Hierarchical Structural Change in the Stress-Induced Phase Transition

Mar 12, 2014 - ... Chemical Society. *(K.T.) E-mail: [email protected]. ...... Davies , G. R.; Smith , T.; Ward , I. M. Polymer 1980, 21, 221. ...
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Hierarchical Structural Change in the Stress-Induced Phase Transition of Poly(tetramethylene terephthalate) As Studied by the Simultaneous Measurement of FTIR Spectra and 2D Synchrotron Undulator WAXD/SAXS Data Kohji Tashiro,†,* Hiroko Yamamoto,† Taiyo Yoshioka,† Tran Hai Ninh,† Masafumi Tasaki,† Shigeru Shimada,‡ Takeshi Nakatani,‡ Hiroyuki Iwamoto,§ Noboru Ohta,§ and Hiroyasu Masunaga§ †

Department of Future Industry-oriented Basic Science and Materials, Graduate School of Engineering, Toyota Technological Institute, Tempaku, Nagoya 468-8511, Japan ‡ Bruker Optics Japan, 1-4-1 Arakawa Chuo-Ku, Tokyo 104-0033, Japan § Japan Synchrotron Radiation Research Institute, 1-1 Koto, Mikazuki-cho, Sayo-gun, Hyogo 679-5198, Japan S Supporting Information *

ABSTRACT: The simultaneous measurement of Fourier transform infrared (FTIR) transmission spectra and 2-dimensional wide-angle X-ray diffraction (WAXD) and smallangle X-ray scattering (SAXS) patterns has been performed successfully to investigate the hierarchical structure changes occurring in the stress-induced phase transition phenomenon of uniaxially oriented poly(tetramethylene terephthalate) film. The molar fraction of the β-crystal form, evaluated from the IR and WAXD data analyses, increased steeply in the plateru region of the stress−strain curve as already known well. The 2D SAXS data have revealed the remarkable and reversible change in the stacked lamellar structure just after the α-to-β phase transition was completed, where the tilting angle of the stacked lamellae measured from the draw axis of the oriented sample became zero, and the lamellar thickness increased due to the inclusion of amorphous region located in the boundary part of the crystalline lamellae. In parallel, the X-ray reflection spots in a wider diffraction angle region became diffuse in the observed WAXD pattern of the β form, indicating the packing disorder of the mechanically stressed chains. In this way, the simultaneous combination of the 3 different types of equipments has allowed us to deduce the detailed structural change from the various levels: the stress-induced α−β transition was found to occur not only with the remarkable changes in the molecular chain conformation and chain packing mode in the crystal lattice, but also with the large and reversible change in the lamellar stacking structure. The stress-induced changes in lamellar thickness and long period were simulated using a mechanical model with these hierarchical structure changes taken into account, giving relatively good reproduction of the observed data.

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data2,10−12,15,17−21 gave the relative content of the β form as a function of stress and strain. It was found that the β form content increases steeply at the critical stress corresponding to the plateau of the stress−strain curve.17−20 The β content increases linearly in proportion to the strain of the bulk sample. The thus-observed stress and strain dependences of the β form content were interpreted reasonably using the concept of the thermodynamic first-order transition.17−20 In a low stress region, the α form is elastically deformed. Once the stress reaches the critical value, then the transition from the α to β form occurs and continues up to the end of the α-to-β conversion. Then the mechanical deformation of the β form starts with further increment of stress. This transition is reversible but some degree of hysteresis is observed.1,2,14,17,22 In the actual sample, a certain residual strain exists even after the

INTRODUCTION A. Stress-Induced Solid-State Phase Transition of PTMT. Poly(tetramethylene terephthalate) (PTMT, −[−OCO-C6H4−COO−(CH2)4−]n−) is one of the most typical engineering plastics and shows the reversible solid-state phase transitions between the two crystalline forms, α and β, which are induced by applying the tensile stress along the chain axis.1,2 This type of tension-induced phase transition can be seen also for poly(ethylene oxide),3 feather keratin,4 poly(butylene succinate),5 etc. In the case of PTMT, the crystalline α form takes the gauchetype conformation in the methylene segmental part, while the crystalline β form takes the all-trans conformation as shown in Figure 1.6−13 The trans-gauche conformational exchange is induced by the tensile stress. This structural transition reflects on the stress−strain curve measured for the oriented bulk sample, where a plateau is observed at a critical stress value.1,2,14−17 The quantitative analysis of wide-angle X-ray diffraction (WAXD) 1 , 7 , 1 7 − 1 9 and infrared spectral © 2014 American Chemical Society

Received: October 3, 2013 Revised: December 31, 2013 Published: March 12, 2014 2052

