Thermal stability of shear-induced precursor structures in isotactic polypropylene by rheo-X-ray techniques with couette flow geometry

Samples and Experimental Procedures

In situ rheo-SAXS and -WAXD measurements were carried out at the X27C beamline in the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL), USA. The X-ray wavelength was 1.371 Å. The sample-to-detector distances for SAXS and WAXD experiments were 1971.4 and 101.5 mm, respectively. A 2D MAR-CCD X-ray detector (MARUSA) with the resolution of 1024 × 1024 pixels (pixel size = 158 μm) was used to collect time-resolved SAXS and WAXD patterns. The calibration procedures and the data analysis schemes were described earlier.55-57 In addition to the parallel plate geometry, a couette flow geometry was also used in this work. The details of the rheo-X-ray experiment using the couette flow geometry are described in the following section.

Parallel Plate Versus Couette Flow Geometry

A couette cell was constructed for the Linkam shear apparatus following the design of Li and de Jeu68 [the diameter of the outer hollow cylinder = 16 mm; diameter of the inner solid cylinder = 14 mm, and length = 4 mm, Fig. 1(A)]. The polymer sample was placed in 1 mm of empty space between the two cylinders or gap of the couette cell. Note that in the rheo-X-ray setup, couette cell length corresponds to sample thickness. Figure 1(A) shows a schematic diagram of the couette flow fixtures, along with the flow profile experienced by polymer sample. For comparison, Figure 1(B) shows the corresponding situation in parallel plate flow geometry. In both geometries, the incident X-ray beam is perpendicular to the flow direction (tangent to the rotating cylinder/plate); however, it is parallel to the imposed shear field (or velocity streamlines) in couette flow and perpendicular in parallel plate. Thus, 2D X-ray scattering projections of the structures obtained in the two geometries are orthogonal to each other. It should be noted that shear field is constant across the gap or sample thickness in couette flow, while it linearly decreases across the gap in parallel plate; strongest at the surface of the rotating plate and zero at the stationary plate.

Another critical aspect of the couette cell design, especially for in situ WAXD measurements, is the length/gap ratio. This is because diffraction signals at large angles are blocked by the metal walls of the outer and inner cylinder. In the case of a cell with the aforementioned dimensions, the scattering/diffraction signals above 2θ = 14° were blocked. Although this 2θ value is above the desired angular range for SAXS measurements of iPP, it is not sufficient to obtain a complete 2D WAXD pattern of iPP, which requires diffraction signals at least up to 2θ = 22°. Note that in the previous report by Li and de Jeu,68 only SAXS data was reported. Hence, we fabricated two set of fixtures: 4.0-mm long with a 1.0-mm gap (mainly for SAXS study) and 2.5-mm long with a 1.5-mm gap (for WAXD study). The latter can capture diffraction signals up to 2θ = 33°. All in situ rheo-WAXD results were obtained using these fixtures. To the best of our knowledge, these are the first rheo-WAXD results using Linkam stage with couette flow geometry.

In Situ Rheo-SAXS

SAXS Results from Couette and Parallel Plate Geometries

As mentioned earlier, one of the advantages of couette flow geometry is that the scattering projection obtained is orthogonal to that obtained in parallel plate geometry. For cylindrically symmetric structures, both projections are identical and the nature of the scattering patterns is expected to be similar in both flow geometries. Conversely, similarity in the two orthogonal scattering projections (images) is evidence of the cylindrical symmetry of the scattering entity. Figure 2 shows two sets of SAXS images obtained in parallel plate and couette (16 × 4 × 1 mm³ couette cell) flow geometries after application of an identical shear condition (rate = 60 s⁻¹, t_s = 5 s, and T = 165 °C). Both sets exhibited the characteristics of shear-induced shish–kebab structures43—the equatorial streak was due to the shish structure oriented along the flow direction and the meridional maxima were due to kebabs oriented perpendicular to the flow direction. The similarity of the scattering projections in these two sets provides unequivocal evidence of the cylindrical symmetry of iPP shish–kebabs. Also, note that the SAXS patterns from the couette geometry appeared stronger/more intense than the corresponding patterns from the parallel-plate geometry. This is because in couette flow geometry, the sample thickness (4 mm, or the couette cell length) is significantly larger than that in the parallel plate (typically 1 mm or lower; higher values limit shear rate that can be imposed in Linkam stage). This is an added advantage of couette flow geometry whereby the scattering sensitivity is increased allowing detection of an even smaller quantity of the oriented structures compared to those detected in parallel plate configuration.

