# Time-Resolving Study of Stress-Induced Transformations of Isotactic Polypropylene through Wide Angle X-ray Scattering Measurements

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{0}of 3.0 mm, width w

_{0}of 1.6 mm, and thickness t

_{0}of 0.25 mm were cut from films obtained by melting the samples in a hot press up to reach a temperature 20–30 °C higher than the melting temperature determined in the DSC scans, using only a small pressure, and by cooling the melt to room temperature while fluxing cold water in the refrigerating system of the press (average cooling rate ≈ 10 °C/min).

^{2}. The strong reflections of the unoriented film specimens are used to determine the correct beam center coordinates and the sample to detector distance. Roughly, the transmission factor is determined measuring the intensity of the direct beam (using an attenuator) in absence of the sample, and in presence of the sample, before stretching, and at the end of stretching experiment. In no case the sample was brought to the rupture. Raw WAXS data are reduced and analyzed using the home made software XESA [36]. In the experiments, the X-ray beam is incident on the central region of the specimens. In this way, the structural changes occurring by effect of mere uniaxial deformation with negligible shear components may be probed. The equatorial profiles are obtained by radial integration of WAXS intensity along arcs in slices spanning an angle of ±20° with respect to the horizontal axis (equator) of the bidimensional WAXS images. We checked that in the stretching conditions adopted for the in situ WAXS measurements, the samples experience uniform deformation. We found that the thickness t decreases according to a power law t = t

_{0}(l

_{0}/l)

^{ν}, with ν comprised between 0.4 and 0.5, depending on the deformation, l being the gauge length of the deformed specimens [19,20]. In the calculation we set, for the sake of simplicity, ν ≈ 0.5, in the whole deformation range, as expected for ideal rubbery materials [37].

## 3. Results

_{start}≈ 200% and is complete at ε

_{end}≈ 400–500% (Figure 1 and Figure 2). In all cases a highly oriented fibrillary morphology is obtained already at the deformations marking the end of transition [19,20].

^{−1}, corresponding to the reflection (111)

_{γ}of γ form at low deformations (images a–c of Figure 1 and curves a of Figure 2), and to the tail of the mesomorphic halo centered at q ≈ 11 nm

^{−1}at high deformations (images d–e of Figure 1A, d of Figure 1B, curves d–e of Figure 2A, and d of Figure 2B). In fact, as shown in Figure 3, the azimuthal intensity distribution at q ≈ 10 nm

^{−1}is uniform for the undeformed samples (curves a of Figure 3) and becomes polarized on the equator with increasing the deformation (curves b–e of Figure 3A and b–d of Figure 3B).

^{−1}relative to the (008)

_{γ}reflections of γ form (curves a of Figure 2), instead, at low deformations is polarized on a layer line off the equator (horizontal direction) and off the meridian (vertical direction), as indicated by the arrows in the images b, c of Figure 1, and only when the transformation into the mesophase is complete, that is, at deformations higher than ε

_{end}, the intensity at q ≈ 12 nm

^{−1}becomes polarized on the equator [19,20]. This indicates that part of the crystals of the initial γ form tend to become oriented at low deformations with the chain axes nearly perpendicular to the stretching direction, as shown in Figure 4, instead than parallel as in the standard fiber morphology [16,38]. It is worth noting that for the perpendicular chain axis orientation of γ form, the polarization of the (111)

_{γ}(at q ≈ 10 nm

^{−1}) reflection occurs on the equator [39].

## 4. Data Analysis and Discussion

^{−1}of Figure 3. A numerical descriptor O that plays the role of an orientation order parameter is introduced from the calculation of the orientation function <P

_{2}> [40]. In general, for uniaxially symmetric materials (such as fibers) the orientation function for a direction normal (pole) to any given {hkl} family of planes <P

_{2}(cosχ)> with respect to a preferred direction (fiber axis) is defined as:

_{2}> = 1 corresponds to an ideal case of perfect alignment of the poles in the preferential direction, <P

_{2}> = 0 corresponds to isotropic case and <P

_{2}> = −0.5 corresponds to an ideal case of perfect perpendicular orientation.

