Time-Resolved High-Resolution SAXS Studies of OOT Process and

Article pubs.acs.org/Macromolecules

Time-Resolved High-Resolution SAXS Studies of OOT Process and Mechanism from Hex-Cylinder to BCC-Sphere in a Polystyrene-blockpolyisoprene Diblock Copolymer Kohtaro Kimishima,†,§ Kenji Saijo,‡,* Tadanori Koga,†,⊥ and Takeji Hashimoto†,‡,∥,* †

Hashimoto Polymer Phasing Project, ERATO, Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi-shi, Saitama 332-0012, Japan ‡ Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan ABSTRACT: The mechanism and process of the thermally induced order−order transition (OOT) of a polystyrene-blockpolyisoprene diblock copolymer from cylinders on a hexagonal symmetry (hex-cyl) to spheres on a body-centered cubic symmetry (bcc-sphere) were investigated by means of timeresolved observation of high-resolution small-angle X-ray scattering (hr-SAXS) profiles obtained with a Bonse-Hart type USAXS apparatus. The USAXS apparatus enabled us to precisely study changes in the scattering peak profiles with time induced by the OOT between the two equilibrium morphologies of hex-cyl and bcc-sphere with a high resolution with respect to magnitude of scattering vector q. The peaks due to hex-cyl and bcc-sphere, which are closely located and hence overlapped one another in q-space when they are observed with conventional SAXS apparatuses, are well resolved into separated peaks with the hr-SAXS, which gave a new insight into the OOT process and mechanism as elucidated in the text.

1. INTRODUCTION In previous papers,1,2 we reported the mechanism of the thermoreversible order−order transition (OOT) between spherical microdomains on a body-centered cubic lattice (hereafter denoted as bcc-sphere) and cylindrical microdomains on a hexagonal lattice (hereafter denoted as hex-cyl) of a polystyrene (PS)-block-polyisoprene (PI) diblock copolymer (bcp). Many studies dealing with the same kind of OOT have been reported for various bcps, and the mechanism of the transition process is found to have the universality of the socalled epitaxial transformation in which the cylinder axis is transformed to the ⟨111⟩ axis of the bcc-sphere, and {10} and {11} lattice planes of hex-cyl are transformed to {110} and {112} lattice planes of bcc-sphere, respectively.1−6 However, the details of the epitaxial process have not yet been well investigated experimentally. This is mainly due to the following two experimental difficulties in exploring in situ and real-time structural evolution of the intermediate structures during the OOT process: (1) Such intermediate structures would be very unstable and have a little retention time. (2) Scattering peaks associated with hex-cyl and bcc-sphere, especially their firstorder peaks, are very closely located in the q-space (the reciprocal space) so that conventional small-angle X-ray scattering (SAXS) apparatuses are not able to resolve the two peaks. Here, q is magnitude of the scattering vector q defined by q = (4π/λ) sin (θ/2) with θ and λ being the scattering angle and the wavelength of the incident X-ray beam. These difficulties give us a serious problem to investigate detailed © 2013 American Chemical Society

processes leading to the symmetry change in the ordered structures via the epitaxial transformation mechanism. In order to overcome the latter experimental difficulty (2) described above, we applied the Bonse-Hart type ultrasmallangle X-ray scattering (USAXS) apparatus7 to the studies of the OOT process. The use of the USAXS apparatus generally has a two-fold merit compared with the use of conventional SAXS apparatuses: It enables us to explore not only (a) large-length scale structures up to order of μm, which influence the scattering in the ultrasmall angle region, but also (b) smallerlength scale structures, which influence the scattering in the conventional small-angle region, with a very high q-resolution of 6 × 10−3 nm−1 or 6 × 10−4 Å−1. In this work we particularly aim to utilize the latter merit (b) in order to resolve the closely spaced SAXS peaks relevant to hex-cyl and bcc-sphere. We hereafter define the SAXS profiles measured with the BonseHart type USAXS apparatus as “high-resolution SAXS (hrSAXS)” profiles. Thus, the strong point in this paper is to apply a time-resolved hr-SAXS to explore the OOT transformation process and mechanism from hex-cylinder to bcc-sphere, allowing us to directly follow the symmetry change with time during the OOT process via the epitaxial mechanism. Received: August 30, 2013 Revised: October 16, 2013 Published: November 11, 2013 9032

dx.doi.org/10.1021/ma401808p | Macromolecules 2013, 46, 9032−9044

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Figure 1. (a) hr-SAXS profiles measured in situ as a function of temperature T in the cooling process. qm,hex and qm,bcc are the q values at the firstorder maximum from hex-cyl and bcc-sphere, respectively, while √3qm,hex and √2qm,bcc are the q values at the second-order maximum from hex-cyl and bcc-sphere, respectively. H and B designate hex-cyl and bcc-sphere, respectively. Each profile was obtained by the step-scanning of the scattered intensity at 10 sec of arc per step with respect to the scattering angle θ with the Bonse−Hart type USAXS apparatus. (b) Same hr-SAXS profiles as part a, except for focusing its first-order scattering maximum by enlarging the q-scale represented by the horizontally directed arrow shown in part a. The profiles include the data shown by red circles at 115.5 °C, which were obtained by heating the sample from 114.5 °C and by a step-scanning with 2 sec of arc per step with respect to θ. The hr-SAXS profiles were vertically shifted to avoid overlaps of the profiles. from the acoustic phonons. The slit smearing effect was also corrected. The sample was put in a vacuum chamber to reduce possible thermal degradation. The sample was annealed at each temperature for 40 min to achieve thermal equilibrium before the SAXS profile measurement. The typical measurement time for the one profile was 60 min. Then the temperature was raised by 1 °C for the next measurement and this procedure was repeated to obtain the in situ SAXS profiles as a function of T to be shown later in Figure 2. Thus, the average heating rate of about 0.6 °C/h was used to obtain Figure 2. 2.3. High-Resolution SAXS (hr-SAXS) Measurements. 2.3.1. Static hr-SAXS. The hr-SAXS measurements were conducted using a Bonse−Hart type USAXS apparatus consisting of an 18 kW rotating-anode X-ray generator (M18XHF-SRA, MAC Science Co., Ltd.), two germanium channel-cut crystals, in which one is to monochromatize and collimate the incident beam and the other is to analyze the scattered X-ray as a detector. The details of the USAXS camera employed in this work have been described elsewhere.9 The wavelength of the X-ray beam can be precisely specified as 0.15406 nm in this apparatus. The measurements were carried out in situ as a function of temperature T with specimens under vacuum to avoid the oxidative degradation of the specimens. The sample was annealed at each temperature for about 3 h to achieve the thermal equilibrium before the hr-SAXS profile measurement. We found the profile did not change with time after a 2 h waiting time at 117.5 °C. The step scanning of θ for the hr-SAXS intensity measurement in Figure 1 to be shown later was extremely fine, i.e., 10 sec of arc/step. The typical measurement time for one profile was about 3 h for the given q-range covered. Then the temperature was decreased by 0.5 °C for the next measurement of the profile and this procedure was repeated to obtain the in situ hr-SAXS profiles as a function of T to be shown later in Figure 1. Thus, an

