Strain-Induced Deformation of Glassy Spherical Microdomains in

Department of Biobased Materials Science, Kyoto Institute of Technology, ... spheres simply deformed into prolate spheroids with its major axis parall...
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Strain-Induced Deformation of Glassy Spherical Microdomains in Elastomeric Triblock Copolymer Films: Simultaneous Measurements of a Stress−Strain Curve with 2d-SAXS Patterns Shogo Tomita,† Li Lei,‡ Yoshimasa Urushihara,‡ Shigeo Kuwamoto,‡ Tadashi Matsushita,§ Naoki Sakamoto,§ Sono Sasaki,† and Shinichi Sakurai*,† †

Department of Biobased Materials Science, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto 606-8585, Japan Synchrotron Radiation Nanotechnology Laboratory, University of Hyogo, Tatsuno, Hyogo 679-5165, Japan § Asahi Kasei Corporation, 1-105 Kanda Jinbocho, Chiyoda-ku, Tokyo 101-8101, Japan ‡

S Supporting Information *

ABSTRACT: Thermoplastic elastomers are elastomeric materials which contain hard domains as physical cross-linking for rubbery chains. Therefore, the hard domains are required permanently rigid. Nevertheless, we have found experimentally deformation of the hard domains upon uniaxial stretching of the thermoplastic elastomer films. In this paper, we report experimental results of deformation of glassy spherical microdomains in elastomeric triblock copolymer films upon uniaxial stretching, as revealed by two-dimensional small-angle X-ray scattering (2d-SAXS) measurements. Actually, shifts of the peak position of the particle scattering toward lower and higher q-regions were detected for q directions parallel and perpendicular to the stretching direction (SD), respectively, where q stands for the scattering vector. By assuming that spheres simply deformed into prolate spheroids with its major axis parallel to SD, 1d-SAXS profiles measured at several strains were successfully reproduced with model calculation of the 1d-SAXS profile. From the results of model calculation, radii of the prolate spheroids were appropriately determined. Since the extent of the deformation of microdomains was found to increase as the initial size of microdomains decreased, it is concluded that the deformation of glassy microdomains may be due to a high extent of the stress concentration at microdomains. Upon unloading, the deformed particle scattering peak in the 2d-SAXS pattern was found to retrieve almost a round shape. At a glance, this fact implies that the deformed sphere (prolate spheroid) recovers an isotropic shape. However, this kind of the elastic behavior cannot be the case for the glassy domain. Alternatively, we have tried to explain the change of the 2d-SAXS pattern by orientational relaxation of the prolate spheroids without changing the shape of the prolate spheroids. It was found that such trial was sound.

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INTRODUCTION Triblock copolymers with glassy microdomains dispersed in a rubbery matrix can be utilized as a thermoplastic elastomer because the glassy domains play a role of physical cross-linking for the rubbery chains. It is needless to say that the glassy domains should be permanently rigid; otherwise, the triblock copolymers are useless as an elastomer. Note that morphologies such as cylinder, lamellae, and double-gyroid are subjected to failure upon the stretching of the specimen.1−14 As for the spherical domains, deformation (namely, changing the shape from spherical to prolate spheroid) may be the case. Inoue et al. are the first to mention the possibility of the deformation of © XXXX American Chemical Society

polystyrene (PS) microdomains upon the stretching of the elastomeric polystyrene-block-polyisoprene-block-polystyrene (SIS) triblock copolymer film.15 They studied on the deformation behavior of the specimen during stretching via small-angle light scattering and two-dimensional small-angle Xray scattering (2d-SAXS) techniques. During the stretching, specific streaks parallel to the stretching direction (SD) were observed in the light scattering pattern. As a first step to Received: October 10, 2016 Revised: December 1, 2016

A

DOI: 10.1021/acs.macromol.6b02206 Macromolecules XXXX, XXX, XXX−XXX

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SIBS sample has a similar chemical structure of SEBS and no double bond in the main chain. This situation is superior as compared to the case of SEBS samples in which there is a trace of unhydrogenated double bond residue remained in the main chain. Therefore, the SIBS sample is thermally more stable. We used two different kinds of SEBS samples, which are SEBS-8 and SEBS-16 with volume fractions of PS being 0.084 and 0.16, respectively. The number-averaged molecular weight (Mn) and polydispersity index of molecular weights (Mw/Mn) of these samples are listed in Table 1, where Mw is the weight-averaged molecular weight.

