Multiscale and Multistep Ordering of Flow-Induced Nucleation of

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Cite This: Chem. Rev. XXXX, XXX, XXX−XXX

Multiscale and Multistep Ordering of Flow-Induced Nucleation of Polymers Kunpeng Cui,† Zhe Ma,*,‡ Nan Tian,§ Fengmei Su,† Dong Liu,∥ and Liangbin Li*,† †

National Synchrotron Radiation Laboratory, Chinese Academy of Sciences Key Laboratory of Soft Matter Chemistry, and Anhui Provincial Engineering Laboratory of Advanced Functional Polymer Film, University of Science and Technology of China, 96 Jinzhai Road, Baohe District, Hefei 230026, People’s Republic of China ‡ Tianjin Key Laboratory of Composite and Functional Materials, School of Materials Science and Engineering, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, People’s Republic of China § Ministry of Education Key Laboratory of Space Applied Physics and Chemistry and Shanxi Key Laboratory of Macromolecular Science and Technology, School of Science, Northwestern Polytechnical University, 127 Youyi West Road, District Beilin, Xi’an 710072, People’s Republic of China ∥ Key Laboratory of Neutron Physics and Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, 64 Mianshan Road, Mianyang, Sichuan 621999, People’s Republic of China ABSTRACT: Flow-induced crystallization (FIC) is a typical nonequilibrium phase transition and a core industry subject for the largest group of commercially useful polymeric materials: semicrystalline polymers. A fundamental understanding of FIC can benefit the research of nonequilibrium ordering in matter systems and help to tailor the ultimate properties of polymeric materials. Concerning the crystallization process, flow can accelerate the kinetics by orders of magnitude and induce the formation of oriented crystallites like shish-kebab, which are associated with the major influences of flow on nucleation, that is, raised nucleation density and oriented nuclei. The topic of FIC has been studied for more than half a century. Recently, there have been many developments in experimental approaches, such as synchrotron radiation X-ray scattering, ultrafast X-ray detectors with a time resolution down to the order of milliseconds, and novel laboratory devices to mimic the severe flow field close to real processing conditions. By a combination of these advanced methods, the evolution process of FIC can be revealed more precisely (with higher time resolution and on more length scales) and quantitatively. The new findings are challenging the classical interpretations and theories that were mostly derived from quiescent or mild-flow conditions, and they are triggering the reconsideration of FIC foundations. This review mainly summarizes experimental results, advances in physical understanding, and discussions on the multiscale and multistep nature of oriented nuclei induced by strong flow. The multiscale structures include segmental conformation, packing of conformational ordering, deformation on the whole-chain scale, and macroscopic aggregation of crystallites. The multistep process involves conformation transition, isotropic−nematic transition, density fluctuation (or phase separation), formation of precursors, and shish-kebab crystallites, which are possible ordering processes during nucleation. Furthermore, some theoretical progress and modeling efforts are also included.

CONTENTS 1. Introduction 2. Conformational Ordering Induced by Flow 2.1. Flow-Induced Conformational Ordering 2.1.1. Coil−Helix Transition 2.1.2. Gauche−Trans Transition 2.2. Flow-Induced Isotropic−Nematic Transition 3. Precursors Induced by Flow 3.1. Flow-Induced Precursors 3.2. Theoretical Considerations for Flow-Induced Precursors 3.3. Nature of Flow-Induced Precursors 3.3.1. Existence of Flow-Induced Precursors 3.3.2. Are Flow-Induced Precursors Crystalline or Not?

3.3.3. Ordering Parameter of Flow-Induced Precursors 3.4. Influences of Precursor on Crystallization 3.4.1. Nucleation 3.4.2. Crystallization Kinetics 3.4.3. Morphologies 4. Factors Influencing the Formation of FlowInduced Precursors 4.1. Flow Parameters 4.2. Temperature 4.3. Molecular Parameters 5. Correlation between Deformation at Whole-Chain Scale and Nucleation 5.1. Shish-Kebab Crystallite

B C C C E F F G G H H

J K K K L M M N O P P

I Received: August 17, 2017

© XXXX American Chemical Society

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DOI: 10.1021/acs.chemrev.7b00500 Chem. Rev. XXXX, XXX, XXX−XXX

Chemical Reviews 5.2. 5.3. 5.4. 5.5.

Hierarchical Structure of Shish-Kebab Coil−Stretch Transition in Polymer Solution Shish-Kebab Formation in Polymer Melt Other Mechanisms for Shish-Kebab Formation 5.6. Advances in Understanding of Shish-Kebab 5.6.1. Coil−Stretch Transition or Stretched Network Model? 5.6.2. Is Long Chain the Only Contributor for Shish Formation? 5.6.3. How Does Polydispersity Influence the Threshold for Shish Formation? 5.6.4. How Does Short-Chain Matrix Influence Shish Formation? 5.6.5. In Situ Observation of Evolution of ShishKebab 5.6.6. Shish Formation under Near-Equilibrium and Far-from-Equilibrium Conditions 5.6.7. Is Shish Formation a Single-Stage or Multistage Process? 5.6.8. Is Shish a Thermodynamic Phase or a Kinetic State? 6. Theories and Models of Flow-Induced Nucleation 6.1. Molecular Theory of Flow-Induced Nucleation 6.1.1. Crystallization Induced by Stretching of Cross-Linked Network 6.1.2. Flow-Induced Nucleation in Free Melt 6.1.3. Quantitative Description of ExtensionInduced Nucleation 6.2. Macroscale Continuum Modeling 7. Final Remarks Author Information Corresponding Authors ORCID Notes Biographies Acknowledgments References

Review

has become a unique aspect in the crystallization field. Obviously, a fundamental understanding of FIC is of great importance for both industrial and academic communities. After decades of effort, two major influences of flow on crystallization have been revealed: acceleration of crystallization kinetics and formation of oriented crystallites, which are associated with raised nucleation density and oriented nuclei.11−15 According to the ultimate morphology (spherulites or oriented texture), flow-induced nuclei can be roughly divided into pointlike nuclei and oriented nuclei. Formation of pointlike nuclei has been recently reviewed by Peters et al.16 and will not be included in the present review. However, a more complex situation is the formation of flow-induced oriented nuclei. A full understanding of oriented nuclei has not been reached yet, even after decades of effort.17−19 Typical unsolved questions include the ordering nature and precise evolution process of the oriented nuclei. On one hand, for a polymer chain, the intrinsic structures at various length scalessuch as segmental conformation, segmental orientation, density fluctuation, stretch of the whole chain, and so oncan all be arranged in an orderly fashion during the crystallization process, especially under the effort of flow. Is there a basic ordering parameter or a combination of multiscale orderings to define nuclei? Do these flow-induced ordering processes at various length scales evolve simultaneously or sequentially? On the other hand, numerous experimental results indicate that nucleation under flow does not simply follow the classical nucleation theory to form stable crystalline nuclei directly and may undergo some intermediate states. In this case, when and how the structural intermediates, if they exist, occur during flow-induced nucleation (FIN) should be answered. This review attempts to emphasize the possible processes of ordering in various length scales. For this purpose, this work is organized by mainly following a bottom-up length scale. We first focus on the formation of conformational ordering on a segmental scale (e.g., helix) in section 2, which acts as a basic ordering unit to arrange into a three-dimensionally ordered crystal unit. Then we introduce flow-induced precursors (FIP), the presence of which can be demonstrated but about which detailed structural information has not been revealed, and their structural analysis in section 3. Concerning precursors, the factors influencing their appearance are summarized to shed light on the formation mechanism in section 4. Then, whether deformation on the whole-chain scale is essential for FIC is discussed with the discovery of shish in section 5. At last, some theoretical and modeling efforts are compared and validated with experimental results in section 6 to explore possible molecular origins. In the meantime, possible multistep processes for structure formation are also discussed for FIP and shish in sections 3 and 5, respectively. Note that the following multiscale and multistep aspects of FIN are generic for polymer crystallization. Especially, the nonequilibrium ordering understood from macromolecular systems may be valid for other types of matter, like small molecules. However, the concrete manifestation of these aspects depends on the polymer investigated. For example, conformational ordering arranges into zigzag conformation for polyethylene (PE),20 syndiotactic polystyrene (sPS),21 and poly(ethylene terephthalate) (PET)22 but forms helices for isotactic polypropylene (iPP),23 isotactic polystyrene (iPS),24 and poly(ethylene oxide) (PEO).25

Q R R S T T U V V W X Y AA AB AB AB AD AF AH AM AN AN AN AN AN AN AN

1. INTRODUCTION Semicrystalline polymers cover more than two-thirds of the global applications of polymeric materials. Just due to their intrinsic capability to arrange macromolecular segments into three-dimensionally ordered crystal units, even in various modifications, the ultimate products are endowed with rich and unique properties.1−3 In practice, polymer processing often starts with molten materials and subsequently utilizes flow to transport the polymeric melt and/or to shape into final products.4−8 This means that flow is an unavoidable factor in polymer processing, and flow-induced crystallization (FIC) is a general phenomenon for semicrystalline materials. Moreover, crystallization is a typical first-order phase transition existing in macromolecular systems. A polymer is a unique substance with anisotropic molecular properties, where atoms along the chain direction are connected by chemical bonds. Thus, a polymer that initially is in quiescent random-coil conformation can be easily deformed into an oriented or stretched state, and the thermodynamic state of the system is varied correspondingly.9,10 The system under such disturbed molecular ordering and thermodynamic state crystallizes in a different manner with respect to the quiescent case or small-molecule system, and this B


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Figure 1. Sketch of coil−helix transition at strained end-to-end distance R. The chain is simplified into a diblock polymer composed of coil and helical domains.

2. CONFORMATIONAL ORDERING INDUCED BY FLOW Since a long-chain polymer needs to orderly arrange its short stems into a crystal lattice, the short stems must adopt proper conformations for ultimate regular packing. For FIN, basic structural ordering concerns the change of segmental conformation. However, in classic nucleation theory, FIN was described in a coarse-grained way. It was often thought that when external flow is imposed, polymer chains are deformed into an oriented or stretched state. The resulting orientation or stretch of the chain reduces system entropy and consequently elevates the melting temperature according to the entropy-reduction model (ERM),26 which introduces an extra undercooling for crystallization. This physical picture is essentially reasonable, since it has been widely demonstrated that flow can effectively enhance crystal nucleation.27 However, molecular details like intramolecular conformational ordering, intermolecular positional ordering, and orientation ordering28,29 are ignored in ERM. In principle, flow can not only give rise to orientation or stretch of individual chain but also change conformational ordering. Moreover, recent ultrafast X-ray scattering results revealed a constant critical strain for nucleation in a wide temperature range under strong flow, which invalidates the prediction of strain− temperature equivalence in classical ERM.30 In this section, we mainly discuss the change of molecular details induced by flow. The ultrafast X-ray scattering results will be discussed in section 5.6.6. Flow can induce conformational ordering. When the concentration or length of conformational ordering segments exceeds a certain threshold, those ordered stiff segments may spontaneously aggregate and organize, as happens in isotropic− nematic transition.31,32 If this is the case, nucleation seems to be completed via multiple steps from the melt, which has been evidenced by experimental observations, especially under flow conditions.33−35 In this section, we decouple the global nucleation induced by flow into two ordering aspects: (i) how flow induces conformational ordering of individual segments and (ii) possible aggregation and parallel permutation of the formed stiff segments. Before going into a deep discussion, it should be first clarified that intermolecular and intramolecular orderings do not necessarily occur simultaneously but may happen individually. As an example, stretching-induced formation of protein α-helix in biopolymers is a conformational ordering without positional ordering.36 On the other hand, PE can crystallize into hexagonal crystals under high pressure, which lacks full conformational ordering.37,38

2.1.1) and gauche−trans transition (section 2.1.2) will be discussed. 2.1.1. Coil−Helix Transition. On the premise of dense accumulation and positioning into a crystal unit, polymer chains adopt conformations with the lowest energy. Helix is a preferred state not only in crystals of synthetic polymers, like iPP, iPS, and PEO, but also in some biological macromolecules, such as DNA and actin filaments.39,40 The coil−helix transition of biopolymers induced by deformation has gained much attention because biological functions are closely associated with the specific structure of the formed helices.41 To better understand the coil− helix transition, we first have a look at some theoretical works about how flow influences conformational transition, and then we discuss the relevant experimental results. Theoretical understanding of coil−helix transition can be dated back to the work of Zimm and Bragg,42 in which the transition was described on a coarse-grained level. In the Zimm− Bragg model,43 segments along a polymer chain are assumed to have only two states, random-coil and helical. The state of a long chain can be described by a simple sequence of segmental status (cchhcchccchh...), where c and h represent coil and helix, respectively. A monomer within a helix gains potential energy Δh by forming hydrogen bonds but bears a loss of entropy Δs. (Here the notation for energy or entropy is lowercase for monomer, but uppercase for total system.) The free energy of each monomer in the helical state can be estimated by Δf = Δh − TΔs. The monomer located at the interface between helical and coil domains suffers entropy reduction but does not form hydrogen bonds, resulting in an increase in free energy of Δf t = −Δh compared to the monomer in helical state. Knowing the microscopic state of the whole chain and the energetic contributions of each segment, the total free energy ΔF can be obtained by a statistical mechanics method. This approach was further extended to deal with the case where an external extension is imposed by Tamashiro and Pincus36 and Buhot and Halperin.44,45 In their approaches, the chain is simplified into a diblock polymer composed of coil and helical domains with an interface energy of Δf t (Figure 1). This means that the mixing entropy from reordering of domains and the interfacial energy are disregarded. The detailed study of Buhot and Halperin45 demonstrated that this simplification has a slight influence on the outcome only quantitatively but not qualitatively. In this case, the total free energy can be expressed as follows:

2.1. Flow-Induced Conformational Ordering

where N is the total number of monomers and ϕ is the concentration of helical segments. The last term describes the free energy of a coil domain, where R is the end-to-end distance of chain, γ is a factor to characterize the shortening of effective polymer length due to formation of helix, and α is monomer

ΔFch = ϕN Δf + 2Δft +

Although early investigations on FIC can be dated back to the 1960s, conformational ordering of chain segments did not get the attention it deserves. Here, the formation of intramolecular conformational ordering including coil−helix transition (section C

3(R − γaNϕ)2 2(1 − ϕ)Na 2


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Figure 2. (a) IR spectra of iPP under quiescent crystallization at 140 °C and (b) the time evolution of normalized relative intensities of different conformational bands. Reprinted with permission from ref 50. Copyright 2007 American Chemical Society.

Figure 3. IR spectra of iPP before and after shear at 140 °C and (b) time evolution of normalized relative intensities of different conformational bands. Reprinted with permission from ref 50. Copyright 2007 American Chemical Society.

940, 1220, 1167, 1303, 1330, 841, 998, 900, 808, 1100, and 973 cm−1 indicate helical structures with different ordering degrees from high to low, of which the 1220, 841, 998, and 973 cm−1 bands correspond to helical lengths with monomer numbers 14, 12, 10, and 5, respectively.49,52 Besides, the concentration of these helices can be indicated by the absorbance intensity. Flow-induced conformational ordering of iPP coil−helix transition has been studied by An et al.50,51 and Geng et al.53 Figures 2 and 3 compare the IR spectra of quiescent crystallization and FIC of iPP at 140 °C. In Figure 2a, the observation of bands at 973, 808, and 900 cm−1 demonstrates that the short helices already exist in amorphous iPP melt. Under quiescent conditions, the intensities of those IR bands remain almost unchanged in the initial 4 h (see Figure 2b). However, when flow is applied, the intensities of IR bands rise sharply just after flow, suggesting the increase in population of helices. As crystallization proceeds further, long helices appear and grow. The saturation time for those IR bands, which under quiescent conditions is 20 h (see Figure 2b), is shortened to around 100 min by shear flow (see Figure 3b). The observation of long helices is often considered as a signature of crystallization. Obviously, these results demonstrated that flow can promote formation of helices and thus crystallization in synthetic semicrystalline polymers. According to the Zimm−Bragg model,46 end-to-end distance is an essential parameter to determine the ratio between coil and helix. This is qualitatively confirmed in a cross-linked iPP by Su et al.,54 who observed a direct correlation between helical content and stress. As stress is determined by the end-to-end distance, helical content is related to end-to-end distance in cross-linked iPP. However, polymer melt is a transient network constructed by entanglements, and there must exist a competition between deformation and relaxation of polymer chain. Thereby, the fraction of helix formed in total sequence is influenced not only by flow strength, like strain or strain rate, but also by temperature

length. This model provides a quantitative correlation between helix concentration and molecular deformation, which can be used to study conformational transition in FIC, as synthetic polymers and biological macromolecules share the same physics. For network, Courty et al.41,46 and Kutter and Terentjev47 formulated a theoretical work by uniting statistical mechanisms of single helix-forming chain under extension (as just described) with the phantom-chain network approach. It was theoretically predicted that extension promotes the formation of helical domains under appropriate conditions, which is in agreement with experimental results.47 Compared with biological macromolecules, flow-induced coil−helix transition was less studied in synthetic polymers, either theoretically or experimentally. As polymer melt is a transient network constructed by entanglements, change of endto-end distance by flow should influence the coil−helix transition, as in biological macromolecules. However, it is not easy to trace the coil−helix transition in polymers. Helix is a short-range order and cannot be characterized with regular scattering techniques like X-ray scattering, which is sensitive to long-range correlation. In this aspect, IR spectroscopy shows superiority to probe conformational ordering. Middle IR bands are mainly vibrational bands due to the existence of dipole moment. Therefore, even though the vibrational modes are the same, differences in helical length and local environment can vary the wavenumber of absorption bands. This was revealed by the calculations of Snyder and Schachtschneider48 and the experiments of Zhu et al.49 Length and concentration of helices are two important parameters for coil−helix transition, which can be characterized by the position and intensity of the characteristic absorption peaks, respectively. iPP with 3/1 helix conformation is chosen here as a representative, as the one-to-one correspondence between helix length of segments and absorption bands in Fourier transform infrared spectra (FTIR) has been well documented.50,51 For iPP, the absorption bands at D


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Figure 4. Schematic of three growth pathways for flow-induced coil−helix transition. Reprinted with permission from ref 50. Copyright 2007 American Chemical Society.

that determines chain relaxation. An et al.51 employed the ratio between height values of band 998 cm−1 after and before shear flow to indicate a conformational order ratio (COR) and assessed the effect of various external parameters on flowinduced helix quantitatively. Under a fixed flow strength with strain rate of 13.5 s−1 and strain of 3375%, COR induced at temperatures below 150 °C decreases linearly with increasing temperature due to the competition between deformation and relaxation. For temperatures above 205 °C, COR has negligible change after flow, probably because relaxation dominates this process. On the other hand, at a constant temperature of 145 °C with strain rate of 6 s−1, a minimum strain is required to significantly vary COR, in line with the prediction of Kutter and Terentjev47 that a threshold extension is required to induce coil− helix transition. As strain increases, COR first increases and then reaches saturation at strain larger than about 4000%. Furthermore, when temperature and strain are both fixed, COR increases with rising strain rate. Therefore, An et al.51 pointed out that, due to relaxation effect on COR, a combination of intense flow (high strain rate or/and high strain) and high temperature has a similar effect as combining weak flow (low strain rate or/and low strain) and low temperature. Besides helical population, Geng et al.53 also revealed the influence of flow on length of formed helices. Unlike the short helices that already exist in original amorphous melt, long helices with more than 12 monomers can be found only under flow. A critical flow strength is required to generate long helices. At 150 °C, an 841 cm−1 band (representing the helix with 12 monomers) appears only for flow rates larger than 18 mm3/s, while a flow rate of 45 mm3/s is required to induce the occurrence of a 1220 cm−1 band (corresponding to the helix with 14 monomers). The flow rate thresholds for appearance of the 1220 and 841 cm−1 bands increase with temperature, suggesting that stronger flow is necessary to generate longer helices at higher temperatures. Geng et al.53 also found that, at temperatures close to the melting point, the intensity of 841 cm−1 band or helices with 12 monomers increases monotonically with time upon cessation of flow, which is accompanied by a decrease in band intensity of short helices. In addition, an induction time exists for helices with 12 monomers. On the basis of those results, they proposed three pathways for the formation of long helices (see Figure 4). The first way is flow-induced growth of the short helices that already existed in amorphous melt, without primary nucleation, known as propagation. The second path is to generate long helices via nucleation and growth. The third one is the merging of short helices, that is, an incorporation process.