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temperature, tensile force etc. Therefore, it is more desirable to utilize the simultaneous measurement system, in which the various kinds of equipments are set around a sample subjected to an external condition. However, when the literature is searched, the number of papers reporting the simultaneous measurements is limited in number.23−31 In a series of papers, we have developed the simultaneous measurement systems of the WAXD, SAXS, and Raman spectral data and applied them to the structural studies of the various kinds of crystalline polymers.27−31,33,34 The Raman spectroscopy was convenient in such simultaneous measurements, but the Raman measurement is not necessarily successful in the structural study of polymer materials. This is because many polymer samples tend to emit the relatively strong fluorescence which covers the weaker Raman signals seriously, making the normal detection of Raman signals difficult or impossible actually.32 In contrast, the infrared spectroscopy does not show such a trouble of fluorescence covering over the spectral region measured, giving us the stable and highly resolved band signals. In this case, it is necessary to collect the transmission-type IR spectral data, not the reflection-type data. Although the reflection-type infrared spectra are often measured as a conventional method, in which the infrared beam is incident on the sample surface and the reflected infrared signals are collected by the detector, the profile, peak position, and relative height of the observed band are more or less deformed from the originally expected regular band shape because of the abnormal dispersion effect of the refractive index.32 Quite contrarily, the transmission-type infrared band may take the regular shape and so it is quantitatively analyzable about the profile, intensity and peak position. In this case of transmission-type infrared spectral measurement, however, we have to use a thin film of several micrometers to several tens of micrometers in thickness. When we want to measure the WAXD and SAXS data for such a thin film of only several micrometers in thickness using a laboratory-level X-ray diffractometer, we need to expose the sample in the X-ray beam for tremendously long time to collect the X-ray scattering data of high signal-to-noise ratio enough for the quantitative analysis. This situation is quite opposite to the easier and prompt measurement of the Fourier-transform infrared (FTIR) spectra, which can be obtained in only 1 s, for example. This dilemma between the X-ray diffraction and transmission-type infrared spectral measurements may be taken away by introducing the synchrotron system as an incident Xray beam. In particular, the synchrotron undulator system can generate an X-ray beam of remarkably high brilliance. The combination of the undulator X-ray beam and highly sensitive X-ray detector makes it quite easy to measure the WAXD and SAXS patterns of the thin film of several micrometer thickness in a time scale shorter than 1 s! As mentioned above, the thin film of several micrometer thickness is suitable for the transmission-type infrared spectral measurement. In other words, the combination of transmission-type infrared spectroscopy and synchrotron undulator X-ray system allows us to perform the simultaneous measurement of FTIR transmission spectra and WAXD and SAXS data at a time interval of 1 s order. Recently we have succeeded to set up a miniature-type FTIR spectrometer into the synchrotron system of SPring-8, Japan.31 The thus-developed simultaneous measurement system has been applied to the study of stress-induced phase transition phenomenon of PTMT sample. It may be emphasized here that

Figure 1. Crystal structures of PTMT α and β forms. The methylene segmental parts (CO−O−CH2−CH2−CH2−CH2−O-CO) take TGGTG̅ G̅ T and TTTTTTT structures for the α and β forms, respectively.

stress is relaxed almost perfectly. The sample goes back to the α form again by annealing above the glass transition temperature (ca. 80 °C) where the residual strain disappears. In our previous papers,17−20 we indicated that the structural change occurring in the crystalline region affects the higherorder structure. The long period of the stacked lamellar structure was found to change in parallel to the strain of the bulk sample as known from the small-angle X-ray scattering (SAXS) measurement. However, the details have not yet been clarified enough well about the relationship of the structural change between the crystalline lattice and the higher-order structure. It is ideal to investigate these structural changes in situ during the stretching process by simultaneously performing the FTIR spectral measurement (for the molecular chain conformational change), the WAXD measurement (for the change in chain packing mode in the crystalline lattice) and the SAXS measurement (for the higher-order structural change). Of course, the stress−strain curve must be measured in parallel to these measurements. B. Application of Simultaneous Measurement System. Here, let us see briefly the usefulness of such a simultaneous measurement system of WAXD/SAXS/FTIR in the study of hierarchical structural change of polymers. As well-known, the individual techniques of WAXD, SAXS and IR (Raman) spectroscopy are useful for the structural study of polymers, but the individual method views the phenomenon from only one direction. It is natural to consider that an organized combination of these various characterization techniques is powerful for the description of the whole structural features viewed from the various directions. However, polymer materials, in more general, soft materials respond quite sensitively to a slight change in such an external condition as 2053

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the combination of all the experimental data presented in the present paper has been able to lead us to the detailed description of the hierarchical structural changes occurring in the mechanically deformed PTMT sample viewed from the various directions.