2. EXPERIMENTAL SECTION 2.1. Sample. The sample used in this study was the same polystyrene-block-polyisoprene diblock copolymer (PS−PI) as used in the previous study.1 The number-averaged molecular weight, Mn, determined by GPC (HLC-8020, THOSO, Co. Ltd.) is 4.39 × 104 and the polydispersity index, Mw/Mn, is 1.02 with Mw being the weightaveraged molecular weight. The weight fraction of PS block determined by 1H NMR (JMR-400, JEOL, Co. Ltd.) is 0.204 ± 0.005 that corresponds to the volume fraction of 0.18. The bcp was dissolved in toluene with a small amount of antioxidant (BHT) and cast into film specimens from a 5% polymer solution. The film specimens thus obtained were then dried under vacuum until no further weight loss was observed. We elucidated that this sample shows various morphologies with changing temperature.1 With decreasing temperature, the microdomain structure changes from latticedisordered sphere (defined as LDS) or spheres with a short-range liquid-like order above the lattice disordering temperature1,8 defined as TLDT =140 °C), bcc-sphere (from 116 to 140 °C), and hex-cyl (below 116 °C), where the order−order transition from bcc-sphere to hex-cyl defined as TOOT =116 °C. 2.2. SAXS Measurements. The static conventional SAXS measurements were conducted in situ as a function of temperature with an apparatus consisting of an 18 kW rotating-anode X-ray generator (M18XHF-SRA, MAC Science Co. Ltd.) with a graphite crystal monochromator, a collimator, and a vacuum chamber for the incident-beam path and the scattered-beam path, and a detector. The sample-to-detector distance was set to 1700 mm. The wavelength of 0.154 nm was used. The SAXS profiles were measured using a onedimensional position sensitive proportional counter (PSPC) with a line-focusing optics and were corrected for the absorption of the sample, background scattering, and thermal diffuse scattering arising 9033


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resolved first-order peaks associated with hex-cyl and bcc-sphere. Hence, the smeared profiles themselves satisfy the necessary and sufficient condition required for exploring the symmetry change in the ordered structures brought by the OOT process. They correctly provide relative time changes in the peak intensities, Im,hext and Im,bcct, and the magnitude of the scattering vectors at the peaks, qm,hext and qm,bcct, to be defined and discussed later in conjunction with Figure 5. 2.4. Pycnometry. The specific volume of the sample, vsp, was measured using a conventional pycnometer method to measure the macroscopic volume change associated with the OOT. A small amount of the sample (about 0.3 g) was placed into a vessel (about 0.5 cm3 in volume), and the bubbles inside the sample were removed in the vacuum oven at 130 °C overnight. After taking it out from the oven and cooled down, the rest of the space in the vessel was filled with ethylene glycol (EG) which is a nonsolvent for both PS and PI. The vessel was sealed with a cap equipped with a capillary having a diameter of 0.2 mm. The entire assembly was placed into an oil bath and controlled at various temperatures within a 0.1 °C accuracy. The meniscus of EG in the capillary was measured as a function of temperature. The volumes of the vessel and capillary were calibrated using EG. The density of EG at 20 °C is 1.109 g/cm3, and the thermal expansion of EG was corrected using the following equation:11

extremely slow average cooling rate of about 0.083 °C/h was used to obtain Figure 1. In a whole temperature range covered in this hr-SAXS, the sample temperature was calibrated using the same standard platinum resistance (Pt100) with an ohmmeter as that used for the temperature calibration for the temperature enclosure and was controlled within ±0.1 °C fluctuation. 2.3.2. Time-Resolved hr-SAXS. The Bonse−Hart type USAXS camera is a step-scanning spectrometer such that one needs to rotate the analyzer to obtain the scattering profile, i.e., scattered intensity distribution I(q), against the scattering angle θ or the magnitude of the scattering vector q. Therefore, the in situ time-resolved measurements during the OOT process are in general difficult with this apparatus, if the time evolution of microdomain structures is faster than the total acquisition time for the scattering profile I(q;t) as a function of q and time t. Nevertheless, we tried time-resolved hr-SAXS measurements on the OOT process under the following special circumstances. The method best utilizes the fact that the sample can attain very reproducibly an equilibrium hex-cyl at a temperature in the hex-cyl phase, e.g. 111 °C, and an equilibrium bcc-sphere at a temperature in the bcc-sphere phase, e.g. 121 °C, on repeatedly changing the sample temperature between the two given temperatures across TOOT = 116 °C. In this work we could firmly confirm the reproducibility of the structural changes between the two temperatures, 111 and 121 °C, with respect to the reproducible changes in the scattering profiles. Practically, we conducted the time-resolved hr-SAXS measurements as follows. The sample was first placed in a holder controlled at 150 °C above the TLDT = 140 °C and then quenched rapidly into water in order to avoid any development of the large grains of hex-cyl as elucidated previously.1 This is to minimize the grain size and ensure the reproducibility of the profile in the repetitive OOT process described earlier. The quenched sample in the holder was annealed at 111 °C in the hex-cyl phase for 1 h to develop the small grains composed of hex-cyl. The annealed sample in the holder was set in the sample stage of the USAXS apparatus controlled at T = 121 °C in the bcc-sphere phase for the T-jump with a corresponding superheating ΔT ≡ T − TOOT = 5.0 °C above the TOOT. Then the scattering intensity at a certain q was measured as a function of time t after the Tjump until the intensity reached a constant level (t up to 480 s). The sample was quenched again to 111 °C and waited for about 1 h to recover the hex-cyl. We repeated the hr-SAXS measurements as a function of t with changing the q only around the first-order SAXS peak from 0.255 nm−1 to 0.275 nm−1 in order to reduce effectively the time period required for the time-resolved hr-SAXS experiments. In each T-jump process, we confirmed the reproducibility of the hr-SAXS profiles both at 111 °C and at 121 °C. Then the intensity distribution at a certain time after the T-jump, I(q; t), was reconstructed from intensity matrix of t and q. Note that the qms for the profiles at t = 0 and t = 480 s thus obtained were almost consistent with those obtained by the static measurements. We did not deliberately conduct the form factor analysis during the OOT process because of the limitation of the q range covered in the time-resolved hr-SAXS experiments as described above: The broad form factor peak for this bcp appears in the q range from 0.6 to 1.2 nm−1 (see Figure 1 in ref 1). The form factor analyses were also ignored, because the broad form factor peak may not allow us to unequivocally analyze the thinning of the cylinder diameter in stage I, the undulation of the cylinder and transformation from the cylinders to the spheres in stage II and the refinement of the bcc-sphere in stage III to be discussed in due course. 2.3.3. Further Notes on Static and Time-Resolved hr-SAXS Measurements. Since the optical system of the USAXS apparatus used in this work9 was a line focus system, the profile measured was the smeared one with respect to the line height, while the width of the line is extremely narrow due to the double-crystal optics7 (thus, only the slit-height smearing effect existing10). The static and time-resolved hr-SAXS profiles to be shown later in Figure 1 and Figures 4−6, 9, and 12, respectively, were not deliberately desmeared with respect to the line height10 in order to avoid any artifacts caused by the desmearing process. However, the smeared profiles sufficiently show the well

