Article Cite This: Macromolecules XXXX, XXX, XXX−XXX
Shish-Kebab Crystallites Initiated by Shear Fracture in Bulk Polymers Yijing Nie,†,‡ Yunfeng Zhao,§ Go Matsuba,§ and Wenbing Hu*,† †
Department of Polymer Science and Engineering, State Key Laboratory of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, 210093 Nanjing, China ‡ Institute of Polymer Materials, School of Materials Science and Engineering, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013, China § Department of Polymer Science and Engineering, Faculty of Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata 992-8510, Japan ABSTRACT: The study of shear-induced polymer crystallization has so far overlooked heterogeneous crystal nucleation of shish-kebab crystallites, which can be initiated by the stretched local polymer chains in the sporadic events of shear fracture upon sudden startup or cessation of polymer shear flow or in the memory of these events. We performed dynamic Monte Carlo simulations of a binary blend of short and long polymers and investigated the formation process of shish-kebab crystallites in a driven field with Poiseuille-flow-like gradient forces presumably generated around the shear layer of melt fracture. The results demonstrated the synergetic coil-extension and segregation behaviors of long-chain fractions upon precursor formation, which lead to a discontinuous crystalline structure along the shish. We found that the shear fracture hypothesis can reconcile several controversial experimental arguments on the precursor formation of shish-kebab crystallites in shear-induced polymer crystallization.
1. INTRODUCTION As a unique morphology for polymers, the shish-kebab crystallites are commonly generated in the industrial plastic molding, which often determine the mechanical performance of semicrystalline polymer products. Dating back to 1955, Keller first observed the row structure of polyethylene lamellar crystallites in the shear flow of polymer solutions.1 In 1963, Blackadder and Schleinitz2 and Mitsuhashi3 separately discovered the shish-kebab crystal morphology, and in 1965 its hierarchical structure was interpreted by Pennings and Kiel.4 Keller believed that in solutions the fully extended chains first formed the crystalline shish and then acted as a template for the lateral overgrowth of the folded-chain lamellar crystallites as kebabs.5 De Gennes proposed an abrupt coil−stretch transition of single polymer in the shear flow of polymer solutions in order to explain the underlying molecular origin of sporadic orientations of the shish.6 This idea has received some experiment evidence.7,8 Indeed, molecular simulations have demonstrated that even a single stretched chain can induce shish-kebab crystal formation in polymer solutions.9 In contrast to that in polymer solutions, the mechanism of shish formation in bulk polymers is still hotly debated. So far, the controversial arguments on the flow-induced polymer crystallization in the bulk polymer phase are mainly focused on the following points: First, since shish-kebab crystallites occur only in the polydisperse polymer systems, the dominant role of long-chain fractions in the shish formation has raised arguments. Keller suggested that only long chains with molecular weight higher than a critical value could be stretched at a fixed strain rate and © XXXX American Chemical Society
be developed into the precursor of shish at the early stage of shear, while short chains remain in random coil states and are dominant in the formation of kebabs at the later stage.5,10 The addition of long chains above the overlapping concentration for entanglement can dramatically enhance the formation of oriented structures.11 However, Kimata et al. presented a different story that short chains can also be involved in the formation of shish.12 Zhao et al. confirmed that the long-chain entanglement network catches short chains upon shish formation.13 Second, the origin of the shear-induced shish precursor still puzzles researchers. Hsiao et al. proposed that only the chain segments between entanglements could undergo the coil− stretch transition, resulting in the appearance of multiple shish concatenating the same stacks of lamellar crystal kebabs.14 Penning et al.,15 Han et al.,16 and Li et al.17,18 believed that the shish was originated from the extension of the entanglement network rather than the coil−stretch transition of single strands. By means of a polarized optical microscope, Kanaya and his collaborators observed micrometer-width stringlike oriented objects at high temperatures even above the normal melting point, acting as the reservoir of precursors for shish formation.19−23 Similar structures were also detected by Winter et al.24,25 On the basis of in situ rheo-SAXS and rheo-WAXD studies, Hsiao et al. have observed that equatorial streaks in the SAXS patterns appear right after the shear cessation, but at the Received: November 4, 2017 Revised: December 14, 2017
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DOI: 10.1021/acs.macromol.7b02357 Macromolecules XXXX, XXX, XXX−XXX
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formation of the shish-kebab structures in extensional flow of polymer solutions.39 On the basis of nonequilibrium molecular dynamics simulations, Jabbarzadeh et al. separated the effects of strains and shear rates on flow-induced polymer crystallization.40 In addition, both the enhanced nucleation and growth of shish-like elongated nuclei under sufficiently fast flows were investigated by Graham et al.41,42 Dynamic Monte Carlo (MC) simulations demonstrated that long chains retain the orientation memory after shear cessation, and crystallize into shish in priority, which will induce short-chain kebabs later on.43 In addition, dynamic MC simulations of strain-induced polymer crystallization have been performed,44−52 which improved our substantial understanding on flow-induced polymer crystallization. On the other hand, dynamic MC simulations were also employed to investigate shear-stress-induced coil deformation in the driven flows.53−57 In the present work, on the basis of the approach developed in previous MC simulations, we further explore how the force field holding the Poiseuille-flow gradient generated by shear fracture can initiate the development of shish-kebab crystallites. Our results will demonstrate that the shear-induced precursor is formed by the aggregation of locally deformed subchains of the long chains. When the precursor transforms into shish, the subchain domains crystallize together with the nearby shortchain segments, and the crystalline structure along the shish appears discontinuous. We find that our observations reconcile many controversial arguments on the mechanism of precursor formation.