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EXPERIMENTAL SECTION

A. Building-up of the Simultaneous Measurement System. Building-up of the simultaneous measurement system was made as illustrated schematically in Figure 2a. The experiment was performed

Figure 3. Block diagrams of a miniature FTIR spectrometer used in the simultaneous measurement system shown in Figure 2 time including the data transfer time was ca. 7 s at the resolution power 2 cm−1. B. Samples. The PTMT sample supplied by Mtsubishi Chemicals Co. Ltd. Japan was dried up in vacuo overnight. The sample was meltpressed and quenched into ice water bath. The film was stretched about 5 times the original length at 80 °C and annealed at 130 °C under tension. The sample thickness was about 15 μm. This sample was set into a miniature stretching equipment (Linkam, 10073A). The sample was stretched symmetrically into the upward and downward directions at the speed of 0.17%/sec. The transmission FTIR spectra were measured at every 7 s. The WAXD and SAXS patterns were measured at the same timing, but the actual X-ray exposure time was only 1 s and the waiting time was 6 s since the longer exposure resulted in the saturation of the X-ray scattering intensity. The experiment was performed in the cycle of increasing and decreasing stresses at room temperature.

Figure 2. (a) Schematic illustration of simultaneous measurement system of FTIR, WAXD and SAXS data. (b) Snapshot of the system actually installed in the beamline BL40XU at SPring-8. at the beamline BL40XU in SPring-8, Japan. Figure 2b is a snapshot of actually setup system in this beamline. The X-ray beam generated from the synchrotron radiation source passed through the sample. A detector of WAXD data was the flat panel (Hamaphotonics Co. Ltd., Japan) installed at the position about 8 cm behind the sample center. The effective area of the detector was 5.2 × 5.2 cm2, limiting the measurement range of the 2-dimensional diffraction pattern. The center of the flat panel was set at a position just above the X-ray beamline so that the SAXS signals passed through. At the same time, the flat panel was 45° tilted from the vertical line so that both of the equatorial- and layer-line X-ray reflections were detected on the small display screen. As for the SAXS measurement, a vacuum path was set between the sample and the detector, which was an image-intensifier CCD camera (Hamaphotonics Co. Ltd., Japan) set about 3.3 m distant from the sample position. The flat panel and CCD camera were controlled synchronously by the computer system. The X-ray beam size at the sample position was 40 μm (vertical direction) × 250 μm (horizontal direction). The wavelength of the X-ray beam was 0.827 Å. The WAXD and SAXS data were collected at every 1 s. The FTIR spectrometer had to be set so that the infrared beam was focused on the same position of the sample into which the X-ray beam was incident as mentioned above. We used the commercially available miniature FTIR spectrometer which could satisfy these requirements, Bruker FTIR spectrometer Alpha. As shown in Figure 3, the mirror system was optionally prepared and set to the sample box position. The infrared beam emitted from the IR source (A) was reflected once on the surface of the concave mirror (B) and focused at the sample position (C), then it was again reflected on the other concave mirror (D) and entered the TGS detector (E). This spectrometer was set on the sample stage so that the X-ray beam could pass through the focal point (C) along the IR optical path. Strictly speaking, the FTIR equipment was a little tilted from the horizontal direction (ca. 2°) so that the two concave mirrors did not disturb the passage of the incident X-ray beam as illustrated in Figure 3. In the space of the sample stage, a Linkam 10073A stretcher was set. The shortest scan

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RESULTS AND DISCUSSION Figure 4 shows the stress−strain curves measured in the simultaneous measurement process during stretching and

Figure 4. Stress−strain curve obtained during the simultaneous measurement experiment of the uniaxially oriented PTMT sample. In the plateau region the α-to-β transition occurs in the stretching process. 2054

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relaxation of the oriented film. Figure 5 shows the change of the infrared spectra measured in parallel. In Figure 6 the change of the corresponding 2-dimensional WAXD and SAXS patterns is reproduced.

Figure 5. Infrared spectral changes of uniaxially oriented PTMT sample measured in the stretching and relaxation processes.