1 ⎛ ∂vsp ⎞ ⎜ ⎟ = 0.565 × 10−3 + 1.7074 × 10−6T vsp ,0 ⎝ ∂T ⎠ + 0.293 × 10−8T 2

(1)

Here T and vsp,0 are the absolute temperature and vsp of EG at 0 °C, respectively.

3. RESULTS 3.1. Change in Microscopic Volume Involved by OOT as Observed by in Situ hr-SAXS Experiments as a Function of Temperature. As mentioned above, the advantage of hr-SAXS measurements is the extremely high angular resolution, much higher than the conventional SAXS measurements, which enables us to investigate more precisely the detailed process leading to the symmetry change in the microdomain structures. We tried to elucidate the microscopic volume change involved by OOT using hr-SAXS as a function of temperature T. Figure 1a shows hr-SAXS profiles of the sample measured in situ at representative temperatures in a cooling process (from bottom to top). At first, the sample was kept at 160 °C where the LDS structure was observed (see Figure 1 in ref 1), then rapidly cooled down to 117.5 °C, just above the OOT temperature (116 °C) but much below TLDT = 140 °C, to avoid the evolution of a large grain structure, as found in the previous report.1 If the size of grains becomes too large compared to the spatial resolution of USAXS, the uniform smearing of the scattering pattern does not occur, and hence irregular peaks will appear at the scattering angle smaller than that at the first-order scattering maximum as elucidated in ref 1. To avoid this effect, we cooled the sample quickly to develop volume-filling small grains impinged one another at the grain boundaries. As for the profiles of 117.0 and 117.5 °C the higher-order scattering peak was observed at the position of √2qm, indicating the microdomain structure of bcc-sphere. Here qm is the magnitude of the scattering vector q at the first-order scattering maximum. On the other hand, at the lower temperatures of 113.5 and 114.5 °C, the position of the higher-order peak changed to √3qm without a peak at √2qm, indicating the microdomain structure changed entirely into hexcyl. However, in the profiles between 115.5 and 116.5 °C, it is clear that the first-order peak splits into the two peaks located 9034


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at qm = 0.262 nm−1 (defined as qm,hex) and 0.269 nm−1 (defined as qm,bcc) which are very closely located in the q space so that they are difficult to be resolved with conventional SAXS optics even with a monochromator crystal for the incident X-ray beam. The peak at qm = qm,hex is attributed to hex-cyl and the other at qm = qm,bcc is attributed to bcc-sphere, indicating a possibility of the two phases (hex-cyl and bcc-sphere) being coexisting in equilibrium at these temperatures, seemingly due to the thermal fluctuation effects, as in the case of the coexistence of the ordered phase and disorder phase over the very narrow temperature interval centered at the order-disorder transition (ODT) temperature (TODT).12−14 The coexistence of the higher-order peaks at √2qm,bcc and √3qm,hex also is consistent with the coexistence of the two phases. Moreover, the third-order peak for the bcc-sphere at √3qm is weak, as seen in the profiles at 117.0 and 117.5 °C, so that only the single third-order peak at √3qm,hex is observed even in the case of the two-phase coexistence, i.e., the peak at √3qm,bcc is invisible due to the weak intensity with a poor S/N ratio. Note that the small difference of the qm between bcc-sphere and hexcyl means the small difference between the corresponding lattice constants. To further highlight the splitting of the first-order peak, the profiles around the first-order scattering maxima in Figure 1a are enlarged in Figure 1b by expanding the q scale between 0.23 and 0.30 nm−1 as shown by the arrow in Figure 1a. A precise measurement with 2 arcsec angular step at 115.5 °C is also presented in Figure 1b (indicated in red circles), which clearly shows the splitting identical to the profile obtained at the same temperature in the cooling process. Note that the measurement with 2 arcsec angular step at 115.5 °C was carried out in the heating process after the measuring the profile at 114.5 °C in the cooling process. The agreement of the profiles between the heating process and the cooling process indicates that this splitting would reflect the coexistence of the two phases in equilibrium. The temperatures 116.5 and 115.5 °C are close to the onset and the completion of the OOT from bcc-sphere to hex-cyl, respectively. We define the TOOT in the cooling process as a midpoint between the two temperatures; i.e., TOOT = 116 °C. The qms for bcc-sphere (0.269 nm−1) and hex-cylinder (0.262 nm−1) correspond to the contraction of the lattice spacing by 2.7% with the transformation from hex-cyl to bccsphere. If this contraction would occur in all directions, it could amount to the microscopic volume reduction by 8%. The conventional SAXS measurements also supported the hr-SAXS observations with respect to the two-phase coexistence in the narrow temperature range centered at TOOT. Figure 2 shows the desmeared SAXS profiles taken at various temperatures in a heating process from 112.7 °C with 1 °C temperature increment. The sample for this SAXS measurement was also pretreated at T ≅ 150 °C > TLDT, where it had the LDS structure, and rapidly cooled down to 110 °C to avoid the growth of the large grain. With increasing temperature, the first-order peak position qm was apparently observed to shift toward a higher q from qm,hex to qm,bcc, while almost no shift was observed in the position of the higher-order scattering peaks at √2qm,bcc, √3qm,hex, √3qm,bcc, and √4qm,hex. The higher-order maxima from hex-cyl at √3qm,hex and √4qm,hex gradually disappeared upon the heating process without a significant change of their peak positions, while the higher order maxima from bcc-sphere at √2qm,bcc and √3qm,bcc gradually appeared without a significant change of their peak positions. These higher-order scattering maxima in the

Figure 2. Desmeared conventional SAXS profiles measured in situ as a function of T in the heating process. The values qm,hex, √3qm,hex, and √4qm,hex are the q values at the first-, second-, and third-order scattering maximum from hex-cyl, while qm,bcc, √2qm,bcc, and √3qm,bcc are the q values at the first-, second-, and third-order scattering maximum from bcc-sphere. The higher-order peaks from both hex-cyl and bcc-sphere in this figure are more distinctly discerned than those in Figure 1 due to a better S/N ratio for this figure than for Figure 1. The symbols H and B have the same meaning as in Figure 1. Note that the first-order scattering maximum from hex-cyl and that from bccsphere are overlapped each other into one broad peak in the temperature range between 115.7 and 118.6 °C where hex-cyl and bccsphere are coexisting.