same time no obvious crystal reflections emerge in the WAXD patterns, also suggesting that the shear-induced precursors contain very little crystallinity.26 By means of the microbeam X-ray scattering measurements, Kanaya et al. found that the precursor holds an oriented gel-like structure with a crosslinking of small crystallites.20 Alfonso’s group reported that the survival time of precursors after the shear cessation is extremely longer than the typical rheological relaxation times for the recovery of unperturbed coil conformation of molten polymer chains.27 Janeschitz-Kriegl et al. stressed that only the entropic reduction of polymer melts due to flow-induced orientation and stretching of chains cannot explain the dramatically accelerating nucleation of sheared polymer.28,29 All the above experimental observations suggest some occasional events to enhance both the range and the extent of chain stretching responsible for the precursor formation toward sporadic shish-kebab crystallites. Third, the transformation process from precursor into shish also attracts lots of attention. Balzano et al. observed that after the shear cessation at a high temperature small-size precursors dissolve, while those large-size ones develop into the shish.30 In addition, Hashimoto et al. reported that the extensional flow could induce phase separation in the solutions of entangled polymers at the early stage of shish-kebab formation.31 Those scenarios appear very different from each other and thus demand further investigation. It is well-known that upon slow cooling crystallization is usually initiated by heterogeneous crystal nucleation on the foreign surfaces of those impurities in bulk polymers, such as fillers, additives, dusts, residual catalysts, or content walls.32 In the shear-induced crystallization of melt polymers, heterogeneous crystal nucleation could even more be initiated by the stretched polymer chains or their memory in the sporadic events of local shear fracture,33 which will bring much stronger acceleration effects than the coexisting foreign surfaces on primary crystal nucleation. Indeed, as a characteristic rheological behavior of bulk polymers, every startup and cessation of shear flow have to pass through an instability region of shear/ extension rates,34 where the extensional viscosity decays with the increase of extensional rate and thus easily generates local melt fracture at everywhere. Because of a stochastic nature, the sporadic events of local shear fracture occur at rather unpredictable locations in bulk polymers, similar to the location of impact fracture on the smooth surface of a sample bar during the measurement of un-notched impact strength. In practice, the elastic breakup and shear banding have been observed by a particle-tracking velocimeter in the middle of the bulk melt,35,36 or near the edge where the heterogeneous structure is commonly generated,37 or more often as the wall slip when the wall binding cannot hold the elastic stretching of polymers.38 The shear fracture crosses over the micrometer-scale width and even much larger length, where the local stretching of polymers, in particular, those long-chain fractions, will be enhanced, acting as the reservoir of shish precursors for heterogeneous crystal nucleation as observed by Kanaya’s group.19−23 So far, the shear-fracture mechanism of heterogeneous crystal nucleation has been overlooked in the investigation of flow-induced polymer crystallization. Whether the details of this mechanism can reconcile the above controversial arguments on the formation of shish-kebab crystallites is worthy of further investigation. Molecular simulations can probe the structural evolution of flow-induced polymer crystallization at the molecular scale. By means of Langevin dynamics simulations, Dukovski et al. confirmed the presence of the coil−stretch transition during the
2. SIMULATION TECHNIQUES In a lattice box of size 64 × 256 × 64 (XYZ), we put 768 long chains, each containing 256 monomers, and 24 576 short chains, each containing 32 monomers, so the occupation density is 0.9375 to mimic bulk polymer phase of a blend with 20% volume fraction of the long-chain component. The unit size of the lattice box was thus presumably corresponding to the monomer size. The remaining vacancy sites were served as free volume. Polymer chains moved in the lattice space via a microrelaxation model, which allowed a monomer jumping from an occupied site to a neighboring vacancy, sometimes with partial sliding diffusion along the local chain.58 The bonds were oriented either along lattice axes or along diagonals, and thus the coordination number of each monomer was 26 (summed over six axes, eight body diagonals, and 12 face diagonals). Each bond contained maximum 13 possible orientations. In addition, both double occupations and bond crossings were forbidden, attributed to the volume exclusion of polymer chains. Periodic boundary conditions were introduced along X, Y, and Z directions. As demonstrated in Figure 1, the shear fracture generates a pair of Poiseuille flows with opposite directions hindering