Yamamoto55 used molecular simulation to study the coil− helix transition by quickly drawing an amorphous iPP to about 9 times elongation within about 350 ps. Statistical results showed that the weight-average length of helical sequence increases with elongation, while elongation has no influence on the length of nonhelical sequences. The detailed distribution of the population of helical sequences as a function of their length indicated that short sequences dominate the initial stage of elongation and long sequences increase considerably with further elongation. A threshold length of helix with about 13 monomers was observed during elongation, in line with the IR experimental results of An et al.50 2.1.2. Gauche−Trans Transition. In addition to helical conformation, planar zigzag is another conformation in crystallites of many polymers, such as sPS,24 nylon,56 PET,57 and PE.20,58 For example, sPS has a trans sequence of (TT)2 in crystals, with T representing trans conformation. It was reported that within the crystallization induction period the content of alltrans sequence increases, whereas the sequence containing gauche conformation decreases.24 For nylon, all-trans sequence can be induced by strong flow, as happens in electrospinning.56 In drawing of PET film, gauche−trans transition may also take place to form a mesomorphic phase constituted of trans conformation.57 In the following, PE is chosen as a representative to discuss the gauche−trans transition. PE is the simplest semicrystalline polymer and often serves as a model material to study phase transitions such as crystallization, melting, and so on.4,59,60 PE can crystallize in various modifications depending on crystallization conditions. For instance, mobile hexagonal crystals may appear under high pressure and then transform to orthorhombic crystals with increasing thickness.61−63 Here we discuss the formation and evolution of locally ordered trans-rich structure in the early stage of crystallization studied with Raman and FTIR spectroscopy.20,58,64,65 Using time-resolved FTIR and small-angle X-ray scattering (SAXS), Sasaki et al.65 concluded that, in the early stage of quiescent crystallization, disordered conformation of trans sequence first increases and then remains at the maximum for a while. After that, the content of regular trans sequences, which can be used to indicate the formation of orthorhombic crystals, increases simultaneously with the decrease of disordered trans sequences. In contrast, the structural intermediate composed of all-trans configurations can be induced by flow even before the onset of crystallization. Flow orientates polymer chains and increases the number of trans bonds, which in turn enhances the possibility for formation of all-trans configurations. Combining a E


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homemade shear device and Raman, Chai et al.58 performed a quantitative study on how shear rate influences all-trans C−C bonds. Three peaks in the Raman spectrum of PE are assigned to intrachain bands, where sharp Raman peaks at 1065 (C−C asym) and 1130 (C−C sym) cm−1 stem from consecutive trans vibrations, and the broad peak at 1080 cm−1 originates from gauche bonds in the amorphous component. When PE melt is sheared at 140 °C, the Raman bands at 1065 and 1130 cm−1 appear and their band intensities increase with increasing shear rate, suggesting the generation of all-trans sequences induced by flow. The all-trans sequence can survive for several hours after cessation of flow, indicating that the flow-induced all-trans sequence is not only oriented but also stable. The experimental results of Chai et al.58 are consistent with the simulation of Meier,64 who calculated vibrational frequencies and intensities of various hexadecanes to address how long a trans sequence is needed for PE to contribute to the all-trans Raman bands. These results showed that sequences with more than 10 trans bonds are responsible for the all-trans Raman bands at 1065 and 1130 cm−1. As only disordered trans sequences exist in PE melt, the appearance of all-trans structure can be expected under strong nonequilibrium conditions before the onset of crystallization, such as under flow field. In addition, trans and gauche conformations may differentiate in the response to external flow. The work of Pigeon et al.20 demonstrated that the trans conformation in amorphous phase is easily oriented along the flow direction, whereas flow has negligible influence on orientating gauche sequences.

helices suggests the occurrence of coupling between conformational and orientational orderings. This means that flow-induced coil−helix transition provides the necessary stiff segments for isotropic−nematic transition, which further form intermolecular ordering that in turn stabilizes the long helices. The recent works of Kanaya and Matsuba and co-workers68−71 in iPS melt gave indirect evidence to support this mechanism. Stringlike objects of iPS with micrometer dimensions were generated by flow above the melting temperature. Microbeam SAXS and wide-angle X-ray scattering (WAXS) characterization demonstrated that those structures are not stacks of lamellae and have no or very limited crystallinity.68 The conformational information in those intermediate structures was further examined with two-dimensional (2D) FTIR. The IR band of long helix was observed in the center and edge of those structures, whereas in the amorphous domain only short helical bands were detected. In addition, the works of Alfonso and co-workers72,73 suggested that the intermediate structure consisted of bundles with conformational ordering and oriented chain segments. Hsiao and co-workers74,75 inferred that the intermediate structure is liquid-crystal phase. It seems reasonable and likely that flow induces the occurrence of isotropic−nematic transition in polymer melt. For a certain helical length, a threshold concentration of stiff segment is also needed to induce the isotropic−nematic transition. Combining extensional rheometry and ultrafast SAXS/WAXS measurements, Cui et al.30 found a constant critical strain to observe iPP intermediate structure for a broad temperature range from 130 to 170 °C. Based on flow-induced coil−helix transition47 and fluctuation−dissipation theories,76,77 the content of helical sequence was calculated as a function of helical length. For helical length exceeding 14 nm, flow not only facilitates compatible alignment of the helical sequences but also increases the helical concentration for the isotropic−nematic transition. In addition, flow may vary the critical concentration for isotropic−nematic transition. With time-resolved birefringence, Lenstra et al.78 studied isotropic−nematic transition in suspensions of fd virus and found that the critical concentration under shear flow is much smaller than in the quiescent case. The formation of conformational ordering discussed in section 2.1, including coil−helix and gauche−trans transitions, can be effectively influenced by external stimuli such as strain, strain rate, and temperature. Some qualitative conclusions can be drawn: (i) flow promotes segmental ordering not only in sequence length but also in content; (ii) the combination of high flow intensity and high temperature has a similar effect to the combination of low flow intensity and low temperature; (iii) stronger flow is needed for the formation of ordering segments with long sequence length than for short ones. However, the quantitative relationship between flow intensity, length, and content of ordering segments is still lacking and requires more investigation. The rigidity of ordering segments leads to intermolecular ordering, that is, isotropic−nematic ordering, which is commonly considered as an intermediate state and will be discussed in section 3.

2.2. Flow-Induced Isotropic−Nematic Transition

The helix induced by flow can be considered as a rigid rod or stiff segment with length L and diameter b. The increased rigidity induced by conformational changes may cause the occurrence of nematic ordering, although flexible polymers have no intrinsic mesogenic unit. The statistical mechanical theory of isotropic− nematic transition for rodlike molecules was first proposed by Onsager66 in colloidal particles and then developed by Flory (see ref 67) for polymers. According to this theory, the excluded volume (Vexcl) of stiff segments increases with increasing helical length. The excluded volume Vexcl can be calculated as Vexcl = 2bL2|sin θ|, where θ is the angle between neighboring stiff segments. When the helical sequences exceed a critical length, they start to orient parallel to each other to reduce the excluded volume or free energy of the system. The critical length of stiff segments for orientation occurrence is given as L = 4.19M0/ bl0ρNA, where ρ is density, NA is Avogadro’s number, and l0 and M0 are the length and molecular weight of monomer, respectively. With this correlation, the critical helical length for parallel ordering of iPP calculated by Zhu et al.49 is 11 monomers, which agrees well with their FTIR experimental observations. It was indicated that the segmental conformation is stable when the length of helical sequences is shorter than 10 monomers, while the helix conformation extends quickly and starts crystallization as soon as the helical length exceeds 12 monomers. Flow may induce isotropic−nematic transition in flexible polymers even above the melting temperature. From the rheoFTIR experiments of iPP conducted by Geng et al.,53 it was found that flow-induced helices with 12 monomers can exist at 170 °C and the intensity of the corresponding absorption band increases after flow. According to coil−helix transition theory, an individual isolated long helix is not stable in free polymer melt, as the raised end-to-end distance of chain tends to relax back to that of coil state due to entropy effects. The growth of long

3. PRECURSORS INDUCED BY FLOW Although segmental conformations are the basic ordering for ultimate crystallites, polymer crystallization often starts with the formation of nuclei, of which the length scale is larger than the segmental conformation. According to the classical nucleation theory (CNT),79 crystalline nuclei are directly generated from initial random coil and no further structural intermediate is considered. However, numerous experimental observations F


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morphology, and even induce the appearance of new crystal modification. The understanding of FIP was further improved by progress in experimental methods. Recently, Lamberti12 produced a review paper on methods to investigate and quantify crystallization. Modeling approaches and main factors acting on crystallization are also included in this review. Here, we just give a brief introduction to the progress in experimental methods. In 1993, Liedauer et al.90 designed a new flow apparatus and proposed a short-term shear protocol, in which the flow duration is short enough to separate nucleation from crystallization processes. This method allows one to study FIP by looking at the subsequent crystallization kinetics and morphology. A similar flow apparatus was developed by Kumaraswamy et al.,91 which allows one to study structural evolution in real time by optical and X-ray probes with only a small amount of sample (several grams). At the same time, the commercial Linkam shear cell with parallel-plate geometry was widely used by the community due to its convenience for X-ray and optical measurements.11 In 2011, Liu et al.92 developed an extensional-type flow device, which can control strain and strain rate independently. More importantly, stress recording and real-time X-ray measurement can be realized simultaneously by this device. Meanwhile, various structure characterization techniques such as optical microscopy,93 light scattering,94 birefringence,95 atomic force microscopy (AFM),96 and X-ray scattering97 have been combined to reveal the formation and evolution of FIP. Especially with the development of synchrotron ultrafast X-ray scatting30,98 and X-ray microdiffraction scanning,68,99 new understanding of FIP has been obtained.

suggest that FIN may be a multistep process and may undergo an intermediate ordered state (also commonly termed as precursor, preordering, mesomorphic ordering, and so on).11,68,80,81 In our opinion, precursors are the structures whose existence can be solidly demonstrated by their substantial influences on crystallization (i.e., kinetics, orientation, morphology, and so on) but whose fundamental ordering nature is still unclear yet. Structural intermediates may exist even in quiescent crystallization. A liquid−liquid phase separation, known as spinodal decomposition, was observed in the first step of polymer crystallization by Kaji et al.,31 and then the relevant theoretical effort was made by Olmsted et al.35 Strobl33 conjectured that crystallization starts with formation of a mesomorphic layer that then develops into a granular crystal layer, followed by a merging process of crystal blocks. Flow is an effective external stimulus to reveal the intermediate state before crystallization, if there is one, because the formation of structural intermediates with mesomorphic ordering in flexible-chain polymers is often attributed to the rigidity based on conformational ordering, which could be considerably enhanced by flow as discussed in section 2. The theory developed by Kim and Pincus82 and experiment conducted by Li and de Jeu83 showed that the coupling between coil−helix transition and orientational ordering could induce a nematic state. Recent results from a combination of FTIR, SAXS, and WAXS suggested that coil−helix transition and orientational ordering indeed happen before crystallization in cross-linked iPP.54 For long-chain polymers, the highly asymmetric nature provides enormous possibility to form precursors with orientational ordering. In this section, the observations of structure intermediatesthat is, precursorswill be discussed for FIN to shed light on the detailed process and formation mechanism of stable nuclei.

3.2. Theoretical Considerations for Flow-Induced Precursors

Flow can induce intrachain conformational ordering, but the conformational ordering alone cannot cause a phase separation in polymer melt. However, the conformational ordering may couple with density. The aggregation and parallel arrangement of oriented segments with conformational ordering may work together to induce phase separation. As mentioned earlier, Kaji et al.31 proposed a spinodal (SD) type of phase-separation model for the induction period of polymer crystallization. In this model, the amorphous random coil first transforms into a stiff helical conformation. As soon as both length and concentration exceed their thresholds, the stiff segments tend to orient with each other. The increase in chain stiffness induces the parallel ordering of polymer segments due to excluded volume effect. According to isotropic−nematic theory67 mentioned in section 2, the completely parallel orientation gives an excluded volume of zero, while the perpendicular orientation gives the maximum value. Such parallel orientation does not occur homogeneously in the system, but it involves a microphase separation into oriented and unoriented domains. Those oriented dense domains grow in size by reactions and diffusion of clusters. Olmsted et al.35 developed a more general phenomenological theory to illustrate the coupling between chain conformation and density for phase separation. Figure 5 shows the temperaturedensity diagram calculated by use of phenomenological free energy, which contains three regions: coexistence region of melt and crystals, metastable region, and unstable region. In Figure 5, the horizontal axis indicates the product of normalized density ρ and w, which is defined as a product of the average mass density ρ of melt and the specific volume w of monomer core. This phase diagram is analogous to the binary component case but has a different ordering parameter, that is, density. While the melt is

3.1. Flow-Induced Precursors

Katayama et al.84 probably were the first to report the formation of flow-induced precursors (FIP) in the 1960s. They studied a melt spinning process by combining a special model-spinning apparatus with an in-house X-ray setup. Their results showed that the structural signal in SAXS is observed much earlier than the crystalline signal in WAXS, which indicates that density fluctuations on the length scale of several tens of nanometers occur before crystallization. This mesomorphic state was deemed as FIP, bridging the transformation from melt to crystals. Several other groups also provided results to support the presence of FIP in PET.85−88 Bonart85 reported that nematic and smectic phases form sequentially during stretching of an amorphous PET sample. Using synchrotron characterization, Blundell and coworkers86−88 announced the existence of mesophase during drawing of PET homopolymer and copolymer, which act as a precursors in strain-induced crystallization. At that time, the investigations of FIP were mainly concentrated on steady melting spinning or polymers with slow crystallization kinetics such as PET,85,86 poly(ethylene naphthalate) (PEN),87,88 and polystyrene (PS),24,89 due to the limitation of time resolution of detection techniques. Besides, the experiments were mostly performed in complex processing conditions like molding or spinning. This means complex flow and thermal histories were imposed on the polymers, which influence both nucleation and growth steps. Despite all aforementioned limitations, some features of FIP are still captured: the formation of FIP can strongly influence the crystallization rate, change the crystallite G


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possibility of liquid−liquid separation. Recently, crystallization studies on the extrusion process of iPP, PS, and PET were conducted by Ryan et al.,106−108 where large-scale ordering before growth of crystals was observed. Moreover, melt spinning investigation of poly(vinylidene fluoride) conducted by Cakmak et al.109 and annealing study of iPP from a highly extended melt conducted by Schultz et al.110 also showed spinodal-type phase separation. 3.3. Nature of Flow-Induced Precursors

Although the formation of FIP has been demonstrated by a large amount of experimental observations, the nature of FIP is still under debate. In this section, we review the debates on the existence (section 3.3.1), structure (section 3.3.2), and ordering parameter (section 3.3.3) of FIP. The concept of FIP is rather vague and is commonly used to describe structures that are not clearly revealed. The term FIP can include various structures; for example, Ma et al.111 sorted four types of FIP according to the sensitivities of different detection techniques. Up to now, there has been no consensus yet reached on the existence and structure of FIP. Various experimental techniques have been employed to characterize dynamic and thermal abilities of FIP. Since scattering methods are powerful for probing structure with long-range ordering, most experimental results presented in this section are based on X-ray scattering. 3.3.1. Existence of Flow-Induced Precursors. Many FIC studies have shown the appearance of metastable FIP before crystallization, among which most experiments were based on the combination of SAXS and WAXS methods. SAXS can detect density fluctuations without long-range order, and WAXS can probe crystalline order. For crystallization with nucleation and growth mechanism, WAXS should appear at the same time as SAXS. However, if FIP forms, development of SAXS due to density fluctuation may occur prior to that of WAXS due to crystalline order. Most early evidence for the appearance of FIP was obtained from extrusion processes. The pioneering works of Katayama et al.,84 Cakmak et al.,109 Ryan et al.,107,108 and Schultz et al.110 showed earlier observation of SAXS than WAXS in various systems like iPP, PE, and PET. They concluded that density fluctuation with large-scale order occurs and that it plays an important role in crystallization. However, Wang et al.112,113 pointed out that the time lag between SAXS and WAXS may be attributed to detector sensitivity. In other words, WAXS may not be able to detect crystals with low volume fraction in the early stage of crystallization, whereas SAXS is capable of probing the structure as long as its density contrast with the surrounding melt is sufficient. Thus, caution should be exercised when comparing the first appearance of SAXS and WAXS. Heeley et al.114 further addressed this issue by using an updated WAXS detector, which has an improvement in count rate with a factor of 104 over that used in previous experiments. Their results demonstrated that the lag between SAXS and WAXS is not caused by detector sensitivity, and the appearance of SAXS before WAXS indicates the formation of unknown structure. In addition to X-ray scattering, some other experimental techniques also lead to the same conclusion on the existence of FIP. As already discussed in section 2, the rheo-Raman study by Chai et al.58 showed that flow can promote the formation of alltrans bands, which can survive for several hours after cessation of flow even above the melting temperature. The birefringence experiments reported by Seki et al.95 and Ma et al.111 suggested the appearance of oriented structure before crystallization. Smallangle light scattering (SALS) experiments conducted by

Figure 5. Generic phase diagram for a polymer melt. Tm, Tc, and Ts are the melting, liquid−liquid binodal and spinodal temperatures, respectively. Dotted line represents quench path. Reprinted with permission from ref 35. Copyright 1998 American Physical Society.

quenched to a temperature below spinodal temperature Ts (that is, the melt is in an unstable region), SD-type phase separation takes place. The melt separates into two coexisting liquids, which differ in conformation distributions (see Figure 6). In the region

Figure 6. Schematic representation of the late stage of spinodal decomposition for coexisting liquid phases with different conformations. Thin and thick lines represent disordered and helical conformations, respectively. Reprinted with permission from ref 35. Copyright 1998 American Physical Society.

of denser liquid, density and conformation are both closer to the state needed for crystal packing than that in the original melt, which lowers the energy barrier for crystallization.100 In fact, numerous experimental results reported the emergence of SAXS signal before crystal diffraction in WAXS, indicating the occurrence of density fluctuation prior to crystallization.31,101−103 For example, Imai et al.101,104,105 investigated the induction period of PET in cold crystallization. In their experiments, the peak position in SAXS is smaller than the ordinary peak position of the intercrystal correlation peak. SAXS signal shows an increase of scattering intensity and a shift of diffraction maximum before crystal growth. The SAXS evolution can be well fitted with the theory for spinodal decomposition, indicating that the scattering behavior obeys the predication of spinodal kinetics in the early stage of crystallization. Spinodal phase separation was mainly observed in melt crystallization under flow. This is because flow aligns polymer chains and enhances density, which thereby increases the H


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Pogodina et al.115 and Zhang et al.116 indicated the formation of highly elongated structures associated with crystallization by flow. The elegant works of Alfonso and co-workers72,117−119 about the existence and lifetime of FIP deserve a separate discussion. They imposed shear flow by pulling a fiber inside a thin layer of molten polymer and chose the crystalline morphology at the fiber−melt interface as a marker to study the existence and memory of flow history. Melt was first sheared at a temperature slightly above the melting point, followed by an annealing at this temperature for different durations, and finally cooled to a lower temperature for isothermal crystallization. For the sheared melt after being annealed for 100 s, a cylindrical morphology was found during isothermal crystallization, while the completely relaxed melt after being annealed for 300 s led to the typical spherulitic morphology (Figure 7). The lifetime of FIP could be

the development of synchrotron radiation and detection techniques, noncrystalline rodlike structures from SAXS, appearing earlier than crystalline scattering from WAXS around the nominal melting point, have been observed by several groups.59,120−122 In contrast, some recent work on PE blends with low and high molecular weight components and lightly cross-linked PE showed that FIP contains crystals at temperature above the equilibrium melting point.59,120,123 However, even with a synchrotron radiation source, the detection sensitivity of SAXS and WAXS is still a disputed issue, which poses an obstacle to understanding whether FIP are crystalline or not. Therefore, experimental techniques with higher detection sensitivity and delicate experimental design are required. Microdiffraction scanning with beam size of a few micrometers is a highly sensitive technique, which allows one to obtain highquality SAXS and WAXS patterns with high time and spatial resolution. For FIP, some notable studies have been carried out recently with this technique by Gutierrez et al.,117 Kanaya et al.,68 and Su et al.,99 just to name a few. Gutierrez et al.117 observed that ordered FIP can be generated under intense flow at temperatures above the nominal melting temperature in iPS. They claimed that those ordered FIP are noncrystalline and are made up by parallel chain bundles oriented along the flow direction, while the lamellae developed subsequently with a crystallinity less than 1%. Their results also suggested that the smallest and least stable FIP may be destroyed by the relaxation of orientation and loss of segments from the oriented clusters, which is consistent with the finding of Balzano et al.120 that FIP stability depends on size. Kanaya et al.68 reported that FIP has a crystallinity of about 0.15% and has a higher melting temperature than the nominal melting temperature of lamellar crystals in iPS. Su et al.99 performed systematic temperature-range research to provide more evidence on the structure of FIP. Their experimental protocol is similar to the fiber pulling experiment of Gutierrez et al.117 A fiber was pulled through iPP films to create an intense shear flow field in a temperature range covering temperatures below and above the nominal melting point, and then the sheared sample was kept at the shear temperature for 10 min, which was finally cooled to 138 °C for isothermal crystallization; see Figure 8. For shear temperatures below 170 °C (slightly above the nominal melting point of iPP, 165 °C), crystalline FIP is observed. For shear temperature at 175 °C, no crystalline FIP is detected but transcrystalline morphology is generated at the fiber−melt surface at 138 °C. The transcrystalline morphology indicates the formation of noncrystalline FIP induced by shear at 175 °C. For shear temperatures above 180 °C, only spherulitic morphology appears at 138 °C. Some may argue that the formation of tiny crystals cannot be detected due to the detection limit of WAXS. This indeed cannot be completely avoided, even with synchrotron radiation scanning microdiffraction. If the structures induced by flow at 175 °C are tiny crystallites below the detection limit, the absence of induction time is expected, because crystals formed could grow straightforwardly when sample was cooled to 138 °C. However, an induction time exists for the sample sheared at 175 °C (S175−138), as shown in Figure 9. Thus, it seems that the existence of induction time demonstrates the formation of noncrystalline FIP, which further develop into stable nuclei during the induction time. As suggested by the results of Su et al.,99 whether FIP is crystalline or not depends on temperature. This dependence is consistent with the findings from different groups.121,124−126 Polec et al.121 observed crystalline FIP for temperature below