conventional SAXS profiles are much more distinct than those in the hr-SAXS, because the S/N is much higher in the former than in the latter, especially at the higher q region (q > qm). This is a big merit of the conventional SAXS compared with the hr-SAXS. The fact that the qm values for the higherorder scattering maximum hardly shift with T in the T range covered as well as the fact that the qm,hex and qm,bcc observed in the hr-SAXS profiles hardly shift with T as shown in Figure 1b indicate that the shift in qm for the first-order peak observed by the conventional SAXS is an artifact; It truly reflects the fact that the change in the peak intensity ratio of the two peaks at the two qms (qm,hex and qm,bcc) which remains unchanged with temperature, as observed in hr-SAXS. Thus, the hr-SAXS technique, which can well resolve the closely spaced two peaks, is powerful to elucidate the phase behavior of the OOT process and hence the symmetry change involved in the OOT process. Nevertheless, the conventional SAXS profiles accurately clarify the OOT from hex-cyl to bcc-sphere with increasing T based on those higher-order peaks: At T ≤ 114.7 °C, hex-cyl is the thermally stable ordered structure; at 115.7 ≤ T(°C) ≤ 9035


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Figure 3. Specific volume vs T measured by the pycnometry. The inset highlights the data near TOOT.

the OOT is a first-order phase transition, it may not necessarily involve the discontinuity in vsp, because the OOT of the bcp here is solid−solid phase transition involving only a symmetry change of the ordered structures without changing the molecular density, except for a density change due to a thermal expansion. 3.3. Time-Resolved Studies of OOT Process. The OOT process was investigated by the time-resolved hr-SAXS measurement. Figure 4 shows a set of the bird-eye-view plots on the time-evolution of the hr-SAXS profile around the firstorder scattering maximum after the T-jump from 111 to 121 °C. Parts a and b present the same data with different view angles. The profiles were plotted in 3D with the axes of log I(q), q, and t; The profiles were plotted with respect to time t in such a way that t increases from the back to the front. The trajectories of the peak intensities of Im,hex(t) and Im,bcc(t) for hex-cyl and bcc-sphere, respectively, were indicated with the black dots. With a close look at the profiles, we found the OOT process could be classified into 3 stages. Part a highlights the time evolution of the two scattering peaks in stage II, while part b highlights the shift of the peak positions in stage I and stage III both toward larger q values. The time change in the profiles in each stage was separately plotted in Figure 5a−c. In the first stage (stage I) from t = 0 to 52.5 s (Figures 4 and 5a), the peak positions continuously shift toward larger q values, as shown by the horizontally directed arrow, from the equilibrium q value for hex-cyl, defined by qm,hexe (=0.2608 nm−1), to the transient q value for hex-cyl, defined by qm,hext (=0.2622 nm−1), keeping the peak intensity almost constant. This fact indicates a decrease in the lattice spacing of hex-cyl between {10} planes from the equilibrium value defined by dhexe = 2π/qm,hexe to the transient value defined by dhext = 2π/ qm,hext. Although this shift that corresponds to the change from dhexe = 24.09 nm to dhext = 23.96 nm was very small (only about 0.5%), it is well resolved by the hr-SAXS method. Although, with Figure 5a alone, it is not self-evident that the profile with the peak at qm,hext is due to the transient hex-cyl, this will be

118.6, hex-cyl and bcc-sphere coexist; at T ≥ 119.6 °C, bccsphere is the thermally stable ordered structure. Thus, 115.7 and 118.6 °C are close to the onset and completion temperatures for the OOT, leading us to define TOOT = 117 °C in the heating process. Therefore, we found the hysteresis in between the OOT from hex-cyl to bcc-sphere and from bccsphere to hex-cyl, judging from the difference of the TOOT by 1 °C in the cooling and heating processes. Note that the average heating rate and cooling rate adopted were extremely small, i.e., 0.083 and 0.6 °C/h, respectively, as clarified in sections 2.2 and 2.3.1., respectively. In the temperature range where the two phases coexist, the peak at √3qm,hex and the peak at √3qm,bcc are expected to coexist and to be overlapped each other, hence resulting in a broadening of the peak. However, the coexistence of the peak and the peak-broadening were not observed. This can be explained by the fact that the peak intensity at √3qm,hex is much higher than that at √3qm,bcc. This is quite natural from the view that the former is the second-order peak from hex-cyl, while the latter is the third-order peak from bcc-sphere. 3.2. Change in Macroscopic Volume Induced by OOT. We measured the temperature dependence of the specific volume of the sample with the pycnometry over a wide temperature range in the first run as well as the second run. Both measurements were conducted in the heating process with ca. 15 min waiting time at each temperature. The error bar in the figure was estimated from the reading error of the meniscus height in the capillary. The specific volume of the sample, vsp, is plotted against the temperature in Figure 3, showing no discontinuity at OOT, although a little change in temperature coefficient was observed above and below TOOT: (∂vsp/∂T) for hex-cyl is slightly small compared with that for bcc-sphere. Because OOT of bcps is a first-order phase transition, the discontinuous change in the specific volume at TOOT could be expected. The discontinuity can be well expected for gas−liquid or liquid−solid phase transition accompanied by a sizable density change, as in the case of the ODT of bcps.13a Even if 9036


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Figure 4. Bird-eye-view plots of log I(q, t), q, and t for the timeresolved hr-SAXS, which highlight the time evolution of the scattering profiles around the first-order peak, during the OOT process induced by the T-jump from 111 °C (hex-cyl) to 121 °C (bcc-sphere). Parts a and b, which present the same data from two different views, led us to find the process being classified into the three distinct stages: stage I, stage II, and stage III, as designated in part a.

proved to be true later by investigating the change of the profiles in the whole stages, including stages II and III (to be discussed below). At the second stage (stage II) from t = 52.5 to 207.5 s (Figures 4 and 5b), the maximum intensity due to the transient hex-cyl at qm,hext was observed to decrease with t as shown by the downward arrow in Figure 5b, while a new maximum corresponding to the transient bcc-sphere phase appeared, and the peak intensity increased with t at a different qm defined by qm,bcct = 2π/dbcct as also shown by the upward arrow in Figure 5b. Both peaks changed only their intensity without changing their peak positions. At the end of stage II, the peak from hexcyl disappeared. Finally at the third stage (stage III) from t = 207.5 to 457.5 s (Figures 4 and 5c), both the peak intensity and position from bcc-sphere changed continuously toward a larger intensity and a larger q value from qm,bcct = 0.2678 nm−1 to qm,bcce = 2π /dbcce = 0.2689 nm−1 as shown by the arrow, indicating a lattice contraction from dbcct to dbcce and a lattice perfection. Note that dhexe and dbcce are, respectively, the lattice spacings for {10} planes of hex-cyl and {110} planes of bcc-sphere in each equilibrium state. The hex-cyl and bcc-sphere with the spacings of dhext and dbcct are considered to be the transient and

Figure 5. Time-resolved hr-SAXS profiles around the first-order scattering maximum in stage I (part a), stage II (part b), and stage III (part c). In stage I, the q value at the first-order scattering maximum shifts with t from qm,hexe to qm,hext as shown by the horizontally directed arrow. In stage II, the scattering maximum at qm,hext decreases with t and eventually disappear, while the scattering maximum at qm,bcct appears at some time and increases with time. In stage III, both the peak intensity and the q value at the peak slightly shift as indicated by the arrow.

intermediate structures appeared during the OOT process. This will be further discussed below in section 4.

