Self-Acceleration of Nucleation and Formation of Shish in Extension

Jun 19, 2012 - Extension flow induced crystallization of isotatic polypropylene (iPP) has been ... of Shish in Extension-Induced Crystallization with ...
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Self-Acceleration of Nucleation and Formation of Shish in Extension-Induced Crystallization with Strain Beyond Fracture Kunpeng Cui, Lingpu Meng, Nan Tian, Weiqing Zhou, Yanping Liu, Zhen Wang, Jie He, and Liangbin Li* National Synchrotron Radiation Lab and College of Nuclear Science and Technology, CAS Key Laboratory of Soft Matter Chemistry, University of Science and Technology of China, Hefei, China ABSTRACT: Extension flow induced crystallization of isotatic polypropylene (iPP) has been studied with a combination of extension rheological and in situ small-angle X-ray scattering (SAXS) measurements at 140 °C. Rheological data of step extension on iPP melt are divided into before and beyond fracture strain zones in strain−strain rate space, where intermediate strains between them lead to fracture of samples. Coincidently, weak and strong accelerations of nucleation are observed in the before and beyond fracture strain zones respectively, where distinctly different features of crystallization kinetics and nucleation form occur in these two zones. The microrheological model explains the acceleration of nucleation in the “before fracture strain zone” well, while a “ghost nucleation” mechanism is proposed to interpret the strong acceleration of nucleation in the “beyond fracture strain zone”. The “ghost nucleation” is due to the displacement of initial parent point nuclei, where daughter nuclei are induced along the trails. This new mechanism explains well the acceleration of nucleation in orders of magnitude and the formation of shish in iPP melt.

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to combine theories of polymer dynamics and nucleation.64−69 One representative example is the microrheological model,65 where the Doi−Edwards theory for polymer dynamics is employed to estimate the flow-induced free energy change (ΔGf) of polymer chains. ΔGf is further incorporated into the Lauritzen−Hoffman theory for polymer crystallization to quantitatively interpret flow accelerated nucleation. Recently, we extended this model to account for FIC of poly(ethylene oxide) (PEO) with a strain smaller than yield strain, where reasonable agreement is reached between experiment and theory.70 Another typical approach is the continuum models of FIC,66−69 which couples the stress fields with the macroscopic crystallization kinetics in a manner consistent with the laws of continuum thermodynamics and kinetics.66 The continuum models are employed to model the structural and viscoelastic parameters (such as velocity, temperature, tensile stress, apparent viscosity, and crystallinity) during industrial processing like fiber spinning67 and injection molding.68 Nevertheless, for a successful prediction either microrheological or continuum models has to rely on the real physical process of flow-enhanced nucleation, which however still remains controversial. Flow-enhanced nucleation is commonly correlated with the occurrence of row-nuclei or shish at strong flow, which is the focus in the whole history of FIC study. Coil−stretch transition is employed by Keller and co-workers to explain the formation of shish-kebab superstructure in polymer solution, which is further extended to polymer melt.71 In Keller’s view, only the

INTRODUCTION Flow-induced crystallization (FIC) has attracted great interest due to its vital importance in polymer science and industry. In polymer processing such as extrusion, fiber spinning, film blowing, etc., polymer melt undergoes intense and complex flow field, which dramatically influences the final morphology and properties of products.1−4 On the basis of large amount of experiments in the last 60 years, it is generally accepted that flow can enhance crystallization rate by orders of magnitude,5−8 induce morphological transition from spherulite to shish-kebab or row-nuclei structure,9−12 and lead to new crystal forms like β crystal of iPP.13,14 Nevertheless, though experimental observations are widely confirmed by different groups, the understanding of mechanisms of FIC are far from satisfactory. Discrepancies on the structures of shish/row-nuclei or precursors8,10,15−31 and the roles of molecular and flow field parameters32−59 still exist, which are debated intensively in recent years. Acceleration of crystallization kinetics is the most common observation in FIC study, which is generally attributed to an increase of nucleation rate. A standard approach to interpret the enhancement of nucleation is based on entropic reduction of polymer melt due to flow induced orientation and stretching of chains, which leads to a decrease of nucleation barrier and consequently an increase of nucleation rate. Thus, accelerating nucleation requires flow field being strong enough to orient or stretch chains. The dimensionless parameter Weissenberg number Wi = ε̇τd > 1 can be employed as a qualitative criterion for FIC, which is essentially a competition between flow with strain rate of ε̇ and chain relaxation with terminal time of τd.60−63 Quantitative interpretation on flow accelerated nucleation needs © 2012 American Chemical Society

Received: February 19, 2012 Revised: June 6, 2012 Published: June 19, 2012 5477

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chains longer than the critical weights (M*) can be stretched and the rest shorter chains remain in the coiled state in a given flow field. The stretched chains crystallize into shish and the coiled chains form the kebab. However, the coil−stretch transition in polymer melt during flow has always been questioned. Pennings et al. believed that stretched network is responsible for shish formation.72 The view of shish consisting of both long and short chains is also not in-line with the coil− stretch transition.11 Our recent rheo-SAXS experiment shows that coil−stretch transition is not a necessary condition for shish formation in polyethylene (PE),29 which seems coincident with the view of stretched network. Nevertheless, it is still open whether the view of stretched network can be generalized to other polymers or not. The heterogeneities of polymer melt and flow field are a grand obstacle on understanding of flow-enhanced nucleation and shish formation. The “short-term shear or extension” protocol proposed by Janeschitz-Kriegl17 is widely adopted in the study of FIC, which assumes a melt rheological behavior without noticeable structural change during flow. However, both the melt and flow are inhomogeneous in most FIC experiments. Distribution of molecular weight is intrinsically heterogeneous in common polymer, which leads to a confused concerning on the roles of long and short chains in FIC,32−44 while additives like nucleation agents and fillers are the examples of extreme heterogeneity,73−81 which are found to accelerate nucleation and to induce row-nuclei or shish due to amplification of local field. Even starting with a homogeneous melt, the occurrence of shear banding results in heterogeneous distribution of flow field 82,83 and flow-induced structures22,32,52,84 like so-called precursors or crystal nuclei turn the initial homogeneous melt into heterogeneous structural flow. All these heterogeneities deviate the rheological behavior from that of the ideal homogeneous melt and affect nucleation behavior, complicating the interpretation of flow accelerated nucleation and shish formation. Thus, the presence of heterogeneities either in flow field or in melt structure leaves the origin of flow enhanced nucleation up orders of magnitude and formation of shish being obscure. In this work, a combination of in situ extensional rheometer and SAXS measurement is used to investigate FIC of iPP focusing on the acceleration mechanism of nucleation and the origin of shish formation. Step extension induced nucleation is comprehensively studied in flow parameter space with different strains ε and strain rates ε̇. Weak and strong acceleration of nucleation zones accompany with transition from point nuclei to shish are observed in the flow parameter space, which coincide nicely with the before and beyond fracture strain zones in rheological space. Our results show that acceleration of nucleation on several orders and formation of shish is more possibly due to a self-acceleration effect by structural flow during extension rather than entropy loss of simple polymer melt.

