Article pubs.acs.org/Macromolecules
Tricontinuous Double Diamond Network Structure from Binary Blends of ABC Triblock Terpolymers Yusuke Asai,† Jiro Suzuki,‡,§ Yoshitaka Aoyama,∥ Hideo Nishioka,∥ Atsushi Takano,† and Yushu Matsushita*,† †
Department of Applied Chemistry, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan ‡ Computing Research Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan § Information System Section, J-PARC Center, 2-4 Shirakatashirane, Tokai, Ibaraki 319-1195, Japan ∥ JEOL Ltd., 1-2 Musashino, 3-Chome Akishima, Tokyo 196-8558, Japan S Supporting Information *
ABSTRACT: We report the tricontinuous double diamond (TDD) structure in binary blends of ABC triblock terpolymers with different chain lengths of the two end-blocks. Although, the TDD structure has been long considered as an unstable phase because of the high energetic barrier associated with stretching energy and interfacial energy due to wider interfacial area than those for known structures such as a lamellar structure or a tricontinuous double gyroid (TDG) structure. The different chain length possibly helps to alleviate the free energy penalty, which resulted in the occurrence of the TDD as a stable phase at wide range of compositions. Transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and TEM tomography (TEMT) results all corroborate the existence of TDD in the present blend system. We present the first solid evidence of the thermodynamically stable TDD structure.
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al.15 and Bates et al.16 experimentally revealed bicontinuous network structures with Ia3̅d symmetry by their careful scattering data analyses, and the new structure was entitled “gyroid”. Matsen et al. theoretically studied the phase stability of the double gyroid (DG) structure over the DD structure for multiarm star-block and linear multiblock systems.17,18 They found that the DG phase is thermodynamically more stable than the DD, and it appears between lamellar and cylindrical phases. Later, Hajduk et al. re-examined the morphologies of PS−PI star-block copolymer and proved the existence of the ordered bicontinuous double gyroid (OBDG).19 Suzuki et al. reported on an tricontinuous double gyroid (TDG) structure for an ISP triblock terpolymer sample with thermal treatment at high temperature to achieve a thermal equilibrium state.20 Considering this history as for cocontinuous network structures, there might be some possibility of structure misidentification in the past.21 It could be caused by low resolution of both scattering data and TEM images. DG and DD structures have several structure similarities. Both the structures have the triply periodic networks, and the intermaterial dividing surfaces are well described by two parallel surfaces derived from the periodic minimal surfaces: “Schoen G
INTRODUCTION Cocontinuous structures formed from block copolymers have attracted much attention because of a wide range of possible technological application such as photonic crystals,1,2 solar cells,3,4 and separations.5 First observation of a cocontinuous structure was presented by Aggarwal in 1976,6 where the TEM image with a wagon-wheel pattern was obtained from a 15armed polystyrene−polyisoprene (PS−PI) star-block copolymer, but the nature of the structure was not discussed. A decade later, Alward et al. reported the formation of an ordered bicontinuous double diamond (OBDD) structure in PS−PI star-block copolymers, in which they first used the phrase “ordered bicontinuous” for representing a morphology of block copolymers.7,8 At nearly the same time, Hasegawa et al. independently reported a “tetrapod” network structure which was geometrically the same as OBDD, from linear PS−PI diblock copolymers.9 Furthermore, in 1992, Matsushita et al. reported on the tricontinuous network structure from ISP (I: polyisoprene; S: polystyrene; P: poly(2-vinylpyridine)) triblock terpolymers, which was the first discovery of the multiply continuous network structure in ABC triblock terpolymers.10,11 Following their pioneering researches, additional experiments also reported on the existence of OBDD and ordered tricontinuous double diamond (OTDD) structures.12−14 In 1994, three research groups independently found a new network structure from diblock copolymers.15−18 Thomas et © XXXX American Chemical Society
Received: February 23, 2017 Revised: May 17, 2017