4. ANALYSES AND DISCUSSION ON THE TIME-RESOLVED hr-SAXS MEASUREMENTS We discovered, for the first time, the three distinct stages in the transformation process from hex-cyl to bcc-sphere with the time-resolved hr-SAXS measurements. Here we aim to analyze 9037


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more precisely and quantitatively each stage in order to explore the detailed mechanism of the OOT. Figure 5 aims to present the overall behavior of the time change in the hr-SAXS profiles. Since the details of the time evolution of the profiles themselves in each stage may not be clearly presented in the figure, we separately present them in Figures 6a, 9, and 12a, in which the scattering profiles are vertically shifted to avoid their overlaps and facilitate an investigation of their time change more precisely.

Figure 7. Time evolutions of the first-order scattering maximum (Im,hext and Im,bcct) and that of the q value at the scattering maximum (qm,hext and qm,bcct) in stages I−III.

scattering vector at the first-order scattering maximum. Here, the time-dependent wavenumber qm(t) in stage I is defined as qm,hext = 2π/dhext and presented in Figure 7 where the subscript “hext” designates the transient hex-cyl in stage I. Figure 6b shows the scaled scattering function I[q/qm(t)]/I[qm(t)] as a function of q scaled with qm, i.e., q/qm. The ten profiles obtained in the time period between 7.5 and 52.5s in stage I fall onto a master curve universal with time: The scaled scattering function at a given time t (in stage I) was found to be identical to that for hex-cyl equilibrium at 111 °C. This result reveals that the structural change with time in stage I is scaled with the time-dependent single length parameter 2π/qm(t). This means that the spacing of hex-cyl dhex = 2π/qm ≡ 2π/ qm,hext (between {10} planes) as well as the radius of the cylinder R gradually decrease interdependently and self-similarly with time because of the structural change fulfilling the scaling hypothesis with the single length parameter. Since there is no macroscopic volume change involved by the OOT, as clarified in Figure 3 with the pycnometry, the contraction of hex-cyl perpendicular to the cylinder axis must be balanced by an elongation of hex-cyl parallel to the cylinder axis so as to the volume fraction of the cylinders being kept constant. Figure 8 schematically presents the structural change occurring in stage I as elucidated by the scaling analysis of the structure factor shown in Figure 6b. The structural change in stage I must satisfy the following two requirements: (1) The contraction of the spacing of hex-cyl from dhexe to dhext and that of the radius of the cylinder from Re to Rt must occur interdependently so as to keep the volume fraction of the cylinder and matrix phase constant (the single-lengthparameter scaling requirement); (2) This contraction of hexcyl perpendicular to the cylinder axis must be compensated by the elongation of the length of the cylinder from Le to Lt so as to keep the macroscopic volume constant (the constant-volume requirement). These structural changes must occur simultaneously in every grains and continuously with time in stage I as revealed by the continuous shift of the peak position qm or qm,hext in Figures 6a and 7 and as also revealed by the constant Im,hext ≡ I(q = qm,hext, t) in Figures 5a and 7. 4.1.2. Spinodal vs Nucleation and Growth. The transition process in stage I appeares to obey the spinodal process rather than the nucleation−growth (NG) process. If the process were the NG, it might involve a nucleation of the transient hex-cyl phase in the matrix of the equilibrium hex-cyl phase, and the

Figure 6. Time evolution of the first-order scattering profiles in stage I which are vertically shifted to avoid overlaps of the profiles (part a) and the universal scattering function in stage I obtained by scaling each profile at a given t with the single length parameter ∼1/qm (t) (part b). The time increases in the order of the increasing profile number (0 to 9).

4.1. Stage I. Figure 6a shows the time evolution of the hrSAXS profiles in Stage I. Here, each profile was consecutively analyzed with the time interval of 5 s, the time at which the profile was taken increases in the order of the profile # 0 to #9. For example, the profile number n represents the profile taken in the time interval between (n + 1)5 and (n + 2)5 s and this profile was designated as the one taken at time t = (2n + 3)5/2 s in Figure 7 to be shown later. Figure 6a reveals that the peak position of the first-order scattering maximum qm continuously shifts with time toward higher q from qm = qm,hexe to qm,hext as shown by the horizontally directed arrow. The time changes in qm as well as the peak intensity Im will be shown later in a part of Figure 7 (see stage I). 4.1.1. Scaled Structure Factor. We investigate whether or not the time-change in the scattering profiles I(q, t) in stage I (Figure 6a) can be scaled with the time-dependent wavenumber qm(t), i.e., the time-dependent magnitude of the 9038


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Figure 9. Time evolution of the first-order scattering profiles in stage II, which are vertically shifted to avoid their overlaps. The time increases in the order of the increasing profile number (9 to 40).

rise to the shape of the profile being the most different from either the profile no. 9 or the profile no. 40. These trends are clearly identified in Figure 7. The time evolution of the profiles from no. 9 to no. 40 can not be scaled at all with a timedependent single wavenumber parameter qm(t) or the length parameter 2π/qm(t), the trend of which is very different from that of stage I. 4.2.1. Epitaxial Transformation Process in Stage II. The time evolution of the scattering profiles in this stage must involve a structural transformation from the transient hex-cyl into the transient bcc-sphere. This structural transformation occurs according to the so-called epitaxial transformation mechanism which gives rise to the special relationship between the crystallographic axes and planes developed, as schematically summarized in Figure 10: The cylinder axis and {11} and {10} planes of hex-cyl (shown in parts a and c) correspond to ⟨111⟩ axis, {112} and {110} planes of bcc-sphere (shown in parts b and d), respectively. The detailed process of the epitaxial transformation has been elucidated, both theoretically3,15−19 and experimentally with static observations as a function temperature1,4−6,20−22 and with time-resolved observations,23 to involve undulation of hex-cyl before breakup of the hex-cyl into bcc-sphere. Figure 11 schematically presents the epitaxial transformation process. Hex-cyl in part a first undergoes cooperative and periodic undulations with their pinching and bulging points having the spatial arrangements of “bcc symmetry” as shown in part b. The undulation with bcc-symmetry has a degeneracy between bcc symmetry A and A′, as shown respectively in the upper and bottom halves of part b, which respectively break up into bcc-sphere A and A′ as shown in the upper and bottom halves of part c.23 The undulated hex-cyl with bcc symmetry A and A′ as well as bcc-sphere A and A′ are in the mirror symmetry with respect to {11} plane of hex-cyl and {112}