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Figure 1. (a) Storage and loss modulus (G′ and G″) curves vs the oscillation frequency for the iPP at 145 °C. (b) Crossover relaxation time at different temperatures. The samples for extension flow test are cut into rectangular shape with length, width and thickness of 30, 18, and 1 mm, respectively. A homemade extensional rheometer used in this study can apply well-defined thermal history and impose extension flow field. Figure 2

Figure 2. Schematic drawing of the extensional rheometer for in situ SAXS measurements. depicts a schematic picture of our homemade extensional rheometer and details of the apparatus have been described in previous publication.70 Its design is similar to Sentmanat extensional rheometer and allows us to obtain the Hencky strain. The ends of samples are secured to two geared drums by means of clamps and the length of samples (Lo) equals to the distance between the axes of the two drums, which keeps constant during test. With a constant linear velocity ν of the drum surface, the extensional strain rate is constant as ε̇ = ΔL/Lo = 2ν/Lo. With this kind of extensional rheometer, the strain and strain rate can be controlled independently. After mounted on the drums of the rheometer by means of securing clamps, each sample is initially held at 210 °C for 10 min to erase thermal history. Then the sample is cooled to the crystallization temperature (Tc). Immediately after Tc is reached, a desired strain rate and strain is imposed to the iPP melt. Temperature stability is maintained within ±0.5 °C and a nitrogen gas flow is used to help to homogenize the system temperature and prevent sample from degradation. SAXS is used to monitor the evolution of structure and morphology during crystallization process. Two-dimension (2D) SAXS measurements are made using an in-house setup with a 30 W micro X-ray source (Incoatec, GmbH), providing highly parallel beam (divergence about 1 mrad) of monochromatic Cu Kα radiation (λ = 0.154 nm). The scattering intensity is collected by a multiwire proportional chamber detector (Bruker Hi-star) with a resolution of 1024 × 1024 pixels (pixel size of 105 μm). The distance between sample and

EXPERIMENTAL SECTION

The iPP was kindly supplied by SABIC-Europe with a melt flow index about 0.3 g/10 min (230 °C/2.16 kg, ASTM D1238). The weightaverage molecular weight (Mw) and number-average molecular weight (Mn) are 720 kg/mol and 150 kg/mol, respectively. The molecular characteristics of iPP melt is derived from small-amplitude oscillation shear (SAOS) measurements using a Physica MCR 301 rotational rheometer equipped with 25 mm parallel plates. The crossover relaxation time τ is about 1.5 s at 145 °C and 0.6 s at 180 °C respectively (Figure 1), which can be extrapolated to low temperature with time−temperature superposition of linear viscoelasticity data. 5478

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detector is 2280 mm. The data acquisition time for each scattering pattern is 20 s during crystallization. Part of the confirmed measurements was performed at the beamline BL16B of the Shanghai Synchrotron Radiation Facility (SSRF). The X-ray wavelength was 0.124 nm. A Mar165 CCD detector (2048 × 2048 pixels with pixel size 80 μm) was employed to collect time-resolved 2D SAXS patterns, which placed 5380 mm from the sample. The date acquisition time was 3 s per frame, with each frame separated by 5 s waiting time. The 2D scattering images were analyzed with Fit2D software from European Synchrotron Radiation Facility.85 Tc is 140 °C in this work. SAXS data are corrected for background scattering by subtracting contributions from the extensional rheometer, air and the homogeneous iPP melt, and corrected for any detector spatial distortion. The 2D SAXS pattern was first integrated azimuthally to obtain the 1D scattering profile as a function of q = 4π sin θ /λ

Deformations with large strain as described in Figure 3a keeps integrality of these samples without fracture. Interestingly, step extension deformation with smaller strains may result in cohesive fracture of sample after the cessation of step extension. Thus, a fracture strain exists under each strain rate as indicated by blue rectangle shadow in Figure 3a. Note here fracture occurs after the cessation rather than during step extension. More step extension rheological experiments performed with different strains and strain rates at 140 °C are shown in Figure 4, which

(1,)

where q is the module of the scattering vector, λ the wavelength of X-ray and 2θ the scattering angle. The half time of crystallization (t1/2), namely the time to reach 50% conversion to the final full crystallinity of the sample, is employed to evaluate the crystallization kinetics introduced in SAXS study, which is determined from the normalized integrated intensity profiles.

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Figure 4. Step extension rheological experimental of iPP with different Hencky strains and strain rates at 140 °C with in situ SAXS measurements: (black lozenge) “before fracture strain zone” where the melt can be stretched with strain smaller than the fracture strain; (red dot) “fracture zone” where the melt fractured after cessation of imposed a certain strain; (blue square) “beyond fracture strain zone” where the melt can be stretched with strain beyond fracture.

RESULTS Before presenting X-ray scattering data on the crystallization behavior, we first show the rheological data of the step extensional strains, which are imposed on iPP melt to induce crystallization. Figure 3a presents representative stress−strain

can be divided into three zones, named as “before fracture strain zone” (black lozenge), “fracture zone” (red dot), and “beyond fracture strain zone” (blue square). In the “fracture zone”, the samples fractured after cessation of extension. In both “before fracture strain zone” and “beyond fracture strain zone”, most samples exhibit homogeneous deformation after the cessation of step extension. Yet some examples show a bit “necking” with strains just near the fracture strain in “beyond fracture strain zone”, which may be due to the postextension nonquiescent relaxation of the sample. An immediate question raised up is why sample can be stretched beyond fracture strain and keep their integrality without fracture. Strain hardening as shown in Figure 3a already gives some hints of the structural origin on the phenomenon of stretching beyond fracture strain, while direct evidence require structural characterization with techniques like SAXS. A distinct boundary is observed on the crystallization kinetics after subjected to step extension with strains smaller and larger than the fracture strain. For conciseness, we only give two representative results for these two situations, respectively. Figure 5 presents a SAXS result of FIC after subjected to a strain smaller than the fracture strain, where step extension with a strain of 0.8 and strain rate of 12.6 s−1 is imposed. The flow direction is horizontal. A series of 2D SAXS patterns at different crystallization time are presented in Figure 5a, which are integrated into 1D SAXS intensity curves as shown in Figure 5b. Immediately after cessation of extension (t = 0 s), the pattern shows a very weak diffuse scattering of melt, indicating the absence of any detectable structure. The scattering maximum around q of 0.16 nm−1 appears at crystallization time of about 1800 s, which concentrates slightly in the horizontal direction, indicating the formation of weakly oriented lamellar stacks. The intensity of scattering peak increases with crystallization time and a weakly oriented scattering ring is observed in 2D SAXS pattern. On the basis of 1D SAXS curves, the evolution of normalized integrated intensity during crystallization process is