^{−1}on the equator, with respect to the fiber axis. This would correspond to values of the orientation function <P

_{2}>

_{exp}ranging from zero at zero deformation (completely isotropic case) to values less than zero with increasing the deformation. The parameter O is calculated by comparing the experimental values of <P

_{2}>

_{exp}at q ≈ 10 nm

^{−1}with that of an ideal model characterized by an extremely narrow equatorial polarization of intensity at this q (that is <P

_{2}>

_{id}= −0.5) as:

^{−1}originates from the perpendicular chain axis orientation of the residual γ form crystals at low and moderate deformations and from the parallel chain axis orientation of the already transformed mesomorphic domains at moderate and high deformations, the value of the parameter O represents a measure of the average degree of orientation of the chain axes with respect to the fiber axis only at high deformations, that is, after complete transformation of the original crystals of γ form into the mesophase, whereas at lower deformation, the values of O represents a measure of the average degree of orientation of the residual crystals of γ form in the perpendicular chain axis orientation, and of the transformed mesomorphic domains in the parallel chain axis orientation. The so obtained values of the parameter O derived for the iPP samples are reported in Figure 5A.

_{γ}reflections of γ forms essentially probe small reorientation of the lamellar crystals along the pathway toward the fibrillary morphology, due to lamellar rotations [26,27,40]. The leading deformation mechanisms in the first plateau region, instead, correspond to interlamellar shear, that is slip of the crystalline lamellae parallel to each other, and/or interlamellar separation [26,27,28,41,42]. At this stage, no phase transitions occur and all movements are assisted by the shear deformation of the compliant interlamellar amorphous phase. Successively, starting from deformations close to the critical strain at which transformation into mesophase starts (ε

_{start}≈ 200%, Figure 1 and Figure 4), the orientational order O increases again up to reach a final plateau value of ≈0.8 at high deformations (Figure 5A). This indicates that after lamellar breaking, further deformation induces collective shear process, up to reach destruction of the preexisting crystals (mechanical melting) and successive recrystallization with formation of fibrils including mesomorphic aggregates [24,25].

_{min}= 3 nm

^{−1}and q

_{max}= 22 nm

^{−1}, using Equation (4):

_{0}/t to account for the thickness contraction, by setting t

_{0}/t = (l/l

_{0})

^{ν}with ν = 0.5 (see Section 2). Therefore, curves a, b and a’, b’ of Figure 5B illustrate the change of the parameter Γ(ε) with increasing the deformation, in the limiting cases of no thickness contraction (Poisson’s ratio = 0, curves a, b) and in the rubbery limit of thickness contraction, corresponding to Poisson’s ratio ν = 0.5 (curves a’, b’). The invariant is expected to change with deformation according to a behavior in between these two limiting cases.

_{ε}(q,χ) can be written as a linear combination of the scattering intensities from each phase:

_{εi}(q,χ) are the scattering intensities of the γ form (phase i = 1), mesophase (phase i = 2) and amorphous component (phase i = 3) and x

_{i}(ε) are the corresponding mass fractions. Therefore, also the total WAXS reduced invariant Q(ε) (Equation (4)) is a linear combination of the contribution from components Q

_{i}(ε).

_{i}(ε), in turn, is proportional to the following quantities [44,45]:

_{i}and N

_{i}

_{ε,}are the electron density and the number of domains of phase i with average volume of coherence equal to V

_{i}

_{ε},. The N

_{i}

_{ε}domains contribute additively to the scattering, whereas the coherent (elastic) scattering occurs only within each domain. The density of γ form, mesophase and amorphous phase in isotactic polypropylene are 0.939, 0.91 and 0.854 g/cm

^{3}[46] and the corresponding values of electron density are 323, 313 and 294 electrons/nm

^{3}respectively. Based on previous analyses [16,17,18], the total degree of crystallinity, due to the γ form and mesophase contributions, apparently, does not greatly change during deformation (x

_{1}(ε) + x

_{2}(ε) ≈ 0.50, see Table 1). Therefore, in the hypothesis that also the total volume of the coherently scattering crystalline domains does not change by effect of deformation (N

_{1ε}V

_{1ε,}+ N

_{2ε}V

_{2ε,}= cost.), the scattering invariant is expected to remain constant or to slightly decrease with increasing the deformation, since the γ form transforms into the mesophase with slightly lower electron density.

_{start}marking the beginning of transformation of the initial γ form into mesophase, may be due to local “densification” of the amorphous intralamellar phase by effect of stretching, since the intralamellar amorphous phase experiences compressive forces in the direction parallel or perpendicular to the layers, depending on the orientation, perpendicular or parallel to the stretching direction, respectively, of the lamellar stacks in which the amorphous layers are embedded [2,20]. At deformations higher than ε

_{start}, marking also the beginning of lamellar destruction, we hypothesize that the increase of invariant may be due to a slight increase of the size of coherent domains located in the mesomorphic aggregates, leading to a remarkable increase of their average volumes V

_{2ε}, even though the total number of these domains N

_{2ε}does not necessarily change. This increase may involve the incorporation of isolated chains, or groups of 2–3 chains located at the boundaries of adjacent domains, into close neighboring larger domains through small movements and/or rotations facilitated by deformation, as shown in the model of Figure 6.