A. FTIR Data Analysis. The infrared bands of the α and β forms changed their intensities oppositely with an increment of stress. The integrated intensities were estimated for these infrared bands by a curve separation method, from which the molar fraction of the α form Xα was evaluated quantitatively (the details of the data analysis is described in Appendix). Figure 7 shows the thus-evaluated Xα plotted against (a) the stress and (b) the strain of the bulk sample. The Xα decreased almost linearly with an increment of strain in the transition region (strain 5−16%), whereas it decreased steeply in the narrow stress region of 40−60 MPa. This phase transition region corresponds to the plateau region in the stress−strain curve. These behaviors are essentially the same as those reported in our previous paper.17 When the stretched sample was relaxed, a large hysteresis was observed and the transition from the β to α form started to occur for the first time when the stress decreased down to ca. 20 MPa. The pure α sample was obtained when the sample was annealed at a high temperature above Tg since the residual strain was erased totally. B. WAXD Data Analysis. From Figure 6, the X-ray diffraction profiles were extracted, as shown in Figure 8 where the equatorial line profiles are given as an example. The molar fraction of the α form was estimated from the integrated X-ray diffraction intensities following the similar treatment to that of infrared band data. Figure 7 compares the results of FTIR and WAXD, in good agreement within the error. The 2D-WAXD data give us the useful information about the structural changes in the phase transition. As shown in Figure 9,

Figure 6. 2D wide-angle and small-angle X-ray scattering patterns of uniaxially oriented PTMT sample measured in the (a) stretching and (b) relaxation processes. The vertical scale in the SASX pattern is 0.4 nm−1.

the WAXD pattern of the highly tensioned β form is quite diffuse, which was measured in the laboratory using Mo Kα Xray beam. The reflections in the higher-angle region are difficult to detect. Additionally the diffuse scatterings are detected along the equatorial line. This indicates that the chain packing mode in the crystal lattice of the β form is disordered, in particular, the relative height of the neighboring chains is appreciably irregular due to the random translational shift along the chain axis. The width of the hk0 reflections is also relatively large compared with that of the α form. From the half width, the crystallite size along the lateral direction was evaluated using a Scherrer’s equation. The β form has a small crystallite of about 28 Å, much smaller than that of the α form, 83 Å. C. SAXS Data Analysis. As shown in Figure 6, the initial α form shows apparently 2-points SAXS pattern, but the pattern 2055

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Figure 9. 2D WAXD diagrams measured for uniaxially oriented PTMT α and β forms, which were taken using a Mo−Kα line as an incident X-ray beam and with an imaging plate detector in the laboratory. The layer lines are numbered. It should be noted that many diffraction spots were diffuse in the β form, different from the α form.

meridional direction. This 2-points pattern returns to the original wide pattern of the α form in the relaxation process. This apparently wide 2-points pattern of the α form sample is not true, but it is actually the 4-points scattering pattern as seen in the SAXS patterns detected in the strain region of 20−8%. This indicates a titling of stacked lamellae by about 20° from the draw direction of the sample. For all the SAXS data the lamellar tilting angle was estimated, where the width of the scattering profile along the horizontal line was converted to the tilting angle since we know the correspondence between the scattering width observed at 15% strain in the relaxation process and the tilting angle of 20° estimated from the maximal intensity peak position. The thus-estimated tilting angle is plotted against the sample strain and compared with the α content (Xα) in Figure 10. The lamellar titling angle was found to change remarkably at the stage where the α form transformed almost completely to the β form. In the relaxation process, the tilting angle increased again largely once the β form started to transform to the α form. The original sample shows the tilted lamellar structure and the α−β phase transition in the crystal lattice occurs without a remarkable change in the stacked lamellar structure, but this higher-order structure changes steeply and reversibly to the vertically standing lamellar structure for the f irst time when the transition to the β form is completed and the β form crystallites are tensioned f urthermore along the stretching direction. The SAXS data give us additional information about the details of the long period and lamellar thickness. The 1Dscattering profiles, derived from the 2D SAXS data, are shown in Figure 11, parts a and c, from which the correlation functions K(z) of the stacked lamellar structure were calculated as shown in Figure 11, parts b and d (details of the data analysis are described in the Supporting Information). The long period LP or the interlamellar distance and the averaged thickness ⟨d⟩ of the lamellae along the drawing direction, which were evaluated from the correlation functions, are plotted against the stress and strain of the sample as shown in Figure 12a, where the lamellar tilting effect was corrected for these two parameters. Both of these two parameters increased almost continuously with an increment of strain and stress. By referring to the difference in the repeating period of the molecular chain between the α and β forms, the lamellar thickness and the LP might be increased by 11.7%. But the actually detected change in lamellar thickness

Figure 7. Stress and strain dependences of molar content of the α crystalline form (Xα) evaluated from the infrared and WAXD data of PTMT sample shown in Figure 5

Figure 8. Change in 1D WAXD profile of PTMT sample measured during the stretching and relaxation processes, where the data were extracted from Figure 6

is appreciably long along the horizontal direction. The β form shows more clearly the 2-points scattering pattern in the 2056

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Figure 10. Strain dependence of the tilting angle of stacked lamellae of the oriented PTMT sample in comparison with the change in Xα. The tilting angle is defined as the angle between the normal vector of the lamella and the draw direction. The tilting angle decreased drastically once the α-to-β transition was completed in the stretching process, and it increased again when the β-to-α transition started.