Thermal Stability of Shear-Induced Oriented iPP Structures

Figure 3 shows a series of 2D SAXS patterns obtained 60 min after shear (rate = 60 s⁻¹, t_s = 5 s) at different temperatures using couette flow geometry (16 × 4 × 1 mm³ couette cell). In each experiment, the patterns were collected continuously (one every 30 s) before, during, and after shear; for brevity only the last patterns are shown here. The corresponding SAXS patterns obtained after cooling the sheared sample to room temperature are also shown in Figure 3. The SAXS pattern at 165 °C clearly exhibited the formation of stable shish–kebab structures in iPP melt, as expected. Note that the scattering intensity is high, both along the equator and meridian, indicative of a large volume fraction of the shish–kebab entities. Upon cooling, all crystallizable species, low and high molecular weight molecules, in the melt crystallize. It is conceivable that the following three processes occur simultaneously during cooling: (1) growth of previously formed oriented crystals; (2) perfection of previously formed oriented crystals, i.e., reorganization of the chain segments within lamellae, which increases contrast for scattering; and (3) nucleation and growth of unoriented crystals. The SAXS pattern at room temperature is a manifest of the above processes. The diffused scattering ring can be attributed to unoriented crystals, which overlap with the scattering from oriented crystals. As the shear temperature was increased to 175 and 180 °C, the volume fraction of the formed oriented structures decreased, evident from the decrease in the scattering intensity in the SAXS patterns (top panel Fig. 3). The pattern at 185 °C did not exhibit any detectable scattering from the oriented structures; this does not necessarily mean that the oriented structures were not present in the deformed melt. In fact, the corresponding SAXS pattern at room temperature in Figure 3(B) clearly showed the meridional scattering due to the oriented crystals in the sheared polymer. This postmortem result is the evidence of preexisting oriented structures in the deformed iPP melt at 185 °C. We conclude that, at the applied shear condition, the stable oriented aggregates indeed form at 185 °C. It should be noted that the scattering streak along the equator, close to the beamstop in the pattern at room temperature, may be due to air and not necessary from the shish structures.

In addition, the SAXS experiments were performed at 195, 205, and 215 °C. The SAXS patterns of deformed melt at all three temperatures did not show any detectable oriented structures throughout the duration of the experiment (60 min) even after shear. A representative pattern of the deformed melt, at 195 °C, and the corresponding pattern of the cooled solid sample at room temperature are shown in Figure 3. The room temperature pattern exhibited the diffused scattering ring due to unoriented crystals; however, there was no trace of scattering due to the oriented crystals. We concluded that the stable oriented structures did not form at and above 195 °C under the present shear condition. With the present data, it is established that the limiting temperature for the stability or presence/absence of the oriented structures in deformed iPP melt is in the range 185–195 °C. The determination of the exact temperature will become the subject for a future study.

In Situ Rheo-WAXD

For in situ rheo-WAXD experiments, a different couette cell of the larger gap (1.5 mm) and shorter length (2.5 mm) was used. This was necessary to capture the diffraction signals of iPP, up to 2θ = 33°. As mentioned in the experimental section, the 4.0-mm long cell (with 1.0-mm gap) could not be used because the diffraction signals above 14° are blocked by the metal wall. The use of larger gap put restrictions on the shear rate; the theoretical maximum is 50 s⁻¹ (for 1.5-mm gap), practically only about 30 s⁻¹ could be imposed due to high viscosity of the polymer sample. However, its advantage that a full iPP diffraction pattern of interest could be obtained outweighed the above. It should be noted that this also resulted in not being able to repeat the shear conditions of SAXS for WAXD experiments. Nevertheless, only SAXS experiments are critical for the thermal stability studies. Since here the detection of oriented aggregates at the early stages of their evolution is of primary importance, SAXS is the preferred technique over WAXD because its sensitivity is at least about one order of magnitude higher than that of WAXD, confirmed by our previous studies with parallel plate fixtures.52 If the oriented aggregates are not detected by SAXS then there is no doubt that they will not be observed by WAXD.