^{3}–1.6

^{3}≈ 1.3–4. As shown in the model of Figure 6, the increase of the coherent length of the mesomorphic domains by incorporation (coalescence) of the isolated sub-domains a-d within the mesomorphic domains, does not necessarily lead to a decrease of the number of domains N

_{2ε}. As a consequence, the total scattering intensity increases by effect of deformation, because the product (N

_{2ε}V

_{2ε}) increases due to coalescence phenomena of the kind depicted in Figure 6.

_{c}) and the total area of the diffraction profile (A

_{tot}) does not apparently change (see Figure 7A), is due to the fact that A

_{c}is often overestimated in this procedure, as it is obtained by the difference of A

_{tot}and the diffraction area from the amorphous component (approximated in Figure 7A by the diffraction profile of an atactic polypropylene, curve b). In other terms, the crystallinity calculated from the radially averaged WAXS curves according to the procedure of Figure 7A, includes not only the Bragg contribution, but also diffuse scattering located in the diffraction region between the amorphous halo and the Bragg peaks (Figure 7A). Instead, in the experimental value of the scattering invariant, the diffuse scattering terms makes a contribution, which is at least one order of magnitude lower than the Bragg component. Diffuse scattering arises from the presence of disorder and its contribution to the scattering intensity is proportional to the fluctuations of the structure factor f (per monomeric unit), given by the term <f

^{2}> − <f>

^{2}, which represent the difference between the average square (<f

^{2}>) and the square of average (<f>

^{2}) of f [48]. Therefore, the higher the local structure factor deviates from the average value <f> because of the presence of disorder, the higher the fluctuations, and the higher the diffuse scattering. By effect of coalescence of the small sub-domains into the large domains, the diffuse scattering decreases and the interference term (Bragg-like contribution) increases. The WAXS invariant increases, because the diffuse scattering term is always lower than the Bragg term.

## 5. Conclusions

_{start}) the γ form starts transforming into the mesomorphic form of iPP, and at 400–500% deformation (ε

_{end}), the transformation is almost complete. The stress induced phase transition of the γ form into the mesophase occurs after the beginning of lamellar fragmentation, concomitant with destruction of the crystalline blocks (mechanical melting) and re-crystallization in fibrillary entities containing mesomorphic aggregates. At the end of transformation into mesophase, a fibrillary morphology develops with a high degree of orientational order of the chain axes parallel to the stretching direction. We show that the chains extracted from the original crystals re-crystallize forming aggregates of mesomorphic domains responsible for the coherent elastic scattering (Bragg-like contribution) which include at the boundaries isolated chains or groups of 2–3 chains, which contribute to diffuse scattering. The coalescence process of these chains with the larger mesomorphic domains, increases the volume of coherence of the mesomorphic domains. Since the number of coherent domains does not decrease, the WAXS scattering invariant increases by effect of coalescence during deformation, even if the sampled q region is narrow. Coalescence starts concomitant with the process of lamellar destruction, and beginning of transformation of the initial γ form into the mesophase and, after complete transformation into the mesomorphic form, continues facilitated by the mechanical stress field.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Stress strain curves (

**A’**,

**B’**) and bidimensional WAXS patterns of the sample iPP-5.9 (

**A**) and iPP-11.0 (

**B**) at the indicated deformations. The critical values of deformation marking the beginning (ε

_{start}), and the complete (ε

_{end}) transformation of the initial γ form into mesophase are indicated by the vertical bold lines in (

**A’**,

**B’**). The stretching direction is vertical. Arrows in b and c indicate the polarization of the (008)

_{γ}reflection of γ form, off the equator (horizontal direction) and off the meridian (vertical direction), defined in the image a of part A of the figure, occurring at low deformations, due to orientation of the crystals of the γ form with chain axes nearly perpendicular to the stretching direction (vide infra). The azimuthal angle χ is defined in the image a of part A.