Figure 7. Morphological evolution of PS sample as a function of isothermal time at shear temperature after cessation of flow. The isothermal times were (a) 100, (b) 300, and (c) 500 s (pulling rate is 5 mm/s and pulling time is 1 s). Reprinted with permission from ref 118. Copyright 2008 American Chemical Society.

estimated from the disappearance of transcrystalline morphology. They investigated a series of isotactic poly(1-butene)s with varying molecular weights and found that the temperature dependence of FIP lifetime follows an Arrhenius-type relationship.72 This relationship is independent of the molecular weight of polymer, but the lifetime of FIP increases with increasing molecular weight. Later, they used the same method to study a series of very narrowly dispersed iPS and found that the exponent of this Arrhenius-type relationship is about 2.118 Although their experimental approach is simple, with that method, the formation of FIP can be corroborated and the lifetime can be quantitatively assessed. 3.3.2. Are Flow-Induced Precursors Crystalline or Not? Concerning FIP, another debated question is whether they are crystalline or not. In the early stage of nucleation, FIP must start with a tiny amount. In addition, FIP is often studied at high temperatures close to the nominal melting point. Those two reasons lead to difficulty in justifying the structure of FIP. With I


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Figure 8. (a1−d1) Microscopic images after crystallization at 138 °C for about 10 min. (a2−d2) One-dimensional (1D) WAXS diffraction profiles integrated from mapping diffraction patterns. (a3−d3) Distribution of crystallinity over time around the fiber surface (which is indicated in the microscopic images) during the second mapping measurement of samples (a) S160−138, (b) S170−138, (c) S175−138, and (d) S180−138. Dashed line indicates the position of fiber. S160−138, S165−138, S170−138, S175−138 and S180−138 represent samples sheared at 160, 165, 170, 175, and 180 °C, respectively. Reprinted with permission from ref 99. Copyright 2014 American Chemical Society.

crystalline FIP to crystallites is too fast to be detected by current experimental techniques. If this is the case, further development of ultrafast structural detection techniques should shed light on this long-standing problem. 3.3.3. Ordering Parameter of Flow-Induced Precursors. Experimental data from X-ray scattering,83 birefringence,128 and simulation results55 all suggest the existence of FIP. What is the fundamental ordering of FIP? This question is still unrevealed for the polymer community. Therefore, the definition of FIP is obscure and has been queried, just due to the lack of full structural information and precise ordering parameter. Generally speaking, the order of polymer includes intrachain and interchain orderings.28,29 Imposing a flow field first leads polymer chains to be oriented or/and stretched, which is accompanied by intrachain ordering. With Fourier transform infrared (FTIR) spectroscopy, it had been demonstrated by Li and co-workers50,51,53 that flow can indeed induce conformational order (helix) in iPP melt, where the effect is more pronounced below the nominal melting temperature than above. Hence, intrachain ordering seems the starting point to study FIP, which, however, is commonly neglected. The effects of strain and strain rate on the coil−helix transition were studied at various temperatures. It was noticed that long helices induced by flow can relax or grow and align to induce interchain ordering. Figure 10a shows an IR spectrum of the helix containing 10 monomers, with conformational band (998 cm−1), before and after shearing at 164 °C. First, flow leads to a sharp increase of IR band intensity, indicating a strong enhancement of long helices. Second, the IR intensity shows a decay process after shear, which can be considered as the melting of helical structures. Finally, crystallization starts and leads to a second increase in intensity of the IR band. The relaxation process of

Figure 9. Evolution of crystallinity during isothermal crystallization at 138 °C of samples after shear at different temperatures. Reprinted with permission from ref 99. Copyright 2014 American Chemical Society.

155 °C, whereas noncrystalline FIP was found for temperatures above 155 °C. Zhao et al.124 reported crystalline FIP of iPP at 148 °C, while Somani et al.125,126 provided evidence of noncrystalline FIP at 165 and 175 °C. In a nice review by Hsiao and coworkers,11 it was pointed out that FIP may be amorphous, mesophase, or crystalline. In the work of Balzano et al.,127 kinetic analysis of early-stage crystallization indicates that unidirectional propagation of a growth front may occur, which facilitates development of crystalline FIP. However, even at low temperature (much lower than the melting point), recent molecular simulation by Yamamoto55 showed the growth of smectic mesophase before crystallization in a highly stretched amorphous iPP. Therefore, probably noncrystalline FIP can be generated at low temperature, but the transformation process from nonJ


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crystallization. This acceleration of transformation under flow is due to two reasons. First, the barrier between crystal and precursor is smaller than that between crystal and melt. Second, the conformation and orientation of chain in precursor are closer to the state in crystal than that of random-coil state. The former is thermodynamically favorable while the latter is kinetically favorable for this transformation, leading to accelerated crystallization kinetics. In addition, with advanced characterization techniques, some other interesting phenomena were observed recently about how the presence of precursors influences the crystallization process, such as nucleation (section 3.4.1), crystallization kinetics (section 3.4.2), and final morphologies (section 3.4.3). 3.4.1. Nucleation. The influence of precursor on nucleation not only refers to its direct transformation into stable nuclei but also facilitates the subsequent appearance of ultimate nuclei by absorbing the surrounding molecules, creating new surface, and even directly catalyzing the growth from relaxed melt. JaneschitzKriegl and co-workers130−132 proposed the presence of dormant nuclei even in quiescent melt, which are local alignments or organized aggregates with a shape of fringe micelle. When flow strength (stress in their work) exceeds a critical level, the dormant nuclei become active as point nuclei and align along the flow direction. With increasing stress, the number and longitudinal dimension of those nuclei are both significantly increased. At this stage, those nuclei have the ability to induce growth of lamellae and can be considered as the precursors for shish nuclei. As the intensity of the flow field further increases, adjacent nuclei merge into shish nuclei. Later in 2002, Seki et al.95 put forward a new model within the framework of Janeschitz-Kriegl and co-workers130−132 that emphasized the role of chain absorbing in the formation of shish nuclei. In this new model (Figure 11), flow promotes the formation of precursors, which interact with the adjacent chains on the surfaces. The absorbed chains are easier to deform during flow and generate more new precursors, which further adsorb adjacent chains and ultimately lead to a trace of precursor clusters, that is, shish nuclei. More recently, a ghost nucleation model has been proposed by Cui et al.97 It was speculated that the formed precursors have movement relative to their surrounding matrix, which creates surface to form nucleation sites. Such an effect can be generated by pulling fiber embedded in polymer melt.133 3.4.2. Crystallization Kinetics. In most cases, FIP develops into an effective nucleus and accelerates crystallization kinetics, which has been demonstrated by many experiments. However, FIP may be destroyed and consequently influence the early stage of crystallization in a different way. Working with extensional rheology and in situ SAXS techniques, Cui et al.134 investigated the FIC of bimodal PEO blends. As shown in Figure 12a, a nonmonotonic change in the onset time of crystallization was observed. For strain smaller than 1.5 or larger than 3.0, only amorphous scattering is observed immediately after cessation of flow, while with intermediate strain of 2.0 and 2.5, an obvious lamellar scattering peak appears. On the other hand, with strain of 3.5, the lamellar crystals have a relatively weak orientation in the initial stage of crystallization but a higher orientation in the late stage (Figure 12b), whereas an opposite evolution trend appears for the sample with smaller strain of 1.5. Cui et al.134 attributed this unusual phenomenon to the destruction of formed precursors by further increasing flow intensity. In the fragmenting process, the precursors may be forced to fracture, rotate, and tilt, leading to an increased onset time of

Figure 10. (a) Intensities of 998 cm−1 band vs time after shear at (a) 164 °C; (b) 172, 177, and 200 °C; and (c) 168 °C (shear rate 13.5 s−1, shear strain 3375%). Reprinted with permission from ref 51. Copyright 2008 American Chemical Society.

helices was analyzed with the model that was widely used for protein.129 Two different relaxation processes were identified, with the nominal melting point (165 °C) as a boundary temperature. For temperatures above the nominal melting point, the IR band intensity follows a first-order decay process (Figure 10b), while for temperatures around or below the nominal melting point, second-order decay fitting is needed to model the relaxation process (Figure 10c). Taking 168 °C as an example, two relaxation times of 315 and 16 428 s are obtained, suggesting the formation of two different states of helices. It was tentatively speculated that the isolated helices have a fast relaxation dynamic and aggregations of helices with interchain ordering have a slow relaxation process. The relaxation time of helices is influenced by strain, strain rate, and temperature, which can reflect the ordered degree of helical aggregation. Thus, Li and co-workers50,51,53 proposed that relaxation time can be considered as an ordering parameter of FIP in some way. Of course, relaxation time is not enough to define the structure of FIP, but the work of Li and coworkers presented a good starting point. A more precise ordering parameter is needed to describe and define the structure of FIP. Interestingly, the crystallization begins after a relaxation process of flow-induced helices rather than directly after cessation of flow (Figure 10a), indicating that an arrangement of helices is required for crystallization. This implies that the helical aggregations induced by flow have a mesomorphic or liquid-crystal ordering, consistent with the viewpoint of Somani et al.74 that FIP are mesomorphic bundles of aligned chain segments. 3.4. Influences of Precursor on Crystallization

Compared with disordered melt, precursors are easier to transform into stable crystalline nuclei and consequently trigger K


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In addition to the onset of crystallization and lamellar orientation, the growth process is also affected by the presence of precursors. Hsiao et al.59 revealed an unexpected multiple shish structure in a sheared PE blend containing 2 wt % crystalline ultrahigh molecular weight (UHMW) component and 98 wt % noncrystalline matrix. From the high-resolution scanning electron microscopic (SEM) image shown in Figure 13a, multiple shish with a diameter of several nanometers, rather than single shish, are presented, different from the conventional view of shish structure. With the presence of multiple shish, a time-dependent growth rate of kebab is observed (Figure 13b), which is demonstrated as diffusion-controlled growth. This result is quite different from crystallization under quiescent conditions, where diffusion is not a limiting step and causes a constant growth rate. The results of Hsiao et al.59 are consistent with AFM experiments conducted by Hobbs et al.,96,135,136 who observed a similar diffusion-controlled growth process for kebab. More recently, Roozemond et al.137 proposed a self-regulation mechanism in flow-induced structure formation of iPP. Combining a slit flow device and in situ ultrafast WAXS measurement (30 frame/s), they found that the kinetics of the crystallization process in all shear layers are identical, regardless of flow rate or flow time. The intensity of flow field only influences the thickness of shear layer. They attributed this abnormal phenomenon to the disturbance of local flow field by the formed shish. Flow first promotes the formation of pointlike precursors, which transform into shish in the same way as in the model of Janeschitz-Kriegl and co-workers130−132 and Seki et al.95 When the density of shish reaches a critical value, the modulus of the shear layer is sufficient to hinder further deformation and stop shish growth. Since the volume flow rate is constant, the material in the inner layer suffers the raised flow rate, which facilitates the appearance of shish and formation of shear layer. 3.4.3. Morphologies. The influence of FIP on crystallization mainly depends on the density and orientation of formed precursors. Mild flow gives rise to chain orientation and promotes the formation of pointlike FIP, leading to a huge number of spherulites that are small in size, while strong flow results in chain stretch and favors the formation of shish precursors, resulting in shish-kebab structure. Some intermediate structures have also been reported, depending on the density and length of FIP. For example, oriented FIP with short length lead to distorted spherulites,138 while those with long length but low density give rise to sausagelike structures.139 Under strong extensional flow, precursors with low and high densities can lead to fibrillar structure and to homogeneous network structure

Figure 11. Schematic diagram of the nature of shear-induced nucleation and subsequent growth of oriented lamellae during short-term shearing. (a) A long chain (bold line) dispersed in a matrix of short chains adsorbs to a pointlike precursor. Dangling segments of adsorbed chains become oriented due to shear. (b) Additional chains adsorb and their dangling segments form streamers upstream and downstream of the pointlike precursor. (c) Increased local orientation of the chain segments increases the probability that long-lived ordered structures will form. (d) More chains adsorb to these new nucleation sites, and the process propagates a string of nuclei along the flow line. (e) The nuclei along this thread lead to lateral lamellar growth. Reprinted with permission from ref 95. Copyright 2002 American Chemical Society.

Figure 12. (a) 1D SAXS meridional integrations I(q) immediately after cessation of extension (t = 0 s). (b) Orientation parameter of lamellar crystals of PEO blends evolving with time under different strains at 52 °C. Reprinted with permission from ref 134. Copyright 2014 American Chemical Society.

crystallization and low orientation of initial lamellar crystals under large strains.

Figure 13. (a) SEM image of toluene-extracted UHMW PE crystallites with a shish-kebab structure having multiple shish. (b) Kebab growth rate G as a function of time. Reprinted with permission from ref 59. Copyright 2005 American Physical Society. L


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Figure 14. Schematic of correlation between precursors and cylindrites at a local wall shear stress. (a) One-dimensional SAXS plots of structural melt after annealing for 10 min at 180 °C (a-1; iPP was heated directly from room temperature to 180 °C) and supercooled melt at 180 °C (a-2; iPP was first heated to 210 °C, kept at this temperature for 15 min to ensure thermal history, and finally cooled to 180 °C). (b) Schematic of shear stress distribution in a slit shear cell. (c) Corresponding optical images obtained under crossed polarizers at wall shear stress of 20 kPa. The bright sections in optical images represent β-form crystals of iPP. Reprinted with permission from ref 142. Copyright 2012 American Chemical Society.

decorated by small highly oriented lamellar stacks, respectively.134 Recently, Shen et al.140 performed an interesting work to establish the relationship between initial precursors and final fibrillar structure (the so-called cometlike shish-kebab morphology in their definition). A combination of two-step shear proposal and in situ optical microscopy was adopted in their experiment. The aim of the first shear step is to generate pointlike precursors. After the second shear step, they observed that all fibrillar structures are initiated from pointlike precursors. In addition to morphologies, crystal modifications are also influenced by the presence of precursor. Zhang et al.141−143 obtained iPP precursors by melting a sample at a temperature between the nominal melting point and the equilibrium melting point. The formation of precursors can be demonstrated by the periodic structure scattering in SAXS but no crystalline scattering in WAXS (Figure 14a). They found that, even with low shear stress, the presence of precursor assists the formation of βcylindrites (Figure 14c). The density and content of β-cylindrites increase with increasing precursor content. Their further work142 indicated that, in a specific structural melt containing precursors, the number of α-cylindrites increases with shear stress at the expense of β-cylindrites. Moreover, lamellar structure also depends on the type of precursor. Four different types of precursornamely, pointlike, scaffold-network, microshish, and shishwere observed sequentially by increasing strain in a lightly cross-linked PE.144 The long period of lamellar stacks resulted from the former three types of precursor increasing in an orderly fashion, while the fourth type of precursor decreased. This is due to the increase of entanglement and cross-link densities in the former three types of precursor, leading to a thick interlamellar amorphous layer. In contrast, the chain con-

formation inside the fourth type of precursor is almost extended, allowing lamellae to grow without preservation.

4. FACTORS INFLUENCING THE FORMATION OF FLOW-INDUCED PRECURSORS FIP formation is influenced by many experimental parameters, such as flow strength, temperature, polydispersity of materials, and so on. Thus, study of the crucial factors determining FIP formation is expected to improve our understanding of the nature and formation mechanism of FIP. 4.1. Flow Parameters

Flow can disturb chain configuration from the initial equilibrium random-coil state to oriented and aligned states and thus can promote the formation of FIP as well as accelerate the crystallization. However, promotion and acceleration happen only when flow is above a certain strength. In this sense, the quantification of flow strength is essential to understand FIC. The flow field can be assessed by several parameters such as strain, strain rate, flow time, stress, and external work. The first three parameters (strain rate, flow time, and stress) are intrinsic flow properties, but the last parameter, mechanical work, is associated with not only flow strength but also molecular properties. Recently, Peters and co-workers98,111,145 carried out some elegant works to study the effects of strain rate on the formation of FIP even during short-term flow. By combining a Linkam shear cell and fast X-ray scattering, they investigated the early stage of FIC from melt of iPP at 145 °C with a total strain ε = 180 but different strain rate ε̇ under strong flow.145 For ε̇ ≥ 90 s−1, crystalline FIP containing 2% crystallinity were already generated during flow, while for ε̇ ≤ 60 s−1, only metastable FIP with no crystallinity were formed during flow, which transform into M


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characterize the effect of flow on FIP formation. Janeschitz-Kriegl et al. found that the number of pointlike precursor increases with the specific mechanical work applied, but a sudden transformation from pointlike to threadlike FIP happens when the specific mechanical work reaches a threshold. Recently, the validity of specific mechanical work was demonstrated by Mykhaylyk et al.150 by using a well-defined model of linear− linear hydrogenated polybutadiene (h-PBD). They found that, for an assigned sample, the specific mechanical works for formation of threadlike FIP are almost the same and independent of strain rate when the strain rate is larger than the inverse Rouse time of long-chain molecules (Figure 15). However, this specific work decreases with increasing fraction of long-chain molecules in blends. Later, Mykhaylyk et al.138,151,152 generalized this conclusion to polydisperse materials and pointed out that the specific mechanical work for threadlike FIP formation depends on the chemical structure and molecular weight distribution of polymer as well as experimental temperature.

crystals when flow stops. Later, combining the characterizations of fast X-ray scattering, birefringence, and final morphology, Ma et al.111 defined several types of FIP for iPP at 145 °C. For ε̇ ≥ 400 s−1, crystalline FIP can be generated during flow, even when the flow duration is only 0.25 s. For ε̇ = 320 and 240 s−1, noncrystalline FIP formed during flow and quickly transformed into crystalline shish after cessation of flow, which are defined as precursor for shish. For ε̇ = 160 s−1, SAXS and WAXS do not show characteristic structural signals, but the birefringence signals, including a birefringence upturn during flow and nonzero relaxation after flow, were observed. The birefringence signals results demonstrate the formation of FIP, which is termed as threadlike precursor. For ε̇ = 80 s−1, the birefringence cannot capture a structural signal, but the accelerated kinetics and orientation indirectly reveal the generation of FIP, which is termed as needlelike precursor. In addition to strain rate, strain also plays an important role in FIP formation. For example, Liu et al.144 studied strain-induced crystallization in lightly cross-linked PE and observed uncorrelated oriented FIP when the applied strain is smaller than 0.6; scaffold-network FIP when the applied strain is on the order of 1.0; microshish-type FIP when the applied strain is up to 1.3; and shish-type FIP when the applied strain is larger than 2.0. Although the strain rate and strain provide useful ways to assess flow strength, the flow time, that is, accumulation effect for the whole flow period, is not fully considered. Many results have shown that the strain rate ε̇ and flow time tflow together influence FIP formation in a complex way. An empirical relationship was constructed by Liedauer et al.90 that the transition from spherulitic to fibrillar morphology (an indicator of fibrillarlike FIP) is proportional to (ε̇)4tflow2. This conclusion is qualitatively consistent with the results of Somani et al.146 in the sense that a flow with large strain rate but short flow time has more remarkable effects on the formation of FIP than a flow with small strain rate but long flow time. According to the work of Doi and Edwards,67 the anisotropy in chain conformation can be directly related to the applied stress. Thus, stress is also a key parameter to influence FIP formation. Kornfield and co-workers95,139,147 carried out some well-defined shear experiments with bimodal iPP blends by not only fixing the stress but also employing similar flow time and applied strain, aiming to control the same average chain orientation at the molecular level. They found a critical shear stress of 0.12 MPa at 137 °C, above which threadlike FIP forms as evidenced by the anomalous stress upturn during flow and shish-kebab structure in the final crystallized sample. For stress below the critical value, flow induces the formation of pointlike precursors, as confirmed by the accelerated kinetics and increased number density of spherulites compared with the quiescent conditions. These results of Kornfield and co-workers are well consistent with that of Balzano et al.,148 who performed shear experiments at temperatures around the nominal melting point (163 °C for the iPP they used). Coincidentally, stable threadlike FIP containing limited crystals form for stress larger than 0.12 MPa, while shortlength FIP with aspect ratios tending to unity (pointlike FIP) are generated for stress smaller than 0.10 MPa and dissolve into the melt with time. In contrast with the parameters describing flow field, such as strain rate, strain, flow time, and stress, Janeschitz-Kriegl et al.149 proposed a concept of specific mechanical work, which is defined t as W = ∫ 0flowη[ε̇(t)]ε̇ 2(t) dt, where η is the strain-rate-dependent viscosity. The specific mechanical work contains the effects of stress and strain, which may be chosen as a decisive parameter to