In the case of WAXD experiments the primary objective was to probe the distribution of the oriented and unoriented crystals in the crystalline phase as a function of shear temperature. The allowable maximum rate of 30 s⁻¹ was chosen for these experiments, and shear duration was t_s = 5 s. Also, the chosen experimental temperatures were such that the shear-induced crystallization process reached a steady state within a reasonable time (of about 60 min). The selected temperatures were 150, 155, 160, and 165 °C. At temperatures >165 °C, the present WAXD setup is not sensitive enough to detect the evolution of aggregates (evident from the WAXD patterns in Figure 6).

As mentioned in the experimental section, a different couette cell (16.5 × 2.5 × 1.5 mm³) was used for in situ rheo-WAXD experiments. The use of this couette cell in Linkam shear stage put restrictions on the imposed shear field due to its larger gap; however, its advantage is that a full iPP diffraction pattern of interest could be obtained, outweighed the above limitation. The imposed shear condition for rheo-WAXD experiments was rate = 30 s⁻¹, t_s = 5 s. At this shear intensity, the thermal stability limit of the oriented crystals is expected to be lower (∼165 °C, based on the results of our previous experiments with parallel plate fixtures at this shear condition43) than that at high shear intensity. Therefore, the selected temperatures for rheo-WAXD experiments were 150, 155, 160, and 165 °C.

It has been well documented that iPP crystals possess three different crystalline forms1: monoclinic α, hexagonal β, and orthorhombic γ. At a wavelength of 1.371 Å, α-form reflections can be indexed as follows43: (110) at 2θ = 12.5°, (040) at 15°, (130) at 16.5°, (111) at 19°, and (−131) at 19.4°. The β-crystals exhibit the following reflections: (300) at 2θ = 14.3° and (311) at 19°. Note that the (311) reflection of the β-form coincides with the (111) reflection of α-form; however, the (300) reflection is distinctly separate from all the α-form reflections. It can be taken as a marker for β-crystals. The γ-crystals are rare and were not present in the studied iPP. Furthermore, crystal orientation can be determined from the azimuthal variation in the intensity of the appropriate crystal reflections in 2D WAXD patterns. When the crystal orientation is high, the azimuthal breadths are relatively narrow, leading to the appearance of arc-like or point-like diffraction features. On the other hand, the crystals without preferred orientation exhibit circular rings of uniform intensity.

Figure 4 shows four sets of 2D WAXD patterns obtained before and after application of shear at the indicated temperature. Note that the data acquisition rate was 30 s/WAXD image; only selected images are shown here. The duration after shear is shown on each image. Figure 5 shows the circularly averaged WAXD intensity profiles as a function of time after shear, extracted from the 2D WAXD images. The time of inception of crystalline structures (peaks) and their growth can be clearly seen in these profiles. At 165 °C, both the WAXD patterns and intensity profiles only showed a diffraction halo due to amorphous polymer melt; no crystalline structures were detected, as expected. This does not necessarily mean that the oriented crystals did not form at this temperature; their volume fraction can be below the detection sensitivity of WAXD that is an order of magnitude poorer than SAXS.51 The postmortem analysis of the structure of the cooled solid sample, described in detail below, would correctly confirm the presence/absence of the oriented crystals in the deformed melt. Similarly, up to about 20 min after shear at 160 °C, both the WAXD patterns and intensity profiles only showed the diffraction halo due to amorphous melt. However, the patterns at longer times showed evolution of (110), (040), and (130) reflection arcs. Obviously, intensity of the reflections is weak at the time of crystal inception; nevertheless, a closer inspection of the WAXD images and intensity profiles revealed their presence. At 155 °C, the crystal reflections were seen to appear at about 2 min after shear (Fig. 5); these reflections grow rather quickly as seen in the WAXD patterns and profiles at later times. In addition, azimuthal breadth of the crystal reflections became narrow, indicative of their large degree of orientation. At 150 °C, as one might expect, the crystals evolved almost immediately after shear; inception time was about 30–60 s. The narrow reflection arcs due to the oriented crystals were observed in the initial patterns. Subsequently, complete reflection rings were also seen to evolve, overlapping with the previously formed arcs. The rings can be attributed to the formation of the randomly oriented or unoriented crystals. Interestingly, these patterns also showed evolution of β-form crystals at about 5 min after shear; the intense (300) reflection of β-form can be clearly seen in the 2D WAXD patterns. The corresponding profiles in Figure 5 show β-crystalline peak and its growth. The formation of β-phase at this shear temperature has been observed before; it is thought that the surface of the shear-induced oriented α-crystals provide nucleation sites for β-crystals.55 The β-crystals were not observed at shear temperatures of 155 and above, since their melting point is about 155 °C93.

