Short-Term Flow Induced Crystallization in Isotactic Polypropylene

Nov 22, 2013 - Short-Term Flow Induced Crystallization in Isotactic Polypropylene: How Short Is Short? Zhe Ma,. †,‡. Luigi Balzano,. †,‡,∥. ...
0 downloads 5 Views 5MB Size
Download PDF
Article pubs.acs.org/Macromolecules

Short-Term Flow Induced Crystallization in Isotactic Polypropylene: How Short Is Short? Zhe Ma,†,‡ Luigi Balzano,†,‡,∥ Tim van Erp,† Giuseppe Portale,‡,§ and Gerrit W. M. Peters*,†,‡ †

Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600MB, Eindhoven, The Netherlands Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands § DUBBLE CRG/ESRF, Netherlands Organization for Scientific Research (NWO), c/o ESRF BP 220, F-38043, Grenoble Cedex, France ‡

S Supporting Information *

ABSTRACT: The so-called “short-term flow” protocol is widely applied in experimental flow-induced crystallization studies on polymers in order to separate the nucleation and subsequent growth processes [Liedauer et al. Int. Polym. Proc. 1993, 8, 236− 244]. The basis of this protocol is the assumption that structure development during flow can be minimized and the rheological behavior, i.e., the viscosity, does not change noticeably. In this work we explore the validity of this assumption for short but strong flows and reveal the structure formation during the early stages of crystallization. Viscosity and structure evolution of an isotactic polypropylene (iPP, Mw ≈ 365 kg/mol and Mw/Mn = 5.4) melt at 145 °C are measured during the short-flow period (0.2−0.25 s) using the combination of a slit rheometer and fast X-ray scattering measurements. For high enough (apparent) shear rates (≥240 s−1) a viscosity rise during flow is observed; i.e., the condition for “short-term flow” is not satisfied. With a time delay with respect to the viscosity rise, the development of shish is observed at a position halfway the length of slit, along the flow direction, by means of ultrafast time-resolved SAXS measurements. Depending on the shear rate, these shish are detected during (shear rates ≥ 400 s−1) or after flow (240 s−1 ≤ shear rates < 400 s−1). For even lower shear rates of 160 and 80 s−1, the viscosity does not change significantly, and instead of shish, oriented row nuclei (X-ray undetectable) are generated. These two shear conditions qualify as short-term flow. A full understanding of the coupled flow and crystallization phenomena requires that the transient and nonhomogeneous behaviors, both in flow and in flow gradient direction, have to be taken into account. This can only be done by a full numerical model, and therefore, the results presented in this paper also provide a valuable data set for future numerical studies. the flow.8,9 When crystals nucleate and subsequently grow, the viscosity and the modulus of the melt increase, and this enhances the effect of flow on crystallization under constant deformation rate, giving rise to a self-accelerating mechanism. To simplify this kind of experiment, Janeschitz-Kriegl and coworkers proposed a “short-term shearing ” protocol,10 where the shear duration is chosen short enough so that during flow the effects of crystallization on viscosity and structure changes are minimized. It is assumed that only nuclei or their precursors are created during flow and that these structures crystallize and grow after the flow ceases. In this way, the features of flowinduced nuclei are revealed indirectly by studying the resulting crystallization kinetics and morphology. This “short-term flow” has been widely used in studies on flow-induced crystallization in order to separate the nucleation and growth processes.10−19

1. INTRODUCTION Semicrystalline polymers, especially polyethylene (PE) and isotactic polypropylene (iPP), are widely used materials because of their low cost, easy processing, good chemical resistance, etc. These materials are most often processed in the molten state and therefore subjected to (strong) flow fields when shaped into final products. It is well-known that these flow fields not only can accelerate crystallization kinetics by orders of magnitude but also can radically change the crystalline morphology from isotropic spherulites to highly oriented shishkebab crystals. Such a morphological transition is important since these building blocks determine the final (mechanical and other) properties of products.1,2 Therefore, a full understanding of the relation between flow fields, crystallization kinetics, and the resulting morphology is required to design processing procedures for optimal properties. Initial studies on flow-induced crystallization of polymer melts focused on the structure evolution during continuous flow fields.3−7 Crystallization of polymers is governed by nucleation and growth, and both processes are influenced by © 2013 American Chemical Society

Received: September 3, 2013 Revised: November 17, 2013 Published: November 22, 2013 9249

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

Figure 1. Combined in-situ synchrotron X-ray scattering and slit rheometer.

applied (168 and 173 °C).30 On the other hand, density fluctuations were observed during extrusion of iPP31 and this was interpreted as a process where crystallization is preceded by spinodal-assisted phase separation enhanced by flow.32 Balzano et al.17 found, using a polyethylene (PE), shear-induced “bundles” generated by flow, in line with a more classical view on crystallization. They suggested that the bundle dimensions determine the subsequent evolution of crystallization or relaxation. Obviously, a variety of interpretations exist for the structures generated by flow. The current understanding on shear-induced crystallization, especially concerning the initial stage during flow, is not yet clear enough to give conclusive answers to the above questions. The present study focuses on viscosity changes (other than the normal transient response of a start-up flow) and structure formation during short-term shear flow (maximum 0.25 s) and explores the flow strength dependency of these events. For this purpose, a slit rheometer and fast X-ray scattering measurements are combined to achieve a time resolution sufficient to resolve the phenomena studied.

Based on the assumption that the viscosity is not changed, the effect of the flow can be characterized by using flow characteristics and rheological properties. For instance, the mechanical work16,20−23 w=