4.2. Temperature

The effect of temperature is obvious in FIP formation, as in nucleation and crystal growth. In this section, we mainly discuss some unusual phenomena about the influence of temperature on precursors with the presence of flow. As already discussed in section 3.3, whether FIP are crystalline or noncrystalline depends on temperature. Generally, in polymer melt, for temperatures around and below the nominal melting point, FIP stay in a crystalline state; for temperatures slightly above the nominal melting temperature but still well below the equilibrium melting temperature, FIP are in a noncrystalline state; and for temperatures above the equilibrium melting temperature, only amorphous melt is expected. However, for PE at 142 °C, close to but above the equilibrium melting temperature Tm0 (141.2 °C), FIP containing limited crystallinity have been observed in blends of LMW (low molecular weight) and HMW (high molecular weight) components by Keum et al.153 and Balzano et al.27,120 Recently, Liu et al.123 reported that, in lightly cross-linked PE, crystalline FIP was observed under extensional flow at 184 °C, about 43 °C higher than the equilibrium melting temperature. Balzano et al.27 pointed out that, in polymer melt, precursors could form if the HMW chains overcome a critical molecular deformation at a time scale when those molecules cannot relax. However, at such high temperatures, the crystalline FIP is not stable even though it could form. Balzano et al.120 studied the structural evolution of FIP at 142 °C after cessation of flow, using in situ SAXS and WAXS. At times before 600 s, some interesting phenomena were observed; see Figure 16. After cessation of flow, the SAXS intensity decreased exponentially, while the corresponding crystallinity built up gradually. Balzano et al.120 speculated that the initially formed FIP show polydispersity in size. The FIP with sizes larger than the critical value transform into crystals, whereas those with sizes smaller than the critical value dissolve into melt. The good correlation between the experimental dissolution process and the modified memory function further indicated that the time scale for dissolution of small FIP is related to the reputation time of HMW chains, in line with the IR results of An et al.51 Intuitively, the threshold of FIP formation is expected to increase with temperature because of the enhanced barrier. In contrast, Kumaraswamy et al.154 found that the flow time for FIP formation under strong shear flow decreases with increasing temperature (Figure 17). However, after rescaling by the N


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Figure 16. Crystallinity and SAXS intensity evolve with time after step shear at 142 °C. The initial drop of SAXS intensity is fitted with Doi− Edwards’ memory function; the fit is represented by the solid line. Reprinted with permission from ref 120. Copyright 2008 American Physical Society.

Figure 15. (a−f) Optical images of sheared blends of high and low molar mass h-PBD (2 wt % 1700 kDa in a 15 kDa matrix). White dashed circles mark a boundary between oriented and nonoriented lamellar structures in samples. The plot superimposed on image d shows the degree of orientation of lamellar structure along the flow direction, measured across the diameter by SAXS. The color-coded scattering patterns above were taken from the areas marked by the green and pink squares. (g) Plot of specific mechanical work vs measured critical shear rates, required for the formation of threadlike FIP. (Inset) Dependence of shear rate required for orientation on shearing time. Reprinted with permission from ref 150. Copyright 2008 American Chemical Society.

Figure 17. Temperature dependence of the time scale at quiescent crystallization, tQ, and of the onset time of the abnormal upturn in birefringence during flow, tu. The solid line presents WLF rheological shift factor with 190 °C as a reference temperature. Reprinted with permission from ref 154. Copyright 2002 American Chemical Society.

short flow duration was adopted (less than 400 ms). By combining SAXS/WAXS and rheological information, they found that FIP already formed during flow and they discovered a constant critical strain for FIP formation for temperatures ranging from 130 to 170 °C. Cui et al.30 proposed a kinetic pathway coupling flow-induced coil−helix transition and isotropic−nematic transition, in which flow provides sufficient concentration and alignment of helices for FIP formation, exhibiting that the barrier is eliminated by flow.

rheological Williams−Landel−Ferry (WLF) time−temperature shift factors, the values of the rescaled onset time for birefringence upturn were approximately the same for various temperatures ranging from 140 to 175 °C. This result implies that the formation of FIP happens at a fixed strain. Thereby, they proposed that the formation of FIP is determined by a critical level of molecular orientation, consistent with the viewpoint of Balzano et al.27 More recently, Cui et al.30 presented a similar result in iPP under strong extensional flow. In their study, the time resolution of SAXS/WAXS was down to 30 ms, and rather

4.3. Molecular Parameters

Most semicrystalline polymers have very broad molecular weight distribution (i.e., polydispersity). Short and long chains differ in their responses to imposed flow, which complicates the O


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to their long orientational memory, and makes them the source for precursor formation.

explanation of FIP formation, especially the role of short and long chains. From the rheological point of view, whether and how much chains can be deformed by external flow depends on the competition between molecular relaxation and flow strength. This competition can be quantified by the Weissenberg number, which is a product of strain rate ε̇ and relaxation time τ (Wi = ε̇τ, which is named as Deborah number in the original reference155). Two characteristic time constants, terminal relaxation time τrep for chain orientation and Rouse relaxation time τRouse for chain stretch, classify flow field in three regions: (i) Wirep < 1, where flow is weak and has negligible influence on chain conformation; (ii) Wirep > 1 and Wis < 1, where only chain orientation occurs without segmental stretch; and (iii) Wirep > 1 and Wis > 1, where flow is strong enough to ensure both chain orientation and chain stretch. The two specific relaxation times follow the relationship τrep = τRouseZ, where Z is the number of entanglements per chain,145 meaning that Wirep is always larger than Wis. Also note that the practical threshold of Weissenberg number may be slightly larger than unity. According to the estimation of van Meerveld et al.,155 the number density of spherulites can be increased for Wis < 1−10, suggesting an enhancement of pointlike FIP in this flow strength region. While shish-kebab structure is generated for Wis > 1−10, implying the formation of threadlike FIP. The validity of this Weissenberg number approach has been further confirmed by Housmans et al.,156 Somani et al.,146 Zhao et al.,124 and many others. According to this picture, it is obvious that molecular weight and polydispersity play key roles in defining the flow regions and in influencing FIP formation. At a given flow condition, long chains are much more easily oriented or stretched than short ones, as long chains have longer relaxation times. To assess the effect of molecular weight and polydispersity on FIP formation, bimodal blends composed of long and short chains in a matrix were commonly used as a model system. Kornfield et al.128 studied the role of long chains in a bimodal blend of iPP under shear flow. They found that the long chains are preferentially involved in the formation of threadlike precursors. Chains longer than about 4.7 times average are effective in promoting threadlike precursor formation. Furthermore, the formation of threadlike precursors is greatly enhanced by long chain−long chain overlap, suggesting a cooperative effect of long chains. Seki et al.95 reported a similar enhancement of threadlike precursor formation by adding long chains in a short-chain matrix, in agreement with the results of Kornfield et al.128 However, Seki et al.95 pointed out that, at low stress, long chains have no priority in accelerating the formation of pointlike precursors. They speculated that the formation of pointlike precursors is determined by the local stress or average orientation of chain segments, which is independent of long chains. The simulation results of Wang et al.157 showed that polydispersity, together with orientational relaxation, determines precursor formation. They first studied athermal relaxation in bulk extended chains and then investigated isothermal crystallization of intermediately relaxed melt by dynamic Monte Carlo simulation. Their results suggested a longer orientational memory of long chains than short ones. For isothermal crystallization, in the melt with uniform chain lengths, the crystallization rate can be increased by the orientational memory, but no precursors formed during crystallization for either long- and short-chain systems. However, in a bimodal blend with different chain lengths, precursors were generated from the highly oriented long-chain component. They argued that orientational relaxation leads to selection of long chains, due

5. CORRELATION BETWEEN DEFORMATION AT WHOLE-CHAIN SCALE AND NUCLEATION Ordering in FIP is not completely clear yet, but flow-induced shish can be characterized much more easily due to their sufficiently large density contrast with the surrounding melt. The length of shish can reach micrometers, comparable with that of extended chain, so shish have been recognized as extended-chain crystals in early times. Hence, the formation of shish nuclei seems correlated with the deformation of polymer at the whole-chain scale. In this section, the formation mechanism of shish nuclei is our primary concern. For this purpose, we will first introduce the discovery and various formation mechanisms of shish nuclei. Then some new understandings of shish-kebab revealed by recent experimental investigations will be delivered, which are essential but still under debate: (i) Is coil−stretch transition (CST) or stretched network model (SNM) responsible for shish formation in polymer melt (section 5.6.1)? (ii) How do polydispersity, long chain, and short chain matrix influence shish formation (sections 5.6.2−5.6.4)? (iii) How does shish evolve and grow under flow and thermal conditions (section 5.6.5)? (iv) How does shish form under near-equilibrium and farfrom-equilibrium conditions (section 5.6.6)?(v) Is shish formation a single-stage or multistage process (section 5.6.7)? (vi) Is shish a thermodynamic phase or a kinetic state (section 5.6.8)? 5.1. Shish-Kebab Crystallite

The chain character of polymer molecules was recognized around 80 years ago. Since then, many studies had been carried out on extension and alignment of polymer chains to exploit the intrinsically anisotropic properties of materials.158−171 First of all, chain stretching in extensional flow benefits fiber spinning, where a uniaxial flow from a spinneret dies and a subsequent mechanical drawing are utilized to induce chain orientation. Ziabicki et al.172,173 and Peterlin174 constructed a relationship between extensional flow and processing parameters for orientation phenomena in melt spinning. Early in 1963, Mitsuhashi175 reported the generation of fibrous stringlike structures in polyethylene solution upon stirring. In the same year, Vanderheijde176 observed a similar crystal morphology in polyoxymethylene crystallized from stirred dilute solution. After observing the stringlike structure (see Figure 18), Pennings and Kiel177 demonstrated that it may consist of extended-chain crystals in 1965. Moreover, similar stringlike structure was also reported for several other polymers.178−180 In these cases, a fibrillar core with diameter of about 10 nm was always found, which acts as a nucleus for epitaxial growth of folded-chain crystals. Such morphology was named shish-kebab. For shish-kebab structure, Pennings and Kiel177 investigated the melting behavior with polarized optical microscopy (POM). It was found that the shish backbone shows strong birefringence and can bear an unexpectedly high temperature up to 151 °C, much larger than the melting point of common lamellar crystals. They conjectured that the shish might be extended-chain crystals. Later, in 1970, Pennings et al.181 studied extensionalflow-induced crystallization in PE solutions with a Couette-type apparatus. They found that shish-kebab could be observed only with Taylor vortices, and they speculated that the extensional flow component of Taylor vortices is responsible for shish-kebab formation. Those essential experimental phenomena lead to the P


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cally showed the difference between macro- and micro-shishkebabs. Moreover, Pennings et al.180 gave the details of microshish-kebab in Figure 19b. In the macro-shish-kebab structure, the macro-kebab can be removed to reveal the central microshish-kebab, while the micro-kebab is intrinsically attached to the central micro-shish core. Figure 19c shows the structure of the central core of a micro-shish-kebab. The core was considered as continuous extended-chain crystals at first, but later shrinkage measurements and dark-field electron microscopic results suggested that the core may be elongated bundlelike crystals connected by fringelike amorphous regions.190 The chains originating from these regions may crystallize later to form the platelets. The ends of the crystalline region are tapered in order to satisfy the lower density of amorphous regions.189 Such a hierarchical structure of shish-kebab has been confirmed by monitoring the thermal and soluble behavior with different techniques like scanning or transmission electron microscopy (SEM or TEM), providing real-space information, and X-ray or neutron scattering, providing details in reciprocal space.71,72,95,117,122,147,190−203 Keller and co-workers190,200 used TEM to study shish-kebab structure before, during, and after the melting process in PE. They observed smooth fibers with diameters around 10−100 nm and small closely packed plateletsthat is, micro-shish-kebabsand fibers with large platelets with spacing distance about 0.4 μmthat is, macroshish-kebabs. The partial melting experiments in iPS of Petermann and co-workers201 suggested that the entire shishkebab structure is composed of the following parts: extendedchain micro-shish crystals, overgrown micro-kebabs that nucleate and connect with micro-shish intrinsically, and macro-kebabs generated by secondary crystallization with micro-kebabs as nuclei. Different parts of shish-kebab structure show different responses to external attack. It was found that macro-kebab can be washed away by fuming nitric acid from micro-shish-kebab.204 Moreover, micro-kebabs can be overheated and are more thermally stable than macro-kebabs, as micro-kebabs are firmly attached to the micro-shish backbone. Recently, Kanaya et al.205 investigated blends of low molecular weight deuterated PE and high molecular weight hydrogenated

Figure 18. Electron micrograph of shish-kebab in stirred PE solution. Reprinted with permission from ref 177. Copyright 1965 Dr. Dietrich Steinkopff Verlag.

genius idea of Frank182 about chain structure and end-use properties of polymer products. Frank realized that the unit cell of PE crystallites is similar to diamond in certain directions and predicted that the Young’s modulus could be on the order of 285 GPa for the crystal consisting of fully extended chains. However, in that era, the Young’s modulus was only on the order of 10 GPa, even for oriented PE. The potential of high-modulus PE, as Frank conjectured, stimulated the polymer community greatly and research on shish-kebab flourished, as shish have been considered as extended-chain crystals.183−186 5.2. Hierarchical Structure of Shish-Kebab

Initially, it was thought that shish-kebab consists of parallel extended long chains as shish or row nuclei, which nucleate the epitaxial growth of folded-chain crystals as kebab.187,188 The observations of shish-kebab at variant scales revealed that the shish-kebab entity consists of two structural levels: micro- and macro-shish-kebab. The macro-shish is constructed by microshish-kebab, and the macro-kebab grows on the surface of macroshish. As shown in Figure 19a, Barham and Keller189 schemati-

Figure 19. Schematic of (a) difference between macro- and micro-shish-kebabs, (b) micro-shish-kebab, and (c) central core of micro-shish-kebab. Adapted with permission from ref 189. Copyright 1985 Chapman and Hall Ltd. Q


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Figure 20. (a) Schematic of flow device consisting of two opposed jets. (b) Birefringent bright line under elongational flow in a PE dilute solution above crystallization temperature. Adapted with permission from ref 207. Copyright 1993 Dr. Dietrich Steinkopff Verlag.

Their results gave the transient rather than the final steady-state chain conformations, which indeed showed fully extended chain conformations and are in line with the predictions of CST. The simulation work conducted by Dukovski and Muthukumar212 also demonstrated the discontinuous CST of isolated chains under extensional flow. Their calculated free-energy landscape showed that chains may be in stretched or coil state depending on the initial conformation under a specified flow field, even for a monodisperse polymer. The stretched chains aggregate into shish, while the coiled chains crystallize as kebabs subsequently.

PE under shear flow by combining small-angle neutron scattering (SANS), SAXS, and depolarized light scattering (DPLS). They elucidated that a large oriented structure, on the micrometer scale, contains some extended-chain crystals with a diameter of approximately 10 nm, which seems in accordance with the picture of macro-shish-kebab. Their work also gave some structural details on both nanometer and micrometer scales. 5.3. Coil−Stretch Transition in Polymer Solution

To generate extended-chain crystals, polymer chains have to be stretched. Coil−stretch transition (CST) was used to account for the formation of shish nuclei under flow. Historically, the CST theory was first developed by De Gennes206 to study single-chain dynamics in polymer dilute solution under external flow. According to the CST theory, only outer segments are exposed to the flow field when polymer is in random-coil conformation, while all segments are subjected to flow when polymer is in extended-chain conformation. Hence the hydrodynamic interactions are decreased by chain stretching and a critical strain rate exists, above which a solute polymer random coil will unwind abruptly. That is to say, the steady flow generates dual populations of chain conformations, random coil and fully extended chains, where no stable intermediate chain conformation exists. The elegant studies of Keller and Kolnaar207 and Mackley208 provided direct evidence of CST in polymer dilute solution under extensional flow. They designed a flow cell that consists of two opposed jets to create an elongational flow field, as depicted in Figure 20a, and used birefringence to characterize chain orientation. In a dilute solution of monodisperse PE, they found that a sharp bright line appeared along the central line of the two jet orifices, corresponding to full chain extension when the imposed flow rate exceeded a critical value (Figure 20b). Mackley and Keller209 later carried out experiments at lower temperatures, where crystallization could happen, and found that shish-kebab morphology was generated within the localized regions only where birefringence appeared. On the basis of these results, they constructed a nice correlation between initial chain conformation and final morphology, that is, the CST model, where extended chain is assigned to form shish and random coil is assigned to form kebab. Experimentally, the direct visualization of CST in individual polymers was reported by Smith et al.,210,211 who observed molecular extension as a function of strain rate through use of fluorescently labeled DNA molecules in an extensional flow.

5.4. Shish-Kebab Formation in Polymer Melt

In concentrated solutions and melts of polymer, chain overlap and entanglements exist. The physical entanglements between different chains can act as network junctions. With an opposedjets flow device and birefringence, Keller and Kolnaar207 demonstrated that, for concentrated solution under elongational flow, there are two critical strain rates ε̇c and ε̇n, corresponding to CST (Figure 21a) and network deformation of stretched polymer chains (Figure 21b). For an entangled polymer solution, it was demonstrated that the chains become disentangled and stretched out individually when the strain rate reaches ε̇c. As the strain rate further increases

Figure 21. Schematic of the response to an elongational flow field for entangled polymer solution. (a) Chain stretch at strain rate window ε̇c−ε̇n and (b) deformation of network of stretched polymer chains for strain rate larger than ε̇n. Reprinted with permission from ref 207. Copyright 1993 Dr. Dietrich Steinkopff Verlag. R


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Figure 22. Strain rate for CST and stretched network rate versus concentration plot in elongational flow. Two cases are shown: (a) CST exists up to pure melt (C = 1); (b) no CST at high concentrations or pure melt. Adapted with permission from ref 207. Copyright 1993 Dr. Dietrich Steinkopff Verlag.

to ε̇n, the chains deform like a mechanically cross-linked network and the viscosity of the polymer solution increases drastically. That means, for entangled polymer solution, there is a strain rate window between ε̇c and ε̇n where stretch of individual chain occurs. Both ε̇c and ε̇n decrease with increasing polymer concentration, while ε̇n decreases much more steeply with concentration than ε̇c. The window ε̇c−ε̇n narrows with increasing concentration, but it is not clear whether there really exists a crossover at high concentrations, due to the lack of welldefined materials. If there is no crossover, as shown in Figure 22a, the CST holds true even in polymer melt (C = 1); but if a crossover exists, as shown in Figure 22b, chains cannot be extended individually but deform as a network in melt. Keller and Kolnaar207 found that the oriented crystal morphology observed in melt under flow displays the same fiber-platelet duality as that in solution. Similar experimental results have been widely obtained in polymer melt under extensional flow.213−215 For example, Schultz and co-workers213 studied the structure development of PET during melt spinning in the early stage of crystallization. They observed the diameter of shish directly by TEM, which is about 5 nm, in accordance with the result of 3−4 nm obtained from X-ray radial distribution function.214 Then the shish would be axially punctuated with kebabs upon modest heat treatment. As mentioned above, the correlation between CST in chain conformation and the resulting crystal morphology of shish-kebab has been firmly established for solution, while no conclusive study on melt was conducted. On the basis of the fact that fiber-platelet duality has been also widely observed in melt, Keller et al.1,216 argued that the final morphology of shish-kebab structure was a pointer to the preexistence of CST, and thus they extended the application of CST model to polymer melt, although there is no direct evidence for CST occurrence in melt. Afterward, the CST model was widely accepted by the community and recognized as a standard to explain shish-kebab formation in both solution and melt. However, it should be emphasized that the CST theory proposed by De Gennes was originally deduced from polymer dilute solution where hydrodynamic effect is an essential ingredient. For polymer melt, this essential ingredient does not exist. Thus, in polymer melt the argument for CST actually lacks the strict physical fundamentals. Therefore, the above experiments conducted by Keller and Kolnaar207 can provide convincing evidence of CST only for dilute and semidilute solutions. Polymer melt is a transient network constructed by a

large amount of entanglements, and the chains seem unlikely to be extended individually. Experimental evidence on shish composed of both short and long chains147 and the critical strain for shish formation217 clearly revealed that CST is not a necessary condition to induce shish in polymer melt. Those works will be discussed in detail later. 5.5. Other Mechanisms for Shish-Kebab Formation

In addition to the dominant role of CST in explaining shishkebab formation, some other models and mechanisms were also developed. In 1979, Hoffman218 proposed that the formation of shish was a multiple nucleation event. In this model, long molecules are more evident to be elongated by flow, which provides a set of sites for the formation of bundlelike or fringedmicellar nuclei. The nuclei are interlinked by short amorphous ciliary bridges, and the interior of nuclei are partly of extendedchain type crystals but with some chain-folding defects and chain ends. Nucleation on the same aligned long chain leads to a set of nuclei, which subsequently crystallize and transform into a very long core fibril, shish. Then Hoffman219 combined continuum mechanics and nucleation theory to describe this model theoretically. The theory predicts several parameters, such as shish diameter and mean characteristic length, that agree well with experimental results. In 1984, Smook and Pennings220 emphasized that elastic flow instabilities play a key role in shish-kebab formation during gel spinning of ultrahigh molecular weight PE. In the model proposed by Smook and Pennings,220 the solution of ultrahigh molecular weight PE can be considered as a highly entangled network constructed by entanglements with different lifetimes. The lifetime of entanglements is mainly dependent on the strand length protruding from an entanglement. During extrusion flow, the entangled network deforms inhomogeneously, since the entanglements of short lifetime can be easily migrated and the entanglements of long lifetime are more resistant to deformation. In this process, parts of chains are stretched out from the cluster of unoriented molecules. The stretched chains are more likely to crystallize even at higher temperature, due to the decrease in conformational entropy and the squeezing effect on solvent. Further increasing flow strength, the large clusters break into oriented chain bundles and small clusters. Finally, the oriented chain bundles evolve into shish and the unoriented cluster crystallize as kebab. This model was further supported by SEM results, which provide a possible mechanism for shish-kebab formation in gel spinning. S


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Figure 23. Engineering stress−strain curves of high-density polyethylene (HDPE) melt with (a) different strains at the same strain rate of 6.3 s−1 and (b) different strain rates. Numbers at the largest stress indicate yield strain. (c) Extensional yield strain evolves with strain rate. Red dashed line indicates the critical strain for shish formation. Reprinted with permission from ref 217. Copyright 2010 American Chemical Society.