A
DOI: 10.1021/acs.macromol.7b00403 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules surface”22 and “Schwarz D surface”.23 In fact, the domain interfaces have large deviation from the minimal surfaces because of the nodes.24 The structural resemblances further cause the difficulty in distinguishing the two morphologies by TEM projections. On the other hand, one crucial difference between the two is the connectivity of each node. The interwoven networks composed of minority components can be divided into “channels” and “nodes”. In the gyroid, each node is constructed by the junction of three channels, whereas diamond networks possess 4-fold nodes. The node structures considerably affect the free energy of the morphology. In short, packing frustration in diamond networks is higher than that in gyroid networks because the minority chains have to stretch more to fill the centers of the 4-fold nodes than that of 3-fold nodes.25−27 From the standpoint of the interfacial energy, a gyroid structure is favored due to the lower distribution of mean curvature on the domain interface and the smaller interfacial area than those of a diamond network.25,26 Theoretical works presented that blends of block copolymer/ homopolymer can stabilize double diamond structures,28,29 where the homopolymer preferentially fills the center of 4-fold nodes to alleviate packing frustration. Furthermore, MartinezVeracoechea et al.30 and Dotera31 suggested by simulations that a plumber’s nightmare phase, which includes 6-fold nodes, was predicted to be stable for AB diblock/A homopolymer and ABC triblock/A/C homopolymers blends, although the 6-fold nodes in the plumber’s nightmare phase cause even higher packing frustration than that in diamond networks. Experimentally, Takagi et al. have demonstrated that an OBDD structure was explicitly identified in PS−PI/PI homopolymer blends by using a scattering technique.32 In addition, Chu et al. have recently found a OBDD structure in a syndiotactic polypropylene−polystyrene (sPP−PS), in which the helical segments in the sPP may reduce the packing frustration in 4fold nodes,33 where both the electron microscopy images and scattering patterns ensured the structure. On the other hand, tricontinuous double diamond (TDD) structure has not yet been found in ABC/A/C blends even though Suzuki et al. carefully investigated the phase behavior of the blend system.34 In order to obtain the DD structure, the following two energetic disadvantages have to be overcome: (1) packing frustration in 4-fold nodes; (2) nonconstant mean curvature (non-CMC) interface. Fortunately, we have already found the hints to solve these two problems in our previous works.35−37 We have reported that ABC triblock terpolymer blends with different chain lengths of two end-blocks exhibited rectangularshaped rods35,36 and cylindrical morphologies with nonuniform domain sizes and shapes.37 These structures revealed two important characteristics: nonuniform domain thickness and the interfaces with nonconstant mean curvature, although domains with uniform thickness are naturally favored to avoid packing frustration and domain interfaces tend to adopt constant mean curvatures to minimize surface area for conventional block copolymers. It has been concluded that localization of short and long chains within domains or unit lattices caused the specific structures to reduce the conformational entropy losses of the components on chain ends. So far, we have merely investigated the blend system with different chain lengths of the two end-blocks in the composition range for the cylindrical morphologies. In the present study, we extend our molecular design of “different chain lengths of two end-blocks in ABC triblock terpolymers” to the cocontinuous structure region and aim to
acquire the TDD structure. Binary blends of two ISP triblock terpolymers with the same total molecular weights but with different chain lengths of two end-blocks were adopted in this work. The difference in molecular weights adopted for I chains was 6.9, and that for P chains was 4.6. Both the chain length differences were estimated to be large enough to fill the center of the 4-fold nodes with longer block chains without further chain stretching. Transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS), and TEM tomography (TEMT) were performed to probe the structures of the blend samples.