Figure 1. Schematic illustrations of (a) the local shear-induced melt fracture, (b) the Poiseuille shear flow model for stress distributions around the direction normal to the layer of shear fracture, and (c) the Poiseuille shear flow model for the driving-force distributions adopted in our present simulations. B
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Macromolecules each other at the fracture layer; therefore, away from the fracture layer, the shear stresses decay presumably linear, like the edge of Poiseuille shear flow. Since we were interested only in polymer behaviors under such a gradient of driven forces, we set up a Poiseuille flow model with a symmetric decay of driving forces away from the middle to mimic the fracture-induced stress field, as illustrated in Figure 1c. To this end, a gradient potential has been introduced into the energy penalty in conventional Metropolis sampling algorithm for a trial move of monomers in each step of microrelaxation process: E = [aEc + pEp + sEs]/(kT ) ⎧0 (Δy = 0, Δx or Δz = ± 1) ⎪ ⎪∓ fz (Δy = ± 1, z ≤ 32, Δx or ⎪ Es = ⎨ Δz = 0) ⎪ ⎪∓ f (64 − z) (Δy = ± 1, z > 32, Δx or ⎪ Δz = 0) ⎩
(1-1) Figure 2. Time−temperature protocol for our simualtions of shearinduced polymer crystallization.
blend. We calculated the extension ratios of the long and short chains, as their time evolution curves shown in Figure 3. (1-2)
where Ec is the potential energy change for noncollinear connection of consecutive bonds along the chain, reflecting the chain inflexibility, Ep is the potential energy change for each pair of nonparallel packed bonds, representing the molecular driving force for polymer crystallization,59 a is the net change in the number of noncollinear connection pairs of bonds along the chain, p is the net change in the number of nonparallel packed pairs of bonds, s is the net amount of monomers moving forward for a distance of one lattice spacing in each step of microrelaxation, Es is the change of flow-field potential that drives a monomer moving from (x, y, z) to (x + Δx, y + Δy, z + Δz) in our lattice model, f is the gradient of the flow-field potential, and y and z are the coordinates in Y (flow direction) and Z (driving-force gradient) directions, respectively, k is the Boltzmann constant, and T is the temperature. Below, we set Ep/Ec = 1 and simplified the reduced system temperature kT/Ec as T. In our previous paper, we have demonstrated that Es/Ec was the external potential field of driving forces, corresponding to the driving-force aspect of shear stress in a shear field imposed along Y-axis onto each monomer.53 The hydrodynamic interactions above the monomer scale were not considered here because in reality they are screened off by the high interpenetration of bulk polymer chains. To obtain the initial state, the fully ordered preset chains were relaxed for 1 × 106 MC cycles to the equilibrium random coil state under athermal conditions. In the definition of the time unit as each MC cycle, the number of microrelaxation steps makes all the monomers to have once trial move on average. Then, like what happened in reality, the flow field with f = 0.04 was employed into the system at a high temperature (Ts = 5.0) for a certain time period to observe the formation of flow-induced precursor. No crystalline structures can be formed at such a high temperature during shearing. After the cessation of shearing, temperature was quenched down to 4.0 (Tc) for the subsequent isothermal crystallization in another certain period. The time−temperature protocol is illustrated in Figure 2. We employed such a protocol as a typical crystallization case during the relaxation process either upon shearing or after shearing.
Figure 3. Time evolution curves of the normalized Y-components in mean square radius of gyration of long and short chains during shearing. The inset snapshot demonstrates the coil deformation of the typical long chain (yellow cylinders) and the typical short chain (blue cylinders) at 1000 MC cycles.