Janeschitz-Kriegl and co-workers130−132 proposed an explanation for the nonlinear relationship between densities of nuclei and mechanical loading times in flow-induced nucleation (FIN). As mentioned in section 3, dormant nuclei exist even in quiescent polymer melt at temperatures below the equilibrium melting point. Those nuclei are local alignments or organized aggregates with a shape of fringed micelle, and they can become effective to induce crystal growth at low temperature or by the action of flow. When the strength of flow field (called stress in their work) is larger than a critical level, the dormant nuclei become active as point nuclei and are aligned along the flow direction. With increasing stress, both the number and longitudinal dimension of those nuclei are significantly enlarged. At this stage, those nuclei have the ability to induce the growth of lamellae and can be considered as precursors for shish. With further increase in the intensity of flow field, the adjacent nuclei merge into shish nuclei.

should be responsible for shish formation. Recent rheo-optical experiments conducted by Zhang et al.116 showed that shish can be generated at a very low shear rate, which cannot be explained by CST. A report on shish composed of both short and long chains in iPP melt by Kimata et al.147 is not reconciled with the CST model either. Hsiao et al.59 found multiple shish with SEM from a solvent-extracted sheared PE blend, where adjacent kebabs are interconnected by several short shish instead of single shish. They argued that CST occurs in the chain sections between kebabs or probably in adjacent entanglement points, leading to extended chain sections. Furthermore, the rheooptical experiments on iPP melt conducted by Seki et al.95 showed that the effect of long chain on shish formation becomes remarkable after exceeding a critical concentration, which is about half the overlap concentration of long chain. Ogino et al.225 reported that, in PE melt, shish was generated when the long chain is above a certain concentration, about 2.5−3 times larger than the overlap concentration. Later, they further pointed out that the critical concentration of long chain is independent of temperature below 125 °C, while it increases with temperature above 125 °C.197 One may argue that the materials used in the above studies were broadly dispersed in matrix or long chain or both. However, the blends of well-defined monodisperse samples of h-PBD in the work of Heeley et al.226 also gave the same conclusion, that is, the formation of shish at a concentration of long chain around the overlap concentration. These results imply that long chains should be deformed as an entangled network rather than individual chain behavior. On the basis of results measured by in situ synchrotron radiation X-ray scattering and homemade extensional rheometer, Yan et al.217 argued that the occurrence of CST does not need chains to undergo a disentanglement process in PE melt. This argument can be justified by a combination of rheological and structural information (Figure 23). On one hand, the disentanglement can be judged by yielding strain. On the other

5.6. Advances in Understanding of Shish-Kebab

In the past 20 years, researchers have made great efforts with time-resolved technologies including synchrotron radiation SAXS and WAXS, AFM, and birefringence to unveil the features of shish-kebab.11,93,95−97,131,150,156,205 New observations have been obtained and are challenging the conventional models or explanations for shish-kebab. In this section, we intend to outline the current understanding of this subject. 5.6.1. Coil−Stretch Transition or Stretched Network Model? Keller and Kolnaar207 reasoned the CST for shish-kebab formation in polymer melt because similar morphologies were observed in polymer solution and melt. Actually, no direct evidence is available hitherto. Recent experiments on entangled polymer melt and cross-linked network suggested that it is unlikely for a long chain to disentangle and undergo CST at typical flow conditions.59,116,217,221−223 On the other hand, more and more researchers tend to accept that the primary nucleus of shish comes from deformed network. Actually, early in 1984, Smook and Pennings224 suggested that a stretched network T


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hand, the appearance of shish structure can be detected by streak scatting in SAXS. As exhibited in Figure 23c, the yield strain increases with increasing strain rate. However, the critical strain for shish formation is constant when the strain rate is sufficiently large to overcome the Rouse relaxation of chains. Meanwhile, the critical strain for shish formation was found to be smaller than the yield strain, which demonstrates that shish have already been generated before CST occurs. These results excluded CST for shish formation, and the stretched network is proved to be the contributor in PE melt. More recently, Cui et al.227 prepared a series of bimodal PE blends with various long-chain concentrations. In all bimodal blends, only the long-chain component meets the requirement of chain stretch to induce shish formation. They utilized the scaling law between entanglement molecular weight and concentration of long-chain component to justify whether CST or stretched network is responsible for shish formation. If the stretched network model holds true, the critical strain to induce shish formation should follow this scaling law. As depicted in Figure 24, the critical extension ratio (strain) for shish formation decrease with increasing long-chain concentration, which is fitted with the stretched network model well.

Figure 25. Correlation between flow-induced nucleation morphologies and strain in polyethylene. Reprinted with permission from ref 144. Copyright 2013 American Chemical Society.

While in iPP, Cui et al.97 revealed that shish is generated after the collapse of entangled network during flow. They studied the rheological and crystallization behaviors in a wide flow parameter space and found that at each strain rate a fracture strain exists. Unexpectedly, a sample can maintain integrity without fracture if a strain larger than the fracture strain is imposed on the sample directly. Before and beyond fracture strain zones were defined, with the fracture strain as boundary. SAXS results indicated that the before and beyond fracture strain zones correspond to weak and strong acceleration in crystallization kinetics, respectively, accompanying the transition from point nuclei to shish nuclei. They proposed a ghost nucleation model, in which whether a sample fractures or not depends on the interplay between the initial entangled chain network and the physical cross-linked network constructed by the ordering structure or point nuclei induced by flow. As exhibited in Figure 27, the formation of point nuclei has two effects. On one hand, the chain segments between point nuclei are more easily oriented or stretched. On the other hand, the movement of initial nuclei provides a dynamic template for surface nucleation. This model explains their experimental results well and provides a new explanation for shish-kebab formation. Wang et al.229 studied the effect of formed ordering structure on nucleation and crystallization in more detail. They utilized a two-step flow protocol and revealed a transition from chain to crystal network in extension-induced crystallization of iPP. During the interval between two extensional operations, the structures induced by the first strain evolve into different stages before application of the second strain. As the interval time increases, large-scale lamellar crystallites are formed, and during the second flow, the resultant concentration of stress on the crystal network increased, leading to an unusual increase of crystallization half-time. However, if the crystal network is continuously perfected, the dynamic symmetry of the system can be rebuilt, and crystallization kinetics is accelerated again. 5.6.2. Is Long Chain the Only Contributor for Shish Formation? As mentioned earlier, whether in the CST model207,209 or from the rheological point of view,155 only chains above a critical molecular weight undergo stretch at a specific flow strength. Thereby, long chains were thought to be mainly responsible for shish formation. Using a crystalline HMW PE in noncrystalline LMW PE copolymer with rheo-SAXS and rheo-WAXS, Yang et al.230 demonstrated that the HMW component dominates the formation of FIP. Balzano et al.120 studied a specially synthesized HDPE bimodal blend at

Figure 24. Critical extension ratio to induce shish formation as a function of chain concentration at 131 °C. The red line presents the fitting with the stretched network model (inset equation). Reprinted with permission from ref 227. Copyright 2015 American Chemical Society.

With a unique PE system consisting of cross-linked network and free chains, Liu et al.144 revealed four types of nucleation morphology in strain space, which coincides nicely with the four regions defined by stress−strain curve. From rheological and structural information, they established a correlation between flow-induced conformations of chains and morphologies of nuclei, as shown in Figure 25. The uncorrelated oriented point nuclei in region I result from the orientation of cross-linked network and free chains, while the formation of scaffold-network nuclei in region II is due to the disentanglement of free chain. Not only orientation but also stretch of chain segments is required to induce the micro-shish in region III, and finally, nearly extended-chain segments give rise to shish nuclei in region IV. As the sample they used is permanently cross-linked, shish formation should be attributed to network stretching instead of CST. Yang et al.228 further detected real chain conformation in a similar lightly cross-linked system, composed of deuterated PE/ hydrogenated PE blend, with real time SANS; see Figure 26. Their results demonstrated an expectedly small chain deformation of about 1.3 for shish formation, which does not support CST. Yang et al.228 pointed out that the coupling between chain conformation and density, rather than intrachain conformation alone, is the key factor for shish formation. U


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Figure 26. Stress−draw ratio curve and in situ 2D SANS patterns of lightly cross-linked PE with different draw ratios (number in the upper left corner of each pattern) of the extension processes at 170 °C. Reprinted with permission from ref 228. Copyright 2016 American Chemical Society.

words, short chains are involved in the formation of shish, consistent with the report of Kimata et al.147 This situation may be the general case in the polymer melt, where highly entangled chains are unlikely to disentangle themselves, while with the appearance of EDT in end-linked network, the long chains are the main contributors for shish formation, in line with the results of Yang et al.,230 Balzano et al.,120 Ogino et al.,225 and Wang et al.157 This situation may be the general case in polymer solution. Actually, the noncrystalline PE in the work of Yang et al.230 and short chains at temperatures above the equilibrium melting point in the work of Balzano et al.120 can be considered as solvent from a general point of view. 5.6.3. How Does Polydispersity Influence the Threshold for Shish Formation? Polydispersity seems to be a prerequisite for shish formation.207 Here we focus on the influence of polydispersity on the threshold for shish formation, in which the effects of concentration and length of long chain are mainly discussed. Mykhaylyk et al.150 reported that the critical specific mechanical work for shish formation is inversely proportional to the long-chain concentration, which stems from the change in Rouse relaxation time of long chain due to polydispersity. With a molecular weight ratio between HMW and LMW components of about 5, Seki et al.95 demonstrated an almost constant critical stress of 0.12 MPa for shish formation, which is independent of HMW concentration. while with use of the same LMW component but an increase of this ratio to 20, the critical stress decreases significantly with HMW concentration.139 Fernandez-Ballester et al.139 ascribed that the differences correlate to the onset of chain stretch during flow. Recently, Cui et al.227 found that the critical strain for shish formation decreases with increasing long-chain concentration, which agrees pretty well with the stretched network model. Their quantitative analysis further demonstrated that the formation of shish is determined by the deformation degree of long-chain entangled network, but not by a sole parameter such as strain or long chain concentration. 5.6.4. How Does Short-Chain Matrix Influence Shish Formation? As discussed above, the role of long chains in shish formation was investigated quite extensively. However, less attention has been paid to the effect of matrix, that is, short chains. The length and concentration of long chain have a strong influence on shish formation. Similarly, the matrix is also expected to have an influence. Using blends of long chains of crystalline PE with two different short chains of noncrystalline

Figure 27. Ghost nucleation model. Path I indicates the chain segments between nuclei are easily deformed to induce new nuclei, and path II indicates that the initial nuclei N0 move to Nt during flow, which induces daughter nuclei along their trails. Reprinted with permission from ref 97. Copyright 2012 American Chemical Society.

temperatures slightly above the equilibrium melting point and concluded that long chains construct the backbone of shish. In addition, Ogino et al.225 combined SAXS and SANS as well as DPLS to investigate the blends of LMW deuterated PE and HMW hydrogenated PE under shear flow. Their results implied that shish were mainly generated from the HMW component. Moreover, the simulation results of Wang et al.157 from a melt of short- and long-chain blend concluded that the crystallization of oriented long chains forms shish, which induces the subsequent crystallization. However, a contrary conclusion was drawn by Kimata et al.147 with deuterium labeling to distinguish different chain lengths in iPP. Their results highlighted the presence of LMW component in shish; that is, shish consist of both short and long chains. They suggested that the long chain may play a catalytic role, recruiting short chains into the formation of shish. Those contradictory viewpoints about shish were recently unified by Zhao et al.231 Two simplified mixtures of free and end-linked PEO were designed to mimic the blends of short and long chains. Their results indicated that, without the entanglement−disentanglement transition (EDT) in end-linked network, the formation of shish is a synergetic effect between the stretch of network and the fast diffusion of free chains. In other V


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Figure 28. AFM amplitude images of the growth process of lamellae from the oriented backbone at various temperatures: (a) 132.5, (b) 132.3, (c) 132, and (d) 131 °C. Scale bars represent 300 nm. Reprinted with permission from ref 136. Copyright 2001 American Chemical Society.

PE copolymer, Yang et al.230 studied shear-induced shish formation by in situ rheo-SAXS and rheo-WAXS. Their results suggested that the matrix viscosity influences the formation of shish in a cooperative manner. When matrix viscosity is low, the long chains have low orientation under flow but a fast diffusion rate. On the contrary, when matrix viscosity is high, the long chains have high orientation but slow diffusion rate. The interplay between those two factors influences the arrangement of shish. Recently, Okura et al.232 gave some quantitative results for the effect of matrix on shish formation. By studying bidisperse blends of HMW h-PBD in LMW polymer matrices under shear flow, they found that the critical specific mechanical work for shish formation (revealed by an oriented morphology) has a power law dependence on the molecular weight of matrix, in which the index is 2.59 ± 0.27. They speculated that the matrix influences the viscosity of blends, which opposes flow and makes the long chain difficult to stretch. Thereby, the critical specific mechanical work increases with increasing molecular weight of matrix. 5.6.5. In Situ Observation of Evolution of Shish-Kebab. With the help of in situ characterization techniques, in both real space (i.e., POM, AFM) and reciprocal space (i.e., SAXS and WAXS), the detailed evolution process of shish-kebab can be traced. Here we take AFM and X-ray scattering as examples to illustrate in situ studies of shish-kebab. AFM is now becoming a standard method to provide realspace information on the nanometer scale. Hobbs and coworkers96,233,234 developed a novel rapid AFM technique (videoAFM) with the capability to detect crystal growth on the

millisecond time scale and applied this technique to study FIC for the first time. Their AFM works on shish-kebab formation are especially interesting, as structure evolution on the lamellar scale was revealed in real time and in real space.96,135,136,235 Oriented PE melt was obtained by dragging a razor blade across the melt on glass coverslip. It should be noted that the direct observation of shish growth was not realized. However, the subsequent overgrowth of kebab could be monitored, which exhibits a number of interesting features. As shown in Figure 28a, when the melt was cooled from 133 to 132.5 °C, a new nucleation event of one lamella occurs on the shish (marked A). When the neighboring shish-kebabs meet each other, interdigitations may happen (marked B in Figure 28b). The kebabs change their directions to avoid joining, implying that the advancing lamella has a strong influence on the melt. In some case, lamellae can even join together to form a single long crystal (marked C in Figure 28d). Hobbs and Miles136 further measured the growth rate of lamella and found different lamellar growth rates. Even for individual lamellae, the growth rate was not constant with time, different from the constant growth rate of spherulites observed by POM. In this AFM study, flow field is difficult to define and only qualitative results were obtained. Quantitative information can be obtained through X-ray scattering techniques. Keum et al.153 investigated the formation and stability of shish-kebab with in situ rheo-SAXS and rheo-WAXS. In their experiment, PE blends with long-chain concentrations of 2 and 5 wt % were used, which were named 2/98 and 5/95 blends, respectively. They chose a high shear temperature (142 °C), to allow the sole formation of W


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Figure 29. Critical strain for nucleation from (a) SAXS and (b) WAXD as a function of temperature. Reprinted with permission from ref 123. Copyright 2014 American Chemical Society.