Figure 3. Engineering stress as a function of Hencky strain for iPP melt under (a) three strain rates at 140 °C and (b) 25.1 s−1 at 180 °C .

curves during the extension of iPP melt with three different strain rates but the same strain of 3.5 at temperature of 140 °C. Here engineering stress rather than so-called true stress vs strain is plotted because polymer melt acts like a solid when extension rate is large enough to overcome relaxation of chain. Stress of rubber network is determined by segment density n between two entanglement points rather than cross section area. Thus, if no disentanglement occurs, it may not be proper to simply divide the cross section area. The stress increases almost linearly with strain in the first stage. Following the linear deformation region, a stress overshoot is observed, which leads to a stress maximum. As the occurrence of the stress maximum, the corresponding strain increases with the increase of strain rate. After exceeding the stress maximum, the evolution of stress with increasing strain undergoes at first declination and then a plateau-like region. By further increasing the strain, the stress−strain curves exhibit a strain-hardening phenomenon, similar to the solid mechanical behavior in tensile deformation. Figure 3b presents a stress−strain curve with a strain of 3.5 and strain rate of 25.1 s−1 at 180 °C. The shape of stress−strain curve is similar to the one at 140 °C until stress maximum, but the stress keeps decreasing rather than entering plateau-like and strain-hardening region with further increasing strain. 5479

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scattering intensity to saturate. The evolution of normalized scattering intensity is plotted in Figure 6c, giving induction time of 0 s (here no detectable induction time is observed within the time resolution of 20 s in our current work) and half time of crystallization of about 45 s. Both induction time and half time of crystallization show that the acceleration of crystallization rate with strain larger than fracture strain is more significantly than that with strain smaller than fracture strain. Since other experiments with strains beyond fracture strain show similar crystallization behaviors to Figure 6, we skip the detailes and only show half time of crystallization to illustrate the effect of strain on FIC directly. Half time of crystallization is employed to compare FIC with step extension strains smaller and larger than the fracture strain, which give a quantitative comparison on the effect of strain. Figure 7 shows the half time of crystallization at different strains Figure 5. (a) 2D SAXS images of the iPP sample at selected time intervals after extension at 140 °C with strain and strain rate of 0.8 and 12.6 s−1, respectively. (b) 1D SAXS intensity profiles. (c) Evolution of integrated intensity with time during crystallization process.

further analyzed, which is presented in Figure 5c. With the evolution of normalized integrated intensity in Figure 5c, the induction time and half time of crystallization can be quantitatively extracted, which reflect nucleation and crystallization rates, respectively. At current experimental condition, the induction time and half time of crystallization are about 1600 and 4000 s, respectively. The integrated intensity reaches a plateau after isothermally crystallized for about 8000 s. Crystallization under other experimental conditions with strains smaller than the fracture strain show similar results as presented in Figure 5. An example for samples subjected to step extension strains beyond fracture strain is exhibited in Figure 6, where step

Figure 7. Plots of half time of crystallization vs strain at three different strain rates at 140 °C.

and strain rates, which are extracted from the evolution of normalized integrated intensity measured with in situ SAXS during crystallization process. Here three different strain rates are studied (6.3, 12.6, and 25.1 s−1), all larger than the inverse of the crossover relaxation time τ estimated with SAOS. The overall trend of half time of crystallization to decrease with increasing of strain, which lies in the general expectation of reported experiments and some existed theory. In addition to this general trend, the plots of half time of crystallization vs strain can also be grouped into three distinct zones, which coincide with the three zones defined by rheological data as presented in Figure 4. With strain smaller than the fracture strain, increasing strain only leads to a weak decrease of half time of crystallization. For example with a strain rate of 12.6 s−1, imposing a strain of 1.0 leads to a reduction of half time of crystallization from 7860 to 6000 s. As soon as extension reaches beyond fracture strain, half time of crystallization drops drastically. With the same strain rate of 12.6 s−1, further increasing strain to 2.0 (beyond fracture strain of 1.2) results in about 3 orders of reduction on the half time of crystallization. This clearly indicates that different mechanisms govern nucleation with extensions before and beyond fracture. Avrami plots are used to evaluate crystallization kinetics from the SAXS intensity. The general expression of Avrami equation that describes isothermal crystallization kinetics is:86−88

Figure 6. (a) 2D SAXS images of the iPP sample at selected time intervals after extension at 140 °C with strain and strain rate of 3.0 and 12.6 s−1, respectively. (b) 1D SAXS intensity profiles. (c) Evolution of normalized integrated intensity with time during crystallization process.

extension with strain of 3.0 and strain rate of 12.6 s−1 is imposed. A series of 2D SAXS patterns during crystallization are presented in Figure 6a. Immediately after cessation of extension (t = 0 s), SAXS pattern clearly shows onset of crystallization with lamellar normal oriented along extension direction, as demonstrated by obvious scattering signal in horizontal direction. The 1D SAXS intensity curve is shown in Figure 6b. It takes about 160 s for the

1 − X(t ) = exp( −kt n)

(2)

where X(t) is the volume fraction of the material crystallized at time t, k is the rate constant of the crystallization process, and n is the Avrami exponent that indicates the geometry of the growing crystallites. The values of n and k are usually 5480

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strain larger than fracture strain, the Avrami exponent n ≤ 1.3, suggesting a fibrillar and disk-like crystal growth. Interestingly, the Avrami exponent n ≤ 1.0 when strain beyond fracture strain. n∼0.5 may suggests a diffusion controlled one-dimensional growth process,89 which is also observed during FIC of PE.12 Falling in the same trend as Avrami exponent n, a sharp change in the rate constant k is observed upon strain exceeding a critical value, which is exactly the fracture strain. The same extension flow induced crystallization of iPP is further studied with in situ SAXS in SSRF to confirm the observation on the difference with strain smaller and larger than the fracture strain. A series of representative 2D SAXS patterns for step extension with different strains and strain rates are presented in Figure 9. Immediately after imposing strains smaller than the fracture strain, the SAXS patterns show very weak diffuse scattering of melt, indicating the absence of any detectable structure. Figure 9 gives patterns with strain of 1.0 as an example. With strain larger than the fracture strain (in the range 2.0−3.5), two scattering streaks, perpendicular to the extension direction, appear immediately after the cessation of step extension, which are commonly taken as the sign of shish formation. On the basis of the scattering streaks in SAXS patterns, the relative content of initial shish after the cessation of the step extension is extracted. The relative content of the shish Xshish is defined by the following equation:

obtained from the double logarithmic form of the Avrami equation: log[− ln(1 − X (t ))] = log k + n log t

(3)

Figure 8 shows an example of Avrami plot for iPP crystallization after the cessation of extension with strain of 0.6 and

Figure 8. Avrami plots from the crystallization curves after extension at 140 °C with strain of 0.6 and 2.5 at strain rate of 12.6 s−1.