∫0

ts

η[γ(̇ t )]γ 2̇ (t ) dt

(1)

with the shear rate, γ̇(t), shear rate dependent viscosity, η[γ̇(t)], and the shear time, ts, is often considered as the controlling factor in flow-enhanced nucleation24 and formation of oriented structures.16,18,20 The shear rate dependent viscosity η[γ̇(t)] is obtained separately from standard rheological measurements.16 When a constant shear rate is applied and the transient behavior of the shear stress at start-up of flow is negligible when compared with the relatively long-time flow, the specific work integral can be simplified into w = η(γ̇)γ̇2ts with the steady state viscosity η(γ̇) only depending on the shear rate.20,22 In more recent work25−27 fast, time-resolved experimental methods were used to investigate structure development, also during the flow pulse, for conditions where the stretch of high molecular weight tail is large, e.g., the condition for flowenhanced nucleation and generating oriented structures. Kumaraswamy et al.25 performed slit-flow experiments with constant wall stress (0.06 MPa) and attributed the observed unusual upturn in birefringence to the generation of long-lived oriented structures. Balzano et al.27 observed the appearance of wide-angle X-ray diffraction peaks during flows shorter than 1 s, indicating the formation of crystalline structures. These evidence imply that the “short-term flow” protocols employed were not always short to prevent structure formation, even though the shear time is much less than the characteristic crystallization time. These findings raise questions concerning short-term flow; can viscosity change during flow? If so, under what conditions and how fast, and finally, what is the relation between a viscosity change and structure formation in these early stages? However, the early stages of shear-induced crystallization, from a structural point of view, are still under debate. It has been proposed that so-called dormant nuclei already preexist in the amorphous melt and are activated by flow to trigger crystallization.28,29 The unusual birefringence upturn observed by Kumaraswamy et al.25,26 during flow experiments on an iPP points toward the formation of “shear-induced oriented structures”.25 However, X-ray scattering measurements could not resolve these structures at the relatively high temperatures

2. EXPERIMENTAL SECTION 2.1. Material. The material used in this work is a commercial isotactic polypropylene (iPP) homopolymer (HD601CF) provided by Borealis GmbH, Austria. This iPP has a weight-average molecular mass Mw ≈ 365 kg/mol and a polydispersity of Mw/Mn = 5.4. Its nominal melting and crystallization temperatures are 163 and 113 °C, respectively.18 A full characterization of the crystallization kinetics of this grade, for both quiescent and flow-enhanced, can be found in the literature.18,33−35 For sample preparation, the material was first compression molded at 220 °C to plates with thickness of 1.5 mm. Next, strips were machined of H × W × Ltot = 1.5 × 6 × 200 mm3 that fit in the slit flow cell. 2.2. Methods. The slit flow cell is operated on a multipass rheometer.36 The specimen is confined between two servo-hydraulically driven rectangular pistons that fit tightly in the slit (see Figure 1). When pistons move together in one direction, they impose a shear field to the polymer melt. The top and bottom barrels are equipped with pressure transducers (distance between the transducers L = 160 mm) to measure the pressure history in the slit during flow. The pressure difference ΔP is used to determine the apparent viscosity. A pair of diamond windows placed in the middle of the flow cell allows for in-situ X-ray characterization during and after flow. The polymer in the slit is first heated to 220 °C and annealed for 10 min in order to erase the sample preparation history. Next, it is cooled to 145 °C and pressurized to 50 bar by moving the pistons toward each other. During cooling, the reference pressure of 50 bar is kept on 9250

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

where az is the azimuthal angle and q is the norm of the scattering vector. The scattering vector q is defined as q = (4π sin θ)/λ with the scattering angle 2θ and the wavelength λ of the X-rays. The shear rate in the a slit flow varies along the thickness direction,37 and this inhomogeneous flow leads to an inhomogeneous crystallization process along the thickness direction. Consequently, the X-ray observation is an average over the thickness. The current work focuses on the earliest stage of crystallization during flow, i.e., the first appearance of shish and the first observation of a viscosity change. For flow-induced crystallization, strongly depending on the flow strength, the first observations (X-ray signal or rise of pressure difference) are related to crystallization at the wall, where the shear rate and stress are highest. Therefore, the term “short-term flow” actually relates to the outermost wall layer, where the flow strength is determined by the wall shear rate instead of the average shear rate. Moreover, the results in section 4.1 will show that the flow is also inhomogeneous in the flow direction, while the X-ray measurements are done at one specific position, i.e., a position halfway the length of slit, along the flow direction, where the X-ray windows are mounted (see Figure 1). Optical microscopy was used to visualize the morphology over the sample thickness direction and to determine the thickness of final shear layers at different positions in the slit. Cross sections 5 μm thick were prepared at a low temperature (approximately −20 °C) using a microtone (Leica RM2165) equipped with a glass knife. Two crossed polarizers are rotated to ±45° with respect to the flow direction, and optical micrographs were taken with an Axioplan imaging-2 microscope combined with an AxioCam camera. The AxioVision software was used to analyze the micrographs and determine the shear layer thickness.

the sample to prevent shrinkage holes. The sample is then sheared and subsequently isothermally crystallized at 145 °C. To avoid fluctuations, the temperature of the cell is stabilized by means of an oil bath. On the other hand, the top and bottom barrels are always kept at high temperature (220 °C) to ensure proper functioning of the pressure transducers. After isothermal crystallization, the slit is cooled to room temperature and the sample is removed for ex-situ analysis. The flow strength was varied by choosing piston speeds, Vpiston, from 20 to 140 mm/s, and the apparent wall shear rate is calculated by37 γ̇ =

6Q WH2

(2)

where Q is the volumetric flow rate (Q = H × W × Vpiston), W is the slit width (6 mm), and H is the slit thickness (1.5 mm). From the viscosity function for this material the real velocity profile can be calculated, and from this, the real maximum shear rate can be obtained as well. These values are given in the Supporting Information. Here, we will use the apparent values to classify the different flows. The corresponding apparent wall shear rates range from 80 up to 560 s−1 (real shear rates range from 117 to 916 s−1). The shear duration is fixed at 0.25 s for apparent shear rates from 80 to 400 s−1 and shortened to 0.23 and 0.20 s for 480 and 560 s−1, respectively, due to limitations in the piston displacement. The wall shear stress and the corresponding apparent viscosity are given by σ=

H ΔP 2(1 + H /W )L

(3)

η=

σ H2 ΔP = γ̇ 12(1 + H /W )L Vpiston

(4)