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EXPERIMENTAL SECTION
Two poly(isoprene-b-styrene-b-(2-vinylpyridine)) (ISP) linear triblock terpolymers, ISP-α and ISP-β, were prepared in tetrahydrofuran (THF) at −78 °C via three-step anionic polymerizations using cumyl potassium as an initiator according to a previously reported procedure.10 Under this condition, polyisoprene blocks are preferentially composed of 1,2- and 3,4-addition microstructures over 90%. Osmometry, multiangle laser light scattering (MALLS), 1H NMR spectroscopy, and size exclusion chromatography (SEC) were used to investigate their molecular information. Osmometry was performed in benzene at 37 °C using an Osmomat 090 of Gonotec GmbH to determine the total number-average molecular weight, and the weightaveraged molecular weights of precursor PI homopolymers were evaluated by MALLS (DAWN EOS, Wyatt Technology). The volume fractions of ISP triblocks were determined by 1H NMR measurements (Varian INOVA, Varian), and the polydispersity indices, Mw/Mns, were measured by SEC, which is composed of a set of pumps, the DP8020 (Shimadzu Co.), and a RI detector, RI-8020 (Shimadzu Co.), equipped with three polystyrene gel columns, TSK-gel G4000HHR of Tosoh Co., using THF as an eluent with 0.1% addition of tetramethylethylenediamine (TMEDA).36 Table 1 summarizes the
Table 1. Molecular Characteristics of the Poly(isoprene-bstyrene-b-(2-vinylpyridine)) (ISP) Parent Triblock Terpolymers Used in This Study sample
Mna (kg/mol)
Mn(I):Mn(S):Mn(P)b (kg/mol)
φI:φS:φPb
Mw/Mnc
ISP-α ISP-β
136 146
10.0:55.2:70.7 68.5:62.1:15.3
0.09:0.42:0.49 0.51:0.40:0.09
1.02 1.03
a Determined by osmometry. bEstimated from a combination of MALLS and 1H NMR spectroscopy using the densities of I, S, and P at room temperature (ρI: 0.926 g/cm3; ρS: 1.05 g/cm3; ρP: 1.14 g/cm3). c Measured from SEC chromatograms calibrated with polystyrene standards.
molecular characteristics of the two ISP parent triblock terpolymers. These ISP triblocks have almost the similar total molecular weights and midblock (S) molecular weights, while the molecular weights ratios for I chains and P chains are 6.9 and 4.6, respectively. In this system, the asymmetric chain lengths of the two end-blocks were adopted accidentally, but fortunately, the two longer chains, which are 6.9 (I) and 4.6 (P) times as long as the corresponding short chains, are long enough to reach the center of the 4-fold nodes, if the chain localization occurs within the nodes of the D phase; the longer chains prefer inside the nodes and the shorter chains concentrate in the channels to avoid packing frustration. Binary blend samples of ISP-α and ISP-β are designated as Blend(α/β), where α is the molar ratio of ISP-α and β is that of ISP-β. The molecular characteristics of the binary mixtures are summarized in Table 2. Considering the phase boundary shift by sharing the common interface with block chains having different chain lengths, which is called the “cosurfactant effect”,38 the volume fractions of S component in the blend samples are designed to be lower than that for the cocontinuous structure region for monodisperse ISP triblocks (φS = 0.48−0.68, φI = φP).39 B
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Macromolecules Table 2. Molecular and Morphological Characteristics of the Blend Samples in This Study sample name
φI:φS:φP
morphologya
Blend(9/1) Blend(8/2) Blend(7/3) Blend(6/4) Blend(5/5) Blend(4/6) Blend(3/7) Blend(2/8) Blend(1/9)
0.13:0.42:0.45 0.18:0.42:0.40 0.23:0.41:0.36 0.27:0.41:0.32 0.31:0.41:0.28 0.35:0.41:0.24 0.39:0.41:0.20 0.43:0.41:0.16 0.47:0.40:0.13
PL DG DG + DD DG + DD DD DD DD DD DD
Figure 1. Representative TEM images of (a) ISP-α and (b) ISP-β stained with OsO4/I2. Both the scale bars represent 100 nm.
a
Morphology identified by TEM and SAXS (PL = perforated lamellae, DG = double gyroid, DD = double diamond). DG + DD represents the coexistence of DG and DD.
