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Structure Development during Stretching and Heating of Isotactic Propylene−1-Butylene Random Copolymer: From Unit Cells to Lamellae Yimin Mao, Xiaowei Li, Christian Burger, and Benjamin S. Hsiao* Department of Chemistry, Stony Brook University, Stony Brook, New York 11794-3400, United States

Aspy K. Mehta ExxonMobil Chemical Company, 5200 Bayway Drive, Baytown, Texas 77520, United States

Andy H. Tsou ExxonMobil Research and Engineering Company, Annandale, New Jersey 08801, United States ABSTRACT: Structure changes in propylene−1-butylene (P−B) random copolymer having low content of butylene concentration (5.7 mol %) during stretching and heating were investigated by combined wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) techniques. On the basis of 2D data analysis, two crystal modifications with three orientation modes were determined: γ-phase lamellae with “tilted cross-β” configuration, aligned α-phase lamellae (with respect to the stretching direction) and α-phase daughter lamellae. It was found that γphase was unstable and could be transformed into α-phase by stretching. The early stage “four-point” SAXS pattern was attributed to the coexistence of both α- and γ-phase lamellae. The c-axis in the γ-phase was parallel to the lamellar long axis, where corresponding polymer chains were perpendicular to this axis. On the other hand, the c-axis in the α-phase was aligned to the stretching direction. After yielding, the SAXS pattern changed into a “two-point” pattern along the meridian, and was superimposed with two tilted streaks near the equator. The origin of the scattering streak might be due to tilted microfibrils with a mean diameter of about 8 nm, which probably served as nucleation sites for epitaxial growth of lamellar crystals. Lamellar fragmentation was observed from comparison of the lamellar lateral width and crystal size derived from SAXS and WAXD results, respectively. During heating, the SAXS pattern exhibited a longer lifetime than the corresponding WAXD pattern, indicating the existence of two-step melting processes, i.e., the disappearance of lattice coherence in block crystals followed by the diffusion of chains in molten microfibrils to the surrounding matrix. The nonmonotonic behavior of scattering invariants of meridional peaks and equatorial streaks provided some insights into stretching-induced structure changes. The results indicated that when lamellae melted away, microfibrils became more visible to X-ray, causing the increase in streak intensity.

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INTRODUCTION

The hybrid arrangement of molecular segments can alter the preference of crystal modification (or polymorph).1−4 For example, by incorporating a small amount of noncrystallizable comonomer, isotactic polypropylene (i-PP) the copolymer inclines to form γ-phase crystals instead of commonly observed and more stable α-phase crystals. New crystal modification can be generated in such copolymers,5−8 especially when the comonomer concentration exceeds a critical value and some comonomer segments are incorporated in the unit cells. The incorporation of comonomer can further change the degree of

Modifications of thermoplastic polyolefin, such as polypropylene, by chemical or physical means have been attractive to the chemical industry because different pathways can produce materials with different properties. One particular application involves the creation of thermoplastic elastomers having both melt processability and rubber-like elastic properties. To produce such materials, one strategy is to hybridize the polypropylene backbone with different species of comonomer(s) using random copolymerization, which can result in statistical arrangement of two (or more) types of molecular segments. Depending on the type of comonomer used and its concentration, random copolymers can differ significantly in the crystallization behavior when compared with homopolymers. © 2012 American Chemical Society

Received: July 25, 2012 Revised: August 21, 2012 Published: August 30, 2012 7061

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disordering in crystals.9,10 For example, at low comonomer concentrations, the crystal structure is identical to that formed in the homopolymer, but corresponding unit cell dimensions become significantly larger.9,11 At high comonomer concentrations, the crystal structure can be different, as large unit cells can form a hexagonal-like packing.5 When such a copolymer is subjected to external force field such as shear or stretching, the crystal structure exhibits an interesting preferred orientation depending on the initial polymorphs.9,11 Several systematic studies of the effects of comonomer type, concentration and statistical distribution on the crystallization behavior of propylene-based random copolymers have been carried out.4,12,13 It was found that comonomers, such as ethylene, 1-butylene, 1-hexene, and 1-octene, are able to induce γ-phase of i-PP at certain ranges of comonomer content. Among them, propylene−1-hexene and propylene−1-butylene random copolymers exhibited very interesting behavior. Propylene−1-hexene copolymer produced a new crystal form having R3c or R3c ̅ symmetry once the content of hexene went beyond 10 mol %.5,14,15 When comonomer concentrations were comparable, propylene−1-butylene copolymer possessed the largest degree of comonomer inclusion in the formed crystal.12,13 At low butylene concentration (50 mol %) could yield crystal form I of poly(1-butene) homopolymer.16 In our previous studies, we investigated the system of propylene−1-butylene random copolymer (P−B) consisting of only a small amount of butylene monomers (5.7 mol %) under shear flow in the molten state9 and strong uniaxial tensile deformation in the solid state11 using in situ X-ray diffraction technique. High quality 2D diffraction patterns were analyzed using the whole-pattern approach, which resulted in the deconvolution of two crystal phases (γ-and α-phases) with distinctive orientation modes. These results are impossible to obtain using only 1D analysis. P−B copolymer with low butylene concentration (5.7 mol %) was chosen because the system demonstrated an interesting interplay between γ- and αphases. In addition, the lattice coherence of crystal could be largely maintained at such a low butylene concentration. The above considerations made the chosen copolymer an ideal model system to study the relationship between polymorphism and crystal orientation in a quantitative way. In the current study, uniaxial stretching of the same polymer system at high temperatures was carried out using combined wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) techniques to reveal the structure changes at multiple length scales (i.e., from the unit cells to crystal lamellae). In addition, subsequent melting of the stretched sample was also carried out, where the results further revealed some new insights into the process of deformation−induced structure change in this random copolymer system.