The extension ratio was defined as ⟨Rgy2⟩/⟨Rgy02⟩, where ⟨Rgy2⟩ is the Y-axis component of mean-square radius of gyration for either short or long chains along the direction of shearing, and ⟨Rgy02⟩ is the initial state of polymer chains right before shearing. One can observe that the long chains immediately deform, while the short chains stay in the relaxed states near to their initial random coil states. Recently, dynamic Monte Carlo simulations demonstrated an entropy-driven phase separation between stretched and free host polymer chains in a blend.52 The different deformation states of the long and short chains may raise spontaneous segregation during shearing. Figure 4 shows the time evolution curve of demixing parameters for the long-chain component during shearing. The demixing parameter was defined as the mean fraction of neighboring sites of each monomer on long chains occupied by other monomers of long chains. One can see that the demixing parameters increase gradually upon shearing, indicating the segregation between the short and long chains. Since the long-chains deform the most at the highest driving forces, the segregation will be the most completed in the middle layer along Z-axis. In other words, the long chains will aggregate around the middle layer, as demonstrated by the snapshots in Figure 4. The stretched long chains do not exhibit a homogeneous stretching along the chain but rather contain highly deformed
3. RESULTS AND DISCUSSION 3.1. Structure Evolution during Shearing. We first focused our attention on the shear-induced coil deformation of polymer chains of two different chain lengths in the binary C
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along the middle layer can be regarded as a synergetic phenomenon of chain stretching and chain segregation in the longchain component. 3.2. Structure Evolution after the Cessation of Shearing. After the cessation of shearing, we quenched the system from Ts = 5.0 to Tc = 4.0 to observe the spontaneous isothermal crystallization. Herein, in order to monitor the crystallinity contributed separately from the long and short chains, we defined the separate crystallinity for the long and short chains as the fractions of the bonds of each component containing more than five parallel neighbors of whatever components in the total amount of bonds of the sample system. As shown in Figure 7, both the long and short chains crystallize immediately after the temperature jump and the cessation of shear flow, implying that the less deformed short chains also participate in the formation of shish, consistent with the experimental observations of Kimata et al.12 To obtain more detailed structure characteristics of shish, we observed the crystalline structures of two states at the early crystallization periods, i.e., 300 and 600 MC cycles, as their snapshots shown in Figure 8. One can see from the side view that some small crystalline clusters oriented along the shear direction first appear. Then, those small clusters develop into a row of crystallites aligning along the shear direction. In addition, those row crystallites are connected by many tie molecules. This observation means that the shish formed at the early stage of crystallization actually contains a string of oriented crystallites connected with tie molecules. Meanwhile, crystal stems formed by short chains are also involved into the formation of oriented crystallites. Crystal nucleation is initiated in priority by the aggregation domains of the deformed subchains. To evidence this point, we traced the time evolution of the volume fraction of the crystalline bonds belonging to the aggregated domains of the deformed subchains of the long-chain component, as the results shown in Figure 9. One can see that in the early stage of crystallization, namely, the formation of shish, the fraction is about 0.7, indicating that oriented nuclei (shish) preferentially form from the aggregation domains. Snapshots in Figure 10 verify the origination of shish. Most of the crystalline bonds (yellow cylinders) of the long chains yield from the aggregation domains of deformed subchains of the long chains (blue cylinders). In this sense, the oriented thin-layer structure, rich of highly oriented subchains, can be considered as the precursors for the formation of shish in the shear flow, which are just the stringlike objects observed from the side view of the local melt fracture (for instance Wang’s group) but much larger sizes from the top as observed by Kanaya’s group. From Figure 10, one can also observed that in the early stage of crystallization the crystalline bonds mainly originate from the deformed subchains of the long-chain component; meanwhile, many short chains are also involved into the crystallization, consistent with the results in Figure 7. The extent of involvement of the short chains very much depends upon the development of chain segregation which is usually slow in the viscous melt of bulk polymers. This fact may explain Kimata et al.’s observation. When the chain segregation stays in a stage far from completing, the crystallization of the short-chain component plays the role of sticks in connecting the small segregated domains into the large crystalline region. In order to confirm the role of the short chains, we also performed the parallel simulations of the binary blend under the same protocols: the same shearing
Figure 4. Time evolution curve of demixing parameters of the long chains during shearing. The insets snapshots at 0 (the initial state) and 20 000 MC cycles demonstrate the aggregation of the long chains (yellow cylinders) in the middle layer during shearing.
subchains, which are responsible for the initiation of straininduced crystal nucleation.45 To reflect the local extension of the long chains, inspired by the work of Hölzl et al.,60 we defined the deformed subchains when the Y-axis parts of the end-to-end distances of consecutive eight bonds along the long chains were larger than 83.3% of their maximum contour lengths. Furthermore, when the fraction of monomers in the deformed subchains occupying in the neighboring sites of a monomer of the same type was larger than 0.5, this monomer was considered as existing in the aggregation domains of deformed subchains. Figure 5 shows that the volume fraction of deformed
Figure 5. Time evolution curve of the volume fraction of aggregation domains in the deformed subchains of the long-chain component during shearing. The inset snapshots at different shear times (0 and 20 000 MC cycles) demonstrate the rich aggregation domains of the deformed subchains (the bonds shown by the green cylinders) around the middle layer of Z = 32.
subchains in the aggregation domains increases almost in parallel with the increase of mixing parameters. The inset snapshots in Figure 5 demonstrate the aggregation domains of deformed subchains around the middle layer. In addition, the distribution of the aggregation domains inside the middle layer is also inhomogeneous, as demonstrated in Figure 6. This heterogeneous distribution of the deformed subchains and their aggregated domains is caused by entropy-driven segregation due to the contrast of deformation between long and short chains in the flow field.52 Therefore, the precursor formation of shish D
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Figure 6. Snapshot of XY plane at Z = 32 for the bonds (shown by the green cylinders) in the aggregation domains of the deformed subchains at the shearing period of 20 000 MC cycles.
