits along with the plateau of the lateral compression. Meanwhile, the largest period of microshish superstructure theoretically is 141.2 nm when ε = 0.

intensity from lamellar periodicity. In region I, the orientation parameter increases with strain and reaches a relatively high level (up to 0.92). Unexpectedly, with further increasing strain to region II, the orientation decreases with the increases of strain, which reaches a plateau in region (III). The orientation jumps to another low level of plateau when strain enters into region IV. Following the nucleation morphology, the final lamellar orientations also fall into four distinctive regions in strain space. The different morphologies of nuclei also affect the fashion of lamellar growth as well as the final morphology. Figure 8c illustrates the time evolutions of long periods of lamellar stacks (LLS) during isothermal crystallization, where four samples with strains of 0.6, 0.9, 1.4, and 2.3 are selected to represent the four regions, respectively. In region I (represented by the data at strain of 0.6), LLS keeps relatively constant in early stage of crystallization, which drops sharply from 67.0 to 45.5 nm in later stage of growth. The later sharp decrease of long period is generally attributed to insertion of lamella. The insertion mechanism is weakening with the increase of strain, and only small drop of LLS is observed in region II and III in the later stage of crystallization. In region IV, no any dropdown of LLS is observed. In contrast, an increase of LLS occurs in the early stage of crystallization, which is attributed to a coupling between nucleation rate and poststretch relaxation.76 The LLS of the final crystallized samples is plotted vs strain in Figure 8d, which shows a nonmonotonic trend. Increasing strain in regions I and II leads to a continuous increase of LLS from 45.5 to 59.8 nm, which reaches a plateau of about 63.0 nm in region III. Further increasing strain from 2.0 to 3.0 in region IV, LLS decreases from 54.1 to 48.6 nm. This three-step transition coincides with the three zones in true stress−Hencky strain curve, which may be related to conformation of chains at different strains. In regions II and III, the periodicity LE related to lateral correlation of microshish continuously decreases with strain. A simple geometric consideration would lead to proportionality between LE and the inverse of the square root of extension ratio

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DISCUSSION Current work studies the relationship between flow-induced nucleation morphology and strain, which is aiming to establish a correlation between extension-induced conformation of chains and morphology of nuclei. On the basis of in situ SAXS measurements, time evolutions of morphological data during extension-induced crystallization with different strains are extracted, which include Bragg periodicities of nuclei, long period of lamella and lamellar orientation. All these morphological data consistently lead to the division of four regions with respect to nucleation morphology in strain space. Figure 10 shows a schematic illustration of nuclei and lamellar crystals in strain-time space, which demonstrates the transitions from uncorrelated oriented, scaffold-network to microshish and shish nuclei with the increase of either strain or crystallization time. Starting with the dynamic asymmetric system containing cross-linked network and free chains, step extension results in orientation and stretch of chains. In region I with strain lying in linear elastic deformation zone in engineering stress−Hencky strain curve, the main consequence generated by step extension is chain orientation, as illustrated in row I. In this region, an induction period up to several hundred seconds always exists before scattering signal from lamellar stacks shows up. Here the primary nucleation is induced by the step extension, as under quiescent condition no crystallization is observed in 2 h at this temperature. Since strain in region I is rather small, the nucleation rate or density is at low level, which results in nuclei 3440

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Figure 10. Schematic illustration of the formation of extension induced nuclei and the subsequent crystallization.

well separated with one another and lacking of spatial correlation. As mentioned in the Results, the scattering signal from nuclei is not detectable with our current SR-SAXS, where crystallization is viewed via scattering from lamellar periodicity. Thus, we name region I as the “un-correlated oriented pointnuclei region”. As the sample system contains cross-linked network, both nucleation and growth processes are affected by extension, which leads to a relatively high orientation of lamellar crystals. In the later stage of crystallization, the continuous decrease of LLS is due to insertion of new lamellae among the crystallized lamellar stacks, as illustrated with the column D of row I in Figure 10. Row II in Figure 10 describes extension-induced nucleation and growth of XL-HDPE in region II. Immediately after the cessation of step extension, the lozenge-shaped scattering pattern appears, which reflects the spatial distribution of extension-induced nuclei. The lozenge-shaped pattern is assigned to stretched network. Nevertheless as scattering maxima exist in both meridianal and equatorial directions, the arrangement of nuclei follows weak periodicities, which are noted as LM and LE in column A. Coalescence of neighbor nuclei may take place during crystallization, which eventually results in shish like structure in the later stage of crystallization evidenced by the appearance of streak signal in SAXS patterns indicated by the red arrows in Figure 5a. This process is illustrated through column B and C of row II, where the growth of the shish may contain the combination of microshish and microkebab. Further increasing strain into region III, the molecular chains are directly stretched into bundle like structure (see column A of row III), which is named as microshish. Here the internal bundle periodicity is preserved, while the periodicity in extensional direction disappears. Similar to that in region II, these bundles or microshish merge and grow into shish in the crystallization process (see column B and C of row III). The fourth row depicts morphological evolution in region IV, where shish is directly induced by extension. The coexistence of scattering signals from periodic microshish and fibril shish supports that shish is composed of microshish structures, as illustrated in row IV.