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weight (Mn) of this copolymer was 56 000 g/mol and the polydispersity index was 1.97. On the basis of differential scanning calorimetry (DSC) measurement, the endothermic melting peak of this copolymer was located at 122 °C. Experimental Procedure. The sample preparation and testing procedures were as follows. The chosen copolymer was first melt pressed at 150 °C for 5 min in a mold (thickness of 1.0 mm), which was then cooled down to room temperature under ambient conditions. The resulting film was stamped into dumbbell-shape specimens having a total length of 30.0 mm. The ends of the dumbbell specimen were 9.0 mm in width and the width of the central portion of the specimen was 4.0 mm. The stretching and subsequent melting measurements were performed in an INSTRON stretching machine. In the stretching measurement, the sample was mounted between two clamps enclosed in a heating chamber, which was heated to 100 °C at a rate of 4 °C/ min. Once it reached 100 °C, the sample was equilibrated for 2 min and then stretched uniaxially at a constant speed of 6.0 mm/min. Scattering patterns were collected simultaneously during stretching in a time-resolved manner. The stretching experiment was terminated at the strain of 3.7. After that, the sample was cooled down to room temperature. For the subsequent melting experiment, the central part of the stretched specimen was cut and sealed between two Kapton films. This sample was then mounted back in the INSTRON device, where the melting process was monitored at a heating rate of 4 °C/ min until it became completely molten. In this experiment, the INSTRON device was used only as a sample holder with heating capability, where no force was applied. Time-Resolved WAXD/SAXS Measurements. Combined wideangle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) measurements were carried out at the X27C Beamline in the National Synchrotron Light Source (NSLS), Brookhaven National Laboratory (BNL). The chosen wavelength of the X-ray beam was 1.371 Å. All scattering images were captured in situ by a 2D MAR CCD detector, having a spatial resolution of 1024 × 1024 pixels. The exposure time for each image was 30 s. The scattering angle was calibrated by Al2O3 for WAXD experiments and by silver behenate for SAXS experiments. The sample-to-detector distances were 116.2 mm and 1937 mm for WAXD and SAXS, respectively. The stretching direction was vertical in all scattering patterns shown in the context. 2D whole-pattern analysis was carried out to deal with both WAXD and SAXS results. For the WAXD analysis, two crystal modifications (γ- and α-phases of i-PP) were considered. Coordinates of each unit cell from i-PP homopolymer were directly adopted from the literature as the first step in the analysis. A full set of coordinates of atomic groups for the corresponding unit cell was generated based on the space group, where the powder diffraction pattern was calculated accordingly. The powder diffraction intensity was then redistributed with the satisfaction of the normalization requirement. Details of this WAXD analysis have been published elsewhere.9,11 For the SAXS analysis, the following principle was considered. As the polar distribution of the typically measured SAXS pattern was quite broad, the corresponding intensity distribution did not have a simple analytic form and it could not be obtained by applying an orientation distribution function separately. To deal with this problem, we adopted the Legendre expansion approach to calculate the 2D scattering pattern. The details of the SAXS analysis can be found later in the appropriate context. For both SAXS and WAXD analyses, simple fiber symmetry was assumed. This approximation was verified in an earlier study.11 In addition, the fiber axis was in parallel to the stretching direction, and it was defined as zero degrees in polar angle ϕ.

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RESULTS AND DISCUSSION Uniaxial Stretching Experiment. It has been shown that under quiescent crystallization conditions (e.g., 100 °C), P−B copolymer exhibited a mixture of two crystal modifications: γand α-phases of i-PP crystals.9,11 This can be seen from either 1D intensity profiles or 2D diffraction patterns. For example, in Figure 1, 2D WAXD patterns from the sample at low and high

EXPERIMENTAL SECTION

Materials. A series of propylene-based random copolymers containing different comonomer type and comonomer concentration were synthesized and kindly provided by ExxonMobil Chemical Company. In this study, the propylene−1-butylene random copolymer (P−B) with low butylene content was chosen, where the mole fraction of the butylene component was 5.7%. The number-average molecular 7062