2.5 at strain rate of 12.6 s−1. The lines are fitting results of experimental data with eq 3. The parameters at different strains and strain rates are obtained through fitting and listed in Table 1. Crystallizing under strain smaller than fracture strain, the samples give Avrami exponents n between 2 and 3, indicating a spherulitic and disk-like crystal growth. While with

Xshish = (Ishish − Ib)/Ib

(4,)

Table 1. Avrami Analysis for iPP Samples at 140 °C with Different Strains and Strain Rates strain strain rate

fitting parameter

0.0

0.4

0.6

0.8

1.0

1.1

6.3 s−1

n log k/s−1 n log k/s−1 n log k/s−1

2.5 −9.9 2.5 −9.9 2.5 −9.9

2.6 −10.3 2.3 −9.2 2.4 −9.5

2.4 −9.0 2.4 −8.0 2.0 −7.7

2.4 −9.0 2.4 −8.1 2.2 −8.3

2.1 −7.0 2.1 −8.3 2.0 −7.8

2.6 −8.5 2.6 −7.6

12.6 s−1 25.1 s−1

1.6

2.0

2.5

3.0

3.5

1.3 −2.1

1.0 −1.6 1.0 −1.9 1.0 −2.1

0.8 −1.4 0.9 −1.7 1.0 −1.8

0.7 −1.3 0.8 −1.3 0.6 −0.8

0.5 −0.9 0.5 −0.6 0.5 −0.8

Figure 9. SAXS patterns immediately after cessation of extension under different strains and strain rates at 140 °C, the number in the parentheses at top left corner of individual pattern represents the strain under a given strain rate. 5481

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interesting findings can be extracted. (i) In the flow parameter space, step extension induced crystallization can be defined into two distinct zones, namely weak and strong acceleration zones, which are divided by the fracture strain. As showed in Figure 7, with a strain rate of 12.6 s−1, the first 1 unit of extension leads to only 24% reduction of half time of crystallization, while increasing of another 1 unit strain from 1.0 to 2.0 would decrease it as large as nearly 3 orders of magnitude. (ii) Both Avrami exponent and SAXS patterns indicated that two different nucleation type occurs in weak and strong acceleration zones, point nuclei is observed in the weak acceleration zone while shish emerges in the strong acceleration zone. (iii) The rheological behavior during step extension can be divided into three zones with the fracture strain as boundary, namely “before fracture strain zone”, “fracture zone”, and “beyond fracture strain zone”. Note that the “fracture zone” covers a range of strains rather than one fracture strain. The “before fracture strain zone” composes of the linear deformation, stress overshoot and post stress overshoot regions, while the “beyond fracture strain zone” starts from the upper boundary of the “fracture zone” and goes beyond, where strain hardening occurs, especially under large strain rates. Coincidently, the before and beyond fracture strain zones in rheological behavior correspond exactly to the weak and strong acceleration zones in crystallization kinetics, which is also accompanied by the transition from point nuclei to shish. This indicates an intrinsic correlation existing between rheological observation and crystallization kinetics. An intriguing question is why crystallization can be accelerated so dramatically in the “beyond fracture strain zone”. First we take the microrheological model to estimate the acceleration of crystallization induced by flow, which is based on Doi−Edwards theory for polymer dynamics and classic nucleation theory. We take the final expression directly and omit the deduction details, which can be found in reference.64,65 The ratio between nucleation rate under flow (Nf) and at quiescent condition (Nq) can be expressed as:

Figure 10. Plots of shish content vs strain at different strain rates at 140 °C.

where Ishish is the scattering intensity of the streaks from the shish and Ib is the background scattering intensity from the melt. The relative contents of shish vs strain are plotted in Figure 10. With three strain rates studied here, shish appears only for strain larger than the fracture strain. In order to investigate the effect of strain and strain rate on average shish length (⟨Lshish⟩), Ruland streak method36,90 is used to analyze the streak in SAXS patterns. Since the experimentally measured azimuthal breadth from contributions of scatterer length and misorientation, the method can also be applied to separate the average length of shish and its average misorientation. The apparent azimuthal width (Bobs) is a function of the length of shish and the azimuthal width (Bϕ) due to the misorientation of shish. If a Gaussian profile can be used to describe the orientation distribution, it follows: Bobs 2 =

4π 2 Lshish 2 q2

+ Bϕ 2

(5,)

If a Lorentzian profile is a proper model for the orientation distribution, instead of eq 5, the relation becomes: 2π + Bϕ Bobs = Lshish q (6,) Here Bobs represents the integral width of the azimuthal profile from the streak at q. On the basis of above equation, ⟨Lshish⟩ can be obtained. In this study, all the azimuthal distributions are fit with Lorentz functions well, Figure 11a is shown as an example using

⎡ ⎞⎤ K1 ⎛ 1 ⎜⎜1 − ⎟⎥ = (1 + ΔGf /ΔGq) exp⎢ ⎢⎣ Tc ΔGq ⎝ Nq (1 + ΔGf /ΔGq) ⎟⎠⎥⎦

Nf

(7,)

where ΔGq is the thermodynamic driven force coming from the volumetric free energy difference between melt and crystalline phase at quiescent conditions and ΔGf is added to account for the effect of flow on free energy change of the melt. K1 is a constant containing energetic and geometrical factor of the crystal nucleus. Tc is the crystallization temperature. Hence, all the parameters can be obtained and compared with experiment results through the above equations. Taking the SAXS data at 140 °C as an example, we calculate ΔGq first. With ΔH0 = 1.4 × 108 J/m3,65 Tm = 467 K, and a crystallization temperature Tc = 413 K, ΔGq = 1.6 × 107 J/m3 is obtained. The prefactor of ΔGf is 3ckBT = 3ρRT/Me = 1.6 × 106 J/m3. Here R is the gas constant, ρ the iPP melt density (0.9 g/cm3), and Me the molecule weight between entanglement, which is 5800 g/mol.91 Note that the memory effect is omitted in calculation of ΔGf for simplification. Here K1 equals 9.0 × 1010 K·J/m3.65 With strain of 1.0 and strain rate of 12.6 s−1, the nucleation rate under flow is 1.53 times faster than that at quiescent condition. This value matches reasonably well with experimental results, where the half time of crystallization under flow is 1.31 times of that at quiescent. Imposing strain of 2.0 at the same strain rate, eq 7, predicts that nucleation rate increases to 4.02 times compare

Figure 11. (a) Plots of azimuthal width (Bobs) vs the value of 1/q, which is used to determine the average shish length (⟨Lshish⟩). (b) Average shish length (⟨Lshish⟩) vs strain at different strain rates.

eq 6, to determine ⟨Lshish⟩. Figure 11b presents ⟨Lshish⟩ after being subjected to different strains and strain rates. ⟨Lshish⟩ increases with the increase of strain. For example, with strain of 2.0 at a strain rate of 25.1 s−1, ⟨Lshish⟩ is about 400 nm. By increasing strain to 3.5 at same strain rate, ⟨Lshish⟩ reaches about as long as 1000 nm.