**Figure 2.**Equatorial profiles extracted from the bidimensional WAXS images of Figure 1 for the samples iPP-5.9 (

**A**) and iPP-11.0 (

**B**). The relevant reflections of α and γ forms are indicated.

**Figure 3.**Azimuthal profiles of intensity centered in the q region around 10 nm

^{−1}, extracted from the bidimensional WAXS images of Figure 1 for the samples iPP-5.9 (

**A**) and iPP-11.0 (

**B**).

**Figure 4.**Structural model of γ form (

**A**), scheme of the perpendicular chain axis orientation of γ crystals (

**B**) and of mesomorphic domains of iPP (

**C**), as they develop by effect of stretching, starting from unoriented specimens.

**Figure 5.**Orientation parameter O (

**A**) and total WAXS scattered intensity (invariant) normalized for the integrated intensity of the unoriented sample Γ(ε) (

**B**) as a function of strain, for the samples iPP-5.9 (○, ●) and iPP-11.0 (○, ●). The parameter O is calculated from the azimuthal intensity distribution at q ≈ 10 nm

^{−1}in the bi-dimensional WAXS images of Figure 1, corresponding to the reflection (111)

_{γ}of γ form at low deformations, to the tail of the mesomorphic halo centered at q ≈ 11 nm

^{−1}at high deformations. It represents a measure of the average degree of orientation of the chain axes with respect to the fiber axis at high deformations (>ε

_{end}), and to the average degree of orientation of the residual crystals of γ form in the perpendicular chain axis orientation, and of the transformed mesomorphic domains in the parallel chain axis orientation at deformations lower than ε

_{end}. In (

**B**), the curves a’ and b’ (open symbols) are obtained by multiplying the curves a and b (full symbols) by the factor t

_{0}/t = (l/l

_{0})

^{1/2}to account for the thickness contraction (see Experimental section).

**Figure 6.**Model of coalescence of mesomorphic domains separated at the boundaries by isolated groups of 1–2 chains (sub-domains a–d) in a completely different arrangement (

**A**) with formation of larger mesomorphic domains (

**B**). By effect of stretching, the sub-domains a–d coalesce with close-neighbors mesomorphic domains.

**Figure 7.**(

**A**) Radially averaged WAXS profile of the undeformed sample iPP-5.9, extracted from the bidimensional WAXS image a of Figure 1A (a) and underlying amorphous contribution, approximated by the diffraction profile of an atactic polypropylene (b). (

**B**) Equatorial profiles extracted from the bidimensional WAXS images of Figure 1B, of the sample iPP-11.0 stretched at 574 and 900% deformations. The diffraction curves are subtracted for the background contribution, approximated as a straight line subtending the whole profiles.

**Table 1.**Molecular mass (M

_{v}), melting temperature (T

_{m}) and content of rr triads of iPP samples prepared by metallocene catalysts as described in ref. [22]

^{a}.

Sample | M_{v} (kg/mol) ^{b} | T_{m} (°C) ^{c} | [rr] (mol %) ^{d} | x_{c} ^{f} (%) | f_{γ} ^{f} (%) |
---|---|---|---|---|---|

iPP-5.9 | 211 | 114 | 5.92 | 55 | 96 |

iPP-11.0 | 123 | 84 | 11.01 | 42 | 100 |

^{a}The polydispersity index of molecular masses is close to 2.

^{b}From the intrinsic viscosities [15,22].

^{c}The melting temperatures were obtained with a differential scanning calorimeter Perkin Elmer DSC-7 performing scans in a flowing N

_{2}atmosphere and heating rate of 10 °C/min [22].

^{d}Determined from solution

^{13}C NMR analysis [22].

^{f}Crystallinity index x

_{c}and relative amount of γ form with respect to the α form f

_{γ}evaluated from X-ray diffraction profiles of compression-moulded samples [16,17,18,19,20].

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**MDPI and ACS Style**

Auriemma, F.; De Rosa, C.; Di Girolamo, R.; Malafronte, A.; Scoti, M.; Mitchell, G.R.; Esposito, S. Time-Resolving Study of Stress-Induced Transformations of Isotactic Polypropylene through Wide Angle X-ray Scattering Measurements. *Polymers* **2018**, *10*, 162.
https://doi.org/10.3390/polym10020162

**AMA Style**

Auriemma F, De Rosa C, Di Girolamo R, Malafronte A, Scoti M, Mitchell GR, Esposito S. Time-Resolving Study of Stress-Induced Transformations of Isotactic Polypropylene through Wide Angle X-ray Scattering Measurements. *Polymers*. 2018; 10(2):162.
https://doi.org/10.3390/polym10020162

**Chicago/Turabian Style**

Auriemma, Finizia, Claudio De Rosa, Rocco Di Girolamo, Anna Malafronte, Miriam Scoti, Geoffrey Robert Mitchell, and Simona Esposito. 2018. "Time-Resolving Study of Stress-Induced Transformations of Isotactic Polypropylene through Wide Angle X-ray Scattering Measurements" *Polymers* 10, no. 2: 162.
https://doi.org/10.3390/polym10020162