3. RESULTS 3.1. Rheological Evolution during Flow. Figure 3a shows the evolution of the pressure difference ΔP between the transducers during flow. This pressure difference scales directly with the wall stress and thus with the apparent viscosity (according to eq 4; see Figure 3b). The apparent viscosity is an average over the material in the flow channel between the two pressure transducers. First of all, Figure 3a clearly shows the expected time dependent pressure rise. Considering this, the apparent wall shear rate seems more suitable to characterize the strength of flow field than the shear stress which significantly evolves with time. Second, different behavior is observed with increasing flow strength; two distinct responses can be distinguished for shear rates ≤160 s−1 and shear rates ≥240 s−1. For relatively low shear rates of 80 and 160 s−1, the pressure difference ΔP first shows an overshoot, then decreases, and eventually approaches a steady-state level. This nonlinear rheological behavior is typical for polymer melts subjected to start-up shear flows with a constant shear rate.37 For shear rates ≥240 s−1, the trend of ΔP becomes different; after the overshoot, ΔP increases with time rather than leveling off. With increasing shear rate, this upturn takes place at shorter times and the time evolution becomes steeper. Such an unusual trend of ΔP indicates that during flow viscosity changes due to formation of new structures associated with crystallization. It is clear that depending on flow strength, viscosity can deviate from the typical melt behavior during short-term flow with shear times as short as 0.25 s when apparent wall shear rate exceeds a critical threshold that lies between 160 and 240 s−1. When we recall the basic assumption of “short-term” flow that viscosity does not change during flow, it is obvious that whether the flow is sufficiently short or not depends on the flow strength. Notice that this 160−240 s−1 threshold relates to the specific shear duration of maximum 0.25 s used in our

Both small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD) were employed to characterize the flow-induced structures. Synchrotron X-ray measurements were carried out at the Dutch-Belgian (DUBBLE) beamline BM26B of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France.38,39 The wavelength used was 1.033 Å. Fast acquisitions of SAXS and WAXD were performed with a Pilatus 1M detector and a Pilatus 300K detector, respectively. These ultrafast measurements are carried out with an acquisition rate of 30 frame/s and last for 1 s. Both detectors are triggered by the start of piston movement. The Pilatus 1M detector (981 × 1043 pixels of 172 μm × 172 μm) was placed at a distance of 7.117 m and used for SAXS; the Pilatus 300K detector (1475 × 195 pixels of 172 μm × 172 μm) was placed at a distance of 0.240 m and used for collecting the equatorial part of WAXD images. Figure 2 shows a typical SAXS pattern (so-called streaks), which is the result of a highly oriented structure. The appearance of such

Figure 2. A typical SAXS pattern with equatorial streaks. The integrating region for determination of the equatorial intensity ISAXS is indicated. Flow direction is vertical. streaks means that the structure formed has an electron density which is different from its surroundings. Their equatorial distribution implies that the maximum density contrast is perpendicular to the flow direction; i.e., these fibrillar objects are oriented along the (vertical) flow direction. To describe the evolution of these SAXS streaks, we define a SAXS equatorial intensity ISAXS integrated over the specific equatorial region: 0.2

ISAXS =

10 °

∫0.018 ∫−10° I(az , q) daz dq

(5) 9251

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

Figure 3. (a) Pressure difference ΔP evolution during flow for different apparent wall shear rates. For shear rates of 560 and 480 s−1, some pressure data points are missing just before flow cessation. These points were extrapolated with a linear function and indicated by the dashed line. The kink in the slope (dΔP/dtime) at very short times (t < 0.02 s) is an artifact due to a small deviation of the piston movement during startup. (b) The corresponding transient apparent viscosities (see eq 4).

experiments. For prolonged shear duration, the threshold shear rate will be of course different. Figure 3b also shows that for weak flows (80 and 160 s−1) the viscosity does not reach the steady-state value. Since for the strong flows (≥240 s−1) the viscosity is changing during the whole period of flow, using “work” to characterize the strength of short flow should be done with precaution. The next question is, what kind of structure is able to change the rheology-related behavior of a polymer melt? Two examples25,40 from the literature that report a deviation from the “normal” rheological behavior during flow are briefly discussed. Scelsi et al.40 found for a high-density polyethylene flowing through a contraction (apparent wall shear rate ≈ 200 s−1, shear time = 2 s at 130 °C) a buildup of ΔP similar to our results presented in Figure 3. They associated this pressure buildup to a growing crystalline layer in the slit after the contraction. Using an iPP (Mw ≈ 300 kg/mol and Mw/Mn ≈ 6−8), Kumaraswamy et al.25 observed a birefringence upturn (which is proportional to the stress) during flow at constant pressure, different from the typical melt rheology, and attributed it to the formation of a “highly oriented structure”. These “highly oriented structures” were studied with in-situ WAXD.30 A correlation between these structures and successive crystal formation was found for relatively low temperatures (141 and 163 °C) only but not for high temperatures (168 and 173 °C). This means that the “highly oriented structure” could be noncrystalline. Therefore, the origin of the deviations (viscosity and birefringence) from the amorphous melt behavior remains unclear. On the other hand, the absence of a viscosity rise during the short flow period at shear rates of 80 and 160 s−1 in our experiments does not mean that flow-induced structures are absent. To reveal the structural evolution during strong flows (shear rates ≥240 s−1) and probe the potential precursors developing in weaker flows (shear rates ≤160 s−1), structural investigations using X-ray scattering were carried out. 3.2. Structural Evolution. The X-ray measurements were done at the slit center of the flow channel (see Figure 1). Illustrative SAXS and WAXD patterns of ultrafast measurements collected during and just after flow, for a shear rate of 400 s−1, are shown in Figure 4. Interestingly, after 0.23 s, starting from the beginning of flow, the SAXS equatorial streaks and WAXD (110) diffraction of monoclinic α-form crystal are

Figure 4. SAXS and WAXD patterns during and just after flow; γ̇ = 400 s−1 and tflow = 0.25 s. Time is accurate to two decimals. Images acquired after flow indicated by time in red. Flow direction is vertical.

observed simultaneously. The SAXS equatorial streaks are associated with the formation of densely packed fibrils oriented in the flow direction. The simultaneous appearance of SAXS streaks and WAXD diffraction suggests that these fibrils are already (partially) crystalline and, therefore, considered as crystalline shish. To further illustrate the differences in terms of the structure formation between relatively strong flows (γ̇ ≥ 240 s−1), the SAXS results for shear rates above and below 400 s−1 (i.e., 560 and 320 s−1) are shown in detail in Figure 5. We do not show WAXD results since the shish formed at 320 and 560 s−1 are also crystalline (a detailed evolution of the crystallization will be presented in a following paper). For the wall shear rate γ̇ = 560 s−1 the SAXS streaks appear at 0.17 s, which is again within the flow period of 0.2 s, while for the wall shear rate γ̇ = 320 s−1 the equatorial streaks appear at 0.33 s, i.e., after cessation of flow. Clearly, flow strength determines the structure formation time. For a flow duration of 0.25 s, the first threshold shear rate for SAXS and/or WAXD observable structure formation exists between 400 and 320 s−1, above which crystalline shish are formed during flow; i.e., for shear rates above the threshold shear rate, the flow duration is not sufficiently short anymore from a structural point of view. Flow has the remarkable effect of generating structures since it effectively orients and stretches polymer chains. Molecules change their conformations and, for iPP, form ordered units of 31 helices.15,41 The equilibrium melting temperature is 9252