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ϕ2, kept increasing in the early stage of stretching, and was equal to 90° − ϕ1. Here we refer to “the early stage” as the period when strain is less than 0.7, during which the yielding process is completed (the yield point is 0.2 according to the stress−strain curve in our early study11). The consistency in the changes of WAXD and SAXS patterns strongly suggests that the “four-point” lobes in the SAXS pattern are related to the orientation of γ-phase lamellae (note that γ-phase is the dominant modification in the initial state of stretching). The geometric relationship between the unit cell and lamella is shown in Figure 3a. The c-axis of the γ-phase unit cell is parallel to the long axis of lamella. This relationship explains the observation that ϕ1 decreased while ϕ2 increased with strain, but the sum of the two angles always equaled to 90°. Since αphase coexisted with γ-phase, it must also contribute to the four-point SAXS pattern. In this case, the c-axis is aligned to the stretching direction, as all (hk0) arcs in the WAXD pattern reside along the equatorial direction. Lamellar fragmentation (as illustrated in Figure 3b) should account for the observed lobes in the SAXS pattern. This behavior has been reported by some other authors.38,39 The “cross-β” configuration is unstable under uniaxial stretching because polymer chains are perpendicular to the stretching direction. As a result, the γ-phase can be transformed into α-phase having parallel chain alignment with respect to the stretching direction (this is seen from the diffraction pattern at high strains in Figure 1). It is clear that the γ-to-α transformation took place during yielding. After that, α-phase became the dominant modification. This also implies that beyond yielding, the tensile load was mainly carried by α-phase crystals. As a result, γ-phase crystals could not be further aligned and the angle ϕ1 could not approach the zero degree. In other words, the “tilted cross-β” configuration was retained until the very late stage (even though at that time only a small amount of γ-phase was present). In Figure 1, the existence of a daughter lamellae in the α-phase was also noticeable. The orientation difference between mother and daughter lamellae was about 80°, resulting in the appearance that one set of the (110) arc was near the meridian.18,19 To investigate the nature of the “two-point” pattern at high strains, a region ϕ = ±20° (ϕ being the polar angle) around the meridian (i.e., without the inclusion of equatorial intensity) was selected. On the basis of the intensity in this region, the 2D pattern was integrated into the 1D profile. Integrated 1D profiles at different strains are shown in Figure 4a. A scattering maximum caused by the interference between lamellae is seen in all these profiles. It is interesting to see that when strain approaches 0.7, the scattering peak moves toward a lower angle and the corresponding scattered intensity decreases. This can be explained by the possibility that when spherulites are

Figure 1. Typical WAXD patterns at low strain (0.5) and high strain (2.2). The upper-left and lower-right quarters are experimental data; upper-right and lower-left quarters are computed ones. The polymorphs used for diffraction pattern computation are annotated; their orientation modes are discussed in the context.

strains during uniaxial stretching are shown. At strain 0.5, the appearance of three equatorial arcs indicates the existence of αphase, and they can be indexed as (110), (040), and (130) reflections, respectively. Since these reflections all belong to the (hk0) family and they are all positioned along the equatorial direction, the orientation mode of the corresponding α-phase unit cell can be determined, i.e., the chain direction (c-axis) is in parallel to the stretching direction. The γ-phase can be identified via the characteristic reflection peak (117). Because the (008) plane of γ-phase and the (040) plane of α-phase are very close in s values (s = 2 sin(θ/2)/λ, with θ being the scattering angle), confusion often arises but it can be eliminated as follows. The off-axis arc in the same s position as the equatorial (040) arc should be assigned as the (008) plane of γphase. This is because if it is assigned as the (040) plane of αphase, the c-axis must be tilted with respect to the stretching direction, then all other planes, such as (110) and (130) would also need to be tilted, which is not observed. The (008) plane of γ-phase lies in the off-axis direction because of the “tilted cross-β” configuration. In the early stages during uniaxial stretching of i-PP, it is possible to have the c-axis orientation of γ-phase with respect to the stretching direction, whereas chains are cross-hatched and in perpendicular to the c-axis of γ-phase. This special orientation mode was termed the “cross-β” configuration by de Rosa et al,17 in contrast to the parallel alignment where the c-axis is perpendicular to the stretching direction. In this study, the (008) arc exhibited a tilt angle with respect to the stretching direction (denoted as ϕ1), and it moved toward (but never reached) the stretching direction with increasing strain. In corresponding SAXS measurements, the scattering pattern changed from isotropic ring to “fourpoint” lobes and then to “two-point” lobes (Figure 2). It is interesting to note that the angle between the off-axis lobes and the stretching direction in the “four-point” pattern, denoted as

Figure 2. Selected SAXS images at different strains. The pattern changes from isotropic ring to “four-point” lobes and finally to “two-point” lobes. 7063

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Figure 3. Illustration of the relationship between unit cell and lamella in (a) γ-phase and (b) α-phase. In γ-phase, the c-axis of the unit cell is in parallel to the long axis of lamella, where chains are perpendicular to this axis. The c-axis of α-phase is in parallel to the stretching direction.