In Figure 6, structure of the deformed melt prior to cooling is compared with the final equilibrium structure after complete crystallization. Both 2D WAXD patterns of the deformed melt 60 min after shear at various temperatures (these images are part of Fig. 4, duplicated here for clarity) and the corresponding patterns of solid sheared polymer at room temperature were compared in this figure. As mentioned above, upon cooling all crystallizable molecules in the deformed melt would crystallize. The WAXD patterns of all four samples exhibited overlap of reflection arcs and rings due to the oriented and unoriented crystals, respectively. The intensity of crystal reflections is strong, as expected. Results from the analysis of crystallinity and varying crystal fractions are summarized as follows.

Total Crystal Fraction

The amount of total crystal fraction was estimated from circularly averaged WAXD (after the Fraser correction,94 which are discussed later) intensity profiles. To illustrate the calculation procedure, Figure 7 shows the circularly averaged WAXD intensity profiles 60 min after shear at various temperatures. A standard peak-fitting software program, described elsewhere,55, 57 was used to deconvolute the crystalline peaks in these profiles. The normalized integrated intensity (peak area) of each crystal reflection and that of the amorphous background were obtained from the above fitting. The percentage of total crystal fraction in the sheared polymer was calculated after subtraction of the area of amorphous background. Note that the above calculation gives a “crystallinity index” and not true crystallinity of the sample. Hereafter, the crystallinity is used to refer to the “crystallinity index” or the crystal fraction. The calculated values of the percentage total crystallinity (X_T) 1 h after shear at various temperatures are shown in Figure 7. At 165 °C, X_T is zero, as expected. Its value progressively increased with the decrease in the temperature. At 160 and 155 °C, mostly the oriented crystals contributed to the total crystallinity, evident from the nature of the corresponding 2D WAXD patterns in Figure 6. On the other hand, at 150 °C oriented and unoriented α-form crystals, as well as β-form crystals, all contribute to the total crystallinity.

Oriented and Unoriented Crystal Fractions

The solid polymer crystalline microstructure or the oriented and unoriented crystal fractions were determined by the Halo method.58 The initial (total intensity) 2D WAXD images were deconvoluted into two 2D images: one of the diffraction patterns due to the oriented crystals, and the other due to the unoriented crystals. The principle of this method is as follows. The total WAXD intensity, I_total [2θ, ϕ], is a function of both the diffraction angle, 2θ, and azimuthal angle, ϕ. It is separated into two components: one azimuthal independent, I [2θ], arising from the unoriented crystals, and the other azimuthal dependent, I [2θ, ϕ], arising from the oriented crystals. At a 2θ position, an azimuthal intensity profile is drawn and the minimum value of the intensity is obtained by a suitable fitting method. A series of azimuthal scans along the diffraction angle gives an envelope of minimum diffracted intensity, i.e., a 2D diffraction pattern due to the unoriented crystals. The image–image subtraction of the above obtained 2D image from the initial, total intensity pattern gives a 2D diffraction pattern due to the oriented crystals. The example analysis of the WAXD data using the above method is illustrated in Figure 8, where the total intensity pattern of sheared iPP sample at room temperature (shear temperature was 150 °C) along with the calculated contributions of the unoriented and oriented components are shown. Note that the total diffracted intensity pattern was determined from the 2D WAXD pattern after the “Fraser correction”94; hence it has a slightly different appearance. Figure 8 also shows the corresponding circularly averaged WAXD intensity profiles. In this figure A_T, A₀, and A_u represent the area sums of all crystalline/diffraction peaks in the profile of total intensity, oriented contribution and unoriented contribution, respectively. The calculated values of the three area sums have the following relationship: A_T = A₀ + A_u. This relationship was also confirmed by the addition rule of the three circularly averaged intensity profiles. The latter method provided an internal check for the accuracy of the image–image subtraction procedure of the Halo method. The total percent crystallinity and oriented and unoriented contribution were obtained from the corresponding area sum. The oriented (X₀) and unoriented (X_u) crystal fractions were obtained from the ratio of area sums, as follows:

(1)

(2)

Note that only the distinction between the oriented and unoriented crystals is critical for the present analyses; hence contribution of α- and β-form crystals was not separately calculated. The crystal ratios of A₀/A_T (= X₀/X_T) and A_u/A_T (= X_u/X_T) in the cooled solid sample corresponding to shear temperature of 150 °C were 0.27 and 0.73, respectively. Similarly, Figures 9-11 show intensity profiles of total, oriented, and unoriented contributions for shear temperatures of 155, 160, and 165 °C, respectively. The calculated values of the total percentage crystallinity, oriented, and unoriented crystal fractions at room temperature are also shown in these figures.