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

of (oriented) precursors during flow cannot be excluded. Therefore, the WAXD diffraction patterns after isothermally crystallizing for 1000 s are presented for the two weakest flows (see Figure 7). For both conditions, the (040) diffraction is

Figure 5. SAXS patterns for flow rates of 560 and 320 s−1. Time is accurate to two decimals; images acquired after flow indicated by the time in red. Flow direction is vertical. The slightly higher intensity left and right of the beam stop for 0.13 s at 560 s−1 and 0.27 s at 320 s−1 is due to the beam itself; they do not correspond to an equatorial SAXS streak signal (illustrated in the Supporting Information). Figure 7. 2D WAXD patterns of isothermal crystallization at 1000 s after flow pulses at shear rate (a) 160 s−1 and (b) 80 s−1. Flow direction is vertical.

increased due to the decreased entropy,42 providing an additional thermodynamic driving force (undercooling) for crystallization.43 Oriented and stretched molecular segments are also more close to their ordered state as in nuclei and crystals.43 Therefore, the kinetic barrier of transforming the chain segments from random coils into ordered structures is lowered. The consequence is the formation of locally ordered aggregates, or precursors, which can be considered as the cradle for nuclei and/or shish. The specific enhancement of nucleation rate and growth rate are both strongly dependent on the flow strength. Consequently, the formation time of shish decreases with increasing shear rate, as shown by Figures 4 and 5. On other hand, the above considerations imply also that no shish is created for too weak flows. To explore whether or not shish can be formed depending on flow strength, the SAXS patterns after 1 s, i.e., the entire ultrafast measurement including the flow period, for all shear rates are shown in Figure 6. Equatorial streaks are observed only for shear rates

mainly distributed at the equatorial region, implying that crystals are oriented, and this anisotropy finds its origin in oriented structures generated by the flow. From this, we conclude that the two weak flows generate oriented precursors, and instead of shish, they develop into oriented nuclei undetectable by X-ray. These precursors do not change the rheology during flow. These results are consistent with the finding of Janeschitz-Kriegl et al.24,44,45 that the shear-induced objects have no noticeable influence on the rheology of melt, which was the basis for the introduction and availability of “short-term flow”. 3.3. Onset of Rheological and Structural Changes. The threshold flow strength and the formation time for crystalline shish are known. The formation of shish may affect the rheological behavior and thus contribute to the deviation of ΔP from a normal meltlike behavior. However, it also might be that a nonobservable structure first changes the viscosity and then develop into shish. The relation between the onset of shish and ΔP is illustrated by first examining the experiment with wall shear rate of 400 s−1. In this experiment, the ΔP upturn time occurs at ∼0.1 s (see Figure 8a). As shown in Figure 8b, ISAXS initially fluctuates around 0.04 but at ∼0.2 s, with the onset of the streaks, starts to rise, and this continues after cessation of the flow. Clearly, the time required to form an amount of shish sufficient to produce a noticeable increase of ISAXS is longer than the time for the ΔP upturn. From this distinct difference in onset times it seems that the apparent viscosity rise (averaged over the 160 mm sample between pressure transducers) does not result directly from shish formation in the slit center (X-ray observation window). There are two possible reasons for the pressure upswing prior to shish observation: (a) the specif ic precursors for shish are SAXS invisible, or (b) shish is f irst created at another (upstream) location in the slit instead of the center equipped with X-ray diamond windows. All results of the ΔP upturn time and the shish onset time are summarized in Figure 9. The SAXS streaks for a wall shear rate of 240 s−1 do appear after flow (see Figure 6), but it is hard to determine the precise onset time for these streaks. The results in Figure 9 show that depending on the shear strength, structure development can occur during or after flow. Summarizing the above rheological and X-ray scattering results: For the applied short-flow conditions two critical apparent wall shear rates are foundone for the deviation of

Figure 6. 2D SAXS pattern at t = 1 s for different shear rates. To improve the signal-to-noise ratio, the patterns of 240, 160, and 80 s−1 were averaged over 10 frames (between 0.67 and 1 s). Flow direction is vertical. The slightly higher intensity left and right of the beam stop for 160 and 80 s−1 is due to the beam itself; they do not correspond to an equatorial SAXS streak signal (illustrated in the Supporting Information).

equal to or above 240 s−1. For shear rates of 160 and 80 s−1, no shish was observed within the ultrafast acquisition lasting 1s (see Figure 6) nor during the subsequent isothermal crystallization (data not shown). A second threshold shear rate is found between 160 and 240 s−1, above which shish can be formed (either during or after flow). This threshold is consistent with the appearance of the viscosity rise during flow as shown in Figure 3. Although neither a viscosity upturn nor shish appearance is found for the low shear rates of 80 and 160 s−1, the generation 9253

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

Figure 8. (a) ΔP evolution during flow and (b) SAXS equatorial intensity during and just after flow. Lines are drawn to guide the eyes. The shear rate is 400 s−1, and the flow duration is 0.25 s.

appearance of shish at the center of the slit where the SAXS is measured. This suggests that the viscosity rise is caused by formation of crystals (or their X-ray undetectable precursors) at an upstream position, before actual scattering objects are formed in the center of the slit.

4. DISCUSSION For short flows of 0.2−0.25 s, when the wall shear rate is high enough (≥240 s−1) both a viscosity rise and shish formation are observed. The viscosity rise and the shish formation are not observed at the same time; unexpectedly, the former is observed first. This implies that prior to shish appearance in the center of the slit, where the SAXS observations are made, some structures have already formed in the flow channel, and they increase the average apparent viscosity. The reason that these structures are not observed with SAXS can be twofold: (a) the density contrast (or concentration) is too low to be detected, and (b) viscosity rise is caused at a location different from the SAXS observation window, i.e., the structure formation is not homogeneous over the slit length. Structure formation may first occur upstream, where the pressure is the highest. Especially the second possibility implies that the interpretation of the delay in occurrence of shish with respect to the viscosity rise should be considered with caution. No strong statements can be made about “case a” unless we can exclude “case b”. In the following we will first discuss the evidence of “case b” and then the possibility of “case a” without excluding “case b”.