Figure 7. Time evolution curves of two crystallinity contributions separately from the long and short chains during isothermal crystallization at temperature 4.0. For the detailed definition of the crystallinity contribution, see the text.
Figure 9. Time evolution curve of the crystalline bond fraction in the aggregated domains of the deformed subchains of the long-chain component during isothermal crystallization, demonstrating the dominant effect of the deformed subchains at the early stage of crystallization.
temperatures and periods and the same crystallization temperatures, but we removed the crystallizability of the short-chain component. We found that in the latter case the crystallization did not develop, and the short chains just act as “solvent” surrounding the aggregated domains of the deformed subchains of the long-chain component. The surrounding solvent will suppress the equilibrium melting point and hence the thermodynamic driving force for crystallization in the long-chain component. Figure 10 also shows a discontinuous structure of the crystallites along the shish at the late stage of crystallization (20 000 MC cycles) exhibiting a row-structure feature of lamellar crystals. This feature is exactly following the microshish-kebab structure discovered by Barham and Keller,61
although the shish inside is actually a bunch of tie molecules as observed by Hsiao et al.14 The amorphous chain segments contain loops and tie molecules, together with dead entanglements, to prevent the complete crystallization. In strain-induced polymer crystallization, we have observed that upon the increase of crystallization temperature the favorite mode of crystal nucleation will switch from the chainfolding mode to the fringed-micelle mode, and those oriented subchains initiate the fringed-micelle nucleation.45 The fringedmicelle mode is distinguished by a less probability of chain folding than the chain-folding mode. We therefore calculated the chain-folding probability of the crystallites during isothermal
Figure 8. Snapshots of (a) oriented nuclei connected with (b) tie molecules (blue cylinders) at 300 and 600 MC cycles, respectively. The tie molecules are those long chains involved in the crystalline region. The yellow cylinders represent the crystalline bonds of the long-chain component, while the red cylinders represent the crystalline bonds of the short-chain component. E
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Figure 10. Snapshots of precursors and crystallites in the middle layer (Z = 32) at 300, 1000, and 20 000 MC cycles. The light blue regions represent the deformed subchains, the yellow cylinders represent the crystalline bonds of the long-chain component, and the red cylinders denote the crystalline bonds of the short-chain component.
folding in the crystallites appears low, indicating that the formation of shish follows the fringed-micelle nucleation mode.45 Then, it increases due to the formation of more folded-chain crystals (kebabs), mainly contributed by the relaxed short-chain component.46 A visual demonstration of shish-kebab structures can be seen in Figure 12, following the characteristic morphology well observed under AFM.62 One can clearly see that the long-chain component contributes the dominant center of the shish crystallites, implying their early stage role in the initiation of this crystal morphology, while the short-chain component occupies the kebab crystallites, implying their later-stage development during crystallization.
4. CONCLUSION By means of dynamic Monte Carlo simulations, we investigated the formation process of shish-kebab crystallites in the Poiseuilleflow-like field presumably generated by the sporadic events of shear fracture in the bulk polymer melt. The subsequent isothermal crystallization behaviors after the cessation of shearing at a low temperature can reproduce many experimental observations on shear-induced polymer crystallization. The synergetic phenomenon of chain extension and chain segregation, followed with the competition between chain segregation and
Figure 11. Time evolution curve of the chain-folding probability of all crystallites during isothermal crystallization. The chain-folding probability was defined as the fraction of stems connected by less than four bonds to the neighboring stems.