Crystallinity Phase Diagram

The effect of shear temperature on the final solid-state polymer microstructure can be concisely represented in the form of a crystallinity phase diagram, i.e., plot of shear temperature versus crystal fraction ratio. Figure 12 shows the constructed crystallinity phase diagram of sheared iPP polymer. Interestingly, the diagram in Figure 12 is shaped like an “hourglass,” closely resembling the phase diagram of many two-phase polymer–polymer systems.95 As the shear temperature was increased from 150 to 155 °C, the ratio of oriented crystal fraction increased from 0.27 to 0.36; while it decreased with further increase in the temperature. The values at 160 and 165 °C were 0.25 and 0.18, respectively. Although the decrease in the oriented crystals fraction with the increase in shear temperature was expected, its increase when the temperature was raised from 150 to 155 °C was not an a priori prediction! Interpretations of these peculiar observations and possible pathways are presented in the discussion section.

Themal Stability and Molecular Relaxation of Shear-Induced Precursor Structures

The in situ rheo-SAXS results of iPP polymer in Figure 3 corroborate the emerging consensus about the formation of ordered long-lived mesomorphic precursor structures in sheared polymer melts at temperatures above its nominal melting point, and their profound effect on the final polymer microstructure. In addition, the results allowed quantitative determination of the thermal stability of oriented iPP structures, and provided insight into its molecular origin, presented below. First, the results clearly showed that, at the applied shear condition of rate = 60 s⁻¹ and t_s = 5 s, the stable oriented iPP structures can be formed up to a temperature of 185 °C, and not at and above 195 °C. It is important to point out that the value of T_limit is indeed valid only for the applied temperature protocol, i.e., the melt was kept at the selected temperature for 60 min after cessation of shear, prior to cooling. This was deliberately designed to ensure their long-term stability. It is entirely likely that, at the initial stages or immediately after the imposed flow, the structures might have evolved in the deformed melt even at and above 195 °C; however, it is certain that they do not remain stable for a long time. Under a different shear and temperature protocol, T_limit will, of course, be different. For example, at a certain flow condition it may be possible to generate the ordered structures at temperatures above 195 °C, and then these can be frozen/preserved by immediately quenching to a low temperature. In this case T_limit will be higher than the value under the present protocol.

On the molecular scale, the Langevin dynamics simulation studies of Dukovski and Muthukumar96 provided insight into the structure of oriented crystals/aggregates and conformation of the participating chains. They probed early stage events during transformation of the oriented chains into oriented crystals in elongational flow. Accordingly, an extended chain segments can crystallize along with other extended chain segments to form long fibrillar entities or shish. At the same time, another chain segment, identical to the previous one, may join other folded chains and become a part of the perpendicularly oriented entities or kebabs. Thus, the flow-induced oriented aggregates, both shish and kebab-like, originate from the extended/oriented chain segments. The question about their relaxation behavior in the melt at high temperatures was recently addressed by Zuo et al.92 in their experimental studies of bimodal PE melts. They report that the thermal stability of flow-induced precursor structures (shish–kebabs) is directly related to the relaxation behavior of stretched long chain segments confined in a topologically deformed entanglement network. With increase of temperature, the relaxation of the deformed entanglement network results in the decrease in the extent of stretched segments and the shish–kebab fraction upon cooling.

Thus, the state (i.e., orientation and extension) of the high molecular weight chains is the most important factor dictating the thermal stability of flow-induced precursor structure. Thermodynamically, the entropy of oriented and extended chain segments is lower than that of random chain segments. Since an extended chain segment is closer to its state in the crystal form, it has a smaller kinetic barrier to overcome during crystallization. The extended and oriented chain crystals, thus formed, are of larger size than that of the folded chain crystals that originate from random chain segments. Their larger size lead to a melting point, T_or = ΔH/ΔS, higher than the nominal one T_mp; as predicted by the well-known Gibbs–Thomson equation.1 In other words, the result of the imposed shear and the resultant molecular orientation is that it produces long nuclei of which the melting point is above the regular one but still lower than the equilibrium melting temperature of the α phase of iPP, which is considered in the literature between 188 and 210 °C.97 The previously published50 results of DSC studies are consistent with the above scenario.