Figure 9. Onset times for ΔP rise and occurrence of the SAXS streaks for different shear rates. The gray region indicates the flow period for various apparent shear rates. Onset time for SAXS streaks at a shear rate of 240 s−1 cannot be determined accurately.

the rheological behavior from the expected meltlike behavior and one for shish formation, respectively. For the iPP used in this work, and at a temperature of 145 °C, this critical value lies between 160 and 240 s−1. When shear rate is beyond this threshold, the viscosity rises during flow, lasting only 0.2−0.25 s, indicating that these short-term flows are not short enough from the rheological point of view. Another critical shear rate threshold is between 320 and 400 s−1 for which shish occur during flow. In this case, the short durations are even not sufficiently short from a structural point of view. The rise of the average viscosity is followed by

Figure 10. Optical microscopy pictures of cross sections of samples along the flow direction for an apparent shear rate of 240 s−1. The sample positions are illustrated by the top drawing, and the corresponding images are viewed between two polarizers at ±45°. The scale bar is 0.2 mm. 9254

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

the differences between flow-enhanced nucleation and shish generation at different locations in the slit. For this purpose, the “nucleation and growth model”47 is applied with the parameters values for this iPP grade as determined by van Erp et al.34,35 In that work the flow enhanced nucleation rate and the longitudinal growth rate of oriented nuclei were determined for a range of temperatures, pressures, and shear histories, using extended dilatometry. Only the pressure difference before the pressure upswing occurs is of importance, since temperature and flow histories are practically the same during that period in most of the slit. With a pressure difference of 100 bar (estimated form the results in Figure 3) between the center and the upstream position, it can be estimated (details given in the Supporting Information) that the flow-induced nucleation rate might be slightly larger (20%), but the nuclei growth rate is considerably enhanced (200%). From this we conclude that indeed the pressure gradient has a significant influence on crystallization in such pressure-driven slit flow, and as a consequence, structure formation is not homogeneous over the slit length and shish will occur upstream first where the pressure is highest A much stronger nonlinear coupling between the viscosity rise and the flow-enhanced crystallization may happen for more severe flows. For the extreme case (apparent shear rate = 560 s−1, shear time = 0.2 s) the resulting morphology distribution along the flow direction is shown in Figure 12. The shear layers appear at all positions but are much thicker than those formed for an apparent shear rate of 240 s−1 (see Figure 10). Qualitatively speaking, and although the shear time is slightly shorter, this is caused by the much higher shear rate of 560 s−1. Notice that for the positions 2, 3, and 4, which are all three in or close to the slit middle region, a gradient in shear layer thickness is clearly visible (average coverage of the shear layers at these positions: 92%, 87%, and 84%). Moreover, a huge difference between the middle position 3 and the downstream position 5 is present. With a pressure difference of 200 bar (see Figure 3), flow-induced nucleation rate and growth rate are increased by 40% and 900%, respectively; i.e., the pressure effects are dramatically increased compared to the case with a shear rate of 240 s−1. Concluding, there is definitely an influence of the location in the slit and structure formation most probably will occur first upstream. Again, this coupling effect will not be quantitatively discussed here since it is too complex without numerical simulation tools, which is out of the scope of this work. 4.2. Conditions of the Viscosity Rise. Although the structural reason for viscosity rise is not fully clear yet, we consider it still to be valuable to examine the conditions for this crystallization-related structure, capable of changing the viscosity. It is normally thought that flow-induced crystallization is determined by the high molecular weight (HMW) tail.49 To illustrate the flow strength dependence of deforming the HMW tail, two characteristic Weissenberg numbers are defined:50 Wio = γ̇τrep, which is related to molecular orientation, and Wis = γ̇τRouse, which is related to molecular stretch. τrep and τRouse are the reptation and Rouse times of the HMW tail, respectively. At 145 °C, the relaxation times τrep and τRouse for the iPP used in this work are 48 and 0.23 s, respectively.18 The values of Weissenberg numbers for the different flows are summarized in Table 1, which shows Wio > 103 while Wis > 10 for all shear rates. This means that all shear rates applied can effectively orient the contour path along the flow direction and stretch molecular

4.1. Nonhomogeneous Crystallization inside the Flow Channel. The choice of a slit geometry has the advantages of allowing for very high shear rates and pressurizing the sample (preventing shrinkage holes) but, at the same time, brings some complications. The pressure gradient, which reaches 100−1000 bar (see Figure 3), causes large differences in thermodynamic properties. High (upstream) pressures will not only shift the equilibrium melting temperature but also change the viscosity, change the (longitudinal) lamellar growth rate and can cause pressure-induced nucleation. As a consequence, the pressure will influence the (flow induced) crystallization kinetics. The coupling between these variables is highly nonlinear. Only with a full numerical model46−48 can the interplay between all these material functions be investigated quantitatively. Here, we will discuss the influence of a pressure gradient on flow-induced crystallization in a qualitative way only. For this purpose, the morphology of the sample subjected to the flow at an apparent wall shear rate of 240 s−1, the shear rate at which the extra pressure upswing occurs is examined along the flowing direction. Ex-situ micrographs of the structure distribution along the flow direction are shown in Figure 10. The outer shear layers, i.e. the bright parts close to the walls, and inner core layer can clearly be distinguished. They result from the inhomogeneous distribution of the shear rate which varies from zero in the center to maximum at the walls. The variation in the thickness of the shear layer between different images demonstrates that the structure formation depends on the position in the flow direction as well. Position 1 is where the polymer being kept at a high temperature (220 °C) enters the test section of the slit where the temperature is set to T = 145 °C. The high temperature of the melt allows for molecular relaxation and leads to a relatively thin shear layer at position 1. Figure 11

Figure 11. Thickness of shear layers at various positions along the flow direction for an apparent wall shear rate of 240 s−1. The X-ray observation is at position x = 0.

shows the quantified shear layer thickness of different slit positions except position 1. It is observed that there is indeed a slight but clear gradient in the shear layer thickness going from high to low pressure zone (i.e., going in the flow direction). Thus, the structure information averaged over the whole channel length (reflected in the pressure upswing) and that specific to the slit middle (reflected in the X-ray observations) may not evolve simultaneously. How large the effect is in terms of the time difference between these observations cannot be determined from these experiments. However, we can make an estimate of the order of 9255

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

Figure 12. Optical microscopy pictures of cross sections of samples along the flow direction for an apparent shear rate of 560 s−1. The sample positions are illustrated by the top drawing, and the corresponding images are viewed between two polarizers at ±45°. The scale bar is 0.5 mm.