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DISCUSSION Combining the results of in situ extension rheological and SAXS measurements during FIC of iPP at 140 °C, some 5482

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discussion on the fracture of polymer melt and the formation of precursors with strain beyond fracture strain, a schematic illustration on FIC is presented in Figure 12. Starting with an

with that at quiescent condition, which is about 2 orders smaller than the experimental result from half time of crystallization. This large discrepancy suggests that the microrheological model is not suitable in the “beyond fracture strain zone”, where different mechanism on the acceleration of nucleation may exist. As mentioned in the Introduction, the microrheological model consider a homogeneous flow, which does not take nonlinear rheological behaviors into consideration and restrict their application in linear rheological region like the “before fracture strain zone” here. To understand the strong acceleration of crystallization in the “beyond fracture strain zone”, we need first to answer why samples are possible to be stretched beyond fracture strain. Before discussing the observation in the “beyond fracture strain zone”, we first explain the fracture behavior of polymer melt under fast deformation, namely Wi = ε̇τd > 1. The interpretation of stress overshoot recently proposed by Wang’s group92,93 on entangled polymer liquid may help to explain this phenomenon. Polymer melt is considered as an entangled network, which follows a viscoelastic deformation with Wi = ε̇τd > 1. With strain larger than the stress overshoot point, the interchain locking force cannot hold the network and sliding of entanglement point occurs. Further increasing strain leads to unbalance between the cohesive force and stretching force from external driver or retraction force stored by molecules, which finally results in fracture of samples either directly by external stress or by internal stress due to retraction force. Note that for iPP material investigated here with large molecular weight distribution, delayed fracture rather than direct fracture is observed in the “fracture zone”. In other words, polymer melt held by its cohesive force can only sustain rather small strain during fast deformation without fracture if no any other structure emerges to hold the samples from tearing apart. This seems straightforward as under fast deformation polymer melt acts like solid, which cannot be deformed in large strain without necking or fracture. At this point, a paradox exists on the accelerating effect in FIC, rooted from the confliction between high strain rate and large strain. The criterion for FIC based on Weissenberg number Wi = ε̇τd > 1 requires high strain rate to prevent chain from relaxing, while high strain rate corresponds to small fracture strain (see Figure 4). Under the assumption of homogeneous flow it seems impossible for flow to accelerate crystallization kinetics in a large extent as this requires both high strain rate and large strain to be the necessary conditions, which however cannot be fulfilled due to the above paradox. The above paradox seems conflicting with experimental observations during the last 60 years, where acceleration of crystallization in orders of magnitude has been widely reported and confirmed by different groups. Untangling of this confliction may just lie in the answer for extension beyond fracture strain in this work. If the cohesive force is not strong enough to hold polymer melt from fracture, there should be other structures to keep its integrality when step extension with strain exceeds fracture strain. In other words, interchain organization has already been induced by flow during step extension, which may be crystal nuclei or precursors as generally assigned by the community. The occurrence of flow-induced precursors with strain beyond fracture strain is supported by the occurrence of strain hardening in the “beyond fracture strain zone” together with no detectable induction time of crystallization. Strain hardening in the “beyond fracture strain zone” directly reflects the formation of precursors, which act as physical cross-link and keep the network from being fractured. Combining the above

Figure 12. Flow induced nucleation model with strain before and beyond fracture strain. In part E, initial nuclei N0 moves to Nt during stretching, which leave trails as indicated with the dashed rectangle blocks. At the top and bottom sides of the dash rectangle blocks, the gray parts represent the daughter nuclei which form through the surface nucleation approach. Note that the daughter nuclei at top and bottom sides may merge together after their parent nuclei moving away and we leave the dash area there for better view on the trails.

entanglement network (Figure 12A), step extension leads to deformation of the network, where chains are either oriented or stretched (Figure 12B). As soon as strain reaches stress overshoot point, entanglement points start to slip, which finally leads to disentanglement of the network (Figure 12C). At this stage, if no interchain structures like precursors or nuclei form, sample will eventually fracture, which corresponds to the “fracture zone” (see Figure 4). The formation of flow-induced precursors or nuclei reinforce the fragile polymer melt with partially disentanglement, which ensures samples to sustain further deformation and eventually enter into the strain hardening zone (Figure 12D). The formation of precursors during step extension not only explains stretch beyond fracture strain with intact sample but also supports the strong accelerating effect in the “beyond fracture strain zone”. As discussed above, even large strain would be imposed on a homogeneous polymer melt, the accelerating effect on crystallization is still rather small with a strain of 2.0. The strong accelerating effect in the “beyond fracture strain zone” is due to structural flow with precursors. Further imposing flow after the formation of precursors may lead to two effects on accelerating crystallization, which can be named as self-acceleration. The approach I is that the point precursors or nuclei act like locks on chains (see Figure 12E, approach I). The locked chains possess slower relaxation time and prefer to be oriented or stretched, becoming prone to form nuclei due to lower nucleation barrier. The stretched chains between point nuclei N0−N0 in Figure 12E are sketched to demonstrate this effect on nucleation. Similar physical picture was suggested before by Zuidema,69 Seki,32 and Heeley52 et al., Zuidema emphasized the influence on the rheological relaxation time of cross-link, while Seki and Heeley emphasized the advantage of long chain or long branched chain being absorbed 5483