The relaxation behavior or how long the oriented chain segments can remain oriented after cessation of flow can be addressed as follows. Keller's conceptual idea of the critical strain rate for coil–stretch transition in flow14 is well known. Accordingly, at a given shear rate, only chains longer than a critical chain length can remain stretched and oriented, while the shorter chains will return to the random coil conformation at the cession of flow. Increasing the shear rate does not affect the degree of chain extension, but will increase the amount of material that becomes extended by increasingly “cutting into” the distribution from the high molecular weight tail downwards. These concepts are schematically shown in Figure 13(A). The reciprocal shear rate represents time (related to relaxation). Thus on the basis of well known time–temperature superposition, we hypothesize that the temperature has a similar effect. That is, at a given temperature, only a certain fraction of chains in the distribution, particularly the chains in the high molecular weight tail, can remain oriented for a sufficiently long time after shear. The low molecular weight chains will quickly lose their orientation. Only the oriented high molecular weight chains participate in the formation of stable oriented structures, the low molecular weight chains do not. Increasing the shear temperature will reduce the amount of oriented high molecular weight species and hence the concentration of stable aggregates. Ultimately, at a certain limiting maximum temperature (T_limit) no chains can remain oriented long enough to form the stable aggregates. The above concepts are schematically shown in Figure 13(B). In this figure, the sharply split molecular weight distribution into one fully stretched part and a random coil one appears very simplistic and requires further explanation. It is important to note that the whole viscoelastic behavior of the melt affects the capability of the molecules to be oriented by the imposed flow and their relaxation time.23, 98-101 The chain–chain overlap and entanglements affect the relaxation behavior of both short and long chains. The short chains may be oriented by the long ones and take longer time to relax; on the other hand, short chains will act as diluents for the long ones and reduce their relaxation time. Thus, for an identical long chains trail embedded in different molecular weight distribution, its relaxation time value will differ. The underlying molecular weight distribution curve will also change. Fundamentally, it is the chain relaxation time (and the corresponding M*) that will dictate whether it becomes stretched or relaxes to random coil at a given flow condition and temperature.

It should be noted that the above arguments are valid for polymer melts above a certain temperature; i.e., there is a lower limit of temperature, namely the crystallization temperature of unoriented crystals (T_u). Below T_u, all crystallizable species, both low and high molecular weight, can crystallize. In fact, the rapid crystallization kinetics of unoriented crystals can overwhelm/hinder the crystallization of oriented crystals44; so much as to significantly change the final microstructure, leading to peculiar shape of the crystallinity phase diagram, as discussed in detail below. SAXS patterns of Figure 3 are consistent with the above scenario.

The Meaning of Crystallinity Phase Dagram

While the construction procedure for the phase diagram was relatively straightforward, its peculiar hourglass shape was not at all an a priori prediction. A progressive decrease in the oriented crystals fraction with the increase in shear temperature was the prediction before the experiments. A thorough inspection of the total, oriented and unoriented crystallization kinetics during cooling of the sheared melt revealed the possible pathways/mechanisms for the experimental observed phenomenon. First, note that the total percentage crystallinity of cooled sheared polymer was about the same (∼40%) for all four samples, independent of the shear temperature. The result was not totally unexpected, since in our previous studies the total percentage crystallinity was found to be independent of the applied shear rate as well as shear duration.43, 44 In other words, the total crystallinity does not depend upon the flow condition. This is because, in a semicrystalline polymer sample there is only a certain fixed amount of crystallizable species or molecules. Upon cooling, all the species crystallize and contribute to the total crystallinity. If melt is in a different state prior to crystallization, either due to flow or prior history, certainly the kinetics and final microstructure will be affected; however, the total crystallinity remains the same.