Figure 12. Stress dependences of (a) Xα, (b) the observed and calculated lamellar thickness ⟨d⟩, and (c) the observed and calculated long period (LP) of uniaxially oriented PTMT sample, where the calculation was performed by taking into account the heterogeneous stress distribution but without any consideration of the additional growth of lamellar thickness. The broken lines are the curves predicted for an ideal phase transition with the sharp critical stress at 53 MPa.

describe the concrete images of the structural changes during the stress-induced phase transition of PTMT in the following way. The α form exhibits the relatively regular crystal structure consisting of the molecular chains with the gauche methylene segments. The X-ray coherent size of the crystallites is 43 Å along the chain axis and 83 Å in the lateral direction (the X-ray coherent size is not necessarily equal to the whole size of lamella, which should be much larger because the aggregation of the coherent crystalline domains). These lamellae are stacked together along the draw direction with the tilting angle of about 20° measured from the draw direction, as illustrated in Figure 13. The sample was tensioned along the draw direction to

Figure 11. (a and c) Tensile strain dependences of the 1D SAXS profile of PTMT sample in the stretching and relaxation processes, respectively, and (b and d) the corresponding correlation functions K(z) calculated for the 1D SAXS data.

and LP is far beyond such an expectation, suggesting that the further increment of the lamellar thickness occurs due to the crystallization of the amorphous region adjacent to the lamellae. D. The Whole Structural Change Deduced from IR, WAXD and SAXS Data. On the basis of FTIR, WAXD and SAXS data analyses mentioned in the previous sections, we may 2057

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Figure 14. Stacked lamellar models of PTMT α and β forms. In the latter case, the molecular chains are shifted more or less randomly along the chain axis to result in the disappearance of lamellar tilting and breakage of larger domains into smaller pieces. The lamellar thickness is increased a little because of the inclusion of the boundary amorphous chains into the crystalline region.

sample was found to change remarkably in the tensile deformation process including the α−β phase transition in the crystal lattice. We will try to reproduce the experimentally obtained stress (and strain) dependences of LP and ⟨d⟩ using a mechanical model on the basis of the thus-estimated structural change. As shown in Figure 13, the mechanical model is assumed to consist of the alternately stacked crystalline lamellae and amorphous regions.17−20 The stress regions are divided into three: 0 < σ < σ*, σ = σ*, and σ > σ*. 1. Lamellar Thickness. a. 0 < σ < σ*. The elastic deformation of the α-form lamellae occurs. The averaged lamellar thickness ⟨d⟩ is expressed as follows.

Figure 13. Deformation process of the mechanical model of PTMT sample. (a) The tilted structure of the α crystalline lamellae, (b) the coexistence of the α and β forms in the phase transition occurring at the critical stress, (c) the tilted lamellar structure of the β form, and (d) the vertically standing lamellar structure of the β form where the lamellar thickness increases by drawing the amorphous region into the crystallites.

⟨d⟩ = d o α*(1 + σ /E o α) ≈ d o α

(1)

where the intrinsic Young’s modulus E α of the α form is 8.7 GPa (observed)35 to 10.1 GPa (calculated),36 and the second term in eq 1 is negligible in the σ range of 10 MPa order. The doα is an initial value of the averaged lamellar thickness, 4.32 nm. b. σ = σ*. The α-to-β phase transition occurs when the stress reaches the critical value σ*, and the lamellar thickness is increased by the difference in the repeating period between the two crystal phases. o

induce the α-to-β phase transition. The chain conformation changes to the all-trans form. These extended chains are packed in the crystal lattice of ca. 52 Å (along the chain axis) and 28 Å (in the lateral direction) at 20−30% strain. In this way the lamellar thickness is increased from 43 to 52 Å. Since the repeating period along the chain axis is increased by 11.7%, the lamellar thickness must be increased to 48 Å in the β crystal, but the observed value is larger, 52 Å. Therefore, as already pointed out above, the amorphous region near the lamellar boundary is included into the lamellae by the tensile force. At the same time, the fully extended molecular chains in the crystal lattice are more or less randomly shifted along the draw direction, and the crystal region is disordered in the packing structure as known from the diffuse X-ray diffraction pattern of the β form. Such a translational disordering of the molecular chain height might result in the disappearance of the tilting of the stacked lamellae (Figure 14). At the same time, this translational shift of chains may induce the breakage of the crystallites into smaller domains: the lateral size of the X-ray coherent domains becomes smaller from 83 Å (α) to 28 Å (β), which is speculated to occur by the slippage of molecular chains along the draw axis, although the slippage itself is only by 2−3 Å as estimated from the increment of the thickness. This slippage induces the irregular packing of the chains and the diffuse X-ray scatterings as mentioned above. E. Simulation of Mechanical Deformation Behavior. In this way, the hierarchical structure of the oriented PTMT