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on the point nuclei or precursors and inducing oriented segments for nucleation. Nevertheless if only conformational entropic effect is considered here, the accelerating effect is still small in the “beyond fracture strain zone”. The previous calculation with eq 7, does not take any relaxation into account and gives only 4.02 times increase of nucleation rate with a strain of 2.0. Moreover, if one chain is locked by one or two point precursors at its ends, the reduction of its conformational entropy will be limited with further increasing of strain, as the surrounding of the precursors is the partially disentangled melt, which cannot transfer strong stress to the locked chains. The approach II is surface or secondary nucleation, which is a combination of self-epitaxial nucleation mechanism and the effect of flow (Figure 12E, approach II). Starting with the physical picture described in Figure 12D with point nuclei or precursors, further stretching the sample leads to a relative displacement between these point nuclei or precursors and their surrounding chains. The movements of these nuclei leave their trails behind, which are illustrated as the space from N0 to Nt. The movements of point nuclei or precursors not only drive surrounding chains to be oriented, but also induce new nuclei along their trails through the initial point nuclei or precursors continuously move on. Taking the strain rate of 25.1 s−1 as an example, increasing strain by 1 unit takes about 40 ms for the point nuclei to move from N0 to Nt. In the extreme case where flow pushes nucleation barrier approaching to zero (homogeneous nucleation limit) and reduces activation energy of diffusion through orienting chain segment, the growth rate can reach the order of 1010 μm/s.94 Referring to homogeneous nucleation temperature at quiescent condition (∼60 °C), the growth rate estimated through extrapolation is on the order of 106 μm/s.95,96 Taking the growth of 106 μm/s, the stretching time of 40 ms allows to grow 4 × 107 nm. Considering that lateral size of critical nucleus is generally in the order of 10 nm, the movements of point nuclei or precursors in 40 ms can amplify nucleation by 106 times. Thus, though the initial point nuclei are moving along their trajectories, there is sufficient time for them to induce secondary nuclei during the moving process, which consequently create crowded nuclei along their trails behind. In this model, as the initial parent nuclei continue moving on and act dynamically, we call them as “ghost nuclei” or “ghost nucleation”. A question might be raised whether the daughter nuclei is detachable from initial parent nuclei or not. Computer simulation from Cacciuto and Frenkel indicates that the nuclei can break away from the heterogeneous seeds when they reach a critical size merely due to the presence of curved substrate in colloidal suspensions system.97 Even in polymer solids, crystal is easy to slip and be destroyed under tensile deformation.98 Thus, it is reasonable for daughter nuclei to be detached from parent nuclei during extension. Induced nucleation through homofiber in iPP melt can be considered as frozen “ghost nucleation”,99,100 where the parent nuclei states statically, while coupling solid interfaces like nucleation agent and filler which can be treated as pseudo “ghost nucleation”.101,102 In analogy, the shish observed in FIC is derived from movements of point nuclei, which indeed coincides with the emergence of the SAXS streak signal after strain entering the “beyond fracture strain zone” for iPP. The “ghost nucleation” mechanism proposed here can explain flow-induced orders increase of nucleation rate and observation on the growth of shish after cessation of flow, which is also consistent with recent experimental results that shish composes of not only long chains but also short ones.11

Determined by the circumstance and chemical structure of polymer chains, different mechanisms may exist for the formation of shish or row-nuclei, which are listed as followings. (i) For polymer chains in dilute solution, only fully stretched out or essentially unoriented random chains can exist. Here, the coil−stretch transition is generally accepted as the mechanism for shish formation.71 (ii) In concentrated solutions, flow induced phase separation plays a dominant role for shish formation, which is reported in PE solution.28 (iii) In PE melt, stretched network, instead of coil−stretch transition, is responsible to shish formation, which is demonstrated with rheo-SAXS measurements.29 (iv) Here in iPP melt, a “ghost nucleation” mechanism is more appropriate for shish formation, which can be generalized to other fillers or additives like carbon nanotube and fibers. As Keller proposed, two routes can be employed to obtain oriented products: (i) drawing an initially random crystalline solid and (ii) to orient chains in their random state (solution or melt) first and “set” this orientation by subsequent crystallization.103 The “ghost nucleation” mechanism origin from structural flow presented here is a hybrid of the two routes to attain orientation mentioned above, which is commonly occurred in real polymer processing. Coupling the “ghost nucleation” mechanism into continuum model may lead to a better prediction on polymer processing.

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CONCLUSION In summary, we combine the rheological technique and in situ SAXS to study FIC of iPP with systematical variation of strain and strain rate in flow parameter space. Weak and strong accelerations of crystallization accompanied by transition from point nuclei to shish after subjected to step extension strains coincide with the rheological behavior in before and beyond fracture strain zones, which are partitioned by the “fracture zone”. In the “before fracture strain zone”, the experimental result of acceleration of crystallization matches well with the prediction of microrheological model, whereas huge discrepancy exists between the theoretical prediction and experimental observation in the “beyond fracture strain zone”. On the basis of the rheological and structural information, we speculate that the strong acceleration effect in “beyond fracture strain zone” stems from the heterogeneity due to the formation of point nuclei or precursors during step extension. The occurrence of point nuclei or precursors leads to two effects of accelerating crystallization. (i) The point nuclei or precursors act as physical cross-link on chains which are incline to be oriented or stretched due to slow relaxation dynamics. (ii) The movements of point nuclei or precursors provide a dynamic template for surface or secondary nucleation, which generate daughter nuclei along their trails. The “ghost nucleation” mechanism proposed here offers a new interpretation for orders of acceleration of nucleation and for the formation of shish.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (51033004, 50973103, 51120135002), the Fund for One Hundred Talent Scientist of CAS, 973 program of MOST (2010CB934504). The research is also in 5484

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part supported by “the Fundamental Research Funds for the Central Universities” and the State Key Laboratory of Polymer Physic and Chemistry (Changchun Institute of Applied Chemistry, CAS). The experiment is partially carried out in National Synchrotron Radiation Lab (NSRL) and Shanghai Synchrotron Radiation Facility (SSRF). We would like to thank Sabic-Europe for providing iPP material and Prof. Shiqing Wang for assistance on SAOS measurements.