the parent triblocks seem to be three-phase four-layer lamellae, although the minor components of two triblocks, that is, I for ISP-α and P for ISP-β, conform partially broken lamellar domains embedded in thick lamellae. Figure S1, which shows a region where the lamellar normal is slightly off perpendicular to the section, reveals that the minor components form perforated phases. The morphologies of the parent triblocks were further confirmed by SAXS, as shown in Figure S1. The d-spacings of ISP-α and ISP-β were estimated to be 69 and 71 nm, respectively, which are consistent with the results of the real space images. The periodicity of the perforated phase generally can be identified by the scattering pattern;42,43 however, the peaks associated with the perforated phase are not obviously observed in Figure S1. This may be due to the poor-ordered perforated phase. Although the perforated lamellar structure is often believed to be a metastable phase structure,44,45 in the present work, they must be the thermal equilibrium structures because of the long solvent casting/annealing process as well as a good reproducibility of the morphology. TEM images of all blend samples are summarized in Figure 2. As a general observation, macrophase separation did not occur in any blend samples, and the most of the blends exhibited complex structures. In the case of Blend(9/1), a perforated lamellar phase was obtained, where I lamellae were thicker than those of ISP-α. A tilted TEM image of Blend(9/1) shown in Figure S2 reveals that the number of perforations reduces from the neat ISP-α due to the higher volume fraction of I component for the blend than that for ISP-α. The SAXS pattern shown in Figure S2 indicates that the relative peak ratio is typical for a lamellar structure, whose domain spacing is estimated to be 73.7 nm from the primary peak (q*). The domain spacing observed from the TEM image in Figure 2a is consistent with that estimated from the SAXS observation. The domain distance is slightly increased by the addition of the small amount of ISP-β with the higher total molecular weight. As for other blend samples, the projection images with wavelike texture suggest the formation of a continuous network structure. For example, the TEM image for the Blend(7/3) in Figure 2c shows a typical (112) gyroid projection, so-called “double wave” pattern.25,45 For Blend(6/4) to (1/9), their projected patterns do not match gyroid projections. However, it is hard to distinguish between TDD and TDG by merely the two-dimensional (2D) micrographs because the 2D projections for some TDD planes are similar to those for the TDG. This projection similarity has caused confusion in the morphological identification, but the tetrahedral connections can generate the specific projection images. Hence, the network structure assignment was made by comparing experimental TEM images
All sample films for the morphological observation were prepared by solvent casting procedure from the solutions of THF, which is a nonselective solvent for all components. The sample amount was accurately measured (within 1% error) and then placed into a glass vessel; successively THF (without an antioxidant) was poured into the vessel to give 3 wt % solution. The polymer solution was stirred for at least 6 h at room temperature. The solution was transferred into a Teflon beaker, and the solvent was evaporated slowly over 2 weeks at 25 °C in a temperature control oven. Subsequently, the resulting films were dried under vacuum at room temperature for 1 day, followed by thermal annealing at 150 °C for 5 days. The phase-separated structures were probed using a combination of TEM observation and SAXS measurements. For TEM observation, the annealed bulk films were embedded in an epoxy resin and ultramicrotomed to a thickness of ca. 50 nm at room temperature. The ultrathin sections were floated on water and collected on Cu 300 mesh grids. They were stained with osmium tetroxide (OsO4) vapor for 2 h at 70 °C and subsequently treated with iodine (I2) vapor for 2 h at 50 °C to enhance the contrast. The combination of OsO4 and I2 is identified as suitable for the I−S−P three-component system. OsO4 stains polyisoprene heavily, whereas I2 gives relatively weak contrast to poly(2-vinylpyridine). By double staining with OsO4/I2, I, S, and P phases appear dark, white, and gray, respectively. TEM experiments were performed using a JEM-1400 (JEOL Co., Ltd., Japan), operated at an accelerating voltage of 120 kV. SAXS experiments were conducted using the beamline BL-40B2 at SPring-8 (Hyogo, Japan) and the BL-6A at Photon Factory (Tsukuba, Japan). The wavelength of the irradiated X-ray was 0.15 nm. A charge coupled device (CCD) camera on BL-40B2 and Pilatus 1M detector on BL-6A were used for two-dimensional detectors. The detectors were calibrated using a collagen and a silver behenate, respectively. All scattering data were corrected for air scattering and dark current. All SAXS experiments were performed under room temperature. In order to obtain the solid evidence of the DD structure, TEM tomography (TEMT) was carried out using a JEM-2100Plus (JEOL Co., Ltd., Japan) operated at 200 kV. The sample for a TEMT observation was prepared in the following manner. A small sample piece cut from the annealed bulk film was stained with OsO4 aqueous solution for 2 h at 70 °C. A rod-shaped specimen with a diameter of approximately 300 nm was fabricated by a focused-ion-beam (FIB) system.40,41 A series of a total of 165 TEM images were taken at tilt angles ranging from −82° to +82° at an angular interval of 1° increment. The aligned micrographs were reconstructed to give a 3D image by the filtered back projection method using a software, TEMography (System in Frontier, Inc., Japan).