⟨d⟩ = Xα[d(α) at σ *] + Xβ [d(β) at σ *] ≈d o αXα + d o β(1 − Xα) =d o αXα + 1.117d o α(1 − Xα)

(2)

The lamellar thickness of the β form, d β is 1.117 times longer than that of the α form (doα) because of the longer repeating period of the β form by 11.7% than that of the α form. c. σ* < σ. The β-form lamellae are deformed by the stress. o

⟨d⟩ = d o β(1 + (σ − σ *)/E o β ) ≈ 1.117d o α

(3)

2. Long Period. The similar derivation was made also for the long period LP. a. 0 < σ < σ*. The elastic deformations of the α lamellae and the amorphous region occur. LP = LPo[1 + σ (Xc /Eα + (1 − Xc)/Ea)] ≈LPo[1 + σ (1 − Xc)/Ea] 2058

(4)

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amorphous region adjacent to the β crystallites (see Figure 14). By taking this situation into account, the equation concerning the lamellar thickness was modified, where the lamellar thickness was simply assumed to increase linearly with stress:

where Xc is the degree of crystallinity = doα/LPo = 0.404 using the initial lamellar thickness 4.32 nm and the initial LP value (10.71 nm). Ea = 0.60 GPa was assumed for the Young’s modulus of the amorphous phase.17 The second term was neglected because of the small elastic deformation of the crystalline phase. b. σ = σ*. The long period is increased in the α-to-β transition process.

dβ = d o β[1 + kβ(σ − 72 MPa)]

(7)

The coefficient kβ was determined so that the calculated ⟨d⟩ curve was in good agreement with the observed one: kβ ∼ 0.001 nm/MPa. This means that the application of additional stress of 1 MPa increases the lamellar thickness along the chain axis by doβkβ × 1 MPa = 0.135 nm in average (doβ = 4.83 nm). The ⟨d⟩ and LP were calculated by taking eq 7 into account in addition to the heterogeneous stress distribution discussed above. The results are shown in Figure 15, parts a and b, respectively, giving a good agreement with the observed data.

LP = contribution of the crystalline regions and the deformation in the amorphous region = d o α(1 + σ */EL α)Xα + d o β(1 + σ */EL β )(1 − Xα) + (LP* − d o α*)(1 + σ */Ea) ≈ d o αXa + d o β(1 − Xa) + (LP* − d o α*)(1 + σ */Ea) (5)

The first and second terms include the elastic elongation and the additional change in the crystallite thickness due to the αto-β phase transition. The third term is the elastic elongation of the amorphous region. c. σ* < σ. The elastic deformation of the β-type lamellae and the amorphous region occurs. LP = d o β(1 + (σ − σ *)/EL β ) + (LP* − d o β) (1 + (σ − σ *)/Ea) ≈ d o β + (LP* − d o β)(1 + (σ − σ *)/Ea) (6)

The first term is the elongation of the β form crystals. The second term is the elongation of the amorphous region. In this equation the partial crystallization of the amorphous region is not taken into account. 3. Numerical Calculations. The numerical calculations were performed for the ⟨d⟩ and LP using these equations. As mentioned above, the α-to-β phase transition is the thermodynamically first-order transition and the α form transforms to the β form at a critical stress point (σ*). Therefore, the α content (Xα) should decrease sharply at the σ* point. This ideal case was adopted at first, where the phase transition was assumed to occur only at the critical stress σ* (=53.7 GPa or the central stress value in the Xα curve given in Figure 12a). Parts b and c of Figure 12 show the results calculated using the Xα curve indicated by a broken line. The ⟨d⟩ and LP change quite sharply at the critical stress. Of course, the calculated curves do not give any good reproduction of the experimental results. As the next trial, we utilized the Xα change occurring in a broader stress region as evaluated by the experimental data (open circles in Figure 12a). This corresponds to the assumption of the heterogeneous stress distribution in the bulk sample. The calculated results of ⟨d⟩ and LP (calcd-1) are shown in Figure 12, parts b and c, respectively, in comparison with the observed data. The calculated curves fit relatively well to the observed data in the stress region lower than 72 MPa, where the α form transformed almost completely to the β form. In the stress region higher than 72 MPa, however, the calculated ⟨d⟩ and LP are much shorter than the observed ones. In other words, we need to consider that the lamellar thickness grew furthermore even after the phase transition to the β form was completed or the additional crystallization of the

Figure 15. Stress dependence of (a) the lamellar thickness ⟨d⟩ and (b) the long period (LP) of the uniaxially oriented PTMT sample, where the calculations were performed by taking into account both of the heterogeneous stress distribution and the additional growth of lamellar thickness.