Table 1. Weissenberg Numbers Wio and Wis for HMW Tail at 145 °C apparent shear rate (s−1) Wio (orientation) Wis (stretch)

80 3.8 × 103 18.4

160 7.7 × 103 36.8

240 11.5 × 103 55.2

320 15.4 × 103 73.6

400 19.2 × 103 92

480 23 × 103 110

560 26.9 × 103 129

forms; for shear rates >400 s−1 they even form during flow. These results could be interpreted in terms of this model and are not contradicting it. However, also other ideas19,46,52−55 on shish formation exist, and our results do not provide a definite answer which of these ideas should be preferred. Especially the third step, the alignment of nuclei from which precedes the fibrillation and shish formation is questioned. In some of the other model the shish grow from a single nucleus. Experiments where the shear time is varied for a shear rate that can generate both shish (during or after flow) or oriented structures (without the shish) could give more conclusive results. A shear rate of 240 s−1 seems to be a good candidate for such (future) experiments. 4.3. Relation between Viscosity Change and Crystallization. Because of the nonhomogeneous crystallization behavior along the slit channel, any final conclusion of the relation between the viscosity rise and shish formation is premature. However, we still want to present our thoughts on viscosity changes and related structure formation (e.g., precursors, nuclei, and crystallites). There is no doubt that flow is able to induce precursors/nuclei. The mobility of molecular segments inside precursors or/and subsequent crystallites is restricted, and as a consequence, the chains involved cannot move as they do in entangled melts. Therefore, these crystallization-related structures are considered to act as physical cross-links that slow down relaxation dynamics and even increase the viscosity as soon as the concentration reaches a sufficiently high level.46 As precursors/crystallites are being generated (and grow) continuously during flow, the very early stages of shear-induced crystallization are thought to be a “cross-linking” process, i.e., forming “physically branched” molecules and not necessarily a network (i.e., a gel). This cross-linking process during flow seems very similar to the physical gelation process found in quiescent crystallization of iPP by Pogodina et al.56,57 They observed gelation at a crystallinity level of about 1%, whereas we did not observe any crystallinity when the viscosity started to change. It should be noted that in the work of Pogodina et al.56 low degrees of undercooling (10−26 K) were used for quiescent crystallization for which the nucleation density is determined by temperature

segments to deviate from the rotational isomerization corresponding to the equilibrium Gaussian configuration.50 However, rheological results in Figure 3 show that viscosity rise only occurs for γ̇ ≥ 240 s−1. This indicates that effectively stretching the HMW tail is the necessary but not a sufficient factor for viscosity rise.16,20 The HMW tail stretch should go beyond a critical value to start the growth of fibrillar nuclei.47 Since the Deborah number >1 (De = relaxation time/shear time) for shear times 160 s−1, while for shear rates ≤160 s−1 this is not the case due to the insufficient molecular stretch. If a critical stretch is the criterion for the start of forming a structure responsible for viscosity rise, a work criterion as defined with eq 1 could also be applicable since these two criteria both reflect the integrated transient history of the flow. An advanced detailed numerical model for flow-induced crystallization, including a fully characterized nonlinear viscoelastic model46,47 from which the relaxation times are coupled to the structural development, could resolve which of these criteria is better (ongoing work). The critical condition of shish formation was not estimated from the onset time of observing SAXS streaks (shown in Figure 9), since the local shear field may have already changed with the average viscosity rise which happens earlier. There are different ideas on how shish is formed during flow. For example, Mykhaylyk et al.51 present a detailed four-stage model for shish formation: (1) molecular orientation and stretch, (2) nucleation, (3) alignment of nuclei, and, finally, (4) fiber (shish) formation. For shear rates shear rates ≥240 s−1 shish 9256

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

Article

5. CONCLUSIONS The rheological and structural evolution during and after shortterm flow of 0.2−0.25 s were studied for iPP at 145 °C. The rheological results show that viscosity rises beyond the normal pressure overshoot for apparent shear rates ≥240 s−1, and the onset time for this rise decreases with increasing shear rate. This viscosity rise implies that these flows do not satisfy the basic requirement for a “short-term flow”, i.e., that the polymer viscosity does change during flow. Ultrafast X-ray characterizations show that shish can form during the short flow (maximum 0.25 s) for apparent shear rates ≥400 s−1. Therefore, 0.25 s is not always short enough from a structural point of view. Interestingly, X-ray measurements (at the center of the slit) do not show simultaneous structure development with the apparent viscosity rise; the observation of shish is delayed, typically ∼0.1 s. It is argued that the influence of the pressure on the local values of rheological and kinetic parameters will cause nucleation events to occur first upstream. This nonhomogeneous crystallization behavior along the slit channel makes the real relation between viscosity rise and crystallization at the identical slit location unclear yet; it requires future numerical studies where all effects can be taken into account and analyzed in detail. Shear rates of 160 and 80 s−1 below the threshold also generate precursors which do not change the melt viscosity and develop into row nuclei. These flows can be considered as “short term shear flows”.