interpret the specific pattern, they attempted to take into consideration of the uniaxial deformation of PS microdomains toward SD. But, the possibility was denied because any shifts in the particle scattering peaks could not be observed in the 2dSAXS pattern. In 1988, the deformation phenomenon was first detected by Seguela and Prud’homme, in which the deformation of the particle scattering peak was seen in the 2d-SAXS patterns measured for a polystyrene-block-polybutadiene-block-polystyrene triblock copolymer specimen. 16 Although the 20% of the deformation of the particle scattering peak can be seen in this literature, it was not clearly mentioned in the text. Prasman et al. have mentioned subtle deformation (2%) of the glassy spherical microdomains in block copolymer specimens.17 They investigated changes in structure and physical properties during stretching of SIS triblock copolymer specimens containing mineral oil (a polymer concentration of 60 wt %) by SAXS. They found that particle scattering originated from glassy spherical microdomains shifted toward lower q region for q∥ (a q-direction parallel to SD), while it shifted toward higher q region for q⊥ (a q-direction perpendicular to SD). Here, q is the scattering vector of which definition will be shown later. This fact may suggest deformation of the glassy spheres into an anisotropic structure with its major axis parallel to SD. However, they finally stated that the physical cross-linking due to glassy spheres might not be affected because the extent of the deformation of glassy spheres was trivial (2%). Actually, the deformation of glassy spheres was not discussed in detail. Another technique used to detect the deformation behavior was the FT-IR dichroism method with polarized beam.18−22 Since this method enables evaluation of the polymer chain orientation, it may be also possible to detect the deformation of PS microdomains. Duan et al. showed experimental results of SAXS and FT-IR measurements conducted during the stretching of polystyrene-graf t-polyisoprene graft copolymer films with PS spherical microdomains.23,24 They concluded the deformation of the PS spheres based on the results of FT-IR measurements showing that the orientation factor of PS block chains increased with strain. However, they failed to clearly detect the particle scattering peak in the 2d-SAXS patterns. Therefore, the deformation of PS was erroneous. Once the fragmentation of the PS spheres due to fracture takes place, the elongation of the PS block chains is induced. Therefore, the detection of the orientation of the PS block chains may not necessarily indicate deformation of the PS spheres. We report in the present paper clear deformation of the particle scattering peak in 2d-SAXS patterns for polystyreneblock-poly(ethylene-co-butylene)-block-polystyrene (SEBS) triblock copolymer specimens. Actually, before stretching the particle scattering peak appears as a round shape in the 2dSAXS pattern, and upon stretching the shape of the particle scattering peak was deformed. Finally, the relationship between the mechanical property and the deformation of PS spheres is discussed. For this purpose, the stress relaxation was measured.

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Table 1. Characteristics of Samples sample code

Mn

Mn of PS

Mw/Mn

ϕPS

SEBS-8 SEBS-16 SIBS

6.7 × 104 6.6 × 104 1.0 × 105

3.1 × 103 6.0 × 103 7.5 × 103

1.04 1.03

0.08 0.16 0.12

Solutions of these block copolymers with a concentration of 5 wt % were prepared by using toluene as solvent for the SEBS-8 and SIBS samples. As for the SEBS-16 sample, a mixture of dichloromethane (DM) and n-heptane was used. The reason for using the mixture as solvent is to force the SEBS-16 sample to form spherical microdomains. As we reported in our previous publication,27 when a selective solvent, which is selectively good and poor for one of the constitutive block chains of a block copolymer, is used, formation of nonequilibrium morphology in the as-cast film would be resulted and kinetically locked by the vitrification of PS (glassy component). This is due to a shift in effective volume fraction in the solution caused by the selective solubility of the solvent to the constitutive block chains. In our case, nonequilibrium spherical morphology can be formed in the as-cast specimen of SEBS-16 by using n-heptane as the solvent, although its equilibrium morphology is cylinder, where n-heptane is selectively good for poly(ethylene-co-butylene) (PEB) component. Since the SEBS-16 sample was hardly dissolved with n-heptane, the common solvent DM was adopted to obtain a homogeneous solution of the SEBS-16 sample. DM evaporates much faster than n-heptane due to its high vapor pressure; therefore, a homogeneous solution of SEBS-16 in n-heptane can be obtained. Solvent evaporation from the solutions of SEBS-8, SEBS-16, and SIBS were fully performed for at least 1 week at room temperature. Formation of spherical PS microdomains in the SEBS-16 as-cast film was verified via transmission electron microscopy (TEM) in our previous study.27 It was further found that such nonequilibrium spheres coalesced to form cylinders upon thermal annealing. This transition was observed in the wide range of the annealing temperatures (150−220 °C).27 Simultaneous Measurements of 2D-SAXS and Stress−Strain Curve. The SEBS-8 and SIBS films were thermally annealed at 210 °C for 10 h. These annealed films and the SEBS-16 as-cast film were cut into rectangular specimens with a dimension of 2.5 × 40 mm2. The specimen was clamped between a couple of grips of a tensile tester apparatus (Island Industry Co., Ltd., Kyoto, Japan) which enabled us to conduct the simultaneous measurements of the 2d-SAXS pattern during the stress−strain (SS) measurement with the constant stretching rate (0.1 mm/s) at room temperature, where the initial gauge length was 5.0 mm for all the specimens. After the distance between grips reached 40.0 mm, these films were then being unloaded gradually with a rate of 0.1 mm/s to the gauge length of 5.0 mm. During the stretching and unloading processes, SS curves and 2dSAXS patterns were simultaneously measured. The SAXS measurement was conducted with an exposure time of 10 s by using a twodimensional digital CMOS camera, C11440-22C (Hamamatsu Photonics K. K., Hamamatsu, Shizuoka, Japan) at BL40B2 in SPring-8 (RIKEN SPring-8 Center, Sayo, Hyogo, Japan). The incident X-ray was focused on the detector position. The wavelength of X-ray was 0.100 nm, and the sample-to-detector distance was 1.3 m. The SAXS measurements were also conducted at BL08B2 in SPring-8 with an exposure time of 10 s by using PILATUS 100 K (DECTRIS Ltd., Baden, Switzerland). The wavelength of X-ray was 0.100 nm, and the

EXPERIMENTAL SECTION

Sample. Three kinds of samples were used in this study, which were SEBS-8, SEBS-16, and polystyrene-block-polyisobutylene-blockpolystyrene (SIBS). The former two samples were synthesized by Asahi Kasei Corporation, Japan, and the details in the synthesis method have been reported before.25 The SIBS sample was supplied by Dr. Taizo Aoyama of Kaneka Corporation, Japan. The details in the synthesis method have been reported in the literature.26 Note that the B