In this way, both of the long period and lamellar thickness were reproduced well by assuming the mechanical model consisting of the crystalline lamellae and amorphous phase with the factors of the heterogeneous stress distribution, the phase transition from the α to β form, and the additional crystallization of the amorphous region taken into account.

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CONCLUSIONS In the present paper, the newly developed simultaneous measurement system of transmission FTIR spectra/2DWAXD/2D-SAXS data has been successfully applied to trace the hierarchical structural changes in the stress-induced phase transition of uniaxially oriented PTMT film during the stretching and relaxing processes. The FTIR data gave us the 2059

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information about the stress- and strain-dependences of the crystalline α-form content. The WAXD data gave also the α content, but the 2-dimensional WAXD data was quite useful for the detection of the disordering in the crystal lattice as well as the change in crystallite size. The SAXS data were quite helpful for getting the information about the change in higher-order structure, i.e., the change in long period and lamellar thickness. In this way, the individual techniques gave us their characteristic information. But, more important point to be addressed here is that these three different data obtained from the various levels was combined together in an organized manner and revealed the whole images of the hierarchical structural change in the mechanical deformation process of oriented PTMT sample. PTMT is now utilized in the various ways as an excellent engineering plastic because of its high toughness against the mechanical fatigue, which is now understood well from the structural changes occurring in the mechanical deformation process, as described in this paper. The phase transition between the α and β forms consumes the mechanical energy so that the sample damage can be escaped and the mechanical toughness is enhanced. But, once the sample is deformed beyond the phase transition region, the mechanical deformation occurs in the already-mechanically deformed β crystallites, resulting in the rupture of the stressed sample.

*(K.T.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The synchrotron radiation experiments were performed at the BL40XU of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2011A1455 and 2012B1079). This study was supported financially by MEXT “Strategic Project to Support the Formation of Research Bases at Private Universities (20102014)”.

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(A1)

where ε is an extinction coefficient (the absorbance is related to the sample thickness but it is neglected here because the thickness is almost constant in this experiment). When only the 2 components of the α and β forms are coexistent in a transition region, the following relation is given for the molar fraction Xi. (A2)

Therefore, we have the following relation (eq A3) between Aα and Aβ, from which the Xα can be evaluated as shown in eq A4. Aα = −(εα /εβ )Aβ + εα

(A3)

Xα = p(Aα /Aβ )/[1 + p(Aα /Aβ )]

(A4)

p = (εα /εβ )

(A5)

The integrated intensities were estimated for the infrared bands at 810 cm−1 (α) and 845 cm−1 (β) after the curve separations were made.