only. A low undercooling corresponds to relatively few nuclei, and therefore, the cross-linking effect is too low to form a sufficiently dense network; gelation is not observed in the very early stage of crystallization. With increasing crystallinity, more chains get involved in the network which can develop sufficient for observing a viscosity rise. So for low undercooling, large clusters (size of ∼1 μm57) and a crystallinity of ≈1%56 are required for achieving a sufficient network for gelling. However, we think that a viscosity change related to crystallization that is significantly enhanced by strong flow, as in current study, will be different from the above quiescent case with low undercooling. Depending on the flow strength, a precursor/ nuclei density increase of orders of magnitude is possible. Once the density of precursors (and nuclei) is high enough, the resulting increase in the local relaxation time is sufficient for a observable change in the viscosity. The viscosity may rise as a consequence of network formation without noticeable crystal formation. At present, there is no direct evidence to prove this “noncrystalline network”, but some interesting clues were found in the work of Roozemond et al.,58 Kumaraswamy et al.,25 and Roozemond et al.58 observed a clear rise of the dynamic viscosity at low levels of crystallinity in quiescent crystallization for a HDPE, but this rise at the early stage of crystallization could not be captured by a suspension model, which implies some unnoticeable structures changing the rheological property of polymer melt.58 A similar experimental result was found by Kumaraswamy et al.:25 a “highly oriented structure”, created in a flow experiment, that changed rheological properties (for an iPP at 168 and 173 °C) could not be detected by WAXD. On the other hand, our results do demonstrate that precursors formed under shear rates ≤160 s−1 (indicated by the appearance of oriented crystals during isothermal crystallization) are too dilute (or weak) to change the viscosity during flow. The detailed properties of these precursors, e.g., structure and concentration, are unknown. In case the specific “cross-linking” capability is the same for different precursors, the precursor concentration would be the major difference. The case of low shear rates (≤160 s−1) is then more similar to quiescent crystallization56 in the sense of absence of significant viscosity change; i.e., a relatively low nucleation density and further crystallization are required to form a sufficient network for a detectable change in the viscosity. Consistent with our low shear rate cases (≤160 s−1), Janeschitz-Kriegl et al. found that the oriented objects have no noticeable influence on the melt rheology and interpreted as that the precursors were too tiny to affect the rheology.24,44,45 On the other hand, the pressure rise is always accompanied by shish formation, indicating that fibrillar precursors and nuclei are more effective in chancing the viscosity. Whether this is a matter of cross-linking or space filling is not clear yet. There are two ways to describe the viscosity change due to flow-induced structures. (1) When the flow-induced number of “physical cross-links” is too little (they do not “feel” each other), the polymer can be treated as a suspension. In this case, the viscosity increase depends on the volume fraction of the flow-induced structures only. The initial small size of these precursors/nuclei implies that the space filling is too little to change noticeably the viscosity. (2) When “physical cross-linking” takes place at a high enough concentration, they can interact and the polymer acts more like a gel. Even if the occupation volume of the cross-links is negligible, it is still possible to raise the viscosity via the network formed.

■

ASSOCIATED CONTENT

S Supporting Information *

Piston speeds and the corresponding shear rates; the equatorial higher intensity of beam; estimation of the influence of pressure gradient on nucleation and longitudinal growth rates. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel +31(0)402474840; e-mail [email protected] (G.W.M.P.). Present Address ∥

L.B.: DSM Ahead, Urmonderbaan 22, Geleen 6167RD, The Netherlands. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors acknowledge Prof. Julia A. Kornfield (Division of Chemistry and Chemical Engineering, California Institute of Technology) for the valuable and helpful discussions. We also thank Pauline Schmit (Department of Chemical Engineering, TU/e) for the optical micrographs. NWO (Nederlandse Organisatie voor Wetenschappelijk Onderzoek) and ESRF are acknowledged for granting the beamtime. This work is part of the Research programme of the Dutch Polymer Institute (DPI), P.O. Box 902, 5600 AX Eindhoven, The Netherlands, Project No. 714. 9257

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258

Macromolecules

■

Article

(33) van Drongelen, M.; van Erp, T. B.; Peters, G. W. M. Polymer 2012, 53, 4758−4769. (34) van Erp, T. B. Structure Development and Mechanical Performance of Polypropylene. PhD Thesis, Eindhoven University of Technology, 2012. (35) Van Erp, T. B.; Roozemond, P. C.; Peters, G. W. M. Macromol. Theory Simul. 2013, 22 (5), 307−318. (36) Ma, Z.; Balzano, L.; Peters, G. W. M. Macromolecules 2012, 45, 4216−4224. (37) Macosko, C. W. Rheology, Principles, Measurements and Application; Wiley-VCH: New York, 1994. (38) Bras, W.; Dolbnya, I. P.; Detollenaere, D.; van Tol, R.; Malfois, M.; Greaves, G. N.; Ryan, A. J.; Heeley, E. J. Appl. Crystallogr. 2003, 36, 791−794. (39) Portale, G.; Cavallo, D.; Alfonso, G. C.; Hermida-Merino, D.; Van Drongelen, M.; Balzano, L.; Peters, G. W. M.; Goossens, J. G. P.; Bras, W. J. Appl. Crystallogr. 2013, accepted, doi: 10.1107/ S0021889813027076. (40) Scelsi, L.; Mackley, M. Rheol. Acta 2008, 47 (8), 895−908. (41) Geng, Y.; Wang, G.; Cong, Y.; Bai, L.; Li, L.; Yang, C. Macromolecules 2009, 42 (13), 4751−4757. (42) Wunderlich, B. Macromolecular Physics; Academic Press: New York, 1980; Vol. 3. (43) Wunderlich, B. Macromolecular Physics; Academic Press: New York, 1976; Vol. 2. (44) Janeschitz-Kriegl, H. Monatsh. Chem. 2007, 138 (4), 327−335. (45) Janeschitz-Kriegl, H.; Eder, G. J. Macromol. Sci., Part B: Phys. 2007, 46 (3), 591−601. (46) Zuidema, H.; Peters, G. W. M.; Meijer, H. E. H. Macromol. Theory Simul. 2001, 10 (5), 447−460. (47) 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 (9), 469−494. (48) Peters, G. W. M.; Swartjes, F. H. M.; Meijer, H. E. H. Macromol. Symp. 2002, 185 (1), 277−292. (49) Steenbakkers, R. J. A.; Peters, G. W. M. J. Rheol. 2011, 55 (2), 401−433. (50) van Meerveld, J.; Peters, G. W. M.; Hutter, M. Rheol. Acta 2004, 44 (2), 119−134. (51) Mykhaylyk, O. O.; Fernyhough, C. M.; Okura, M.; Fairclough, J. P. A.; Ryan, A. J.; Graham, R. Eur. Polym. J. 2011, 47 (4), 447−464. (52) Fernandez-Ballester, L.; Thurman, D. W.; Zhou, W.; Kornfield, J. A. Macromolecules 2012, 45 (16), 6557−6570. (53) Seki, M.; Thurman, D. W.; Oberhauser, J. P.; Kornfield, J. A. Macromolecules 2002, 35 (7), 2583−2594. (54) Zhao, B.; Li, X.; Huang, Y.; Cong, Y.; Ma, Z.; Shao, C.; An, H.; Yan, T.; Li, L. Macromolecules 2009, 42 (5), 1428−1432. (55) Liu, D.; Tian, N.; Cui, K.; Zhou, W.; Li, X.; Li, L. Macromolecules 2013, 46 (9), 3435−3443. (56) Pogodina, N. V.; Winter, H. H. Macromolecules 1998, 31 (23), 8164−8172. (57) Pogodina, N. V.; Siddiquee, S. K.; van Egmond, J. W.; Winter, H. H. Macromolecules 1999, 32 (4), 1167−1174. (58) Roozemond, P.; Janssens, V.; Van Puyvelde, P.; Peters, G. Rheol. Acta 2012, 51 (2), 97−109.