crystallization, as the results shown in Figure 11. One can see that in the early stage of crystallization the probability of chain
Figure 12. Snapshot of the shish-kebab structure at 4000 MC cycles during isothermal crystallization. The yellow cylinders represent the crystalline bonds of the long-chain component, while the red cylinders represent those of the short-chain component. F
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(13) Zhao, B. J.; Li, X. Y.; Huang, Y. J.; Cong, Y. H.; Ma, Z.; Shao, C. G.; An, H. N.; Yan, T. Z.; Li, L. B. Inducing crystallization of polymer through stretched network. Macromolecules 2009, 42, 1428−1432. (14) Hsiao, B. S.; Yang, L.; Somani, R. H.; Avila-Orta, C. A.; Zhu, L. Unexpected shish-kebab structure in a sheared polyethylene melt. Phys. Rev. Lett. 2005, 94, 117802. (15) Smook, J.; Pennings, A. J. Elastic flow instabilities and shishkebab formation during gel-spinning of ultra-high molecular weight polyethylene. J. Mater. Sci. 1984, 19, 31−43. (16) Zhang, C.; Hu, H.; Wang, X.; Yao, Y.; Dong, X.; Wang, D.; Wang, Z.; Han, C. C. Formation of cylindrite structures in shearinduced crystallization of isotactic polypropylene at low shear rate. Polymer 2007, 48, 1105−1115. (17) Yan, T.; Zhao, B.; Cong, Y.; Fang, Y.; Cheng, S.; Li, L.; Pan, G.; Wang, Z.; Li, X.; Bian, F. Critical strain for shish-kebab formation. Macromolecules 2010, 43, 602−605. (18) Cui, K.; Ma, Z.; Wang, Z.; Ji, Y.; Liu, D.; Huang, N.; Chen, L.; Zhang, W.; Li, L. Kinetic process of shish formation: from stretched network to stabilized nuclei. Macromolecules 2015, 48, 5276−5285. (19) Hayashi, Y.; Matsuba, G.; Zhao, Y.; Nishida, K.; Kanaya, T. Precursor of shish-kebab in isotactic polystyrene under shear flow. Polymer 2009, 50, 2095−2103. (20) Kanaya, T.; Polec, I. A.; Fujiwara, T.; Inoue, R.; Nishida, K.; Matsuura, T.; Ogawa, H.; Ohta, N. Precursor of shish-kebab above the melting temperature by microbeam X-ray scattering. Macromolecules 2013, 46, 3031−3036. (21) Zhao, Y. F.; Hayasaka, K.; Matsuba, G.; Ito, H. In situ observations of flow-induced precursors during shear. Macromolecules 2013, 46, 172−178. (22) Zhao, Y. F.; Matsuba, G.; Nishida, K.; Fujiwara, T.; Inoue, R.; Polec, I.; Deng, C.; Kanaya, T. Relaxation of shish-kebab precursor in isotactic polystyrene after short-term shear flow. J. Polym. Sci., Part B: Polym. Phys. 2011, 49, 214−221. (23) Zhao, Y. F.; Matsuba, G.; Moriwaki, T.; Ikemoto, Y.; Ito, H. Shear-induced conformational fluctuations of polystyrene probed by 2D infrared microspectroscopy. Polymer 2012, 53, 4855−4860. (24) Pogodina, N. V.; Lavrenko, V. P.; Srinivas, S.; Winter, H. H. Rheology and structure of isotactic polypropylene near the gel point: Quiescent and shear-induced crystallization. Polymer 2001, 42, 9031− 9043. (25) Pogodina, N. V.; Siddiquee, S. K.; van Egmond, J. W.; Winter, H. H. Correlation of rheology and light scattering in isotactic polypropylene during early stages of crystallization. Macromolecules 1999, 32, 1167−1174. (26) Somani, R. H.; Yang, L.; Hsiao, B. S.; Agarwal, P. K.; Fruitwala, H. A.; Tsou, A. H. Shear-induced precursor structures in isotactic polypropylene melt by in-situ rheo-SAXS and rheo-WAXD studies. Macromolecules 2002, 35, 9096−9104. (27) Cavallo, D.; Azzurri, F.; Balzano, L.; Funari, S. S.; Alfonso, G. C. Flow memory and stability of shear-induced nucleation precursors in isotactic polypropylene. Macromolecules 2010, 43, 9394−9400. (28) Janeschitz-Kriegl, H.; Eder, G. Shear induced crystallization, a relaxation phenomenon in polymer melts: A re-collection. J. Macromol. Sci., Part B: Phys. 2007, 46, 591−601. (29) Eder, G.; Janeschitz-Kriegl, H.; Liedauer, S. Crystallization processes in quiescent and moving polymer melts under heat-transfer conditions. Prog. Polym. Sci. 1990, 15, 629−714. (30) Balzano, L.; Kukalyekar, N.; Rastogi, S.; Peters, G. W. M.; Chadwick, J. C. Crystallization and dissolution of flow-induced precursors. Phys. Rev. Lett. 2008, 100, 048302. (31) Murase, H.; Ohta, Y.; Hashimoto, T. A new scenario of shishkebab formation from homogeneous solutions of entangled polymers: Visualization of structure evolution along the fiber spinning line. Macromolecules 2011, 44, 7335−7350. (32) Cormia, F. L.; Price, F. P.; Turnbull, D. Kinetics of crystal nucleation in polyethylene. J. Chem. Phys. 1962, 37, 1333−1340. (33) Tanner, R. I.; Keentok, M. Shear fracture in cone plate rheometry. J. Rheol. 1983, 27, 47−57.