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(33) Somani, R. H.; Hsiao, S.; Nogales, A.; Srinivas, S.; Tsou, A. H.; Sics, I.; Balta-Calleja, F. J.; Ezquerra, T. A. Macromolecules 2000, 33, 9385−9394. (34) Yang, L.; Somani, R. H.; Sics, I.; Hsiao, B. S.; Kolb, R.; Fruitwala, H.; Ong, C. Macromolecules 2004, 37, 4845−4859. (35) Zuo, F.; Keum, J. K.; Yang, L.; Somani, R. H.; Hsiao, B. S. Macromolecules 2006, 39, 2209−2218. (36) Keum, J. K.; Zuo, F.; Hsiao, B. S. Macromolecules 2008, 41, 4766−4776. (37) Lagasse, R. R.; Maxwell, B. Polym. Eng. Sci. 1976, 16, 189−199. (38) Ogino, Y.; Fukushima, H.; Takahashi, N.; Matsuba, G.; Nishida, K.; Kanaya, T. Macromolecules 2006, 39, 7617−7625. (39) Kanaya, T.; Matsuba, G.; Ogino, Y.; Nishida, K.; Shimizu, H. M.; Shinohara, T.; Oku, T.; Suzuki, J.; Otomo, T. Macromolecules 2007, 40, 3650−3654. (40) Matsuba, G.; Sakamoto, S.; Ogino, Y.; Nishida, K.; Kanaya, T. Macromolecules 2007, 40, 7270−7275. (41) Elmoumni, A.; Gonzalez-Ruiz, R. A.; Coughlin, E. B.; Winter, H. H. Macromol. Chem. Phys. 2005, 206, 125−134. (42) Song, S. J.; Wu, P. Y.; Ye, M. X.; Feng, J. C.; Yang, Y. L. Polymer 2008, 49, 2964−2973. (43) Hashimoto, T.; Murase, H.; Ohta, Y. Macromolecules 2010, 43, 6542−6548. (44) Zhao, B. J.; Li, X. Y.; Huang, Y. J.; Cong, Y. H.; Ma, Z.; Shao, C. G.; An, H. N.; Yan, T. Z.; Li, L. B. Macromolecules 2009, 42, 1428− 1432. (45) Mackley, M. R.; Keller, A. Philos. Trans. R. Soc. 1975, 278, 29− 65. (46) Odell, J. A.; Keller, A.; Muller, A. J. Polymer 1985, 26, 1219− 1226. (47) Ito, H.; Minagawa, K.; Takimoto, J.; Tada, K.; Koyama, K. Int. Polym. Proc. 1996, 11, 363−368. (48) Janeschitz-Kriegl, H.; Eder, G. J. Macromol. Sci.-Chem. 1990, A27, 1733−1756. (49) Tanner, R. I. J. Non-Newtonian Fluid Mech. 2002, 102, 397−408. (50) Bove, L.; Nobile, M. R. Macromol. Symp. 2002, 185, 135−147. (51) Vleeshouwers, S.; Meijer, H. E. H. Rheol. Acta 1996, 35, 391− 399. (52) Heeley, E. L.; Fernyhough, C. M.; Graham, R. S.; Olmsted, P. D.; Inkson, N. J.; Embery, J.; Groves, D. J.; McLeish, T. C. B.; Morgovan, A. C.; Meneau, F.; Bras, W.; Ryan, A. J. Macromolecules 2006, 39, 5058−5071. (53) Lellinger, D.; Floudas, G.; Alig, I. Polymer 2003, 44, 5759−5769. (54) Zhu, P. W.; Edward, G. Macromolecules 2004, 37, 2658−2660. (55) Vleeshouwers, S.; Meijer, H. E. H. Rheol. Acta 1996, 35, 391− 399. (56) Mykhaylyk, O. O.; Chambon, P.; Graham, R. S.; Fairclough, P. A.; Olmsted, P. D.; Ryan, A. J. Macromolecules 2008, 41, 1901−1904. (57) Housmans, J. W.; Steenbakkers, R. J. A.; Roozemond, P. C.; Peters, G. W. M.; Meijer, H. E. H. Macromolecules 2009, 42, 5728− 5740. (58) D’Haese, M.; Mykhaylyk, O. O.; Puyvelde, P. V. Macromolecules 2011, 44, 1783−1787. (59) Martins, J. A.; Zhang, W. D.; Brito, A. M. Macromolecules 2006, 39, 7626−7634. (60) Acierno, S.; Palomba, B.; Winter, H. H.; Grizzuti, N. Rheol. Acta 2003, 42, 243−250. (61) Elmoumni, A.; Winter, H. H.; Waddon, A.; Fruitwala, H. Macromolecules 2003, 36, 6453−6461. (62) Somani, R. H.; Yang, L.; Hsiao, B. S.; Sun, T.; Pogodina, N. V.; Lustiger, A. Macromolecules 2005, 38, 1244−1255. (63) van Meerveld, J.; Peter, G. W. M.; Hutter, M. Rheol. Acta 2004, 44, 119−134. (64) Marrucci, G.; Grizzuti, N. J. Rheol. 1983, 27, 433−450. (65) Coppola, S.; Grizzuti, N.; Maffettone, L. P. Macromolecules 2001, 34, 5030−5036. (66) Doufas, A. K.; Dairanieh, I. S.; McHugh, A. J. J. Rheol. 1999, 43, 85−109.

REFERENCES

(1) Peterlin, A. Colloid Polym. Sci. 1987, 265, 357−382. (2) White, J. L.; Cakmak, M. Adv Polym Technol. 1986, 6, 295−337. (3) White, J. L.; Cakmak, M. Adv Polym Technol. 1988, 8, 27−61. (4) Choi, K. J.; Spruiell, J. E.; White, J. L. J. Polym. Sci., Polym. Phys. 1982, 20, 27−47. (5) Kumaraswamy, G.; Issaian, A. M.; Kornfield, J. A. Macromolecules 1999, 32, 7537−7547. (6) Kornfield, J. A.; Kumaraswamy, G.; Issaian, A. M. Ind. Eng. Chem. Res. 2002, 41, 6383−6392. (7) Janeschitz-Kriegl, H.; Ratajski, E.; Stadlbauer, M. Rheol. Acta 2003, 42, 355−364. (8) Li, L. B.; De Jeu, W. H. Adv. Polym. Sci. 2005, 181, 75−120. (9) Pennings, A. J.; Kiel, A. M. Kolloid-Z. Z. Polym. 1965, 20, 160− 162. (10) Somani, R. H.; Yang, L.; Zhu, L.; Hsiao, B. S. Polymer 2005, 46, 8587−8623. (11) Kimata, S.; Sakurai, T.; Nozue, Y.; Kasahara, T.; Yamaguchi, N.; Karino, T.; Shibayama, M.; Kornfield, J. A. Science 2007, 316, 1014− 1017. (12) Hsiao, B. S.; Yang, L.; Somani, R. H.; Avila-Orta, C. A.; Zhu, L. Phys. Rev. Lett. 2005, 94, 117802. (13) Somani, R. H.; Hsiao, B. S.; Nogales, A.; Fruitwala, H. A.; Srinivas, S.; Tsou, A. H. Macromolecules 2001, 34, 5902−5909. (14) Sun, X.; Li, H.; Wang, J.; Yan, S. Macromolecules 2006, 39, 8720−8726. (15) Somani, R. H.; Yang, L.; Hsiao, B. S.; Agarwal, P. K.; Fruitwala, H. A.; Tsou, A. H. Macromolecules 2002, 35, 9096−9104. (16) Li, L. B.; De Jeu, W. H. Macromolecules 2003, 36, 4862−4867. (17) Jerschow, P.; Janeschitz-Kriegl, H. Int. Polym. Process 1997, 12, 72−77. (18) Pogodina, N. V.; Lavrenko, V. P.; Winter, H. H.; Srinivas, S. Polymer 2001, 42, 9031−9043. (19) Balzano, L.; Kukalyekar, N.; Rastogi, S.; Peters, G. W. M.; Chadwick, J. C. Phys. Rev. Lett. 2008, 100, 048302. (20) Garcia Gutierrez, M.; Alfonso, G. C.; Riekel, C.; Azzurri, F. Macromolecules 2004, 37, 478−485. (21) Janeschitz-Kriegl, H.; Ratajski, E. Polymer 2005, 46, 3856−3870. (22) Balzano, L.; Rastogi, S.; Peters, G. W. M. Macromolecules 2009, 42, 2088−2092. (23) Azzurri, F.; Alfonso, G. C. Macromolecules 2008, 41, 1377−1383. (24) Janeschitz-Kriegl, H. Macromolecules 2006, 39, 4448−4454. (25) Geng, Y.; Wang, G. L.; Cong, Y. H.; Bai, L. G.; Li, L. B.; Yang, C. L. Macromolecules 2009, 42, 4751−4757. (26) Hayashi, Y.; Matsuba, G.; Zhao, Y. F.; Nishida, K.; Kanaya, T. Polymer 2009, 50, 2095−2103. (27) Cavallo, D.; Azzurri, F.; Balzano, L.; Funari, S. S.; Alfonso, G. C. Macromolecules 2010, 43, 9394−9400. (28) Murase, H.; Ohta, Y.; Hashimoto, T. Macromolecules 2011, 44, 7335−7350. (29) Yan, T. Z.; Zhao, B. J.; Cong, Y. H.; Fang, Y. Y.; Cheng, S. W.; Li, L. B.; Pan, G. Q.; Wang, Z. J.; Li, X. H.; Bian, F. G. Macromolecules 2010, 43, 602−605. (30) Azzurri, F.; Alfonso, G. C. Macromolecules 2005, 38, 1723−1728. (31) An, H. N.; Zhao, B. J.; Ma, Z.; Shao, C. G.; Wang, X.; Fang, Y. P.; Li, L. B.; Li, Z. M. Macromolecules 2007, 40, 4740−4743. (32) Seki, M.; Thurman, D. W.; Oberhauser, J. P.; Kornfield, J. A. Macromolecules 2002, 35, 2583−2594. 5485