REFERENCES

(1) Meijer, H. E. H.; Govaert, L. E. Prog. Polym. Sci. 2005, 30 (8−9), 915−938. (2) Schrauwen, B. A. G.; Von Breemen, L. C. A.; Spoelstra, A. B.; Govaert, L. E.; Peters, G. W. M.; Meijer, H. E. H. Macromolecules 2004, 37 (23), 8618−8633. (3) Haas, T. W.; Maxwell, B. Polym. Eng. Sci. 1969, 9 (4), 225−241. (4) Wereta, A.; Gogos, C. G. Polym. Eng. Sci. 1971, 11 (1), 19−27. (5) Lagasse, R. R.; Maxwell, B. Polym. Eng. Sci. 1976, 16 (3), 189− 199. (6) Sherwood, C. H.; Price, F. P.; Stein, R. S. J. Polym. Sci., Polym. Symp. 1978, 63, 77−94. (7) Wolkowicz, M. D. J. Polym. Sci., Polym. Symp. 1978, 63, 365−382. (8) Jay, F.; Haudin, J. M.; Monasse, B. J. Mater. Sci. 1999, 34 (9), 2089−2102. (9) Pantani, R.; Coccorullo, I.; Volpe, V.; Titomanlio, G. Macromolecules 2010, 43 (21), 9030−9038. (10) Liedauer, S.; Eder, G.; Janeschitz-Kriegl, H.; Jerschow, P.; Geymayer, W.; Ingolic, E. Int. Polym. Process. 1993, 8, 236−244. (11) Liedauer, S.; Eder, G.; Janeschitz-Kriegl, H. Int. Polym. Process. 1995, 10, 243−250. (12) Kumaraswamy, G.; Verma, R. K.; Kornfield, J. A.; Yeh, F. J.; Hsiao, B. S. Macromolecules 2004, 37 (24), 9005−9017. (13) Somani, R. H.; Yang, L.; Zhu, L.; Hsiao, B. S. Polymer 2005, 46 (20), 8587−8623. (14) 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 (15), 5058−5071. (15) An, H.; Zhao, B.; Ma, Z.; Shao, C.; Wang, X.; Fang, Y.; Li, L.; Li, Z. Macromolecules 2007, 40 (14), 4740−4743. (16) Mykhaylyk, O. O.; Chambon, P.; Graham, R. S.; Fairclough, J. P. A.; Olmsted, P. D.; Ryan, A. J. Macromolecules 2008, 41 (6), 1901− 1904. (17) Balzano, L.; Kukalyekar, N.; Rastogi, S.; Peters, G. W. M.; Chadwick, J. C. Phys. Rev. Lett. 2008, 100 (4), 048302. (18) Housmans, J. W.; Steenbakkers, R. J. A.; Roozemond, P. C.; Peters, G. W. M.; Meijer, H. E. H. Macromolecules 2009, 42 (15), 5728−5740. (19) Yan, T.; Zhao, B.; Cong, Y.; Fang, Y.; Cheng, S.; Li, L.; Pan, G.; Wang, Z.; Li, X.; Bian, F. Macromolecules 2009, 43 (2), 602−605. (20) Mykhaylyk, O. O.; Chambon, P.; Impradice, C.; Fairclough, J. P. A.; Terrill, N. J.; Ryan, A. J. Macromolecules 2010, 43 (5), 2389−2405. (21) Okura, M.; Mykhaylyk, O. O.; Ryan, A. J. Phys. Rev. Lett. 2013, 110 (8), 087801/1−5. (22) Holland, C.; Vollrath, F.; Ryan, A. J.; Mykhaylyk, O. O. Adv. Mater. 2012, 24 (1), 105−109. (23) Stadlbauer, M.; Janeschitz-Kriegl, H.; Lipp, M.; Eder, G.; Forstner, R. J. Rheol. 2004, 48 (3), 611−629. (24) Janeschitz-Kriegl, H.; Ratajski, E.; Stadlbauer, M. Rheol. Acta 2003, 42 (4), 355−364. (25) Kumaraswamy, G.; Issaian, A. M.; Kornfield, J. A. Macromolecules 1999, 32 (22), 7537−7547. (26) Baert, J.; Van Puyvelde, P.; Langouche, F. Macromolecules 2006, 39 (26), 9215−9222. (27) Balzano, L. G.; Rastogi, S.; Peters, G. W. M. Macromolecules 2009, 42 (6), 2088−2092. (28) Janeschitz-Kriegel, H.; Ratajski, E. Polymer 2005, 46 (11), 3856−3870. (29) Roozemond, P. C.; Steenbakkers, R. J. A.; Peters, G. W. M. Macromol. Theory Simul. 2011, 20 (2), 93−109. (30) Kumaraswamy, G.; Kornfield, J. A.; Yeh, F. J.; Hsiao, B. S. Macromolecules 2002, 35 (5), 1762−1769. (31) Terrill, N. J.; Fairclough, P. A.; Towns-Andrews, E.; Komanschek, B. U.; Young, R. J.; Ryan, A. J. Polymer 1998, 39 (11), 2381−2385. (32) Olmsted, P. D.; Poon, W. C. K.; McLeish, T. C. B.; Terrill, N. J.; Ryan, A. J. Phys. Rev. Lett. 1998, 81 (2), 373−376. 9258

dx.doi.org/10.1021/ma401833k | Macromolecules 2013, 46, 9249−9258