peak is related to the long period, or the average distance between two neighboring lamellae. The change of long period as a function of time is shown in Figure 4b. It is seen that in the early stage of stretching, the long period increases because lamellae become separated. However, the recrystallization process allows the lamellae to become densely packed again, where the long period returns to the original value. In principle, one can also estimate the lamellar thickness based on the 1D profile. But the process requires additional information, such as higher order interference peaks. For example, the SAXS profile can be modeled by the two-phase layered (lamellar) model involving crystal and amorphous phases.22 For stacking layers that are rigorously periodic, the ratio of positions of interference peaks should be 1:2:3.... The intensity of each peak is determined by the structure factor, or more specifically, by the thickness of one phase. Furthermore, the intensities of higher order peaks are also influenced by the disorder effect.23 Thus, without higher order peaks, the fitting of the 1D profile will not be significant. As a result, the long period is the only parameter that can be confidently decided through the 1D profiles in this study. This is in part because of the nature of random copolymer crystallization, whereas the lamellar thickness distribution is broad and the disorder effect plays an important role in the lamellar arrangement.24,25 However, as shown in Figure 2, when strain went beyond 0.7, the SAXS intensity became strongly aggregated near the meridian. This scattering feature allowed us to examine the lamellar lateral width and preferred lamellar orientation (via analysis of the ϕ dependence of scattered intensity). For systems with simple fiber symmetry, the scattered intensity can be described in a 2D orthogonal coordinate, using only two components of scattering vector, s12 and s3, as shown in Figure 5. The absolute value of scattering vector s is equal to (s122 + s32)1/2. For the lamellar system, if lamellae are perfectly oriented, i.e., their normals are exactly in parallel to the fiber axis, which is the s3 direction as defined, the intensity will only distribute along the horizontal lines.26 For example, in Figure 5, at given s = sa, the intensity was spread along the horizontal line s12 = sa, and the reciprocal of the integral width (denoted as w12) could provide an estimation of the average lateral width of lamellae (denoted as w).22 If the system has preferred orientation, the intensity could be further distributed along the circle,26 as shown by the dashed line in Figure 5. In this case, the measured meridian intensity was created by the

Figure 4. (a) 1D SAXS profiles of P−B copolymer being stretched at 100 °C and different strain and (b) the change of long period derived from part a as a function of strain. The 1D profiles are integrated from −20° to +20°, close to the meridian.

destructed by the tensile force, the residual lamellae can form microfibrils under stretching.20,21 Because the experimental temperature was high and polymer chains were sufficiently mobile, these oriented microfibrils could further serve as nucleation sites to induce secondary crystallization. Such a recrystallization process could consequentially increase the meridional intensity and allow the scattering peak to return back to the original position. The position of the scattering 7064

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cn =

anbn 1 + 4n

(4)

In practice, cns are obtained from experimental data, whereby the problem can be reduced to the fitting of cn with an, and bn. An example of fitting is shown in Figure 6, where polar

Figure 5. Orthogonal coordinates for description of scattering from entities with simple fiber symmetry.

combination of two effects: size and orientation. Through the ϕ dependence analysis, it is possible to decouple these two factors using the procedures described as follows. Generally, the fiber-averaged intensity J(s,ϕ) can be written in the following form26−28

∫0

J(s , ϕ) =

π /2

I(s , ϕ′)F(ϕ , ϕ′) sin ϕ′ dϕ′

(1)

where I(s,ϕ′) is the intensity distribution in the primary coordinate without the consideration of orientation, F(ϕ,ϕ′) is the integral kernel describing the orientation effect. The detail of the relationship between F(ϕ,ϕ′) and orientation distribution function g(β) in real space can be found elsewhere.21−23 We note that eq 1 is the general expression of fiber-averaged intensity, and it can be reduced to a simpler form using the same principle employed in our earlier 2D WAXD studies.9,11 In brief, as the diffraction peaks are usually sharp, they can be approximated by a series of δ-functions appearing only at given shkl. The integration of a δ-function is trivial and eq 1 can be written in the multiplication form as follows J(s , ϕ) = I(shkl)F(ϕ , ϕhkl)

Figure 6. Example of polar distributions of intensity at three different s positions and corresponding fitting curves obtained using the Legendre expansion approach. The applied strain was 1.0.

distributions of the scattered intensity at three different s values in the SAXS pattern (strain =1.0) and their fitted curves are illustrated. Hermans’ orientation function, ⟨P2⟩, is related to the value of a1 (⟨P2⟩ = a1/5). In this study, we used a Gaussian distribution to describe I(ϕ′); the lamellar lateral width thus could be estimated using the reciprocal of integral width of the Gaussian distribution. Figures 7 and 8 exhibit the change of ⟨P2⟩ and lateral width during stretching; the corresponding values obtained from WAXD measurement are also shown for comparison purposes.

(2)

where I(shkl) represents the powder diffraction intensity of a given (hkl) plane. However, in most cases, eq 2 is not applicable to SAXS pattern computation, especially for synthetic semicrystalline polymers, since the lamellae in these systems often have finite lateral sizes at this length scale where the sharp peak approximation is invalid. In this scenario, eq 1 does not have a simple analytical solution, but one can still carry out the integration numerically. Following Ruland’s work,29,30 we treated this problem with the Legendre expansion approach. At a given s, g(β), I(ϕ′), and J(ϕ) can be expanded using Legendre polynomials as follows: ∞

g (β ) =

∑ anP2n(cos β) 0 ∞

I(ϕ′) =

∑ bnP2n(cos ϕ′) 0 ∞

J(ϕ) =

∑ cnP2n(cos ϕ) 0

Figure 7. Change in lamellar lateral width as a function of strain. Hollow circles represent the values derived from the polar angle distribution of SAXS intensity, as described in the context. The dashed line represents the estimated value obtained through the WAXD line profile analysis.