Figure 8. Schematic illustration of the structural change occurring in stage I: The elongation and contraction of the grains of hex-cyl parallel and perpendicular to the cylinder axis, respectively, while keeping the volume fraction of the two microphases and the total volume unchanged with t.

former phase grows with time at the expense of the latter phase. If this would be the case, the two peaks at qm,hexe and qm,hext should coexist, and the corresponding peak intensities, Im,hexe and Im,hext, should decrease and increase with time, respectively. However, this is not consistent with our experimental finding, which elucidates the scaled structure factor with a single timedependent length parameter. The deformation of hex-cyl in stage I involves an increase of the interfacial area per unit volume [=2(1/Rt − 1/Re)] and hence the cost of an extra interfacial free energy. However this cost will be well compensated by the gain of the conformational entropy of the bcp chains at the transition temperature (121 °C). 4.2. Stage II. Figure 9 highlights the time evolution of the hr-SAXS profile in stage II. Here again each scattering profile was consecutively analyzed with the time interval of 5 s, and the relation between the profile number n and the time when the profile was taken is defined earlier in conjunction with Figure 6a. Close observations of the profiles in Figures 5b and 9 indicate that the profile at a given time in stage II is generally composed of the two components: one having a peak at a fixed qm value defined by qm ≡ qm,hext independent of time t with the peak intensity Im,hext ≡ I (q = qm,hext;t) decreasing with t ; the other at another fixed qm value defined by qm = qm,bcct also independent of time t with the peak intensity Im,bcct ≡ I (q = qm,bcct ; t) increasing with t. These two peaks have almost the same peak intensity for profile no. 23 (122.5 s), so that the effect of the two peaks being overlapped is very strong, giving 9039


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the bcc symmetry A and A′ (Figure 11b) in the matrix of the transient hex-cyl (Figure 11a); The former with a fixed value of qm,bcct grows at the expense of the latter with a fixed value of qm,hext ; Upon a further elapse of time, the former may breakup into bcc-sphere A and A′ with time and with the timeindependent value of qm,bcct, as shown in the change from Figure 11b to Figure 11c. If this process involves the spinodal process, it may involve a simultaneous transformation from the transient hex-cyl to the undulated hex-cyl with bcc-symmetry A and A′ everywhere in the sample space or in every small grains, which is followed by the breakup of the undulated hex-cyl to bcc-sphere. It is beyond the scope of this paper to identify which process, either the NG process or the spinodal process, is plausible to our system. The time-resolved real-space analysis with transmission electron microscopy as reported previously,23 which clarified the NG process, would be one of the best direct method to clarify this point. 4.3. Stage III. Figure 12a presents the time-evolution of the hr-SAXS profiles in stage III. Here again each profile was

Figure 10. Schematic illustration of the epitaxial transformation from hex-cyl (parts a and c) to bcc-sphere (parts b and d).

Figure 11. Schematic illustration of the epitaxial transformation in stage II from transient hex-cyl (part a) to transient bcc-sphere (part c) via undulating hex-cyl (part b).

plane of bcc-sphere, respectively, as shown in Figures 10a,b and 11b,c. Hence, the undulated hex-cyl with bcc symmetry A and A′ as well as bcc-sphere A and A′ satisfy the twin relationship with the twin axis and twin plane as ⟨111⟩ axis and {112} plane, respectively (Figures 11b,c or 10b). Hex-cyl shown in Figure 10c and bcc-sphere B and B′ shown in Figure 10d are respectively the same structure as that shown in Figure 10a and the one as shown in Figure 10b: The formers are obtained by rotating the latters by 90° around the cylinder axis and ⟨111⟩ axis, respectively. Bcc-sphere B and B′ are in the mirror images with respect to {112} plane, which is the plane parallel to the plane of this paper. The time-evolution of the first-order scattering peak shown in Figures 5b and 9 reflects the time changes in the diffraction from {10} plane of the transient hexcyl and {110} plane from the transient bcc-sphere. 4.2.2. Nucleation−Growth vs Spinodal in Stage II. The epitaxial transformation process from the transient hex-cyl to the transient bcc-sphere may occur according to either NG process or spinodal process. If the process involves the NG process, it may involve nucleation of the undulated hex-cyl with

Figure 12. Time evolution of the first-order scattering profiles in stage III which are vertically shifted to avoid their overlaps (part a) and universal scattering function obtained by scaling with a single timedependent length parameter 1/qm (t) (part b). The time increases in the order of the increasing profile number (40 to 90).

consecutively analyzed with the time interval of 5 s, and the number n = 40 to 90 indicated in each profile has the same meaning as those in Figures 6a and 9. Both of the first-order peak position qm(t) and the peak intensity Im(t) tend to increase continuously with t from qm,bcct to qm,bcce and from Im,bcct to Im,bcce, respectively, as shown in Figure 7. We investigated whether or not the time change in the scattering profiles I(q, t) in stage III is scaled with the time9040


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from 111 to 121 °C causes the contraction in the Bragg’s spacing (2.99%) from dhexe = 2π/qm,hexe = (2π/0.2608) nm =24.09 nm for {10} plane of the equilibrium hex-cyl to dbcce = 2π/qm,bcce = (2π/0.2689) nm =23.37 nm for {110} plane of the equilibrium bcc-sphere. If this contraction would occur in all directions, it could amount to about 8.6% volume reduction. However, there is no reduction in the macroscopic volume as observed by the pycnometry (see Figure 3) in the narrow temperature range, defined as ΔTOOT, between the onset temperature (∼115.5 °C) and the completion temperature (∼116.5 °C) shown in Figures 1 and 2. Instead, the thermal expansion by 0.7% in volume is observed by the T-jump from 111 to 121 °C. The question arises on how these results can be explained. Figure 14 summarizes our hypothesis to interpret this result. The polygons with circles inside them in part (a) represent a

dependent single wavenumber qm(t). Figure 12b shows the scaled scattering function I[q/qm(t)]/I[qm(t)] vs q/qm(t). All the profiles obtained in stage III fall onto a master curve universal with time. This means that bcc-sphere contracts selfsimilarly with time, keeping essentially the volume fraction of the spheres constant (the single length parameter scaling requirement) to attain the more perfect bcc-sphere equilibrium at 121 °C. This process corresponds to a relaxation process of an extra volume generated during the OOT process in stage II as manifested by the change from qm,hext to qm,bcct. Figure 13 schematically presents the contraction of the lattice spacing from dbcct for the transient bcc-sphere (shown in part a)