Consider the melt structure after shear at different temperatures but prior to cooling. The higher the temperature, the lower the amount of oriented high molecular weight species can contribute to the formation of stable aggregates. This is true at temperatures above T_u, where only the oriented crystals can remain stable. Note that T_u is usually a few degrees below T_mp, since a driving force or a certain degree of subcooling (δT = T_mp − T_u) is required to overcome the barrier for the nucleation of unoriented crystals. The magnitude of δT will depend upon the imposed shear condition; maximum for the quiescent or no shear condition. The WAXD patterns and intensity profiles at 155, 160, and 165 °C in Figures 4 and 5, respectively, manifest the above scenario. The patterns at 155 and 160 °C showed only arcs due to the oriented crystals; no rings were observed throughout the duration of the experiment, 60 min after shear. Clearly, the unoriented crystals did not develop in the sheared melt. At 165 °C neither oriented nor unoriented crystals could be detected in the WAXD patterns. This temperature is probably close to the maximum limiting temperature for the formation of stable structures at the applied shear (rate = 30 s⁻¹ and t_s = 5 s). Therefore, at and above 155 °C, the sheared iPP melt primarily consisted of the oriented crystals, and their amount progressively decreased with the increase in temperature, as expected. On the other hand, both the intensity arcs and rings due to the oriented and unoriented crystals, respectively, were observed in the WAXD patterns at 150 °C. That is, δT was sufficient to induce nucleation and growth of the unoriented crystals.

After the deformed melt was cooled to room temperature, the WAXD patterns showed strong intensity rings overlapped with the arcs (Fig. 6), as expected. The cooling process can be divided into two stages: one between initial temperature and T_u, and the other between T_u and room temperature. As the melt is cooled, all the available “crystallizable species” contributed to and were consumed by (a) growth and perfection of previously formed crystals, both oriented and unoriented (if present), and (b) nucleation and growth of new unoriented crystals. When the melt temperature is above T_u, (a) dominates with no competition from (b). Below T_u, both (a) and (b) compete for the “crystallizable species.” Here, the relative kinetics of (a) and (b) will determine the final amounts of the oriented/unoriented crystals. The quantitative details of the kinetics are not known beyond the scope of the present study. However, our previous studies have shown that at temperatures below T_u, the new and previously formed unoriented crystals grow so rapidly that they overwhelm the growth of oriented crystals.55, 56 For example, the results of in situ rheo-SAXS/-WAXD experiments performed at 140 °C showed that the amount of unoriented crystals was significantly higher than that of oriented crystals. Therefore, below T_u, the amount of oriented crystals in the cooled polymer was less than its unoriented counterpart.

The peculiar hourglass shape of the crystallinity phase diagram of sheared polymer is a manifest of the above. When shear temperature was above the optimum temperature of 155 °C, the oriented crystals fraction decreased with the increase in the temperature, as shown in the top part of the hourglass shape curve in Figure 12. Below the optimum temperature, not only does the melt already consist of both the oriented and unoriented crystals, the rapid growth of new unoriented crystals depletes the major portion of the “crystallizable species.” Therefore, the oriented crystals fraction decreased with the decrease in the shear temperature; the lower half of the hourglass shape curve. It should be noted here that the method to obtain the oriented crystal fraction does not take into account the relative amounts of α and β phases, which will vary with temperature. Also, that the orientation function for each phase is likely to be different. In addition, the α phase itself consists of both parent and daughter lamellae, with each having a different orientation function.102, 103 The calculated crystallinity values of X_T, X₀, and X_u refer to the combined α and β crystalline phases; this is important because the growth rate as well as the contributions of α and β crystals are significantly different from each other. Moreover, only if both the α and β crystalline phases are considered then the unoriented crystals growth rate is faster that of the oriented crystals.

It is safe to extrapolate the left and right curves of the hourglass to obtain the two extreme temperature conditions, where the oriented crystals fraction is zero; i.e., the two points of intersection with the corresponding Y-axis: (1) a high temperature corresponding to T_limit, where the oriented aggregates cannot survive, and (2) a low temperature, where the crystallization of the unoriented crystals is so fast, as under spontaneous nucleation condition, that there is no time for the formation of the oriented crystals even at a strong shear intensity. It should be noted that the shape of the hourglass, i.e., location of the neck (the optimum temperature) and its width, in Figure 12 is specific to the applied shear flow intensity: rate = 30 s⁻¹ and t_s = 5 s in the present case. The location of the neck will shift up/down and its width will become narrow/broad, depending on the applied flow intensity. For example, at higher shear rates, the neck will shift upwards or the optimum temperature will be higher, while its width will become narrower. We conjecture that the hourglass shape of the crystallinity phase diagram may not be specific to sheared iPP, but universal to all thermoplastic semicrystalline polymers in flow. Future experimental studies of other polymer systems will substantiate the above.