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to 70 °C, changes in microdomain structures are analyzed with simultaneous measurements of SS and 2d-SAXS at room temperature. Figure 2 shows the results of stress measurements which were simultaneously measured with 2d-SAXS patterns. Here, it

sample-to-detector distance was 1.5 m. Refer to the publication in detail for BL40B228 and for BL08B2.29,30 DSC Measurements. DSC measurements were conducted for the thermally annealed SEBS-8 and SIBS films and for the as-cast film of SEBS-16 to evaluate Tg of PS. Several milligrams of each sample were weighed and placed in aluminum pans. The DSC measurement was conducted with a heating rate of 10 °C/min with a temperature range from −50 to 150 °C by using the DSC 2920 apparatus (TA Instruments Co., Ltd., New Castle, DE). During the measurement, nitrogen gas was continuously purged to prevent thermal degradation of specimens.

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RESULTS AND DISCUSSION Figure 1 shows DSC curves for the SEBS-8, SEBS-16, and SIBS specimens, respectively. Tg’s of PS were evaluated as 60.6, 55.9,

Figure 2. Results of stress measurements as a function of (d−d0)/d0 (see the main text for the definition of d and d0). for the (a) SEBS-8, (b) SEBS-16, and (c) SIBS specimens. Open and filled circles are for stretching and unloading processes, respectively. The labels A−E indicate points at which the 2d-SAXS patterns shown in the panels a− e of Figures 3−5 were measured, respectively.

should be noted that the definition of strain is not (l − l0)/l0, where l0 and l represent the length of the specimen before stretching and that of the stretched specimen, respectively, because slippage of the specimens from the grips took place. To correct for strain, we utilized the change in the position of lattice peaks as an internal reference. When the specimen was stretched, the lattice peak in the direction parallel to SD moved to a lower q region because the plane spacing increases proportionally to the stretching ratio. This relationship is known as the affine deformation. For SEBS-8 and SEBS-16, the affine deformation was confirmed up to the stretching ratio of 5. Therefore, in the present paper, we employed (d − d0)/d0 as a definition of true strain, where d0 represents the spacing of (110) planes in body-centered cubic (BCC) lattice before stretching and d is that of (110) planes in the direction parallel to SD for the stretched specimen. The really measured SS curves (as a function of strain calculated from the distance between crossheads of the stretching apparatus) are shown in Figure S1 of the Supporting Information. For SEBS-8 (Figure 2a), the stress dramatically decreased in the unloading process, and the residual strain of 0.46 was found when the stress reached finally zero. These tendencies were very much contrast to the case of SIBS (Figure 2c), showing an elastomeric property where the stress level was almost same both in the stretching and unloading processes and residual strain was small (0.04). As for SEBS-16 (Figure 2b), a mostly elastomeric property was observed where some extent of stress decrease in the unloading process and small value of the residual strain (0.09) were recognized. It is possible to evaluate the energy loss per a cycle as the area between the elongation and contraction curves. By the independent measurements of the SS curves up to the fifth cycle, the resulted energy loss is summarized in Table 3. It was found for all samples that the energy loss for the first cycle is biggest as compared to those for the other cycles, and therefore the simultaneous measurements of SS with 2dSAXS only conducted for the first cycle are found satisfactory for the discussion on the major effect of the cycled stretching.

Figure 1. DSC curves for SEBS-8, SEBS-16, and SIBS specimens.

Table 2. DSC Results on Tg sample code

Tg(onset)/°C

Tg(mid)/°C

Tg(end)/°C

SEBS-8 SEBS-16 SIBS

55.6 48.1 67.3

60.6 55.9 70.6

65.5 63.6 73.8

and 70.6 °C, respectively, as shown in Table 2 which summarizes the results of DSC. It should be noted that these are much lower than 100 °C, which is a value for PS with sufficiently high molecular weight. The reason for such lower value may be explained by the fact that the molecular weights of PS block chains in these samples were low. Lu and Krause have reported molecular weight dependence of Tg of PS for block copolymers.31 From their result, Tg’s for SEBS-8, SEBS-16, and SIBS are estimated to 40, 62, and 74 °C, respectively, based on Mn’s of PS with 3.1 × 103, 6.0 × 103, and 7.5 × 103. It was found that our DSC results do not agree with the results of Lu and Krause.31 Especially for SEBS-16, the measured Tg was quite low. Not only were the Tg values lower, but also the transition width was larger for the SEBS-16 specimen as compared to SEBS-8. This is because the SEBS-16 specimen was not thermally annealed (as-cast specimen), and an unfavorable effect of solvent evaporation may remain in the specimen. Using these three specimens with Tg ranging from 50 C

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Macromolecules Table 3. Changes in Energy Loss (%) as a Function of Cycle Number Cycle number

SEBS-8

SEBS-16

SIBS

1st 2nd 3rd 4th 5th

32 13 11 11 11

20 6 6 5 4

28 13 13 13 12

From the results of SS measurements, it is implied for SEBS-8 that the glassy PS domains might suffer from fracture and for SEBS-16 that the PS microdomains might be slightly damaged. In either case, PS spherical domains would be deformed upon stretching although they are glassy at room temperature. To confirm the deformation, 2d-SAXS patterns which were simultaneously measured with SS curves were closely examined. Note that labels A−E in the SS curves in Figure 2 denote positions at which 2d-SAXS patterns shown in the panels a−e of Figures 3−5 were measured, respectively. The 2d-SAXS patterns shown in Figures 3−5 are for the SEBS-8, SEBS-16, and SIBS specimens, respectively, during stretching and unloading processes, where the gray scale of the scattering intensity is not according to the linear scale but to the logarithmic scale. A broad round-shaped peak was observed in a range of 0.57 < q < 0.80 nm−1 (q is the magnitude of the scattering vector q, defined as q = |q| = (4π/λ) sin(θ/2) where λ and θ represent the wavelength of X-ray and the scattering angle, respectively) in Figures 3a, 4a, and 5a for specimens

Figure 4. 2d-SAXS patterns measured for the SEBS-16 him (a) before stretching and measured at strains of (b) 1.22 and (c) 2.52 during the stretching process and at strains of (d) 0.77 and (e) 0.09 during the unloading process, where all 2d-SAXS patterns are depicted according to a gray scale of the logarithmic intensity.