(3)

Here an, bn, and cn are the coefficients of Legendre polynomials. By using an additional theorem, their relationships can be established as 7065

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sample in SAXS measurement. This is because the orientation effect can be decoupled from the size effect in this case. Thus, it is not clear if this mosaic block crystal structure is present in lamellae at the quiescent state. For stretching experiment, the observation can be naturally attributed to the fragmentation of lamellae, or the intralamellar slip resulting in the separation of crystal blocks that are datable by WAXD.31−33 Further evidence to this explanation can be seen in Figure 8, where WAXDgenerated ⟨P2⟩ values derived by fitting the polar distribution of diffraction intensity with the Onsager function21,23 were shown against strain. The increasing ⟨P2⟩ value with strain was clearly seen in this figure. Eventually, ⟨P2⟩ became close to 1 in the late stage, indicating polymer chains were almost perfectly aligned along the stretching direction. It is interesting to note that the ⟨P2⟩ values derived by SAXS were systematically smaller than those derived by WAXD. This is consistent with the hypothesis that small crystal blocks are basic units in the lamellae under stretching, which bear the tensile force. In this scenario, it is reasonable to observe a very high degree of crystal orientation by WAXD, but relatively low degree of lamellar orientation by SAXS. In other words, lamellae cannot be easily oriented with the fiber axis due to lamellar fragmentation (or block slippage), resulting in the decrease in SAXS-generated ⟨P2⟩ as seen in Figure 8. Melting Experiment. The motivation of performing the subsequent melting experiment after stretching was as follows. Tilted scattering streaks around the equator were observed in the “two-point” SAXS patterns, but they were too weak for structural analysis. It was thought a sequential melting experiment could give us more insight into the nature of this scattering feature and the corresponding deformation-induced morphology. Figure 9 shows a spectrum of combined WAXD and SAXS patterns taken after stretching at different temperatures during heating. The change of WAXD patterns was as expected, in which diffraction arcs became weaker and broader, and the amorphous halo also became visible at high temperatures. This behavior can be explained by the crystal melting process. The change of SAXS patterns is more interesting with a few distinct features. First, the position of the meridional scattering peak is shifted toward a lower angle during heating. This can be understood because the melting of smaller lamellar crystals, the average distance (long period) between the residual lamellae would become larger. Second, it seems that the cross-streaks near the equator become more apparent at a certain high temperature region (the corresponding intensity of the meridional scattering peak also increases in

Figure 8. Change of Hermans’ orientation function, as a function of strain. Both values obtained from SAXS and WAXD methods are exhibited.

In Figure 7, the lateral width derived from the SAXS method ranges from around 25 to 45 nm, which increases as stretching proceeds. This behavior is reasonable and can be explained by the recrystallization process; i.e., at high temperatures, polymer chains are sufficiently mobile allowing the epitaxial crystal growth from the surface of existing lamellae. The WAXD line profile analysis can also be used to estimate the crystal size. For this purpose, we used the Lorentzian distribution to fit the diffraction peak and the reciprocal integral width was directly related to the size in the normal of the corresponding (hkl) plane. In principle, one is free to choose any (hkl) plane to estimate the sizes in different directions. But, in practice, the planes with one or two Miller indices being equal to zero are more useful. For α-phase crystal of i-PP, we choose the (040) plane for calculation since its normal represents the crystal growth direction. It is interesting to find out that during stretching there was no noticeable size change as derived through the WAXD method, and the size obtained was around 9 nmmuch smaller as compared to the lateral width derived through the SAXS method. A possible explanation for this observation is that the lamella may consist of multiple mosaic block crystals, as previously proposed by several groups.31−33 The boundaries of these blocks define the crystal size in the length scale datable by the WAXD technique, while the entire lamella contributes to the intensity distribution of the scattered intensity in SAXS along the s12 direction. The information on the lateral dimension can only be extracted from the oriented

Figure 9. Selected WAXD and SAXS patterns of the stretched sample at different temperatures during the subsequent melting experiment. 7066

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this region). This is somehow counterintuitive because the melting process should decrease the scattered intensity, which will be discussed later. Finally, it is seen that the SAXS pattern can survive at a higher temperature than its WAXD counterpart. For example, at 130 °C, the diffraction peaks in WAXD are very weak, but the corresponding SAXS intensity is still strong. When the temperature reaches 134 °C, only an amorphous halo is present in WAXD, while the main scattering features, i.e., the two meridional peaks and cross-streaks still exist, although weaker, in SAXS. The quantitative WAXD and SAXS results (crystallinity from WAXD and scattering invariant from SAXS) during melting are shown in Figure 10. For the

In WAXD, crystallinity can be obtained by dividing the invariant value integrated from all diffraction peaks by the overall invariant (i.e., including the invariant from the amorphous portion). Since there have been many misuses of the term “crystallinity” derived from the WAXD method, we wish to briefly point out several important facts about it. As suggested by its name, crystallinity refers to the fraction of crystalline portion in the entire system. First, the use of scattering data for the calculation of crystallinity should be guaranteed by Rayleigh’s (or Parseval’s) theorem, which can be written as34