dx.doi.org/10.1021/ma300338c | Macromolecules 2012, 45, 5477−5486

Macromolecules

Article

(67) van Meerveld, J.; Hutter, M.; Peters, G. W. M. J. Non-Newtonian Fluid Mech. 2008, 150, 177−195. (68) Custodio, F. J. M. F.; Steenbakkers, R. J. A.; Anderson, P. D.; Peters, G. W. M.; Meijer, H. E. H. Macromol. Theory Simul. 2009, 18, 469−494. (69) Zuidema, H.; Peters, G. W. M.; Meijer, H. E. H. Macromol. Theory Simul. 2001, 10, 447−460. (70) Tian, N.; Zhou, W. Q.; Cui, K. P.; Liu, Y. P.; Fang, Y. Y.; Wang, X.; Liu, L. B.; Li, L. B. Macromolecules 2011, 44, 7704−7712. (71) Keller, A. Kolnaar, H. W. H. Flow Induced Orientation and Structure Formation; VCH: New York, 1997; Vol. 18. (72) Smook, J.; Pennings, A. J. J. Mater. Sci. 1984, 19, 31−43. (73) Li, Z. M.; Li, L. B.; Shen, K. Z.; Yang, W.; Huang, R.; Yang, M. B. Macromol. Rapid Commun. 2004, 25, 553−558. (74) Zhong, G. J.; Li, L. B.; Mendes, E.; Byelov, D.; Fu, Q.; Li, Z. M. Macromolecules 2006, 39, 6771−6775. (75) Chen, Y. H.; Zhong, G. J.; Lei, J.; Li, Z, M.; Hisao, B. S. Macromolecules 2011, 44, 8080−8092. (76) Xu, J. Z.; Chen, C.; Wang, Y.; Tang, H.; Li, Z. M.; Hsiao, B. S. Macromolecules 2011, 44, 2882−2818. (77) Haggenmueller, R.; Fischer, J. E.; Winey, K. I. Macromolecules 2006, 39, 2964−2971. (78) Byelov, D.; Panine, P.; Remerie, K.; Biemond, E.; Alfonso, G. C.; De Jeu, W. H. Polymer 2008, 49, 3076−3083. (79) D’Haese, M.; Van Puyvelde, P.; Langouche, F. Macromolecules 2010, 43, 2933−2941. (80) Phillips, A. W.; Bhatia, A.; Zhu, P. W.; Esward, G. Macromolecules 2011, 44, 3517−3528. (81) Hwang, W. R.; Peters, G. W. M.; Hulsen, M. A.; Meijer, H. E. H. Macromolecules 2006, 39, 8389−8398. (82) Tapadia, P.; Ravindranath, S.; Wang, S. Q. Phys. Rev. Lett. 2006, 96, 196001. (83) Fang, Y. Y.; Wang, G. L.; Tian, N.; Wang, X.; Zhu, X. Y.; Lin, P. P.; Ma, G. L.; Li, L. B. J. Rheol. 2011, 55, 939−949. (84) Mitchell, J. C.; Meier, D. J. J. Polym. Sci: Part A-2. 1968, 6, 1689−1703. (85) Hammersley, A. P., FIT2D V9.129 Reference manual v3.1, ESRF report 98HA01T, 1998. (86) Avrami, M. J. Chem. Phys. 1939, 7, 1103−1112. (87) Avrami, M. J. Chem. Phys. 1940, 8, 212−224. (88) Avrami, M. J. Chem. Phys. 1941, 9, 177−184. (89) Yoo, C. S.; Nicol, M. J. Phys. Chem. 1986, 90, 6732−6736. (90) Ruland, W.; Perret, R. J. Appl. Crystallogr. 1970, 3, 525−532. (91) Rubinstein, M.; Colby, R. H. Polymer Physics: Oxford University Press: London, 2003; p 371. (92) Wang, S. Q.; Ravindranath, S.; Wang, Y. Y.; Boukany, P. J. Chem. Phys. 2007, 127, 064903. (93) Wang, Y. Y.; Wang, S. Q. J. Rheol. 2008, 52, 1275−1290. (94) Pantani, R.; Coccorullo, I.; Volpe, V.; Titomanlio, G. Macromolecules 2010, 43, 9030−9038. (95) Janimak, J. J.; Cheng, S. Z. D.; Giusti, P. A.; Hsieh, E. T. Macromolecules 1991, 24, 2253−2260. (96) Xu, J. N.; Srinivas, S.; Marand, H.; Agarwal, P. Macromolecules 1998, 31, 8230−8242. (97) Cacciuto, A.; Auer, S.; Frenkel, D. Nature 2004, 428, 404−406. (98) Bowden, P. B.; Young, R. J. J. Mater. Sci. 1974, 9, 2034−2051. (99) Sun, X. L.; Li, H. H.; Zhang, X. Q.; Wang, D. J.; Schultz, J. M.; Yan, S. Macromolecules 2010, 43, 561−564. (100) Li, H. H.; Yan, S. K. Macromolecules 2011, 44, 417−428. (101) Balzano, L.; Rastogi, S.; Peters, G. W. M. Macromolecules 2008, 41, 399−408. (102) Nogales, A.; Mitchell, G. R.; Vaughan, A. S. Macromolecules 2003, 36, 4898−4906. (103) Keller, A.; Kolnaar, J. W. H. Prog. Colloid Polym. Sci. 1993, 92, 81−102.

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