Figure 5. 2d-SAXS patterns measured for the SIBS film (a) before stretching and measured at strains of (b) 2.79 and (c) 3.70 during the stretching process and at strains of (d) 2.67 and (e) 0.09 during the unloading process, where all 2d-SAXS patterns are depicted according to a gray scale of the logarithmic intensity.

detailed description of the sector-averaging range is given in the Supporting Information (Figure S2). Thus-obtained 1d-SAXS profiles for the SEBS-8, SEBS-16, and SIBS specimens are shown in Figures 6−8, respectively. Note here that some first-order lattice peak measured for SEBS16 in Figure 7 were truncated due to the strong scattering Figure 3. 2d-SAXS patterns measured for the SEBS-8 him (a) before stretching, and measured at strains of (b) 1.73 and (c) 3.18 during the stretching process and at strains of (d) 1.73 and (e) 0.46 during the unloading process, where all 2d-SAXS patterns are depicted according to a gray scale of the logarithmic intensity.

before stretching. These peaks are ascribed to the particle scattering, which is due to the intraparticle interference of Xray. Upon stretching, deformation of the particle scattering peaks from the round shape to elliptic ones was observed for the SEBS-8 and SEBS-16 specimens. The extent of the deformation of the particle scattering peak was increased with strain. On the other hand, for the SIBS specimen, such deformation of the particle scattering peak was not clearly observed even at the strain of 3.70. However, even for the SIBS specimen, some extent of deformation was found when closely examined. To examine the changes in position of the particle scattering peaks, 1d-SAXS profiles in q∥ and q⊥ directions were extracted from 2d-SAXS patterns. The 1d-SAXS profiles were extracted by conducting sector-averaging of corresponding 2dSAXS patterns within an anomalously designated sector area. A

Figure 6. ld-SAXS profiles for the SEBS-8 specimen as a function of strain with q directions (a) parallel and (b) perpendicular to the stretching direction. The red curves are the results of the model calculation. D

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SEBSS-16 specimens under the stretched states. The detailed discussion will be reported in our subsequent publication.32 Before going in detail for the model calculation of the SAXS intensity using prolate spheroid, we discuss the deformation of the lattice peaks upon stretching. First of all, a round peak appeared in a range of 0.2 < q < 0.3 nm−1 before stretching, which is ascribed to the (110) reflection of the BCC lattice. Upon stretching, it was observed that higher-order lattice peaks showed up as apparently streaklike, which are elongated in the q⊥ direction. The relative q positions of those lattice peaks in q∥ direction (at q⊥ = 0) can be assigned to 1:√3:√6 (for the determination of the position of the lattice peaks in the q∥ direction, see Figure S3). This tendency is commonly observed for the SEBS-8, SEBS-16, and SIBS specimens. Generally speaking, (110), (200), and (211) reflections appear at relative q positions with 1:√2:√3. Therefore, the fact that the √3 ((211) reflection) and √6 ((222) reflection) peaks are selectively evolved is specific. Such characteristic evolution was observed and reported in our previous publication.33 However, in that report the evolution was found for √n peaks with n of odd number. The detailed discussion on this discrepancy is beyond the scope of the present paper. We now attempt to calculate the 1d-SAXS profiles for a prolate spheroid. For block copolymer microdomains which regularly packed in a lattice, the scattering intensity I(q) is formulated using the form and lattice factors.34

Figure 7. ld-SAXS profiles for the SEBS-16 specimen as a function of strain with q directions (a) parallel and (b) perpendicular to the stretching direction. The red curves are the results of the model calculation.

I(q) ∝ ⟨f 2 (q)⟩ − ⟨f (q)⟩2 + ⟨f (q)⟩2 Z(q)

(1)

where f(q) represents the scattering amplitude of a particle, ⟨x⟩ denotes the ensemble average of x, and Z(q) is the lattice factor. Before stretching, spherical domains are packed in the BCC lattice, for which Z(q) is given in the literature.33,34 As for f(q) for a spherical particle with a radius of R f (q) = 3V

sin qR − qR cos qR (qR )3

(2)

4 πR3 3

where V = (volume of the sphere). To obtain ensemble average, the size distribution in R was taken into account. When stretched, the lattice is deformed so that the BCC symmetry does not hold. However, it is assumed here that the abovestated formulation for Z(q) of the BCC lattice can be used to conduct model calculation of the SAXS profiles both in q∥ and q⊥ directions. As for the form factor f(q), the domain shape matters. Namely, we assume a prolate spheroid due to deformation of a sphere upon stretching. For a prolate spheroid, the structure amplitude f(q) can be formulated as

Figure 8. ld-SAXS profiles for the SIBS specimen as a function of strain with q directions (a) parallel and (b) perpendicular to the stretching direction. The red curves are the results of the model calculation.