Figure 30. Schematic of morphologies and structures of four regions in the strain−temperature space, deduced from both WAXD and SAXS. Reprinted with permission from ref 123. Copyright 2014 American Chemical Society.

the driving force of nucleation in classical nucleation theory, which lowers nucleation barrier and enhances nucleation rate. The ERM predicts a strain−temperature equivalence; that is, lowering temperature and increasing strain have the same effect for nucleation. However, it should be noted that in ERM the external work is treated as a perturbation, restricting itself to an equilibrium thermodynamic framework, which may be not applicable to far-from-equilibrium conditions. Recently, Liu et al.123 and Cui et al.30 designed two model experiments to study nucleation under near-equilibrium and far-from-equilibrium conditions. In the near-equilibrium experiment, Liu et al.123 verified the validity of ERM and found that free energy determines the transition from point nucleus to shish, while in the far-from-equilibrium experiment, Cui et al.30 invalidated the prediction of strain−temperature equivalence in classical ERM but demonstrated a constant critical strain for nucleation in a wide temperature range, which reveals the nonequilibrium nature of nucleation under strong flow. 5.6.6.1. Near-Equilibrium Experiments. With a series of lightly cross-linked HDPE, step extension with a strain rate of 0.02 s−1 and a total strain of 2.8 were imposed to induce nucleation. A slow strain rate was selected in order to approach a near-equilibrium experimental condition. By a combination of SAXS, wide-angle X-ray diffraction (WAXD), and stress−strain results, the incipient strain (εi) for nucleation can be obtained by the first appearance of shish scattering in SAXS or crystalline scattering in WAXD. As shown in Figure 29, for each sample εi increases with temperature, while at the same temperature εi decreases with increasing irradiation dose or cross-link density. S15, S30, and S50 represent the absorbed doses of 15, 30, and 50

shish without kebab, and performed isothermal measurements at this temperature. In both blends, shish scattering intensity decreases within the initial 400 s and afterward increases with time. They reasoned the initial intensity decrease was due to the decrease in volume fraction of shish due to internal stress and relaxation of stretched chains, in line with the viewpoint of Gutierrez et al.117 and Balzano et al.120 that defective or small-size shish are unstable and may relax into melt. Interestingly, in 2/98 blend, the length of shish was found to increase after 400 s, which can be explained by the autocatalytic growth mechanism proposed by Petermann et al.236 For 5/95 blend, the length of shish decreased monotonously during isothermal process, consistent with the recent report of Cui et al.,227 who argued that if only defective and short shish melted during isothermal process, the average length of shish should increase rather than decrease. Cui et al.227 pointed out a new relaxation process by which some defective sections in a long shish may relax and give rise to several short shish, hence decreasing the average length of shish. Note that Ma et al.237 recently found that, during relaxation, the disappearance of SAXS signal does not mean the complete relaxation of shish into ideal random coil, since the partially ordered intermediate structures that are below SAXS detection limit may be formed, which can crystallize into shish again upon further cooling. 5.6.6. Shish Formation under Near-Equilibrium and Far-from-Equilibrium Conditions. From the thermodynamic point of view, entropy-reduction model (ERM) is the most recognized mechanism for FIN, which is based on the idea of flow-induced reduction of conformational entropy.238−240 In ERM, the entropic reduction or external work is directly added to X


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kGy, respectively. Meanwhile, four regions can be defined in strain−temperature space according to the formed crystal morphology and structure (Figure 30): orthorhombic lamellar crystal (OLC), orthorhombic shish crystal (OSC), hexagonal shish crystal (HSC), and oriented shish precursor (OSP). This work indicates that flow not only reduces the entropy of initial melt but also modifies the free energies of final states, which were often overlooked in classical ERM in FIN. They incorporated the free energies of various final states in ERM, which agrees with their results pretty well. With this modified ERM, the estimated critical thicknesses for OLC, OSC, and HSC nuclei are on the order of 10, 100, and 500 nm, respectively, implying that the critical thickness of nuclei determines the transition from point nuclei to shish nuclei. This work demonstrates the validity of classical nucleation theory for FIC under near-equilibrium conditions, provided that the entropy reduction of initial melt and the free-energy changes of final states induced by flow are taken into consideration. 5.6.6.2. Far-from-Equilibrium Experiments. Nucleation under strong flow is a typical kinetics-controlled process, where the equilibrium ERM may not be applicable. Validation of the equilibrium ERM theory under strong flow condition requires simultaneous acquisition of nucleation and stress−strain information during flow, which is rather challenging. As FIN is extremely fast (on the order of tens of milliseconds) under strong flow, a structural detection technique with high time resolution is a precondition, which restricts most studies on FIC that can only detect crystallization after the cessation of flow rather than during flow.98,124 To construct a strain−temperature diagram for nucleation, the capability to collect stress−strain during flow is another precondition. Cui et al.30 combined extensional rheological and ultrafast Xray scattering measurements to reveal the nucleation in iPP melt under strong flow, with a strain rate of 12.6 s−1, flow duration less than 400 ms, and time resolution of X-ray scattering up to 30 ms. By combining SAXS/WAXS and rheological information, the critical strain for nucleation can be defined precisely by the appearance of streak scattering in SAXS, crystalline scattering in WAXS, and stress-upturn in the stress−strain curve in Figure 31. Unexpectedly, they discovered that the critical strain for shish formation remains almost constant in the temperature range from 130 to 170 °C (Figure 32), which breaks the strain− temperature equivalence predicted by ERM but unveils the nonequilibrium nature of FIN. To account for this temperature independence of FIN, Cui et al.30 proposed a tentative kinetic pathway of nucleation containing stretch-induced coil−helix and isotropic−nematic transitions, in which flow provides both the concentration and the compatible alignment of helixes for nucleation. These two transitions are dictated by strong flow rather than thermal fluctuation, manifesting that FIC is a strong external-field-driven nonequilibrium phase transition. 5.6.7. Is Shish Formation a Single-Stage or Multistage Process? Early mechanisms for shish-kebab formation, such as CST or SNM, only propose the correspondence between initial chain conformation and final crystal morphology. However, it is unclear how extended chains or stretched networks transform into shish. Massive studies on FIN imply that shish may nucleate via a precursor or metastable stage rather than a direct transformation.72,120,124,241−243 On the basis of X-ray scattering results, Balzano et al.145 and Zhao et al.124 argued that precursors first generated during flow, which may transform to shish crystals or dissolve gradually. Works by Kanaya and co-workers68,70,71,121 provided more details on the nature of shish precursors. Their

Figure 31. (a) Engineering stress (σengr) and corresponding 2D (b) SAXS and (c) WAXS patterns evolve during flow at 140 °C. The flow direction is horizontal. Reprinted with permission from ref 30. Copyright 2015 American Chemical Society.

Figure 32. Critical strain for shish formation at different temperatures. Dashed red line indicates the average critical strain measured from 130 to 170 °C. Reprinted with permission from ref 30. Copyright 2015 American Chemical Society.

results showed that large stringlike precursors, on the micrometer scale, form above the melting point, which are able to induce shish when cooled. Microbeam WAXS measurements indicated that the crystallinity of inner structure of the stringlike precursors is rather low, about 0.15%. By studying the structure evolution in solution of UHMW PE under shear flow and along spinning line, Hashimoto and coworkers194,222,244 proposed a new scenario, in which flowinduced phase separation, mediated by the dynamic asymmetry and the stress−diffusion coupling245−247 preceding nucleation, was taken into account. As shown in Figure 33, the nucleation process can be divided into four regions. In the t1 region, PE entangled network is swollen homogeneously in solvent, as evidenced by no feature in the optical image. In the t2 region, plane-wave-type concentration fluctuations with wave vectors oriented along the flow direction appear. In the t3 region, demixed domains are generated and distributed in space randomly. In the t4 region, the domains are aligned into strings Y


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Figure 33. Schematic illustration of shish-kebab formation during (A) spinning and (B−D) shear flow. B and D are optical and birefringent results, respectively. Reprinted with permission from ref 222. Copyright 2011 American Chemical Society.

Figure 34. Schematic illustration of kinetic process for shish formation. (A) Stretched network, (B) type I shish without lamellar structure, (C) type II shish with sporadic lamellae, and (D) type III shish containing periodic lamellae. The flow direction is horizontal. Reprinted with permission from ref 227. Copyright 2015 American Chemical Society.

by flow to create bundles of stretched chains. The stretchedchain bundles and the nearly isotropic demixed domains transform into shish and kebab, respectively. This model is further supported by the transient structures revealed by TEM along spinning line with a special fixation method, which is rational and may be general for dynamically asymmetric polymer systems. Very recently, Cui et al.227 revealed a kinetic process for shish formation from initial chain conformation to final stable nuclei. They first demonstrated that the stretched entangled chain network is responsible for shish formation. Then, with a delicately designed thermal history and real-time SAXS method, they further observed three types of shish with different stabilities

by increasing strain, which can be considered as three stages in the formation of stable shish nuclei; see Figure 34. When the deformation of entangled network reaches a critical degree, the stretched chains couple with each other to transform into fibrillar type I shish, which is similar to nematic phase. Type I shish has density contrast to surrounding matrix but no embedded lamellar structure. Type I shish further transforms into type II shish, containing sporadic lamellar structure, and type III shish, containing lamellar stacks with well-defined periodicity. The barriers for those transformations can be overcome by flow. It should be noted that the lamellar structure mentioned here is within shish, which is different from the kebab that grows on the surface of shish. Z


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Figure 35. (a) True stress−time curve during extension of cross-linked PE with strain rate of 3 s−1 at 172 °C, and corresponding SAXS and WAXD images. (b) Nonequilibrium phase diagram of cross-linked PE in stress−temperature space. L, δ, H and O are melt, noncrystalline shish, H-crystal and O-crystal, respectively. Reprinted with permission from ref 248. Copyright 2016 Springer Nature.

Figure 36. (a) Nonequilibrium phase diagram of cross-linked iPP in strain rate−temperature space. M, S, α, and β are melt, noncrystalline shish, α crystals, and β crystals, respectively. (b) Relative content of β crystals in strain rate−temperature space. Reprinted with permission from ref 249. Copyright 2016 Wiley−VCH.

Figure 37. Strain rate−temperature flow structural (a) and morphological (b) diagrams of poly(1-butene). Reprinted with permission from ref 250. Copyright 2017 Royal Society of Chemistry.

5.6.8. Is Shish a Thermodynamic Phase or a Kinetic State? Noncrystalline shish has been observed at temperatures near or above the melting temperature of lamellar crystals. However, whether the noncrystalline shish is a thermodynamic phase or a kinetic state remains unclear. Wang et al.248 studied flow-induced phase behaviors of a cross-linked PE (with gel fraction 43.5%) in a wide temperature range up to 240 °C with ultrafast X-ray scattering. By combining SAXS, WAXD, and extensional rheology, they could determine the onset or critical stress for various structure formations, such as shish structure (named δ-phase in their work), hexagonal crystal (H-crystal), and orthorhombic crystal (O-crystal). Figure 35a is an example to show structural evolution during extension at 172 °C, where melt, noncrystalline shish, and H-crystal appear sequentially. On the basis of critical stress for the structures formed at various temperatures, they constructed a nonequilibrium thermodynamic phase diagram for FIC of PE in stress−temperature space.

This phase diagram has four regions: melt (L), noncrystalline shish (δ), H-crystal (H), and O-crystal (O) (Figure 35b). Increasing stress (σ) leads to a sharp increase of L → δ transition temperature, a moderate increase of δ → H transition temperature, and a decrease of O → H transition temperature. Wang et al.248 verified the reversibility of flow-induced phase transitions by conducting a stress reduction experiment. The structure evolution follows a pathway L → δ → H with increasing stress, while a reversed transition H → δ→ L occurs with decreasing stress. Interestingly, the critical stresses for H → δ and δ → L transitions during stress reduction are smaller than their reversed δ → H and L → δ transitions during stress increase, indicating that δ ↔ H and L ↔ δ are two pairs of nonequilibrium phase transitions with stress hysteresis. Considering the facts that shish (δ) can be observed solely without crystalline diffraction even at temperatures above 200 °C and that Figure 35b shows a clear direction and pathway for shish (δ) structure transition in AA


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stress−temperature spaces, Wang et al.248 claimed that shish is a thermodynamic phase and can be stable or metastable depending on the stress and temperature. Ju et al.249 constructed a similar flow diagram of iPP in strain rate−temperature space, which is composed of melt (M), noncrystalline shish (S in their work), α crystals, and an α/β crystal coexistence regions (Figure 36). What needs to be emphasized here is that the noncrystalline shish presents alone in a small region at temperatures above the melting point of α crystals. This region is located at the most violent competition zone in the strain rate−temperature phase diagram, where dynamic competitions happen among four involved phases. Ju et al.249 attributed the formation of noncrystalline shish to the kinetic competitiveness of shish over α and β crystals but not to thermodynamic stability. The frustration effect due to the violent competitions among four phases leaves the noncrystalline shish winning out. For poly(1-butene),250 the constructed structural and morphological diagram (Figure 37), the same in strain rate− temperature space, revealed that metastable form III can be crystallized from the melt, which may further transform into form II during flow. Concerning the crystallite morphology, a transition from flow-induced network to the shish structure was also observed upon elevating flow temperature from below to above the melting temperature for form II. A recent work of Liu et al.251 even gave a quantitative estimation of the thermodynamic parameter of noncrystalline shish in cross-linked PE. They calculated the critical external works for melt−noncrystalline shish and noncrystalline shish− crystal transitions based on rheology and X-ray scattering methods. The critical external work of melt−noncrystalline shish transition is larger than that of noncrystalline shish−crystal transition at low temperature, but the situation is reversed at high temperature. Thermodynamic parameters such as the enthalpy and surface energy of noncrystalline shish were analyzed by incorporating the critical external work into a modified stretch network model.123 Their results help to illustrate the following two issues: (1) the energy barrier of noncrystalline shish formation increases with increasing temperature, and (2) the surface free energy and bulk free energy of noncrystalline shish are much smaller than those of corresponding crystals.

cooling becomes larger, and thus the crystallization is facilitated. This is the widely accepted molecular mechanism for flowinduced polymer nucleation. The quantitative description of FIC needs a specified chain model to calculate the conformational entropy. At the very beginning, it is worth pointing out that crystallization of polymer mostly happens under a large undercooling, while for the sake of simplification, the equilibrium thermodynamics of crystallization is used to describe the phase transition. Furthermore, the enthalpy of crystallization is considered as a constant at different crystallization temperatures, and the entropy of undercooled melt is considered the same as that at equilibrium temperature. With these assumptions, the conformational entropy change is the only parameter that needs to be calculated. Various models will give different expressions of this entropy change. With the quantified entropy change, a predictable model for crystallization can be obtained. In the following subsections, we will discuss some molecular theories to describe the crystallization of polymer under either strain or flow. This section dates back to the independent works focusing on cross-linked network and melt. Although the external field is macroscopically imposed by extensional or/and shear flow, it is believed that molecular deformation, rather than macroscopic flow, is the substantial reason for changes in crystallization behavior, so strain-induced crystallization in crosslinked network and FIC in melt will not be distinguished. However, crystal morphology and chain relaxation behavior differ in the two conditions, which make these models slightly different. 6.1.1. Crystallization Induced by Stretching of CrossLinked Network. A cross-linked network like vulcanized natural rubber can sustain strain without significant relaxation, which provides a model system to link chain deformation with the resulting crystallization. Flory developed a thermodynamic theory to describe the strain-induced crystallization in crosslinked natural rubber, which hardly crystallizes at ordinary temperatures. The segments between cross-link points are defined as an individual chain, of which the end-to-end distance increases with strain. During stretch, chains are elongated and the number of possible conformations gradually decreases, which reduces the entropy. Gaussian distribution is still used to describe the conformation distribution. It is assumed that crystallization does not happen before chains are stretched to the final length, so the entropy change coming from deformation can be calculated from the strain. When crystallization begins, the conformational entropy change is further divided into two parts. The first part comes from the transition from oriented amorphous segments to crystals, where the involved segments are completely frozen by crystallization. This reduction in entropy is monotonic. The second part originates in the (partial) release of chain stretching of the residual amorphous segments. Since crystals in natural rubber are found to orient well along the stretch direction, the crystals in this theory are assumed to align along the stretch direction. Segments in the crystals have a more extended conformation than that in the amorphous phase; thus, for the same end-to-end distance, the stretching of amorphous segments will release partially. When crystallinity is low, the second part of entropy change is positive. With increasing crystallinity, the segment number may become so small that the entropy decreases again. This decrease in entropy will prevent full crystallization of the segments between cross-link points. Obviously, calculation of the entropy change of the amorphous part under stretch is a major problem. Fully

6. THEORIES AND MODELS OF FLOW-INDUCED NUCLEATION 6.1. Molecular Theory of Flow-Induced Nucleation

Nucleation of polymer can be greatly influenced by flow, from kinetics to crystal morphology. From the prediction point of view, it is necessary to understand experimental phenomena on a molecular level. Conformational entropy reduction is commonly considered as the origin of FIC. Polymer crystallization is different from the crystallization of small molecules because of the long-chain feature. The covalent connection of polymer not only restricts the diffusion of chain segments but also leads to a huge amount of conformational entropy. For a single chain with a fixed end-toend distance, the position of segments varies with time and a great number of conformations can be obtained. The freedom to form a large number of possible conformations corresponds to large entropy. Evidently, when a coiled polymer chain is deformed, the number of possible conformations is reduced. If equilibrium phase transition is still assumed with no change of free energy, the reduction of entropy directly leads to the increase of equilibrium melting temperature. Equivalently, the underAB


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Figure 38. Schematic illustration of the free energies of different morphologies and structures: (a) under quiescent conditions, (b) classical stretched network only involves the effect of flow on the entropic reduction of melt, and (c) modified stretched network considers different crystal morphologies and structures in the final stage of nucleation as well. G is free energy, where subscripts L and N represent melt and nuclei, respectively; ΔG* is the nucleation barrier of critical nucleus; ΔGfN is the free-energy change of nuclei induced by flow. Reprinted with permission from ref 19. Copyright 2016 American Chemical Society.

where sf is the entropy of fusion per segment and is obtained by the lattice model. Sb is calculated by employing the Boltzmann relationship:

crystallized state is chosen as the reference state, and partial melting of crystals is considered to give the equilibrium crystallinity. The detailed theory is briefly described as follows. The number of probable conformations of an amorphous chain is assumed to be dependent on their end-to-end distance r by Gaussian function: r = (x 2 + y 2 + z 2)1/2

(1)

W (x , y , z) = (β /π 1/2)3 exp[−β 2(x 2 + y 2 + z 2)]

(2)

S = k ∑ ν ln W

S b = k ∑ ν(x , y , z) ln W ′(x , y , z′) xyz

− k ∑ ν′(x , y , z′) ln W ′(x , y , z′)

ν(x , y , z) = σ(β /π

2

2

2

2

The obtained entropy change is given in eq 10: S = σk⎡⎣(n − ξ)sf /k − (ξβl)2 n/(n − ξ) + (2αξβl /π 1/2)n /(n − ξ)⎤⎦ − (α 2/2 + 1/α)n/(n − ξ) + 3/2

) exp[−β (αx + αy + z /α )]

The free energy of the system, with perfectly ordered and totally crystalline chains as the standard state, becomes

where σ is the total number of chains under consideration and α is the stretch ratio. The freely jointed chain model with independently oriented rigid segments is used. For such chains, the reciprocal most probable displacement length is given by

β = (3/2n)1/2 /l

F = σ(n − ξ)hf − TS

(11)

If we define λ = (n − ξ)/n and θ = sf/k − hf/kT, the equilibrium state can be obtained by eq 12 and the result is given by eq 13:

(4)

where l is the length of each segment and n is the number of segments per chain. The product nl is taken to equal the maximum extension L of the actual chain. When ξ of the n segments of the chain participate in crystallization, the relative number of configurations available to the remaining n − ξ segments becomes

∂F/∂λ = 0

(12)

1/2 ⎧⎡ ⎤⎫ ⎤ ⎡ λ = ⎨⎢⎣ 3 2 − ϕ(α)⎦⎥ ⎣⎢ 3 2 − θ ⎥⎬ ⎦⎭ ⎩

(13)

where ϕ(α) = (6/π )1/2 α /n1/2 − (α 2/2 + 1/α)/n

(5)

where

1/Tm = 1/Tm 0 − (R /hf )ϕ(α)

β′ = β[n/(n − ξ)]

(14)

The incipient crystallization temperature T m , at which crystallization just happens, can be obtained by assigning λ = 1 in eq 13:

W ′(x , y , z′) = (β′/π 1/2)3 exp[−(β′)2 (x 2 + y 2 + z′2 )]

1/2

(10)

2

(3)

(15)

The force can be obtained by

(6)

and z′ is the algebraic sum of the z displacement lengths of amorphous sections of the chain. To calculate the conformation entropy change with respect to the fully crystallized state, two hypothetical steps are considered by Flory: (a) n − ξ segments per chain are first melted and the chain ends are assumed to be free, and (b) the free chain ends are reassigned to the cross-link points, which leads to a transformation of conformation distribution from ν′(x, y, z′) to ν(x ,y ,z): Sa = σ(n − ξ)sf

(9)

xyz ′

where x, y, and z represent the coordinates of one end of the chain with respect to the other end and 1/β equals the most probable value of chain displacement length, r. After stretching along the z-axis, the distribution of chain coordinates becomes 1/2 3

(8)

f=

⎛ ∂F ⎞ ⎛ ∂F ⎞ ⎜ ⎟ = ⎜ ⎟ ⎝ ∂α ⎠e ⎝ ∂α ⎠ λ

= σRT[(α − 1/α 2) − (2nβl /π 1/2)(1 − λ)]/λ

(16)

When no crystal forms, λ equals 1 and f becomes f = σRT(α − 1/α 2)

(17)

Force is an easily measurable parameter; thus, for an approximation, the integration of force with strain can be used to indicate the entropy change. Particularly, there should be no

(7) AC


Chemical Reviews

Review

⎛ E ⎞ ⎡ Kn ⎤ Ṅ = CkBT ΔG exp⎜ − a ⎟ exp⎢ − ⎥ ⎣ T (ΔG)n ⎦ ⎝ kBT ⎠

crystallization during stretch. Crystallization is the mostencountered reason for deviation from Flory’s theory. Based on this approach, several recent works have been reported.123 In addition to the aforementioned entropic reduction of initial melt, Liu et al.123 also considered the flow-induced free-energy change of the final nuclei, which was quantitatively expressed as

(

2

where C includes energetic and geometrical constants, kB is Boltzmann’s constant, T is crystallization temperature, ΔG is thermodynamic driving force (the volumetric free-energy difference between melt and crystal), and Ea is diffusion activation energy across the liquid−nucleus interface. Kn is a constant containing energetic and geometrical factors of nuclei. For primary nucleation, n equals 2, and for secondary nucleation, n is 1. When flow is imposed, the volumetric free energy of melt is raised and ΔG changes into

)

vk αi2 + α − 3 1 1 i = − 4σ Tc(αi) Tc(1) 2ΔH 1 − ΔHle *

(

(18)