∫ |f (x)|2 dx= ∫ |F(s)|2 ds

In eq 6, F(s) is the Fourier transform of f(x). If f(x) is the density distribution, then the right-hand term in eq 6 becomes the invariant (not the intensity) in the reciprocal space. This equation simply acclaims that the overall scattering power in reciprocal space (the invariant) is related to the inhomogeneity in real space. Therefore, it is the invariant (or the integration of Lorentz-corrected intensity as preferred by some authors) that should be used for the crystallinity calculation. A ratio of intensity from crystalline portion and the overall intensity is sometimes called “relative crystallinity” or “crystallinity index”. It does not have a significant physical meaning and should only be used for the purpose of showing general trend. Second, as seen in eq 6, the crystallinity as obtained by using the two invariants (i.e., the invariant from crystal peaks and the total invariant) is neither weight fraction nor volume fraction. If necessary, it can be converted to weight or volume fraction by assuming that densities in the crystalline phase and amorphous matrix are constants. Finally, the s integration in the invariant should be extended to infinity theoretically; but in reality, this is limited by the detection method. In this respect, it is advantageous to use a conventional diffractometer which can cover a much broader s-range. The maximum s value in the crystallinity calculation shown in Figure 10a was 0.4 Å−1, below which all significant reflections could be included. Qs and Qb in Figure 10b refer to the invariants from equatorial streaks and meridional peaks, respectively. They are not the invariant in the true sense because of the integration limits, but they do represent the scattering power in the given regions. In Figure 10a, following the trend of the crystallinity change, we can extrapolate the data points to zero crystallinity where the temperature is about 133 °C. As seen from Figure 10b, there are still some scattering contributions from the meridional peaks and cross-equatorial streaks in the SAXS pattern at 133 °C, although both invariants are decreased significantly. Since WAXD only “detects” structures in the molecular length scale and SAXS in the lamellar length scale, the longer lifetime of SAXS pattern indicates that the melting of lamellae, perhaps, is not a continuous process. That is, polymer chains in the crystal domain do not melt and diffuse into the amorphous matrix simultaneously. Heating first destroys the coherence of crystal lattice, but these polymer chains are still restricted within the original boundary, or more specifically, in lamellar layers, due to relatively low thermal mobility. This would cause the disappearance of the diffraction peaks in WAXD but allow some scattering to persist in SAXS. This is because the initial crystal regions, composed of now “molten” chains, still have higher density than those of the surrounding amorphous matrix. However, this state cannot last long. At higher temperatures (or with sufficient thermal mobility), the chains

Figure 10. (a) Change of crystallinity (calculated from WAXD data) and (b) scattering invariant as a function of temperature during heating. Plot b shows invariant integrated within regions of the meridian point (Qb) and the streak that is slightly tilted from the equator (Qs).

system having fiber symmetry (as in this study), the invariant, Q, no matter whether it is from WAXD or SAXS can be defined as: π

Q=

∫0 ∫0

∞

I(s ,ϕ) sin ϕs 2 dϕ ds

(6)

(5) 7067

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once the fractions of the two phases cross the inversion point (i.e., φ1 = 0.5 in the φ1 (1 − φ1) term). But this process has no influence on the change of Qs. As long as the surrounding lamellae are melted away and the residual microfibrils can still maintain their integrity, Qs will continue to increase. It is seen that 132 °C is the temperature where both Qs and Qb exhibit a dramatic drop. For Qb, this corresponds to the disappearance of the lamellae (we note that the WAXD pattern almost has no detectable diffraction peaks at this temperature). For Qs, this indicates that the molten chains in microfibrils begin to diffuse into the surrounding matrix. On the basis of the above results, we may now address the following two questions. Are these microfibrils extended chain crystals? If not, what are they made of? We believe the microfibrils are not extended chain crystals for the following reason. Extended chain crystals should be much more thermodynamically stable and thus have a higher melting point. This is opposite to our observationthe diffraction peaks associated with microfibrils disappear at a relatively low temperature indicating they have a lower melting point. It is interesting to note that the chains in microfibrils begin to diffuse into the matrix almost simultaneously with the disappearance of lamellae. This indicates that the surrounding lamellae may be essential to maintain the stability of microfibrils, e.g., the lamellae may play the role of “clamps”, restricting microfibrils in a confined space. That said, we may consider microfibrils as tightly aggregated polymer chain bundles, extended, but twisted and entangled as well, and hence are semicrystalline because of the chain entanglements, defects and geometrical confinement. The cross pattern of equatorial streaks may be due to the misorientation of microfibrils with respect to the stretching direction. When the tensile force is applied to the polymer network, which exhibits both elastic and plastic behavior, the load is not localized only at microfibrils but is distributed in a complicated way throughout the network. This might explain why microfibrils cannot be oriented perfectly. A question arises as to why split meridional peaks (i.e., a 4-point pattern) were not observed if the lamellae are attached to the microfibrils and also possess a tilt angle. This may be due to the following reasons. In fact, the tilt angle of the equatorial streak is very small; only 5°. Because of the relatively broad distribution of scattered intensity in both polar and s directions, the separation of the meridional peaks may not be possible to differentiate, and other effects such as intralamellar slip and lamellar flipping, as described earlier, may further smear the meridian scattered intensity. A schematic diagram showing the possible relationship between the morphology and SAXS patterns is illustrated in Figure 11a, in which the observed scattered intensity results from the superposition of two split meridional peaks. Two possible models that can account for the observed SAXS pattern are shown in Figure 11, parts b and c, respectively. In Figure 11b, polymer chains in lamellae also have the same tilt angle with respect to the stretching direction, the lamellar normal are parallel to the axis of the microfibril. Since the tilt angle is small, no splitting in diffraction arcs in WAXD pattern can be observed. The alternative model in Figure 11c represents the lamellar with intralamellar slipping. The small crystal block is the basic unit in the lamella, which can bear the tensile force. In this model, although the lamellae are tilted, polymer chains within the block can still be parallel to the stretching direction.