intensity beyond the detection limit. As clearly seen in the series of 1d-SAXS profiles, the particle scattering peaks in q∥ and q⊥ directions shifted toward lower and higher q regions, respectively. This result indicates that radii of microdomains in q∥ and q⊥ directions increased and decreased, respectively, which in turn suggests that the shape of the particle is no more spherical and that spheres may “deform” into an anisotropic shape during the stretching. One may have a doubt about the deformation of glassy spheres because it has been considered that glassy substances hardly deform. Actually, as another possibility giving an interpretation for the shift of the particle scattering peaks, it is considered that anisotropic microdomains are already existing in the initial specimen (before stretching), and these are oriented with their major axis parallel to SD. However, this consideration was found to be erroneous from the fact that the particle scattering peaks in q∥ and q⊥ directions continued to shift toward lower and higher q regions, respectively, during holding the specimen at stretched states. The shifts of the particle scattering peaks were detected by time-resolved measurements of 2d-SAXS for the SEBS-8 and

f (q , v , R min , ϕ , μ) = 3V

sin U − U cos U U3

(3)

4

where V = 3 πR min 2R maj (volume of the prolate spheroid) and U (q , v , R min , ϕ) = qR min sin 2 ϕ + v 2 cos2 ϕ

(4)

for q being parallel to SD, or U (q , v , R min , ϕ , μ) = qR min

1 − sin 2 ϕ cos2 μ + v 2 sin 2 ϕ cos 2 μ

(5)

for q being perpendicular to SD. In eqs 3−5, ν = Rmaj/Rmin (ν > 1) with Rmaj and Rmin being radii of the prolate spheroid parallel and perpendicular to the major axis, respectively. As shown in Figure 9, we defined the polar angle ϕ of the major axis of the E

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profiles in low q region especially for the profiles measured at strain higher than 0.94 in Figure 6b. Nevertheless, the particle scattering peak is perfectly reproduced for all profiles. Since the purpose of the model calculation is to confirm the deformation of the glassy PS spheres, the fact that the particle scattering peak can be reproduced by the model calculation using the prolate spheroid indicates clearly the deformation in the SEBS8 specimen. As for the SEBS-16 specimen, the calculated curves deviate from the measured profiles in low q region in Figure 7a,b. However, it is also seen that the particle scattering peak is perfectly reproduced. Thus, we can deduce the same conclusion of the deformation of the glassy PS spheres for the SEBS-16 specimen. Also for the SIBS specimen, the particle scattering peaks shown in Figure 8a,b can be reproduced well by the model calculation. From the distributions Ξ(Rmin) and Ω(ν), the average values of Rmin and ν were calculated, respectively. Thus, the average value of Rmaj can be evaluated as R maj = v ̅ R min . The evaluated values, R maj and R min , are shown in Figure 10a−

Figure 9. Schematic illustration of orientation of a prolate spheroid with its major axis inclined to the stretching direction with an angle ϕ. μ defines the angle between x axis and projection of the major axis of the prolate spheroid onto the x−y plane.

prolate spheroid from SD and the angle μ between the x-axis and the projection of the major axis of the prolate spheroid onto the x−y plane. In the calculation of 1d-SAXS profile, the size distribution in Rmaj and in Rmin and the orientational distribution in ϕ should be taken into account, and the ensemble averages ⟨f 2(q)⟩ and ⟨f(q)⟩2 are calculated as follows: ⟨f 2 (q)⟩ = 2π

π /2

∞

∫0 ∫0 ∫0

∞

f 2 (q , v , R min , ϕ)Ω(v)

× Ξ(R min)Ψ(ϕ) sin ϕ dv dR min dϕ ⟨f (q)⟩2 = (2π

π /2

∞

∫0 ∫0 ∫0

(6)

∞

f (q , v , R min , ϕ)Ω(v)

× Ξ(R min)Ψ(ϕ) sin ϕ dv dR min dϕ)2

(7)

For this purpose, we introduced Ω(ν), Ξ(Rmin), and Ψ(ϕ) for these distributions. Note here that complete orientation of the prolate spheroids with their long axis parallel to SD was assumed in the stretching process because it can be considered that the deformation of spheres is occurring as the radii increased and decreased respectively in the direction parallel and perpendicular to SD. Namely, Ψ(ϕ) = 1 for ϕ = 0°, and Ψ(ϕ) = 0 for ϕ ≠ 0°. As for Ω(ν) and Ξ(Rmin), the Gauss function was assumed (see Figure S4 for the example of the particular functions used to obtain the model profiles). The results of model calculation of the 1d-SAXS profiles are shown together in Figures 6−8 with red curves. To obtain the results for the specimens before stretching, the distribution in R was appropriately introduced using the Gauss function. Furthermore, randomization of the BCC lattice orientation was conducted according to the method described in the literature.33,34 For the specimens during stretching, first Ξ(Rmin) was determined using the Gauss function to obtain the results of model calculation of 1d-SAXS profiles in the q⊥ direction, and then Ω(ν) was determined from the 1d-SAXS profiles in the q∥ direction. Examples of Ξ(Rmin) and Ω(ν) are shown in Figure S4. It is found that the model calculation reproduces well the 1d-SAXS profiles before stretching as shown in Figures 6−8. This indicates that all of the specimens form BCC lattice with PS spherical domains. In Figure 6a, the calculated 1d-SAXS profiles almost perfectly reproduce the measured profiles during stretching. On the other hand, the calculated curve deviates from the measured