Figure 14. Schematic illustration of the structural change occurring between the equilibrium hex-cyl (part a) and the equilibrium bccsphere (part b) where the cross sections of the grains normal to the cylinder axis (part a) and ⟨111⟩ axis of bcc-sphere (part b) are shown. The OOT from hex-cyl to bcc-sphere involves first the contraction and elongation of grains of hex-cyl perpendicular and parallel to the cylinder axis, respectively, and then its transformation into the corresponding grains of bcc-sphere with its ⟨111⟩ axis perpendicular to the plane of this paper or parallel to the cylinder axis via the three stages as illustrated schematically in Figures 8, 11, and 13

cross-section of grains of hex-cyl perpendicular to cylindrical axes, while the polygons with circles inside them in part (b) represent a cross-section of grains of bcc-sphere perpendicular to ⟨111⟩ axis of bcc-sphere and hence parallel to the cylindrical axis in part (a). The circles schematically represent the cross sections of the cylinders or spheres. The transition may involve a cooperative deformation of the grains. In the case of the OOT from hex-cyl to bcc-sphere, a contraction of the grains parallel to the plane of this paper as illustrated by the decrease of the spacing from dhexe to dbcce, as schematically shown by the change of the structure from part a to part b of Figure 14, and an expansion of the grains perpendicular to the plane of this paper (parallel to the cylinder axis of hex-cyl or ⟨111⟩ axis of bcc-sphere) could occur cooperatively so as to keep the total volume and volume fraction of each component constant over the narrow temperature range of ΔTOOT ∼ 1 °C. One can imagine just an opposite grain deformation occurs in the transformation in the opposite direction. Note that the sample was composed of numerous number of grains and grains in the sample would have the random orientation. Hence, the small changes in the shape and the size of each grain may be averaged out so that the total dimension of the sample is not necessarily changed.

Figure 13. Schematic illustration of the structural change occurring in stage III from the transient bcc-sphere (part a) to the equilibrium bccsphere (part b).

to dbcce for a more perfect bcc-sphere close to the equilibrium bcc-sphere (shown in part b), as manifested both by the increase in the first-order peak position for {110} plane of bccsphere from qm,bcct = 2π/dbcct to qm,bcce = 2π/dbcce (dbcct = 23.46 and dbcce = 23.37 nm, corresponding to the reduction only by 0.4%) and by the relevant intensity increase from Im,bcct to Im,bcce. The change in the volume fraction of the spheres is so small that the single-length-parameter scaling hypothesis is approximately satisfied. 4.4. Change in Microscopic and Macroscopic Dimensions Induced by OOT. We consider here the consistency between microscopic and macroscopic dimensional changes as observed respectively by the hr-SAXS and by the pycnometry during the OOT process. As seen in the hr-SAXS measurements, our OOT from hex-cyl to bcc-sphere due to the T-jump 9041


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5. COMMENTS ON SPINODAL PROCESS AND NG PROCESS ON THE OOT PROCESS The OOT process between hex-cyl and bcc-sphere has been predicted18 to occur either by spinodal process or NG process, depending on a temperature difference between the TOOT and the temperature where the OOT experiment is conducted. Figure 15a defines the characteristic temperatures TOOT,

in the parameter space composed of energy G and the morphology coordinate comprising the hex-cyl and bcc-sphere morphologies. On the other hand, Figure 15c similarly shows the expected energy pathway and the energy barrier for the OOT from bcc-sphere to hex-cyl. When an equilibrium hex-cyl stable below TOOT is brought about at the temperature exactly equal to TOOT, the energy pathway in the parameter space of the energy vs the morphology coordinate has a double minimum with an equal minimum value at the hex-cyl morphology and at the bccsphere morphology as shown by the red line in parts b and c. Hence, hex-cyl and bcc-sphere coexists at thermal equilibrium at TOOT. When it is brought about at Tbn above TOOT, the energy pathway is schematically presented by a green line in part b so as to hex-cyl becoming thermodynamically a metastable state. If the thermal energy assists the system to jump over the nucleation barrier ΔGN as defined in part b, the metastable hex-cyl is transformed into the equilibrium bccsphere with the energy G(T = Tbn). When it is brought about at Tbs, the energy pathway is schematically presented by a blue line so that hex-cyl becomes thermodynamically unstable as shown in part b. Thus, hex-cyl is transformed into the equilibrium bcc-sphere with energy G(T = Tbs). This process occurs without the nucleation barrier [ i.e., ΔGN(T = Tbs) = 0 ] and hence follows the spinodal process. The same principle as described above can be applied to the OOT from bcc-sphere to hex-cyl induced by the T-drop from a T above TOOT to Thn or Ths. The energy G vs the morphology coordinate in this case is shown in part c. We have elucidated the OOT process induced by the T-jump from hex-cyl at 110 °C to bcc-sphere at 121 °C involves the three distinct characteristic stages, denoted as stage I, stage II, and stage III as discussed in section 4. In particualr, stage I (the thinning and elongation of hex-cyl grains perpendicular and parallel to the cylinder axis, respectively) was discovered for the first time to our best knowledge by using the time-resolved hrSAXS analyses that were also conducted for the first time. The experimental finding may give a new theoretical problem on how the NG process or the spinodal process can be theoretically treated in conjunction with the three stages, especially with stage I and stage II emerging in the OOT process. Our previous report23 on the time-resolved in situ synchrotron SAXS (SR-SAXS) and ex situ TEM analyses on the OOT from hex-cyl to bcc-sphere on a shear-aligned polystyrene-block-polyisoprene-block-polystyrene at different temperature concluded that the OOT is composed of three step: step I associated with cooperative undulation of hex-cyl, step II associated with evolution of bcc-sphere in the matrix of the undulated hex-cyl, and step III associated with the perfection of bcc-sphere toward the equilibrium bcc-sphere. Since the SR-SAXS did not have such a high q-resolution as the hr-SAXS employed in this study, the first-order peaks from hexcyl and bcc-sphere are completely overlapped and unable to be resolved in the q-space. Thus, the previous SR-SAXS may overlook stage I found in this work: Step I and step II in the previous work may hence correspond to stage II in this work: step III in the previous paper is identical to stage III in this work. However, rigorously speaking, this confirmation reserves future work, as the sample and temperatures involved are different. It should be noted that the present work with hrSAXS could not capture the undulated hex-cyl phase in step I and step II in the previous paper.