Interestingly, the division of these four nucleation morphology regions coincides nicely with the transitions in both engineering stress−Hencky strain and true stress−Hencky strain curves. The nucleation morphological transition from region (I) to (II) occurs around the yield point of engineering stress−Hencky strain curve, which can be attributed to the emergence of dynamic asymmetric nature of the system. XLHDPE used in this work is composed of 23 wt % cross-linked network and 77 wt % free chains, which mimics a blend of long and short chains and is a typical dynamic asymmetric system. In the elastic deformation zone, homogeneous deformation of the blend is expected to take place, where free chains and crosslinked network suffer deformation equally. In region I, the cross-linked network and the free chains share the same extension-induced conformation with chain oriented in extensional direction, which implies that all chains enjoy equal opportunity to form nuclei and homogeneously spatial distribution of nuclei is expected. A combination of low nucleation density due to small strain and homogeneous spatial distribution of nuclei certainly leads to nuclei well separated with each other, which make region I deserving the name of “un-correlated oriented point-nuclei”. As strain exceeds the yield point, disentanglement of free chains occurs, which leads to discrimination between free chains and cross-linked network due to dynamic asymmetry nature of the system. Following the concept of stressconcentration coupling in dynamic asymmetric system, inhomogeneous distribution of free chains and network may be induced by stretch, which is reflected by butterfly or lozengeshaped patterns in neutron scattering.78,79 In region II, the lozenge-shaped SAXS patterns are due to scaffold-network of nuclei, which reflect the heterogeneous distribution of free chains and cross-linked network. As the stress is mainly taken by the cross-linked network, it may contribute more to nucleation. Nevertheless as nucleation takes rather short time, it is hard to imagine that free chains can be excluded out from nucleation within such a short time. Moreover, as we showed before, nucleation rate can be enhanced dramatically through synergistic effect between stretched cross-linked network with a low nucleation barrier and free chains with a fast diffusion rate.80 3441

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homogeneous deformation with small strain, where orientation is evenly generated in cross-linked network and free chains. Increasing strain into region II differentiates the cross-linked network from free chain and triggers the dynamic asymmetric nature, where “scaffold network nuclei” mimic the heterogeneously deformed chain network. The formation of microshish in region III requires both orientation and stretch of chains, where these conformational information is evidenced by the level-up of stress in true stress−Hencky strain curve. The sharp shoot-up of stress in region IV comes from chains with a nearly full extended conformation, which corresponds to the formation of shish.

Further increasing strain, a transition from scaffold-network of nuclei to microshish takes place around the onset point of the second zone in true stress−Hencky strain curve, where true stress starts to level up slightly from linear deformation. This coincidence suggests that the transition from region II to region III may correspond to the transition from orientation to stretch of cross-linked network, where chain segments among crosslinked points begin to be partially stretched. With partially extended chain segments in region III, it is natural to form microshish. As strain enters into region IV, stress shoots up sharply due to nearly full extension of chain segments in the cross-linked network. Transition from partial extension to full extension of chain segments corresponds to the transition from microshish to shish, which defines the boundary between regions III and IV. The long period data shown in Figure 8, parts c and d, suggest that indeed a distinctive difference between microshish and shish exists. The long period of lamellar stacks (LLS) in the final crystallized samples increases with the increase of strain and reaches a plateau in region III, which, however, turns down in region IV. The increase of LLS from regions I to III can be attributed to orientation and stretch of chain segments in the network, which may impose constraint on crystallization and result in thicker interlamellar amorphous layer with high entanglement and cross-link densities. Crystallinity obtained with differential scanning calorimetry indeed shows reduction with strain (which is not presented here). Here, the initial nucleation density as well as the nucleation in insertion plays dominant role in controlling the final long period of lamellar stacks (LLS). In region IV, shish with nearly full extended chain conformation allows kebab to grow on its surface without preservation, though entanglement and cross-link points still exist. In this case the final LLS is determined by the spatial availability for the growth of kebab rather than nucleation site. In summary, combining experimental data from stress−strain curves and the corresponding morphologies of nuclei, the correlation between extensional strain and nucleation morphology is established through extension-induced conformation of chain as a bridge. This indicates that the rheological characterization should not be neglected in the study of FIC. Furthermore, the dynamic process concerning the evolution from oriented scaffold network nuclei, microshish to shish with strain and time may provide a reference for the strain thresholds of polymer processing such as biaxially oriented film. It also suggests that description of different nuclei morphologies may need separate nucleation kinetics.

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AUTHOR INFORMATION

Corresponding Author

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank Prof. Gerrit Peters (TUE) for his suggestion in Figure 9 and other fruitful discussions. We acknowledge Prof. Xuewu Ge’s group (Hefei) for their kindly help on the sample irradiation. We also acknowledge Prof. Zhigang Wang’s group (Hefei) and Mr. Shiwang Cheng (Akron) for the rheology measurement and discussions. This work is supported by the National Natural Science Foundation of China (51033004, 50973103, 51120135002, 51227801), the Fund for One Hundred Talent Scientist of CAS, 973 program of MOST (2010CB934504) and China Postdoctoral Science Foundation (2012M521233). The research is also in part supported by “the Fundamental Research Funds for the Central Universities”. The experiment is partially carried out in National Synchrotron Radiation Lab (NSRL) and Shanghai Synchrotron Radiation Facility (SSRF).

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REFERENCES

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CONCLUSION Current work is aiming to establish the correlation among strain, chain conformations, and nucleation morphologies in flow-induced crystallization of polymer. The combination of extensional rheological technique and in situ SR-SAXS allows us to link morphologies of flow-induced nuclei with strain, meanwhile the stress−strain curves reflect chain conformations at different strains. All morphological data, including Bragg periodicities of nuclei, long period of lamella, and lamellar orientation, consistently lead to the division of four regions with respect to nucleation morphology in strain space, namely uncorrelated oriented point-nuclei, scaffold-network nuclei, microshish nuclei, and shish nuclei. The definition of these four regions coincides nicely with the transitions in engineering stress−Hencky strain and true stress−Hencky strain curves. The “un-correlated oriented point-nuclei” in region I stem from 3442

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