Figure 10. (a−c) Changes in R maj (filled symbols) and R min (open symbols) as a function of strain for SEBS-8, SEBS-16, and SIBS, respectively. (d) Changes in strain of PS domains, γm, as a function of strain for SEBS-8 (circles), SEBS-16 (triangles), and SIBS (squares).

c for SEBS-8, SEBS-16, and SIBS, respectively, as a function of strain. It was found for all specimens that R maj increased and R min decreased immediately upon stretching. These results imply that there is no threshold of strain (no yielding) for deformation. This is very striking because the glassy domains are so easy to deform. We will discuss more in detail in Figure 11. Furthermore, it seems that small PS domains easily deform (SEBS-8) and large PS domains hardly deform (SIBS). To clearly show these tendencies, we introduced the strain of PS R maj

R

domain γm as γm = R − 1 or γm = Rmin − 1, where R̅ stands ̅ ̅ for the average radius of spherical PS domains before stretching. In Figure 10d, γm is shown as a function of strain. The value of γm being 0.12 for SEBS-8 is strikingly larger as F

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scattering peaks upon unloading, we assume that plastically deformed PS domains can never recover spherical shape, but the perfect orientation of prolate spheroids is relaxed. Recall that we assumed perfect orientation of prolate spheroids with respect to SD to conduct model calculation of the 1d-SAXS profiles in Figures 6−8. Namely, the orientational distribution function Ψ(ϕ) = 1 for ϕ = 0° and Ψ(ϕ) = 0 for ϕ ≠ 0°. For the orientational relaxation upon unloading, we set the Gauss function for Ψ(ϕ), while Ω(ν) and Ξ(Rmin) are fixed with those obtained for the specimen at maximum strain. Figures 12 and 13 show 1d-SAXS profiles obtained for unloading process for SEBS-8 and SEBS-16, respectively,

Figure 11. Changes in γm (strain of the PS domains) as a function of stress for SEBS-8 (circles), SEBS-16 (triangles), and SIBS (squares).

compared with the case of PS homopolymers (tensile strain of ∼0.02 at break).35 Furthermore, it is clearly found that the extent of deformation is highest for SEBS-8 and lowest for SIBS even for the similar stress level around 1 MPa (see the SS curves shown in Figure 2). To clearly rationalize the deformation of PS domains to the tensile stress of the specimen, the stress dependence of γm is depicted in Figure 11. For all specimens, the PS domains suffered from deformation immediately in the initial stages of stretching where the stress was low. This fact would imply that the glassy PS domains can be deformed easily with such low stress. Since PS homopolymers have tensile modulus of 3.4 GPa,36 the stress of 33 MPa should be required for 1% tensile deformation of PS. Nevertheless, from Figure 11, it can be recognized that only small stress ranging from 0.2 to 0.7 MPa was loaded for these specimens at γm = 0.01. At present, we do not have a clear explanation for this amazing behavior. For SEBS-8, γm abruptly increased at the stress of 0.75 MPa, while γm gradually increased for SIBS. These two contrasted results may be ascribed to difference in the extent of the stress concentration. For small domains, the stress is much concentrated at the domains, and therefore they are easily deformed. This may explain easy deformation of the PS domains for SEBS-8 even at such low stress (∼1.0 MPa). On the other hand, for larger PS domains the stress concentration is not so large, and therefore the deformation of the PS domains is trivial. This explains the behavior of the SIBS specimen. One may point out the effect of Tg on the deformation behavior even though the stretching was conducted below Tg. As for three different samples, the molecular weight of PS is in the order of SEBS-8 < SEBS-16 < SIBS. For such short chains, Tg depends on the molecular weight so that the Tg values should also show the same order. However, our result of DSC shows quite low Tg for SEBS-16 because the specimen was not thermally annealed, as mentioned above. Fortunately, this unanticipated order of Tg excludes the effect of Tg on the deformation behavior for SEBS and SIBS specimens. As stated above, on unloading from the maximum strain, the 2d-SAXS patterns shown in the panels of d and e in Figures 3−5 changed such that the deformed lattice and particle scattering peaks almost returned back to isotropic shape. At a first glance, this behavior implies the elastic deformation. However, it should not be the case for the deformation of glassy PS domains. To understand the behavior of the particle

Figure 12. Changes in the ld-SAXS profiles for the SEBS-8 specimen in the unloading process with q directions (a) parallel and (b) perpendicular to the stretching direction. The red curves are the results of the model calculation.

Figure 13. Changes in the ld-SAXS profiles for the SEBS-16 specimen in the unloading process with q directions (a) parallel and (b) perpendicular to the stretching direction. The red curves are the results of the model calculation.

together with results of the model calculation shown with the red curves. It is clearly found that the model calculation can reproduce the changes in the 1d-SAXS profiles perfectly (particularly for the particle scattering peaks). This in turn implies that the changes in the 2d-SAXS patterns upon unloading are due to the orientational relaxation of plastically deformed PS domains. Refer to Figure S5 for the changes in G

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stress decrease in the SS curves from second to fifth cycle, the SEBS-8 specimen was the worst. To examine most effectively temporal stability of the mechanical property, the stress relaxation measurement is suitable. The results obtained at room temperature are shown in Figure 15. Note that all the

Ψ(ϕ) used for the model calculation. From Ψ(ϕ), the secondorder orientation factor, F, can be evaluated as 3⟨cos2 ϕ⟩ − 1 2

F=

(8)

with π

2

⟨cos ϕ⟩ =

∫0 Ψ(ϕ) cos2 ϕ sin ϕ dϕ π

∫0 Ψ(ϕ) sin ϕ dϕ

(9)