in the high density region will diffuse into the low density surrounding, making the system homogeneous. At this point, SAXS scattering will disappear completely. Figure 10b can give us some insights into the change of stretching-induced structure. It turns out that both Qs and Qb first increase and then decrease during heating. To explain this, we should first discuss the possible origin of meridional peaks and tilted equatorial streaks in the SAXS patterns. The former is generally assigned to the layered structure with its normal parallel to the stretching direction. In this study, it is the periodic arrangement of epitaxially grown lamellar crystal that produces the meridional peaks. According to Babinet’s principle, when two complementary structures generate the same scattering pattern, the SAXS pattern alone cannot distinguish which structure represents the lamellae or amorphous matrix. The invariant for the two-phase system is related to the density contrast, Δρ, as well as the volume fraction of one phase φ1, by35 Q ∝ Δρφ1(1 − φ1)

(7)

The term φ1 (1 − φ1) can explain the parabolic behavior of the meridional peak, since during heating the fraction of crystal phase decreases monotonically. The origin of equatorial streaks needs more consideration. The questions we can ask are two: what is the origin of equatorial streaks and why they are tilted. The SAXS equatorial streak can be generated by any long and thin entities of suitable dimensions, including microvoids, fibril bundles, sharp interfaces, etc., with their long axes vertically aligned. The possibility of microvoids should be seriously considered in the material stretching experiment, as stress-induced whitening frequently occurs. We have observed this phenomenon during low temperature stretching, but not at high temperatures. In the present study, the sample remained transparent in the very late stage of stretching. Furthermore, a microvoid usually produces very large density contrast as its density is almost negligible. Therefore, its presence usually leads to a very strong scattering streak, which was not seen in this case. In addition, microvoidinduced scattering streaks cannot be used to explain the increase or decrease of the scattered intensity that was seen in the study. Finally, we note that inappropriate sample mounting may cause X-ray beam irradiation on the sample’s edge (i.e., the air-sample interface), producing a very strong equatorial streak. This possibility can also be excluded based on the same consideration of the change in scattered intensity. We therefore believe that the equatorial streaks in our SAXS patterns primarily originate from the material structure, i.e., microfibrils, which are coupled with lamellae. Oriented microfibrils can provide ideal nucleation sites for polymer chains to attach to. We hypothesize that in the late stage of stretching (the crystallinity was around 70% as indicated by Figure 10a), the individual fibril is surrounded by densely packed lamellae making it invisible to SAXS. As lamellae melting proceeds, microfibrils become more apparent, which may be the major reason to explain the increasing intensity in equatorial streak. Careful examination of Figure 10b indicates that the temperature when the maximum Qb appears is lower than that of the maximum Qs. To be specific, Qb starts to decrease at around 122 °C while Qs starts to decrease at around 132 °C. This further suggests that the changes in meridional peaks and equatorial streaks stem from different mechanisms. The change of the meridional scattered intensity is related to the nature of the two-phase model, whereby the intensity begins to decrease 7068

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Figure 11. Illustration of (a) stretching-induced SAXS pattern and (b, c) possible structures corresponding to it. The meridian intensity is possible to be a superposition of split points in part a. Illustration of (a) stretching-induced SAXS pattern and (b,c) possible structures corresponding to it. The meridian intensity is possible to be a superposition of split points in part a. Intralamellar slip is demonstrated in part c.

Since equatorial streaks became more intense during heating, this feature allowed us to carry out further structural analysis on the scattering streak using the following procedures. The average diameter of microfibrils can be calculated using the 1D profile of the streak. Since microfibrils are well oriented, the 1D profile can be modeled using a 2D hard-disk model. In this case, the form factor is related to Hankel transformation, which is essentially the 2D Fourier transformation for the system with circular symmetry.29 For perfectly oriented long cylinders with a radius of R, the form factor is |F(s)|2 = [RJ1(2πRs)/s]2

Figure 12. Example of fitting the tilted equatorial streak profile using 2D hard-disk model.

which can explain the behavior of gradual changes in SAXS/ WAXD patterns (Figures 9 and 10) that continues until the very late stage of melting. The fact that scattering peak signals in SAXS can last longer than the diffraction signals in WAXD suggests the following melting pathways: vanishing of lattice coherence followed by disappearance of entire lamellar boundary. This hypothesis can be further supported by the results in Figures 13 and 14. Figure 13 is the change of

(8)

where J1 is the Bessel function of the first kind. Considering the asymptotic behavior due to orientation, another s should be divided in eq 8. The final expression of 1D intensity profile thus can be expressed as: I1D = S(s)[RJ1(2πRs)]2 /s 3