fringed-micelle crystal nucleation, dominate the shish formation. Because of incomplete segregation in bulk polymers, the short chains are necessary to be involved into shish formation, in order to connect the small segregated domains of oriented subchains of the long-chain component; while in polymer solutions, the chain segregation is rather complete in the less viscous system, thus the shish can be formed mainly by the long-chain component. With the molecular level observations from the simulation approach, we found that the melt-fracture hypothesis for the initiation of shish-kebab crystallites in the shear flow reconciles the previously controversial arguments raised from various experimental approaches.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (W.H.). ORCID
Wenbing Hu: 0000-0002-7795-9004 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The financial support from National Natural Science Foundation of China (No. 21734005) and the Program for Changjiang Scholars and Innovative Research Teams in University are gratefully acknowledged. Nie also appreciates National Natural Science Foundation of China (No. 21404050).
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REFERENCES
(1) Keller, A. Unusual orientation phenomena in polyethylene interpreted in terms of the morphology. J. Polym. Sci. 1955, 15, 31−49. (2) Blackadder, D. A.; Schleinitz, H. M. Effect of ultrasonic radiation on the crystallization of polyethylene from dilute solution. Nature 1963, 200, 778−779. (3) Mitsuhashi, S. On Polyethylene crystals grown from flowing solutions in xylene. Bull. Text. Res. Inst. 1963, 66, 1−9. (4) Pennings, A. J.; Kiel, A. M. Fractionation of polymers by crystallization from solution, III. On morphology of fibrillar polyethylene crystals grown in solution. Colloid Polym. Sci. 1965, 205, 160−162. (5) Keller, A.; Machin, M. Oriented crystallization in polymers. J. Macromol. Sci., Part B: Phys. 1967, 1, 41−91. (6) De Gennes, P. G. Coil−stretch transition of dilute flexible polymers under ultrahigh velocity gradients. J. Chem. Phys. 1974, 60, 5030. (7) Keller, A.; Mackley, M. R. Chain orientation and crystallization. Pure Appl. Chem. 1974, 39, 195−224. (8) Pope, D. P.; Keller, A. Study of chain extending effect of elongational flow in polymer solutions. Colloid Polym. Sci. 1978, 256, 751−756. (9) Hu, W. B.; Frenkel, D.; Mathot, V. B. F. Simulation of shishkebab crystallite induced by a single prealigned macromolecule. Macromolecules 2002, 35, 7172−7174. (10) Somani, R. H.; Yang, L.; Zhu, L.; Hsiao, B. S. Flow-induced shish-kebab precursor structures in entangled polymer melts. Polymer 2005, 46, 8587−8623. (11) Seki, M.; Thurman, D. W.; Oberhauser, J. P.; Kornfield, J. A. Shear-mediated crystallization of isotactic polypropylene: The role of long chain-long chain overlap. Macromolecules 2002, 35, 2583−2594. (12) Kimata, S.; Sakurai, T.; Nozue, Y.; Kasahara, T.; Yamaguchi, N.; Karino, T.; Shibayama, M.; Kornfield, J. A. Molecular basis of the shish-kebab morphology in polymer crystallization. Science 2007, 316, 1014−1017. G
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Macromolecules
(56) Li, J.; Ma, Y.; Hu, W. B. Dynamic Monte Carlo simulation of non-equilibrium Brownian diffusion of single-chain macromolecules. Mol. Simul. 2016, 42, 321−327. (57) Tao, H. C.; Gao, H. H.; Hu, W. B. Role of chain ends in coil deformation of driven single polymer. Mater. Chem. Front. 2017, 1, 1349−1353. (58) Hu, W. B. Structural transformation in the collapse transition of the single flexible homopolymer model. J. Chem. Phys. 1998, 109, 3686−3690. (59) Hu, W. B.; Frenkel, D. Polymer crystallization driven by anisotropic interactions. In Interphases and Mesophases in Polymer Crystallization III; Springer: New York, 2005; Vol. 191, pp 1−35. (60) Holzl, T.; Trautenberg, H. L.; Goritz, D. Monte Carlo simulations on polymer network deformation. Phys. Rev. Lett. 1997, 79, 2293. (61) Barham, P. J.; Keller, A. High-strength polyethylene fibres from solution and gel spinning. J. Mater. Sci. 1985, 20, 2281−2302. (62) Hobbs, J. K.; Miles, M. J. Direct observation of polyethylene shish-kebab crystallization using in-situ atomic force microscopy. Macromolecules 2001, 34, 353−355.