)

where Tc(αi) and Tc(1) are the crystallization temperatures at elongation ratios of αi and 1, respectively, and v is the networkchain density. Concerning the final nuclei, melting entropy ΔH depends on their specific crystal modification formed, while surface free energy σe and critical nucleus thickness l* both are determined by the crystallite morphology. For instance, the surface free energy σe can be varied from folded-chain to fringe micellar structures, due to the morphological transition from folded-chain lamellae to shish. In this way, the flow-induced change of free energy is also considered for the final nuclei, as shown by Figure 38.19 6.1.2. Flow-Induced Nucleation in Free Melt. Different from the permanent constraint on chain mobility in cross-linked networks, the constraint from entanglements is temporary in melt and the chain can relax via chain movement; for instance, the terminal time for a single chain to move out the original tube is on the order of seconds or less. Two effects must be considered due to the occurrence of relaxation in melt: (i) during flow, the deviation between macroscopic strain and molecular deformation is probably significant, which hinders a direct correlation between chain deformation and crystallization; and (ii) after flow cessation, the continuous decay of chain deformation may make crystallization also dependent on time after flow. A more comprehensive model is needed to include strain rate and timedependent chain deformation, in addition to the thermodynamic model of crystallization. Rheological theory of polymer melt is a good candidate to describe chain deformation during and after flow. From the rheological point of view, the stress response due to flow is determined by chain deformation, which is commonly described by the constitutive equation. The correspondence between macroscopic stress and microscopic chain deformation makes the theory verifiable and gives abundant information about the strain rate and time-dependent chain deformation. Two models have been proposed: the microrheological model (section 6.1.2.1) and the dumbbell model (section 6.1.2.2). 6.1.2.1. Microrheological Model. The Doi−Edwards theory, based on the tube model proposed by De Gennes, is widely used as a rheological theory of polymer melt. This theory gives an analytical expression of the constitutive equation in orientation or even strong chain-stretch conditions. With this theory, Coppola et al.252 have calculated chain deformation and the corresponding entropy change during flow. For the sake of simplification of mathematical analysis, the independent alignment approximationthat the segments are still of the same length and number as at equilibrium and that deformation has only changed their orientation in spaceis introduced.253 Note that this approximation excludes chain stretch, which is actually important in crystal morphology change. As described by the Lauritzen and Hoffman theory, nucleation rate can be expressed as

ΔG = ΔGq + ΔGf

(19)

Here ΔGq is the thermodynamic driving force under quiescent conditions and can be written as ⎛ T ⎞ ΔGq = ΔH0⎜1 − 0 ⎟ Tm ⎠ ⎝

(20)

where ΔH0 is the latent heat of fusion and Tm0 is the equilibrium melting point. ΔGf is the driving force contributed by external field, as the step strain in this work. If ΔGf is known, nucleation rate under flow can be predicted. The Doi−Edwards theory with independent alignment approximation (IAA) was proposed to describe the effect of flow in the linear region. The general form given by Marrucci and Grizzuti253 is t

ΔGf = 3ckBT

∫−∞ μ(̇ t , t′)A[E(t , t′)] dt′

(21)

where c is the primitive chain-segment concentration, equivalent to entanglement density. It can be expressed as c=

ρ NA Me

(22)

where ρ is the density of melt, Me is molecule weight between entanglements, and NA is Avogadro’s number. The Doi−Edwards memory function μ(t,t′) gives the memory of flow at time t when flow was imposed at time t′. It can be written as μ(t , t ′) =

8 π2

∑ podd

⎡ (t − t ′)p2 ⎤ 1 ⎥ ⎢− exp τd p2 ⎦ ⎣

(23)

where τd is the terminal relaxation time. For steady-state flow, ΔGf can be rewritten as ΔGf = 3ckBT

∫0

+∞

μ(̇ z)A[Wiz] dz

(24)

Wi is the Weissenberg number (named as Deborah number in the original reference252), that is, deformation rate multiplied by polymer relaxation time. z is a dimensionless value defined as time divided by relaxation time τd. For uniaxial elongation deformation with an elongation ratio λ, we have A(λ) = ln λ +

tan−1(λ 3 − 1)1/2 (λ 3 − 1)1/2

−1 (25)

and for shear deformation with strain γ, we can write AD


Chemical Reviews A(γ ) =

1 2

∫0

1

Review

⎡ 1 + γ 2x 2 + [x 4(γ 4 + 4γ 2) − 2γ 2x 2 + 1]0.5 ⎤ ln ⎢ ⎥ dx 2 ⎣ ⎦

6.1.2.2. Dumbbell Model. The dumbbell model considers the polymer chain as two rigid beads linked by a flexible spring. The vector R, giving the relative position of the two beads, is the only parameter to describe chain deformation. Evidently, this model is simpler than the Doi−Edwards theory. Several works have been reported to describe the crystallization of polymer based on this model. The configurational distribution function of the end-to-end vector R can be written as

(26)

In the small Wi limit, the integration in eq 24 has the form shown in eqs 27 and 28 for shear and extension: ΔGf π4 = Wi 2 3ckBT 600

(27)

ΔGf π4 = Wi 2 3ckBT 200

(28)

⎞ 2kBT ∂ ∂ψ 2 ∂ ⎛ =− ψ − Feψ ⎟ ⎜[κ·R]ψ − ⎠ ∂t ∂R ⎝ ζ ∂R ζ

In the large Wi limit, the form for shear and extension will be expressed as shown in eqs 29 and 30: ΔGf = ln Wi − 2.41 3ckBT

(29)

ΔGf π2 = Wi − 1 3ckBT 12

(30)

where κ is the velocity gradient tensor, kB is Boltzmann’s constant, ζ is bead friction coefficient, and Fe is elastic force of the spring. For a Hookean spring, the force is Fe = K R

Fe =

KR 1 − ⟨(R /R 0)2 ⟩

(35)

where R0 is the maximum length of the dumbbell. The free energy of the system A, for the deformed chain under flow, is A = nkBT ln⟨ψ /ψ0⟩

(36)

where ψ0 is the equilibrium distribution and n is the number density of molecules. In entangled melt, n is equivalent to the entanglement density. With eqs 33−35, when flow field is assigned by the tensor κ, the distribution function ψ can be obtained by eq 33. When ψ is known, the free-energy change after flow can be calculated by eq 36. In the work of Coppola et al.,252 the free-energy change by dumbbell model is also used as a comparison. The free-energy change obtained by eq 36 is assigned directly as ΔGf. The formula describing crystallization kinetics follows the Lauritzen− Hoffman theory. It is found that the simplification of chain conformation gives a larger free-energy change than that in the Doi−Edwards theory. Bushman and McHugh256 further use the Hamiltonian to derive the time evolution of crystallinity. When crystallization is taken into account, the free-energy change of the remaining amorphous part by the dumbbell model becomes

(31)

This deduction assumes a monodisperse sample, while in practice a polydisperse sample is commonly used. To demonstrate the validity of the theory, Acierno et al.254 also use this model to describe a long- and short-chain blend of polybutene. The only change is the form of the memory function, which is modified as μDR (t , t ′, τdH , τdL) = [ϕHμSR (t , t ′, τdH) + ϕLμSR (t , t ′, τdL)]2

(34)

where K is the spring elastic constant. For a finite extendable nonlinear elastic dumbbell, the force will be

Clearly, the microrheological model only describes steady-state flow, which is not valid after crystallization happens. The authors thus compared the predicted induction period with experimental value, where the crystallinity is rather low. Nq̇ Θ= Nḟ ⎡ Kn ⎛ 1 1 ⎜ = exp⎢ n⎜ n 1 + ΔGf /ΔGq ⎣⎢ T (ΔGq ) ⎝ (1 + ΔGf /ΔGq ) ⎞⎤ − 1⎟⎟⎥ ⎠⎦⎥

(33)

(32)

where ϕH and τdH are the volume fraction and relaxation time of long chain and ϕL and τdL are the volume fraction and relaxation time of short chain, respectively. The effects of crystallization temperature were also investigated.255 Qualitatively, as temperature increases, chain relaxation becomes faster. To quantitatively capture this change, the time−temperature equivalence principle was used, which is a standard approach in rheology. The Weissenberg number is modified by a shift factor α, and other parts of the theory remain the same. Good agreement was obtained on the experimental and modeling induction time. In summary, the microrheological model developed by Coppola et al.252 gives the free-energy change induced by flow in steady state and correlates it with the acceleration of crystallization kinetics. The introduction of independent alignment approximation intrinsically neglects chain stretch and only accounts for the effect of orientation. The use of memory function clearly shows the importance of chain relaxation in melt.

A=−

+

⎡ ⎤ nkBT ⎢ ⎛ 3⟨R cR c⟩ ⎞⎥ ⎟ ln det⎜⎜ 2 ⎢⎣ ⎝ ⟨R N ⟩(1 − ϕ ) ⎟⎠⎥⎦ 2 c 0 ⎤ ⟨R c 2⟩ 3nkBT ⎡⎢ ⎥ 1 − ⎥⎦ 2 ⎢⎣ ⟨R N0 2⟩(1 − ϕc)

(37)

Upon conversion of Rc to the end-to-end distance of whole molecules, RN, the free-energy change in extension becomes AE


Chemical Reviews

Review 1/2 ⎤ ⎡ 6Nc11 ̅ c ̅ c 22 c 22 ̅ c33 ̅ − ϕc π ̅ c33 ̅ ⎥ ∂ c11 ̅ = 2ε ̇c + 1 ⎢⎢ 11 ⎥ 11 ̅ 2 ∂t λ ⎢ c11 ⎥ ̅ c 22 ̅ c33 ̅ + 3ϕc Nc 22 ̅ c33 ̅ ⎦ ⎣

3 2 nkBT ⎛ ⟨RN ⟩(1 − ϕc) ⎞ ⎜ ⎟ ln ⎜ A= ⎟ 2 3 ⎝ ⎠ ⎤ nk T ⎡ ⎛ 8c ⎞1/2 − B ln ⎢det c + c 22c33l 2 − ⎜ 11 ⎟ lc 22c33⎥ ⎝ π ⎠ ⎢⎣ ⎥⎦ 2

+

( )

1/2 ⎛ 24Nc11 1 ̅ ⎟⎞ c c − − ϕc⎜ 22 ̅ 33 ̅ ⎝ π ⎠ λ(1 − ϕc)

⎡ ⎛ 8c11 ⎞1/2 ⎤ 3nkBT 2 ⎜ ⎟ ⎢ tr c l l⎥ − + − ⎝ π ⎠ ⎥⎦ 2 2⟨RN 2⟩(1 − ϕc) ⎢⎣

1/2 ⎤ ⎡ ⎛ 6Nc11 ̅ ⎟⎞ ⎥ ⎢ c11 − ϕc⎜ ̅ ⎝ π ⎠ ⎥⎦ ⎢⎣

3nkBT

(42a)

(38)

where c is the conformation tensor of the whole molecule and l is the length of crystal. The Hamiltonian can be expressed as follows: ⎧ ⎪ 1 ⎨ M·M + σem H= Ω⎪ ⎩ 2ρ ⎛ ρ T ⎞ 3nkT ⎟+ − ϕcΔHu⎜1 − ln (1 − ϕc) Mu 2 Tm 0 ⎠ ⎝ 1/2 ⎤ ⎛ 24Nc11 nkT ⎡ ̅ ⎞⎟ c c ⎥ − + 3ϕc 2Nc 22 − ϕc⎜ ln ⎢ c11 c 22 c33 c33 22 33 ̅ ̅ ̅ ̅ ̅ ̅ ̅ ⎝ π ⎠ ⎢⎣ ⎥⎦ 2

∫

+

1/2 ⎤ ⎫ ⎪ ⎛ 24Nc11 nkT ⎡ ̅ ⎞⎟ ⎥ − 3nkT ⎬ ⎢tr c̅ + 3ϕc 2 − ϕc⎜ d3x ⎪ ⎝ π ⎠ ⎥⎦ 2(1 − ϕc) ⎢⎣ 2 ⎭ (39)

weight of a single chain, σem is the interface energy between crystal and amorphous melt, and c ̅ = 3c/Nb2 is the nondimensionalized conformation tensor. Upon introduction of a parameter Z describing crystallization kinetics, the time evolution of crystallinity can be given by

∂t

= −νβ∇β ϕc − Z

δH δϕc

(40)

where νβ is a component of the velocity tensor and Z is a fitting parameter. When the expression for the Hamiltonian is substituted, the rate of crystallization is ∂ϕc ∂t

=

⎛ ρ T ⎞ ⎟ Z ΔHu⎜1 − Mu Tm 0 ⎠ ⎝ −

⎤ ⎛ 24Nc11 ⎞1/2 nkTZ ⎡ ⎟ ⎢tr c̅ − ⎜ + 6Nϕc − 3Nϕc 2 ⎥ 2 ⎝ π ⎠ ⎥⎦ 2(1 − ϕc) ⎢⎣

1/2 ⎤ ⎡ 24Nc11 ̅ c 22 6ϕcNc 22 ⎥ ̅ c33 ̅ − ̅ c33 ̅ nkTZ ⎢ π + ⎥ ⎢ 1/2 2 ⎢ c c c + 3ϕ 2Nc c − ϕ 24Nc11̅ ⎥ c c 11 22 33 22 33 22 33 ̅ ̅ ̅ ̅ ̅ ̅ ̅ c c ⎦ ⎣ π (41)

(

) (

(42b)

∂ c33 c33 1 ̅ = − 1 ε(1 ̅ ̇ − p) c33 + − ̅ 2 λ λ(1 − ϕc) ∂t

(42c)

where λ is the characteristic relaxation time of the medium, which is chosen to reproduce the known result for a noncrystalline system. The dumbbell model used above has two interesting points making it different from other models, as the authors pointed out. First, it can simultaneously account for the dynamics of flow and the crystallization that is occurring. Second, the finite extensibility of molecules is taken into consideration in the finite extendable nonlinear elastic dumbbell. These two characters are clearly different from the model of Marrucci and Grizzuti,253 in which only induction time under orientation conditions can be obtained. Titomanlio and co-workers focus on the modeling of crystallization during real polymer processing, for example, film casting257,258 and injection molding.259 In their works, both the evolution of crystallinity and crystal morphology under nonisothermal crystallization processes are modeled. The dumbbell model is used in their model to describe chain extension, which is transformed to entropy change and further to elevation of the melting temperature of crystals. The complete model is rather complicated, since many factors affecting the crystallization have to be considered. Introduction of the details is beyond the aim of this review. 6.1.3. Quantitative Description of Extension-Induced Nucleation. 6.1.3.1. Relaxation-Related Long Period Evolution. It is widely accepted that, during flow, molecular deformation depends on the competition between flow strength and chain relaxation. However, whether chain relaxation plays a role in FIC after flow is a question that is paid little attention. Optical microscopic results show that all spherulites have the same dimension, which indicates all nuclei form at the same time. Besides, the rate of lamellar growth is mainly determined by the crystallization temperature. Then, it seems that chain relaxation does not affect the FIC after flow. Intuitively, just after flow, the chain relaxation affects chain conformation, which leads to a time-dependent entropy loss. According to nucleation theory, the nucleation rate should correspondingly change with time. It is convincing to us that the apparent discrepancy is rooted in the length scale covered by the experiments, which is spherulite scale for microscopic experiments but lamellar details for X-ray methods. It was found that at high extensional rate the long period of PEO first increases just after flow; see Figure 39.260 The abnormal increase upon flow cessation is different from the increase of long period induced by lamellar thickening; the latter takes a long time for chain segments in crystals and amorphous

Here M = ρv is the momentum density, Mu is the molecular

∂ϕc

∂ c 22 c 22 1 ̅ = − 1 ε(1 ̅ ̇ + p) c 22 + − ̅ 2 λ λ(1 − ϕc) ∂t

)

The conformational tensor during crystallization can be obtained as AF


Chemical Reviews

Review

quantitatively. Generally, when a deformation with finite time is considered, the free-energy change can be calculated as A(t ) = A[E(t , 0)] −

∫0

t

A[E(t ′, 0)] μ(̇ t − t ′) dt ′

(44)

τd−1

When step strain with a strain rate much higher than is considered, it is a good approximation that no relaxation happens during stretch. The free-energy change at time t after cessation of deformation (t = 0 s) is the product of the memory function and a constant, A0, which is the free-energy change in the absence of relaxation: ΔGf = 3ckBTA(t ) = 3ckBTA 0μ(t )

(45)

The nucleation rate of unit volume can be written as eq 46, following the microrheological model:

Figure 39. Abnormal increase of long period during extension-induced crystallization of PEO. (a) Two-dimensional scattering patterns. (b) Lorentz-corrected one-dimensional intensity profiles. (c) Time evolution of the long period. Reprinted with permission from ref 260. Copyright 2011 American Chemical Society.

⎤ ⎡ ⎛ E ⎞ Kn ⎥ Ṅ = CkBT ΔG exp⎜ − a ⎟ exp⎢ − ⎢⎣ T (ΔGq + ΔGf )n ⎥⎦ ⎝ kBT ⎠ (46)

The volume is estimated by assuming that the filling rate has a linear relationship with the unoccupied volume, as eq 47 shows:

phase sliding collectively. A model based on relaxation is proposed to explain the increase in the distance between two lamellae, as shown in Figure 40.

d V (t ) = B[V0 − V (t )] dt

(47)

where V(t) is the volume occupied by nuclei and V0 is the total volume. B is a constant with units of reciprocal seconds and reflects the speed of nucleation. B will be referred as the volume filling rate hereafter. Solving eq 47, we get V (t ) = V0[1 − exp( −Bt )]

(48)

The total nucleation rate depends on the remaining volume; hence eq 46 has to be multiplied by exp(−Bt). Subsequently the number of nuclei N(t) can be obtained: N (t ) ∼

After cessation of the step strain at time t0, the highly oriented molecular chains tend to gradually relax back to equilibrium random-coil state, during which FIN takes place. In the situation of high orientation, the long period is assumed to be proportional to the inverse of linear density of nuclei, as shown in eq 43: V (t ) N (t )

t

Ṅ (t ′) exp( −Bt ′) dt ′

(49)

With the time-dependent number of nuclei and the occupied volume, the long period obtained from SAXS is numerically fitted. The fitted curves of the long period are presented in Figure 41. The volume filling rate B, reflecting the speed of nucleation, is given in Figure 42, which shows good agreement with the time of onset of a distinct scattering peak. One drawback of this model is the exclusion of chain stretch, which is rooted in the microrheological model by Coppola et al.252 Nevertheless, chain stretch is definitely very important in FIC of polymer. Besides the abrupt morphology change, some interesting changes in long period evolution have been found.261,262 How to describe these transient changes is still an open question in modeling. 6.1.3.2. Crystallization under Single Molecular Stretching. Crystallization theories, particularly those based on rheological models, often assume that material system studied is monodisperse. The assumption simplifies the derivation of theory but impedes its comparison with experimental results. As the material practically used is polydisperse, sometimes the response to flow is dominated by the long-chain portion, which composes only a minority of the material.221,230,263 Even with a monodisperse sample, the inhomogeneous flow in strong flow field may also disrupt the comparison between experimental and theoretical results.264,265 How to stretch a polymer chain in a controllable way and how to correlate deformation with subsequent crystallization are still unsolved issues.

Figure 40. Schematic illustration of nucleation model after step strain. The nucleation density decreases (long period increases) with nucleation time, due to relaxation of polymer chains. Reprinted with permission from ref 260. Copyright 2011 American Chemical Society.

L (t ) ∼

∫0

(43)

Here the symbol ∼ means the coefficient is omitted. The density of nuclei decreases with time due to relaxation of the oriented polymer network. Correspondingly, the long period increases with nucleation time; namely, Lt1< Lt2, with t1< t2 as schematically illustrated in Figure 40. The long period obtained with SAXS is the inverse of nucleation density averaged over total nucleation time, which also increases with time. The original microrheological theory is extended to the step strain case to interpret the evolution of long period AG


Chemical Reviews

Review

Figure 43. Illustration of single molecular stretch and the effect of temperature. Reprinted with permission from ref 266. Copyright 2011 American Chemical Society.

The induction time is obtained by the decrease of SAXS intensity, since after PEO crystallizes the density contrast begins to decrease. The fitted induction time is presented in Figure 44. The good agreement indicates a well-controlled single molecular stretch.

Figure 41. Comparison of calculated and observed long period. Reprinted with permission from ref 260. Copyright 2011 American Chemical Society.

6.2. Macroscale Continuum Modeling

Modeling provides a very powerful tool to understand FIN. Focusing on different length and time scales of polymer crystallization, there are various classes of modeling methods, including full molecular dynamics simulations,267−269 lattice Monte Carlo,270,271 coarse-grained kinetic Monte Carlo,272,273 and macroscopic continuum models.274,275 The bottom-up strategy is to develop detailed models by resolving the motion of individual atoms. However, the corresponding high computational cost hinders its wide application to the crystallization of polymers on practical length and time scales, especially under the mutual influence of severe processing-relevant (flow, temperature, and pressure) conditions. Alternatively, the top-down investigation starts with derivation of macroscopic continuum models from the empirical relationships obtained from abundant experimental observations. Unlike molecular models, which are capable of presenting many details of nucleation, macroscopic models are disadvantaged by the absence of molecular details, and consequently, the macroscale continuum model requires initial assumptions as input to build the quantitative relationship between flow strength and resultant nucleation features like density and orientation. A detailed comparison between different model methods and recent progress of coarse-grain kinetic Monte Carlo and molecular dynamics models can be found in the recent reviews of Graham13 and Rutledge.276 In this section, macroscale continuum models will be mainly discussed. Besides the potential application to practical processes, the macroscopic model can directly use experimental results to test and to improve mechanism understanding, in the form of assumptions. Also note that only modeling of FIN is introduced; other models describing the subsequent crystallization process, including crystallite growth, are outside the scope of this work, and readers are referred to ref 277. Under severe flow strength, the formed nuclei have a fibrillar geometry, where the length is much larger than the lateral diameter. It was suggested that formation of fibrillar nuclei may start with pointlike objects and subsequently grow in the longitudinal direction to form the ultimate fibrillar shape. The first model aspect concerns what determines the appearance of fibrillar nuclei in a quantitative manner. The

Figure 42. Comparison of 1/B and the time of onset of scattering peak. Reprinted with permission from ref 260. Copyright 2011 American Chemical Society.