(9)

where S(s) is the structure factor due to the interfibril interference. In this study, we used the 2D Percus−Yevick hard-disk model to calculate the structure factor. The details can be found elsewhere.36,37 Figure 12 illustrates the fitting of the experimental 1D SAXS profile from a tilted equatorial streak using the model just described. The calculated diameter was about 8 nm. Since there were only three frames of images that had quality good enough for such analysis, we could not obtain the trend of the change in microfibril diameter during heating. Nevertheless, the calculation gave us an estimation that the diameter of the microfibril is in the same order of magnitude as the size of block crystals. The subsequent melting experiment allowed us to examine the change of strain-induced structure at high temperatures. We find that after the destruction of the original texture (i.e., spherulites dispersed in the amorphous matrix), some chains are stretched into bundles (microfibrils) that can serve as nucleation sites for crystallization, forming the shish-kebab like structure, featured with central fibrils and epitaxially grown lamellar crystals. This structure can be readily defragmented by tensile stress through intralamellar slippage. Thermodynamically speaking, as melting is a first-order phase transition, one expects to observe a discontinuous change of parameters, such as density, during melting. However, in polymer crystallization, very often lamellae have a broad spectrum of size distribution,

Figure 13. Hermans’ orientation function (derived from WAXD data) change as a function of temperature during heating. The inset shows orientation distribution functions in real space at three typical temperatures.

Hermans’ orientation function derived by the WAXD method as a function of temperature. The inset shows the orientation distribution functions in real space at selected temperatures. The key point in this plot is that even at the very late stage, the remaining lamellae still maintain a very high degree of orientation, again suggesting that crystal melting and chain diffusion into the amorphous matrix is not a simultaneous process, but a subsequent one. Parameters in Figure 14 were derived by fitting the polar distribution of SAXS intensity using the Legendre expansion approach. The behavior of Hermans’ 7069

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3.

4.

Figure 14. Changes of the lamellar lateral width and Hermans’ orientation as a function of time during heating. The lateral width and Hermans’ orientation function shown are derived from the polar distribution of SAXS intensity.

5.

orientation function of lamellae (derived from SAXS) is quite different from that derived from WAXD. For one, the Hermans’ orientation function derived from SAXS was significantly less than that from WAXD, which is consistent with the notion that the former represents the lamellar orientation and the latter represents the crystal orientation. It was seen that the lamellar orientation remains unchanged until the very late stage of melting around 130 °C, above which it shows an abrupt decrease. In addition, the change in the lateral size of lamellae is also slightly different. It increases slightly first before decreasing. This increase is not caused by the increase in crystal size, but due to the melting of small crystals, making the residual crystals appear larger.

6.

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CONCLUSIONS The structure development of propylene−1-butylene (P−B) copolymer containing 5.7 mol % content of butylene during uniaxial stretching and subsequent melting, using combined WAXD/SAXS techniques, was investigated in this study. The stretching experiment was performed at 100 °C, during which the polymorphism, preferred orientation of the unit cells and lamellar crystals were examined as a function of strain. Subsequent heating experiments of the stretched sample also provided further insights into the strain-induced structure. The main observations in this study are as follows. 1. Three orientation modes in the length scale of unit cell were identified during stretching of the chosen P−B copolymer at high temperatures (i.e., 100 °C), as identified by the 2D WAXD analysis. They were γphase with “tilted cross-β” configuration, α-phase with parallel chain alignment with respect to the stretching direction, and daughter lamellae of α-phase. It was found that γ-phase was not stable and it could be transformed to α-phase by stretching. 2. At the early stage of stretching, the primary morphological change was featured by the destruction of preexisting spherulites followed by recrystallization induced by stretching. The observed “four-point” SAXS pattern

could be attributed to both α- and γ-phase lamellae. In γphase, unit cells are arranged with their c-axes parallel to the long axis of the lamellae; while the c-axes of α-phase are aligned to the stretching direction. Analysis of the combined 2D WAXD/SAXS results provided evidence of lamellar fragmentation during stretching, since the lateral width derived from the SAXS data is significantly larger than that from the WAXD data. The main feature of the SAXS pattern after yielding included two meridian peaks superimposed with a fair amount of tilted equatorial streaks. These streaks are probably caused by tilted microfibrils that are composed of highly oriented chain bundles but with partial crystallinity. The diameter of these bundles was analyzed from the stretched sample at high temperatures, and was about 8 nm, which was in the same order of magnitude as the size of crystal blocks. These microfibrils can serve as nucleation sites for epitaxially grown lamellae. The meridian peaks could be attributed to the assembly of oriented lamellae also with a low degree of misorientation. Changes of the invariants from meridian peaks and equatorial streaks during heating showed nonmonotonic behavior due to the different mechanisms involved. The gradual decrease of lamellae could lead to an inversion of scattering invariant in the two-phase model, resulting in a maximum in the invariant of meridian peak. Melting of surrounding lamellar crystals could reveal further the existence of microfibrils, yielding the enhancement of equatorial streaks. A two-step melting process was identified in this study. Upon heating, the coherence of crystal lattice is first destroyed in crystal blocks, resulting in the disappearance of diffraction peaks in WAXD. The persistence of molten microfibrils due to insufficient chain mobility can lead to the longevity of SAXS pattern. Molten chains diffuse into the amorphous matrix at higher temperatures.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Telephone: 631-6327793. Fax: 631-632-6518. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We wish to acknowledge the assistance of Drs. Lixia Rong and Jie Zhu for the synchrotron WAXD experimental setup. The financial support of this work was provided by the National Science Foundation (DMR-0906512) and ExxonMobil Chemical Company.

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