Note that ⟨cos ϕ⟩ = 0 for the perfect parallel orientation and thus F = 1, while ⟨cos2 ϕ⟩ = 1/3 and thus F = 0 for the random orientation. Figure 14a shows changes in F as a function of strain in the unloading process for the SEBS-8 (open circles) and SEBS-16 2

Figure 15. Stress relaxation curves for SEBS-8, SEBS-16, and SIBS specimens stretched at a strain of 4.0 at room temperature.

specimens were prepared in a similar manner with the 2d-SAXS measurements and then stretched at a strain of 4.0. It is also noted that each stress relaxation curve was normalized with the stress at the time equaled to 0 s. It is clearly found that the SEBS-8 specimen shows the large stress relaxation and is easily fractured (at 380 s). This is much earlier even as compared to the case of SEBS-16 (fractured at 8.0 × 104 s, almost 1 day). On the other hand, the stress relaxation process is very moderate for SIBS. Namely, the stress finally reached 60% of the original value at 1.2 × 106 s (almost 2 weeks) without fracture. These behaviors are in very good accord with the deformation behaviors of PS spheres. Thus, strong correlation between mechanical properties and the deformation of PS spheres are suggested. In the future publication, we will clearly discuss the relationship with a more direct manner.32

Figure 14. (a) Plots of the second-order orientation factor, F, of prolate spheroids as a function of strain in the unloading process for SEBS-8 (open circles) and SEBS-16 (filled circles). (b) Plots of F as a function of normalized strain where the stress is normalized by 2.1 and 3.3 for SEBS-8 and SEBS-16, respectively.

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CONCLUSION We have shown clear evidence of the deformation of glassyspherical microdomains upon stretching of thermoplastic elastomer films by using various types of styrenic triblock copolymers. For this purpose, the simultaneous measurements of SS curves and 2d-SAXS patterns have been conducted using synchrotron radiation facility. Both of 1d-SAXS profiles parallel and perpendicular to SD were successfully reproduced by the model calculation assuming prolate spheroids. The deformation behaviors of PS domains were quantitatively discussed by the changes in radii of the prolate spheroids estimated by the model calculation. For all specimens, it was strikingly recognized that the PS domains suffered from deformation immediately in the initial stages of stretching where the stress was low. However, the deformation behaviors were found to differ depending on specimens. Namely, the extent of the deformation was higher for the smaller PS domains. This fact reminds that the deformation of the PS domains is ascribed to stress concentration. The 1d-SAXS profiles in the unloading process were successfully reproduced by the model calculation using prolate spheroids, where it was assumed that plastically deformed PS domains never recovered spherical shape but the perfect orientation of prolate spheroids was relaxed. There would be another explanation for the changes in the 2d-SAXS patterns upon stretching of the specimens, which is the possibility that anisotropic microdomains are already existing in the specimen before stretching and these are being oriented. In this case, it is expected that orientational relaxation

specimens (filled circles). In the initial stage of the unloading process, F did not decrease from 1 but started to decrease at the strain of 2.1 and 3.3 for SEBS-8 and SEBS-16, respectively. Thereafter, F was linearly decreasing with strain and finally reached 0.3−0.4 at the completely unloaded state where the stress was zero (the strain was remained for SEBS-8). The difference in the behaviors for SEBS-8 and SEBS-16 may exist in the fact that the onset point of the orientational relaxation differs. Therefore, the strain was normalized with the value where F started to deviate from 1. Namely, the strains of 2.1 and 3.3 were chosen as the onset points of the deviation for SEBS-8 and SEBS-16, respectively. Figure 14b shows the changes in F as a function of the normalized strain. As clearly seen, the two behaviors of orientational relaxation almost overlapped to each other until 0.34 of the normalized strain. Thereafter, a dramatic decrease in F was recognized for SEBS-8. Finally, the relationship between the mechanical property and the deformation of PS spheres is discussed. As stated above, we conducted the cycled SS measurements, and the resulted energy loss is summarized in Table 3. At first glance, the energy loss for SEBS-16 is lower than that for SIBS. Although this implies that SEBS-16 maintains the mechanical property for the cycled stretching better than SIBS, in reality the SS curves from second to fifth cycle for SEBS-16 gradually changed such that the stress decreased as a function of the number of cycle, while the SS curves did not change at all for SIBS from second to fifth cycle. With respect to the extent of H