■

REFERENCES

(1) Jakeways, R.; Smith, T.; Ward, I. M.; Wilding, M. A. J. Polym. Sci., Polym. Lett. Ed. 1976, 14, 41. (2) Davies, G. R.; Smith, T.; Ward, I. M. Polymer 1980, 21, 221. (3) Takahashi, Y.; Sumita, I.; Tadokoro, H. J. Polym. Sci., Polym. Phys. Ed. 1973, 11, 2113. (4) Ciferri, A. Trans Faraday Soc. 1963, 59, 562. (5) Ichikawa, Y.; Suzuki, J.; Washiyama, J.; Motekim, Y.; Noguchmi, K.; Okuyama, K. Polymer 1994, 35, 3338. (6) Mencik, Z. J. Polym. Sci., Polym. Phys. Ed. 1975, 13, 2173. (7) Yokouchi, M.; Sakakibara, Y.; Chatanim, Y.; Tadokorom, H.; Tanakam, T.; Yodam, K. Macromolecules 1976, 9, 266. (8) Hall, I. H.; Pass, M. G. Polymer 1976, 17, 807. (9) Desborough, I. J.; Hall, I. H. Polymer 1977, 18, 825. (10) Stambaugh, B. D.; Koenig, J. L. J. Polym. Sci., Polym. Lett. Ed. 1977, 15, 299. (11) Stambaugh, B.; Koenig, J. L.; Lando, J. B. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1053. (12) Stambaugh, B.; Lando, J. B.; Koenig, J. L. J. Polym. Sci., Polym. Phys. Ed. 1979, 17, 1063. (13) Tonelli, A. E. Polymer 2002, 43, 6069. (14) Strohmeier, W.; Frank, W. F. X. Colloid Polym. Sci. 1982, 260, 937. (15) Davidson, I. S.; Manuel, A. J.; Ward, I. M. Polymer 1983, 24, 30. (16) Gillette, P. C.; Lando, J. B.; Koenig, J. K. Polymer 1985, 26, 235. (17) Tashiro, K.; Nakai, Y.; Kobayashi, M.; Tadokoro, H. Macromolecules 1980, 13, 137. (18) Tashiro, K.; Hiramatsu, M.; Ii, T.; Kobayashi, M.; Tadokoro, H. Sen-I Gakkaishi 1986, 42, T659. (19) Tashiro, K.; Hiramatsu, M.; Ii, T.; Kobayashi, M.; Tadokoro, H. Sen-I Gakkaishi 1986, 42, T597. (20) Tashiro, K.; Abe, Y.; Araki, Y.; Sasakim, S.; Kobayashi, M.; Ohguchi, M. Rep. Progr. Polym. Phys. Jpn. 1996, 39, 333. (21) Dobrovolny-Marand, E.; Hsu, S. L.; Shih, C. K. Macromolecules 2001, 51, 21. (22) Brereton, M. G.; Davies, G. R.; Jakeways, R.; Smith, T.; Ward, I. M. Polymer 1978, 19, 17. (23) Bras, W.; Derbyshire, G. E.; Ryan, A. J.; Mant, G. R.; Felton, A.; Lewis, R.; Hall, C.; Greaves, N. NIM 1993, A 326, 587. (24) Bras, W.; Derbyshire, G. E.; Ryan, A. J.; Cooke, J.; Devine, A.; Komanschek, B. E.; Clark, S. M. J. Appl. Crystallogr. 1995, 28, 26. (25) Bras, W.; Derbyshire, G. E.; Bogg, D.; Cooke, J.; Elwellm, J. E.; Naylor, S. N.; Komanschek, B. E.; Ryan, A. J. Science 1995, 267, 996. (26) Bryant, G. K.; Gleeson, H. F.; Ryan, A. J.; Fairclough, J. P. A.; Bogg, D.; Goossens, J. G. P.; Bras, W. Rev. Sci. Instrum. 1998, 69, 2114. (27) Tashiro, K.; Sasaki, S. Prog. Polym. Sci. 2003, 28, 452. (28) Tashiro, K.; Kariyo, S.; Nishimori, A.; Fujii, T.; Saragai, S.; Nakamoto, S.; Kawaguchi, T.; Matsumoto, A.; Rangsiman, O. J. Polym. Sci., Polym. Phys. Ed. 2002, 40, 495. (29) Tashiro, K.; Nakamoto, S.; Fujii, T.; Matsumoto, A. Polymer 2003, 44, 6043.

APPENDIX The molar fraction of the α crystalline form (Xα) was estimated in the following way on the basis of the infrared spectral data (Figure 5). The infrared band absorbance Ai is proportional to the molar fraction Xi of the crystalline form i (i = α or β) as shown below.17

Xα + Xβ = 1

AUTHOR INFORMATION

Corresponding Author

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A i = εiX i

Article

ASSOCIATED CONTENT

S Supporting Information *

Calculation of correlation function K(z) and a figure showing the stacked lamellar structure (Figure B1). This material is available free of charge via the Internet at http://pubs.acs.org/. 2060

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Macromolecules

Article

(30) Tashiro, K.; Sasaki, S.; Saragai, S. J. Polym. Sci. Part B: Polym. Phys. Ed. 2004, 42, 4175. (31) Tashiro, K.; Yamamoto, H.; Yoshioka, T.; Ninh, T. H.; Shimada, S.; Nakatani, T.; Iwamoto, H.; Ohta, N.; Masunaga, H. KobunshiRonbunshu 2012, 69, 213. (32) Chalmers, J. M., Griffiths, P. R. Eds. Handbook of Vibrational Spectroscopy; John Wiley & Sons: New York, 2002. (33) Tashiro, K. Chin. J. Polym. Sci. 2007, 25, 73. (34) Tashiro, K.; Nishiyama, A.; Tsuji, S.; Hashida, T.; Hanesaka, M.; Takeda, S.; Cao, W.; Reddy, R. K.; Masunaga, H.; Sasaki, S.; Ito, K.; Takata, M. J. Phys., Conf. Ser. 2009, 184, 012002. (35) Nakamae, K.; Kameyama, M.; Toshikawa, M.; Matsumoto, T. J. Polym. Sci., Polym. Phys. Ed. 1982, 20, 319. (36) Tashiro, K. Prog. Polym. Sci. 1993, 18, 377−435.

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