Stretching a single chain directly is a promising way to solve the above problem. A poly(L-lactic acid) (PLLA)−poly(ethylene oxide) (PEO) diblock copolymer was designed and synthesized.266 PLLA has a relatively higher melting temperature and crystallizes first at 90−130 °C. The different variations of crystallization temperature will cause different lamellar thicknesses. After crystallization, the contraction of PLLA makes the PEO chains deviate from random-coil state. An equivalent chain stretch, which originates in the surface crowding of PEO, can be obtained. The thickness of PLLA lamellae determines the strength of stretch imposed on PEO. By use of this block copolymer, a single molecular stretch was achieved, as presented in Figure 43. The crystallization kinetics can also be described by classical nucleation theory (CNT) incorporating free-energy change induced by stretch. The free-energy change by stretch can be given through surface crowding theory, as shown in eq 50: ΔGf =

π 2kBTcNA 16NMb2

lPEO2

(50)

where N is the number of segments with Kuhn length b, M is the molecular weight of PEO block, NA is Avogadro’s number, and lPEO is the length of PEO block and is calculated from the density of crystals and amorphous region. AH


Chemical Reviews

Review

Figure 44. (a) SAXS intensity during crystallization of PEO. The temperature indicates the crystallization temperature of PLLA. (b) Fitted induction time. Reprinted with permission from ref 266. Copyright 2011 American Chemical Society.

Figure 45. Model for growth of nuclei. Reprinted with permission from ref 275. Copyright 2009 Wiley−VCH.

quantity of formed fibrillar nuclei is often macroscopically indicated by the sharp morphology transition from fine-grained layer to oriented layer observed with a polarized microscope. Janeschitz-Kriegl and co-workers90,278 found that a parameter (the product of the fourth power of shear rate and the square of shear time) remains approximately constant at the boundary between fine-grained layer and oriented skin layer in a rectangular shear slit. This parameter was linked to the density of flow-induced fibrillar nuclei, and the developed model interpreted such dependence as meaning the creation rate of nuclei and their longitudinal growth rate are both proportional to the square of shear rate. However, this empirical correlation is restricted to specific material (molecular weight and molecular weight distribution). The model needs to relate nucleation with deformation on the molecular level in order to be more generally applicable to other materials and flow conditions, as McHugh et al.279 suggested that molecular strain due to flow may be the dominant process in FIN. Systematic work has been done by Peters and co-workers on macroscale continuum models to describe the onset of formation of fibrillar nuclei, the detailed longitudinal growth rate, and the influence of generated nuclei on rheology. Zuidema et al.274 first proposed that the recoverable strain, that is, elastic deformation, dominates FIN. Later, Steenbakkers and Peters280 replaced the recoverable strain by molecular stretch, and Custodio et al.275 applied it on injection molding processes. It has been demonstrated that the high molecular weight (HMW) tail dominates FIN; the part controlling molecular stretch should be the HWM tail. Thus, flow-enhanced nucleation rate was modeled to be fourth-order-dependent on the molecular stretch ΛHMW of the slowest relaxation mode, Ṅ f = gn(ΛHMW4 − 1), with a scaling parameter gn dependent on temperature. Next, when the molecular stretch of HMW tail surpasses a threshold, the formed nuclei change from pointlike to fibrillar, resulting in the morphology transition from spherulite to oriented crystallites, as shown in Figure 45. After formation, the fibrillar nuclei grow longitudinally. The HMW tail plays a crucial role in triggering the formation of fibrillar nuclei, but Kimata et al.147 found that shish structure has

a comparable concentration of HMW parts as the rest of polymer melt. This implies that the development of fibrillar nucleithat is, L̇ , the growth along longitudinal directionshould be participated in by all chains in the melt. Thus, the longitudinal growth rate of fibrillar nuclei was determined by the average stretch of all chains and written as L̇ = gLJ2(Be,avgd), where J2(Be,avgd) is the second invariant of the deviatoric elastic Finger tensor of a mode representing whole-chain-length distribution of the melt, indicating the combined effect of molecular stretch and orientation, and gL is a scaling factor. In addition, the fibrillar nuclei and the caps can grow in the radial direction at a lamellar growth rate G; see schematic illustration in Figure 46.

Figure 46. Growth of isotropic and oriented crystalline structures. Reprinted with permission from ref 275. Copyright 2009 Wiley−VCH.

Another important aspect of this model is inclusion of the link between flow-induced nuclei and rheological properties of the corresponding melt, which often was not considered by the simulation of the length and time scales of individual molecules. FIP or nuclei are usually envisioned as clusters of chain segments, in which the mobility of chain segments is lower than that of free chains in the melt due to dense packing effects; as a consequence, the flow-induced nuclei can act as physical cross-linking points. Zuidema et al.274 proposed that the relaxation times of HMW chains in the flow melt depend on the number of flow-induced nuclei in a linear function. This model was then applied to two sets of well-defined injection molding experiments employing isothermal and nonisothermal protocols, respectively. A finite element code was utilized to implement the model, and a decoupled approach was employed to compute the flow kinematics. From the growth AI


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Figure 47. Distribution across half the normalized slit thickness of (i) total length of fibrillar nuclei, (ii) number of flow-induced nuclei per volume, and (iii) average length of fibrillar nuclei for flow conditions MPR1 and MPR 2. Reprinted with permission from ref 275. Copyright 2009 Wiley−VCH.

modeled criteria are applicable to other flow conditions. Figure 47 right column (MPR2) clearly shows that the critical values predicted from MPR1 (○) are almost on top of the prediction curve for flow condition MPR2, indicating that the morphological criteria modeled are applicable to both MPR1 and MPR2 conditions. Further applied to conditions MPR3 and MPR4, the model predicted a lower value of total length per volume of fibrillar nuclei than the MPR1 criteria; see Figure 48. This agrees well with the fact that no oriented layer is observed under these two flow conditions, implying that a critical total length of fibrillar nuclei is required to cause a detectable oriented layer. In addition, the relative volume fraction of oriented crystals can be obtained as Vori = ψ0/(ϕ0 + ψ0), as shown in Figure 49, which interestingly shows that the values of Vori at the transition from fine-grained layer to oriented layer for MPR1 and MPR2 are both around 0.025.

rate of fibrillar nuclei, Eder rate equations278 were employed to calculate the total undisturbed length, surface, and volume of oriented crystallites per unit volume. Figure 47 compared the modeling and experimental results for isothermal crystallizations. The features of flow-induced fibrillar nuclei, in terms of (i) total length per volume, (ii) total number density, and (iii) average length, are predicted along the slit thickness direction, where various locations along the thickness direction experienced distinct flow strengths. Experiment MPR1 serves as the reference experiment, and its microscopic images show three distinct regions of spherulitic core layer, fine-grained layer, and oriented layer, moving from the slit center to the wall. These two transition locations along the thickness direction are used in the predicted curves to determine critical points modeled for flow condition MPR1 (shown by ●, which change to ○ under other conditions). These critical values obtained from experimental condition MPR1 are further compared with those values of transitions under other flow conditions, to test whether MPR1 AJ


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Figure 48. Distribution across half the normalized slit thickness of (i) total length of fibrillar nuclei, (ii) number of flow-induced nuclei per volume, and (iii) average length of fibrillar nuclei for flow conditions MPR3 and MPR4. Reprinted with permission from ref 275. Copyright 2009 Wiley−VCH.

presented in Figure 50a, which shows a relatively larger ultimate molecular stretch for 100 s−1 at 1200 bar than for 180 s−1 at 500 bar. According to the aforementioned model using the critical molecular stretch as a criterion, fibrillar nuclei are more likely to be generated in 100 s−1 at 1200 bar. However, the experimental result displayed that fibrillar nuclei appear in 180 s−1 at 500 bar. To understand this deviation, van Erp et al.281 compared the time integrals over the stretch history during the shear time ∫ t0sΛHMW dt between these two conditions (see Figure 50b). Interestingly, it was found that the accumulative molecular stretch of 180 s−1 at 500 bar is always larger than that of 100 s−1 at 1200 bar, which is consistent with experimental results that fibrillar nuclei are observed under the former flow conditions. This indicates that, different from the critical value of the transient molecular stretch, the accumulative molecular stretchthat is, the integral of transient molecular stretch over flow timeseems to be the controlling parameter to determine the formation of fibrillar nuclei under the combined influences of flow and pressure.

The model was also applied to nonisothermal experiments, where the criterion based on the relative volume of oriented crystals shows good agreement between predictions and experimental observations (see Figure 22 in ref 275). The agreement between modeling predictions and experimental results shows that the molecular assumptions about criteria for the formation of fibrillar nuclei, longitudinal growth rate, and correlation between nuclei and melt viscosity, are reasonable for these flow conditions. However, the authors also point out that the predicted critical average length of fibrillar nuclei is up to 1 mm, which seems too high and needs more experiments to calibrate the model parameters.275 Meanwhile, alternative insights are given into the formation mechanism of FIN. Van Erp et al.281 studied the combined effect of shear and pressure on FIN in iPP. Among flow conditions, two typical cases are 180 s−1 at 500 bar and 100 s−1 at 1200 bar, respectively causing distinct isotropic and oriented morphologies. Again the molecular stretch during flow is calculated and AK


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Figure 49. Distribution of relative volume of oriented material, Vori = ψ0/(ϕ0 + ψ0), across half the normalized slit thickness under flow conditions (a) MPR1, (b) MPR2, (c) MPR3, and (d) MPR4. Reprinted with permission from ref 275. Copyright 2009 Wiley−VCH.

Figure 50. (a) Molecular and (b) cumulative molecular stretch over time (shear time ts = 1 s). Reprinted with permission from ref 281. Copyright 2013 Wiley−VCH.

Figure 51. (a) Pressure drop and (b) apparent crystallinity during and after flow with piston of 100 mm/s for 0.2 s. Symbols show experimental data; solid lines show the model of Roozemond et al.282 (indicated as current model); and dashed lines show the model of Zuidema et al.274 Reprinted with permission from ref 282. Copyright 2015 AIP Publishing LLC.

modified multipass rheometer and an advanced ultrafast synchrotron X-ray method to successfully track time evolution of rheological properties during severe flows close to the

The experimental results used to compare with modeling results are the final crystallite morphologies ex situ examined after complete solidification. Recently, Ma et al.98 utilized a AL


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parameter. Although relaxation time was proposed as an ordering parameter of precursors, this parameter lacks structural information and depends on temperature. Finding a suitable ordering parameter of precursors is essential to construct the molecular mechanism of FIN and to understand how precursors influence the nucleation process. (3) Nonequilibrium nature of FIN: Current theoretical considerations of FIN are based on the framework of classical two-phase nucleation model. The effect of flow is incorporated into nucleation driving force through a simple add-up method. However, nucleation under strong flow is a typical nonequilibrium phase transition, which is not a simple extension of equilibrium phase transition and cannot be described by small modifications of the equilibrium case. On the other hand, the intrinsic nature of multiple lengths and multiple relaxation modes makes polymers a rather suitable model system to study nonequilibrium phase transition. Meanwhile, flow is an effective trigger to reveal the nonequilibrium nature of nucleation. Therefore, exploring the nonequilibrium nature of flow-induced polymer nucleation not only helps to underscore the molecular mechanism of FIN but also enriches the study of nonequilibrium science. (4) Diversity in mechanism of FIN: Concerning FIN, the general effects revealed for all polymers include raised nucleation density, oriented nuclei, and even altered crystallite modifications. However, the mechanism of FIN may vary greatly in different polymers, or even for the identical polymer with changes in experimental conditions like temperature and flow strength. It seems difficult, at least presently, to build one universal mechanism to describe FIN for all polymers. Therefore, molecular structures and flow conditions should be studied in a systematic manner, rather than under a single condition, to identify all similarities and differences to comprehensively understand the FIN mechanism. Moreover, experimental conditions should be well-defined to precisely specify the mechanism under certain limited molecular and experimental conditions as well as to avoid occurrence of unintended effects like inhomogeneous flow and melt fracture. (5) Developing new and powerful experimental and modeling approaches: Nucleation of polymer under flow is a multiscale and multistep process. The spatial uniformity and fast dynamics of this process require robust detection techniques with sufficiently high space and time resolution. As the development of synchrotron radiation-based X-ray scattering benefits the understanding of structural evolution during crystallization, innovative techniques with ultrahigh time and space resolution can shed light on the complex nucleation process and help to construct the molecular mechanism. Meanwhile, multiscale modeling approaches are also expected to give verification and new understanding of nucleation at the molecular level and bridge gaps between different detection techniques in both time and length scales. (6) FIN in real polymer processing: Different from most FIN studies that were performed under relatively mild conditions in the lab, real polymer processes have much stronger flow strength and more complex flow conditions. For instance, in film blowing and casting, flow gradients are two-dimensional and exist along both stretching and lateral directions. More attention should be paid to FIN events under complex real processing conditions. In the meantime, based on these obtained experimental results, the mesoscale simulation and modeling need to be developed to gain understanding of mechanism and to also validate/modify the current mechanism.

processing strength and lasting only 0.2−0.25 s. A significant rise in melt viscosity was found during the severe flow pluses, instead of the steady-state plateau. On the basis of these experimental results, Roozemond et al.282 modeled the FIN at such high shear rates and found that, when describing the dependence of nucleation rate on molecular stretch of the HMW tail, an exponential relationship works better than the power law used before by Zuidema et al.274 and van Erp et al.;281 see the comparison of various models in Figure 51. Actually, Pantani et al.283 also proposed a molecular stretch model to describe the transition from spherulitic to fibrillar morphology. By employing the elastic dumbbell model, the constitutive equation was written as D 1 A̿ − (∇ν ̅ )T A̿ − A̿ (∇ν ̅ ) = − A̿ + (∇ν ̅ ) + (∇ν ̅ )T Dt λ (51)

where A̿ is the deformation tensor with respect to equilibrium state, ν̅ is the velocity field, and λ is the relaxation time. If a flow at the constant shear rate (γ̇) is applied to melt at the reference time and the relaxation time λ is considered as constant during flow, then the deformation tensor A̿ at time t can be written as follows: ⎡ ⎛ t ⎞⎛ t ⎞⎤ A11 = 2λ 2γ 2̇ ⎢1 − exp⎜ − ⎟⎜1 + ⎟⎥ ⎝ λ ⎠⎝ ⎣ λ ⎠⎦

(52)

⎡ ⎛ t ⎞⎤ A12 = λγ ⎢̇ 1 − exp⎜ − ⎟⎥ ⎝ λ ⎠⎦ ⎣

(53)

The difference between the two main eigenvalues of the deformation tensor can be taken as a measurement of the elongation of the system. For simple shear, the system elongation becomes Δ = (A112 + 4A12 2 )1/2 . When the Deborah number (defined as the ratio between relaxation time and shear time) is much larger than 1, the molecular stretch reaches its maximum value, Δ = 2Wi[(1 + Wi 2)1/2 ], where Wi = λγ̇. Then, to form fibrillar morphology, molecular stretch Δ needs to reach a certain critical value of Δc. Thus, the relaxation time (λ) is considered as a fitting parameter to reproduce the measured boundary of shish formation in shear rate−shear time space.

7. FINAL REMARKS After decades of effort, a wealth of phenomenological accumulations and substantial progress in theory and modeling have been achieved in FIN. However, there are still many challenges in unveiling the multiscale and multistep process of FIN, which are summarized as follows. (1) Molecular mechanism of FIN: The long-chain nature of polymers endows them with multiscale structure and relaxation time. During nucleation induced by flow, the anisotropic long chain assembles into hierarchical structures, where the multiscale ordering involves via both intra- and interchain ordering. As discussed in section 3, those ordering processes may occur sequentially, leading to appearance of structural intermediates like precursors. The occurrence of precursor challenges the traditional two-phase nucleation model, and the future molecular mechanism of FIN should incorporate structural intermediates. (2) Ordering parameter of precursors: Fast X-ray scattering studies have demonstrated the formation of precursors during flow, which have a large influence on nucleation, crystallization kinetics, and final crystal morphology. However, the definition of precursors is still obscure due to the lack of a precise ordering AM


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In summary, FIN is a very fundamental and industrially core subject. The intrinsic multiscale features of polymer chain lead to multiscale ordered structures and multistep ordering process for nucleation. The multiscale structures include segmental conformation, packing of conformational ordering, deformation on the whole-chain scale, and macroscopic aggregation of crystallites. The multistep process involves conformation transition, isotropic−nematic transition, density fluctuation (or phase separation), formation of precursors, and shish-kebab crystallites. The molecular mechanism of FIN, incorporating both multiscale and multistep considerations, is in urgent demand. A full understanding of nucleation under flow will ultimately benefit the precise control of polymer products and the understanding of nonequilibrium phase transition.

analysis in polymer science with the help of neutron and X-ray scattering. Fengmei Su received a B.S. (2011) in polymer material and engineering from Sichuan University and obtained a Ph.D. (2016) in nuclear science and technology from the University of Science and Technology of China. She is currently a postdoctoral fellow in the Synchrotron Radiation Laboratory, University of Science and Technology of China. Her primary research interest is flow-induced polymer crystallization, such as conformation ordering and flow-induced precursors, etc. Liangbin Li received a B.S. (1994) from Sichuan Normal University and M.S. (1997) from Sichuan University in physics and a Ph.D. (2000) in polymer material processing from Sichuan University. From 2000 to 2004, he was a postdoctoral fellow in FOM-Institute for Atomic and Molecular Physics and Technology University of Delft, The Netherlands. From 2004 to 2006, he worked as a materials scientist at Unilever Food and Health Research Institute. Since 2006, under the OneHundred Talent Program of Chinese Academy of Science, Dr. Li joined National Synchrotron Radiation Laboratory, University of Science and Technology of China as a full professor and started the Soft Matter Group. His primary research interests are polymer physics relevant to processing, such as flow-induced crystallization of polymer and stressinduced deformation and phase transitions of crystalline polymers.

AUTHOR INFORMATION Corresponding Authors

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

Nan Tian: 0000-0003-1822-876X Liangbin Li: 0000-0002-1887-9856 Notes

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (51325301, 51633009, 51573132, and 51227801) and the key research and development tasks of MOST (2016YFB0302501).

The authors declare no competing financial interest. Biographies Kunpeng Cui received a B.S. in material science and engineering from Zhengzhou University in 2010. Then he joined the research group of Professor Liangbin Li at the University of Science and Technology of China, where he investigated flow-induced polymer crystallization and received a Ph.D. in 2015. He is currently working as a JSPS (Japan Society for the Promotion of Science) research fellow at Hokkaido University. His research interests include polymer crystallization, toughening mechanism of hydrogels, and synchrotron-based X-ray scattering techniques.

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Zhe Ma received a B.S. in polymer science and technology from Zhejiang University of Technology in 2005 and obtained his M.S. in polymer material processing from Sichuan University in 2008. Later, he joined Eindhoven University of Technology, where he received a Ph.D. in polymer materials in 2012 and worked as a postdoctoral researcher from 2012 to 2015. He is currently working as an associate professor of polymer science and engineering at Tianjin University. His research focuses on the crystallization behaviors of polyolefins and their correlations with molecular structures. Nan Tian received a B.S. in polymer materials and engineering from the University of Science and Technology of China in 2009 and obtained a Ph.D. in nuclear science and technology from the University of Science and Technology of China in 2014. Since then, he has worked as an associate professor of polymer chemistry and physics at Northwestern Polytechnical University. His research focuses on the relation between entanglement, chain dynamics, and crystallization of polymers. Dong Liu received a B.S. in chemistry from the University of Science and Technology of China in 2009. Later, he joined Professor Liangbin Li’s Soft Matter Group at National Synchrotron Radiation Laboratory, University of Science and Technology of China, where he received a Ph.D. in nuclear science and technology in 2015. He is currently working as a research assistant in neutron scattering, based at the China Mianyang Research Reactor (CMRR) at Key Laboratory of Neutron Physics and Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics (CAEP). His research focuses on structure AN


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