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(5) Sakamoto, J.; Sakurai, S.; Doi, K.; Nomura, S. Molecular Orientation of Poly(styrene-block-butadiene-block-styrene) Triblock Copolymer with Cylindrical Microdomains of Polystyrene. Polymer 1993, 34, 4837−4840. (6) Sakurai, S.; Sakamoto, J.; Shibayama, M.; Nomura, S. Effects of Microdomain Structures on the Molecular Orientation of Poly(styrene-block-butadiene-block-styrene) Triblock Copolymer. Macromolecules 1993, 26, 3351−3356. (7) Lee, H. H.; Register, R. A.; Hajduk, D. A.; Gruner, S. M. Orientation of Triblock Copolymers in Planar Extension. Polym. Eng. Sci. 1996, 36, 1414−1424. (8) Dair, B. J.; Honeker, C. C.; Alward, D. B.; Avgeropoulos, A.; Hadjichristidis, N.; Fetters, L. J.; Capel, M.; Thomas, E. L. Mechanical Properties and Deformation Behavior of the Double Gyroid Phase in Unoriented Thermoplastic Elastomers. Macromolecules 1999, 32, 8145−8152. (9) Daniel, C.; Hamley, I. W.; Mortensen, K. Effect of Planar Extension on the Structure and Mechanical Properties of Polystyrenepoly(ethylene-co-butylene)−polystyrene Triblock Copolymers. Polymer 2000, 41, 9239−9247. (10) Honeker, C. C.; Thomas, E. L.; Albalak, R. J.; Hajduk, D. A.; Gruner, S. M.; Capel, M. C. Perpendicular Deformation of a NearSingle-Crystal Triblock Copolymer with a Cylindrical Morphology. 1. Synchrotron SAXS. Macromolecules 2000, 33, 9395−9406. (11) Sakurai, S.; Isobe, D.; Okamoto, S.; Yao, T.; Nomura, S. Collapse of the Ia3d Cubic Symmetry by Uniaxial Stretching of a Double-Gyroid Block Copolymer. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2001, 63, 061803. (12) Adhikari, R.; Michler, G. H. Influence of Molecular Architecture on Morphology and Micromechanical Behavior of Styrene/Butadiene Block Copolymer Systems. Prog. Polym. Sci. 2004, 29, 949−986. (13) Kwee, T.; Taylor, S. J.; Mauritz, K. A.; Storey, R. F. Morphology and Mechanical and Dynamic Mechanical Properties of Linear and Star Poly(styrene-b-isobutylene-b-styrene) Block Copolymers. Polymer 2005, 46, 4480−4491. (14) Duan, Y.; Thunga, M.; Schlegel, R.; Schneider, K.; Rettler, E.; Weidisch, R.; Siesler, H. W.; Stamm, M.; Mays, J. W.; Hadjichristidis, N. Morphology and Deformation Mechanisms and Tensile Properties of Tetrafunctional Multigraft Copolymers. Macromolecules 2009, 42, 4155−4164. (15) Inoue, T.; Moritani, M.; Hashimoto, T.; Kawai, H. Deformation Mechanism of Elastomeric Block Copolymers Having Spherical Domains of Hard Segments under Uniaxial Tensile Stress. Macromolecules 1971, 4, 500−507. (16) Seguela, R.; Prud’homme, J. Affinity of Grain Deformation in Mesomorphic Block Polymers Submitted to Simple Elongation. Macromolecules 1988, 21, 635−643. (17) Prasman, E.; Thomas, E. L. High-Strain Tensile Deformation of a Sphere-Forming Triblock Copolymer: Mineral Oil Blend. J. Polym. Sci., Part B: Polym. Phys. 1998, 36, 1625−1636. (18) Painter, P. C.; Koenig, J. L. A Normal Vibrational Analysis of Isotactic Polystyrene. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 1885− 1903. (19) Noda, I. Two-Dimensional Infrared Spectroscopy. J. Am. Chem. Soc. 1989, 111, 8116−8118. (20) Zhao, Y. Structural Changes upon Annealing in a Deformed Styrene-Butadiene-Styrene Triblock Copolymer as Revealed by Infrared Dichroism. Macromolecules 1992, 25, 4705−4711. (21) Sakurai, S.; Sakamoto, J.; Shibayama, M.; Nomura, S. Effects of Microdomain Structures on the Molecular Orientation of Poly(styrene-block-butadiene-block-styrene) Triblock Copolymer. Macromolecules 1993, 26, 3351−3356. (22) Kraus, G.; Rollmann, K. W. Effects of Domain and Molecular Orientations on the Mechanical Properties of a Styrene-butadiene Block Polymer. J. Macromol. Sci., Part B: Phys. 1980, 17, 407−425. (23) Duan, Y.; rettler, E.; Schneider, K.; Schlegel, R.; Thunga, M.; Weidisch, R.; Siesler, H. W.; Stamm, M.; Mays, J. W.; Hadjichristidis, N. Deformation Behavior of Sphere-Forming Trifunctional Multigraft Copolymer. Macromolecules 2008, 41, 4565−4568.

of the deformed domains would take place for the case when the tensile stress decreases in the specimen which is fixed at a stretched state. To check this possibility, we have conducted time-resolved measurements of 2d-SAXS for the SEBS-8 and SEBS-16 specimens under the stretched states. The results will be reported in our subsequent publication.32

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.6b02206. (1) Original stress−strain curves obtained by the simultaneous measurements with 2d-SAXS; (2) the sector averaging method with an anomalous sector range to obtain the 1d-SAXS profile from the 2d-SAXS pattern; (3) the method to determine the peak position of (110) reflection in q direction parallel to SD from the 2d-SAXS pattern; (4) examples of size distributions used for the model calculation of the 1d-SAXS profiles; (5) examples of orientational distribution, Ψ(ϕ), used for the model calculation of the 1d-SAXS profiles in the unloading process (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel +81-75-724-7864; Fax +81-75-7247547 (S.S.). ORCID

Shinichi Sakurai: 0000-0002-5756-1066 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are deeply indebted to Dr. Taizo Aoyama of Kaneka Corporation, Japan, for kindly supplying the SIBS sample. This study was partially supported by Grant-in-Aid for Scientific Research C with Grant No. 25410226, and Grant-inAid for Scientific Research on Innovative Areas “New Polymeric Materials Based on Element-Blocks” (No. 25102524) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. The SAXS experiments were performed at BL08B2 in SPring-8, Japan (under the Approval No. 2014B3306). The authors appreciate the technical assistance from Dr. Noboru Ohta in the SAXS measurements at BL40B2 in SPring-8 (under the Approval No. 2015B1071). We also thank Prof. Hideki Yamane of Kyoto Institute of Technology for his kind arrangement of the tensile testing machine for the cycled SS measurements.

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REFERENCES

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