(34) Marrucci, G.; Ianniruberto, G. Interchain pressure effect in extensional flows of entangled polymer. Macromolecules 2004, 37, 3934−3942. (35) Tapadia, P.; Ravindranath, S.; Wang, S. Q. Banding in entangled polymer fluids under oscillatory shearing. Phys. Rev. Lett. 2006, 96, 196001. (36) Wang, S. Q. The tip of iceberg in nonlinear polymer rheology: Entangled liquids are “solids. J. Polym. Sci., Part B: Polym. Phys. 2008, 46, 2660−2665. (37) Li, Y.; Hu, M.; McKenna, G. B.; Dimitriou, C. J.; McKinley, G. H.; Mick, R. M.; Venerus, D. C.; Archer, L. A. Flow field visualization of entangled polybutadiene solutions under nonlinear viscoelastic flow conditions. J. Rheol. 2013, 57, 1411−1428. (38) Wang, S. Q. Molecular transitions and dynamics at melt/wall interfaces: Origins of flow instabilities and wall slip. Adv. Polym. Sci. 1999, 138, 227−275. (39) Dukovski, I.; Muthukumar, M. Langevin dynamics simulations of early stage shish-kebab crystallization of polymers in extensional flow. J. Chem. Phys. 2003, 118, 6648. (40) Jabbarzadeh, A.; Tanner, R. I. Flow-induced crystallization: unravelling the effects of shear rate and strain. Macromolecules 2010, 43, 8136−8142. (41) Graham, R. S.; Olmsted, P. D. Coarse-grained simulations of flow-induced nucleation in semicrystalline polymers. Phys. Rev. Lett. 2009, 103, 115702. (42) Graham, R. S.; Olmsted, P. D. Kinetic Monte Carlo simulations of flow-induced nucleation in polymer melts. Faraday Discuss. 2010, 144, 71−92. (43) Wang, M. X.; Hu, W. B.; Ma, Y.; Ma, Y. Q. Orientational relaxation together with polydispersity decides precursor formation in polymer melt crystallization. Macromolecules 2005, 38, 2806−2812. (44) Liu, Q.; Gao, H. H.; Zha, L. Y.; Hu, Z. M.; Ma, Y.; Yu, M. H.; Chen, L.; Hu, W. B. Tuning bio-inspired skin-core structure of nascent fiber via interplay of polymer phase transitions. Phys. Chem. Chem. Phys. 2014, 16, 15152−15157. (45) Nie, Y. J.; Gao, H. H.; Yu, M. H.; Hu, Z. M.; Reiter, G.; Hu, W. B. Competition of crystal nucleation to fabricate the oriented semicrystalline polymers. Polymer 2013, 54, 3402−3407. (46) Nie, Y. J.; Gao, H. H.; Hu, W. B. Variable trends of chain-folding in separate stages of strain-induced crystallization of bulk polymers. Polymer 2014, 55, 1267−1272. (47) Nie, Y. J.; Gao, H. H.; Wu, Y. X.; Hu, W. B. Thermodynamics of strain-induced crystallization of random copolymers. Soft Matter 2014, 10, 343−347. (48) Zhang, M. M.; Zha, L. Y.; Gao, H. H.; Nie, Y. J.; Hu, W. B. How polydispersity of network polymers influences strain-induced crystal nucleation in a rubber. Chin. J. Polym. Sci. 2014, 32, 1218−1223. (49) Nie, Y. J.; Gao, H. H.; Wu, Y. X.; Hu, W. B. Effect of comonomer sizes on the strain-induced crystal nucleation of random copolymers. Eur. Polym. J. 2016, 81, 34−42. (50) Guan, X. C.; Zha, L. Y.; Wu, Y. X.; Hu, W. B. Strong memory of strain-induced copolymer crystallization revealed by Monte Carlo simulations. Polymer 2016, 98, 282−286. (51) Zha, L. Y.; Wu, Y. X.; Hu, W. B. Multi-component thermodynamics of strain-induced polymer crystallization. J. Phys. Chem. B 2016, 120, 6890−6896. (52) Zha, L. Y.; Zhang, M. M.; Li, L. B.; Hu, W. B. Entropy-driven segregation and its competition to crystal nucleation in the binary blends of stretched and free guest polymers. J. Phys. Chem. B 2016, 120, 12988−12992. (53) Li, J.; Nie, Y. J.; Ma, Y.; Hu, W. B. Stress-induced polymer deformation in shear flows. Chin. J. Polym. Sci. 2013, 31, 1590−1598. (54) Ma, Y.; Zhang, X. H.; Hu, W. B. Extensional flow of bulk polymers studied by dynamic Monte Carlo simulations. Chin. J. Polym. Sci. 2013, 31, 1463−1469. (55) Li, J.; Hu, W. B. Biased diffusion induces coil deformation via a ’cracking-the-whip’ effect of acceleration generated by dynamic heterogeneity along polymer chain. Polym. Int. 2015, 64, 49−53. H
DOI: 10.1021/acs.macromol.7b02357 Macromolecules XXXX, XXX, XXX−XXX