Figure 15. Characteristic temperatures relevant to the OOT process between hex-cyl and bcc-sphere (part a) and the energy-pathway for OOT from hex-cyl to bcc-sphere (part b) and from bcc-sphere to hexcyl (part c) in the parameter space of energy G and the morphology coordinate composed of the hex-cyl and bcc-sphere morphology. In part a, TS,H→B is the spinodal temperature for OOT from hex-cyl (H) to bcc-sphere (B), while TS,B→H is the spinodal temperature for OOT from bcc-sphere to hex-cyl. At temperature T = TbS > TS,H→B, the OOT from hex-cyl to bcc-sphere occurs according to the spinodal process, and its energy-pathway is given schematically by the blue line at TbS, as shown in part b, with G showing an inflection point at the hex-cyl coordinate and the minimum value of G(T = TbS) at the bccsphere coordinate. At T = Tbn satisfying TOOT < Tbn < TS,H→B, the OOT from hex-cyl to bcc-sphere occurs according to the NG process, and its energy pathway is given by the green line, as shown in part b, with G showing a nucleation barrier given by ΔGN and with the minimum value G (T = Tbn). At T = TOOT, the energy pathway has a double minimum with the equal minimum value as shown by the red line in part b. The energy pathways at Ths, Thn, and TOOT in the parameter space of energy G vs morphology in part c can be read in the same way as those in part b.

TS,H→B, and TS,B→H. TOOT is the equilibrium OOT temperature, above and below which bcc-sphere and hex-cyl are stable ordered structures, respectively. TS,H→B is defined as the spinodal temperature for the OOT from hex-cyl (H) to bccsphere (B), and TS,B→H is defined as the spinodal temperature for the OOT from bcc-sphere to hex-cyl. The T-jump from a T below TOOT to a T above TS,H→B, e.g., Tbs, involves the OOT from hex-cyl to bcc-sphere via the spinodal process, while the T-jump from a T below TOOT to a T between TOOT and TS,H→B, e.g., Tbn, involves the OOT from hex-cyl to bcc-sphere via the NG process. Similarly, the T-drop from a T above TOOT to a T below TS,B→H, e.g., Ths, involves the OOT from bcc-sphere to hex-cyl via the spinodal process, while the T-drop from a T above TOOT to a T between TOOT and TS,B→H, e.g., Tbn, involves the OOT from bcc-sphere to hex-cyl via the NG process. Figure 15b schematically presents the expected energy pathway and the energy barrier for the OOT from hex-cyl to bcc-sphere 9042


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If we apply the hr-SAXS method to the shear-aligned hex-cyl, we may be able to explore more in deep stage I and stage II in the OOT process from hex-cyl to bcc-sphere. Especially we may be able to explore clearly not only the stage where undulating hex-cyl grains are developed and grown in the matrix of the transient hex-cyl phase (developed earlier in stage I) but also the stage where bcc-sphere grains are developed and grown in the matrix of the undulated hex-cyl phase in stage II. However, we should carefully note the smearing effects due to the infinite slit-hight on hr-SAXS profiles from the shearaligned hex-cyl and bcc-sphere; Especially, the smearing effects will not allow us to distinguish either undulated hex-cyl with bcc-symmetry A and A′ or “bcc-sphere with symmetry A and A′”.23

We found that the time-evolution of these two peaks can be interpreted to reflect the epitaxial transformation of hex-cyl into the bcc-sphere, as detailed in section 4.2.1 in conjunction with Figure 10, via the formation of the undulating hex-cyl (as an intermediate structure) with their pinching and bulging points arranged spatially the “ bcc symmetry ” (Figure 11b). The process in stage III involves the ordering process of the transient bcc-sphere toward the equilibrium bcc-sphere at the given ΔT, as illustrated in Figure 13 and as revealed by the gradual and continuous increase of the peak intensity Im,bcct and the peak position qm,bcct toward Im,bcce and qm,bcce, respectively (Figures 7 and 12a). The structural changes with time occur self-similarly, giving rise to the universal scattering function scaled with a time-dependent single-length parameter 2π/ qm,bcc(t) (Figure 12b), so that the volume fraction of the spheres are essentially conserved with t.

6. CONCLUSIONS We have elucidated the mechanism and process of the thermally induced OOT of the PS−PI diblock copolymer from an equilibrium hex-cyl to an equilibrium bcc-sphere by using the static and time-resolved high-resolution SAXS (hrSAXS). The hr-SAXS experiments were performed with a Bonse-Hart type USAXS apparatus with a q-resolution of ∼0.006 nm−1, which is at least by 1 order of magnitude higher than that of a conventional SAXS apparatus. The static hr-SAXS was conducted in situ as a function of temperature across the OOT temperature TOOT, while the time-resolved hr-SAXS was focused on the scattering profile just around the first-order peak at the given reduced superheating ΔT/TOOT = 1.285 × 10−2 where ΔT ≡ T − TOOT with T = 394 K and TOOT = 389 K. The hr-SAXS successfully resolved the closely located the two firstorder peaks from hex-cyl and bcc-sphere in a q-space, which are overlooked as a broad single peak with conventional SAXS apparatuses due to the limited spatial resolution. Hence, the use of hr-SAXS enables us to directly follow and analyze unequivocally the symmetry-change process induced by the OOT. The time-resolved hr-SAXS elucidated for the first time that the ordering process involves the three distinct stages defined as stages I, II, and III. Stage I involves a self-similar deformation of the hex-cyl grains with time t under a constant volume fraction of the two microphases, as revealed by the universal scattering function scaled with a single time-dependent length parameter 2π/qm,hext(t) (shown in Figure 6b). This indicates that the grains are compressed and elongated perpendicular and parallel to the cylinder axis, respectively, as schematically illustrated in Figure 8. This process increases the interfacial area density and hereby the cost of the interfacial free energy. However, this cost will be well compensated by the decrease of the segmental interaction parameter and gains of the conformational entropy of block chains at the elevated temperature of 121 °C, where bcc-sphere is the equilibrium morphology. We proposed that the process in stage I is triggered by the thermodynamic instability of hex-cyl at the given superheating ΔT /TOOT, judging from the time evolution of the hr-SAXS profiles as detailed in section 4.1. The process in stage II involves the time evolution of the first-order peak which is composed of the two distinct peaks originated from (1) the time-evolution of the transient hex-cyl, which gives rise to the decrease of the peak intensity Im,hext, while keeping the peak position qm.hext invariant with time and (2) the time-evolution of the transient bcc-sphere, which gives rise to the increase of the peak intensity Im,bcct, while keeping the peak position qm,bcct constant with time (Figures 5b and 9).

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: (K.S.) [email protected]. *E-mail: (T.H.) [email protected]. Present Addresses

§ Toray Battery Separator Film Co.,Ltd., 1190−13 Iguchi, Nasushiobara City, Tochigi 329−2763, Japan ⊥ Department of Materials Science and Engineering, Department of Chemistry, Stony Brook University, Stony Brook, NY 11794 ∥ Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319−1195, Japan

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge Dr. Tsuyoshi Koga for his useful comments on the OOT processes. REFERENCES

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