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RESULTS AND DISCUSSION TEM micrographs of the two parent ISP triblock terpolymers are presented in Figure 1. Note that I and P phases appear dark and gray, respectively. At the first glance, the structures of both C
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Figure 2. TEM images of the blend samples: (a) Blend(9/1), (b) Blend(8/2), (c) Blend(7/3), (d) Blend(6/4), (e) Blend(5/5), (f) Blend(4/6), (g) Blend(3/7), (h) Blend(2/8), and (i) Blend(1/9). All scale bars represent 100 nm.
with simulated projection images.46,47 The TEM simulation was carried out based on the assumption that the cocontinuous structures possess the tricontinuous nature in which I and P domains form mutually interwoven and triply periodic networks embedded in an S matrix, and hence their I/S and S/P interfaces are created by the pseudo parallel shift of the three-dimensional periodic minimal surfaces.47 Four parameters were considered to generate simulated images: (1) TEM contrasts, (2) volume fractions of three components, (3) the direction of projection, and (4) thickness of a sample film. The relative TEM contrasts (1) of I, S, and P were set as 1.0 (black), 0.1 (white), and 0.5 (gray), respectively, because the sample films were stained with OsO4/I2. The exact volume fractions (2) of each sample, listed in Table 2, were employed for the calculation. The other two parameters (3) and (4) were adjusted as needed. Figure 3 compares the experimental TEM images with the computer-generated TEM simulation results. Inset capitals and numbers in the simulation results express the type of cocontinuous structure and the plane of projection: e.g., G(122) indicates TDG from the projection of (122) plane, and D(112) represents TDD from (112) plane. To show more explicit evidence, additional comparison data and TEM images at lower magnification are presented in the Supporting Information (Figures S3−S11). All the TEM simulation results show a good agreement with the experimental images.
According to the comparison, Blend(8/2) and Blend(7/3) exhibited the TDG structures, and Blend(6/4) through Blend(1/9) revealed the TDD structures. However, as shown in Figures S4 and S5, TDD was partially found in Blend(7/3), whereas TDG was partly developed in Blend(6/4), suggesting that Blend(7/3) and Blend(6/4) are in a transition region for TDG and TDD. Here, it should be stressed that the continuous network structures have been found at a wide range of volume fractions: φI:φS:φP = 0.18:0.42:0.40−0.47/0.40/0.13, where they maintain the almost constant φS. In general, tricontinuous network structures such as double gyroid and double diamond are considered to be stable only when the alternative networks occupy the similar volume. Thus, it has never been predicted theoretically and observed experimentally that TDG and TDD structures stabilize in ABC triblock terpolymers with highly asymmetric end-block compositions. To our knowledge, neat monodisperse ISP triblock terpolymers with the same compositions as the present samples, φ I :φ S :φ P = 0.18:0.42:0.40−0.47/0.40/0.13, exhibit three-phase four-layer lamellar structures. The phase boundary shift of continuous network structure toward a lower φS can be well explained by the cosurfactant effect.38 TEM experiment is a useful and powerful tool to determine the detailed microdomain structures, but the historic background for “continuous network structure” study as noted in Introduction tells the difficulty in the structural assignment of D
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Figure 3. Comparison of TEM images and computer-generated images: (a) Blend(8/2), (b) Blend(7/3), (c) Blend(6/4), (d) Blend(5/5), (e) Blend(4/6), (f) Blend(3/7), (g) Blend(2/8), and (h) Blend(1/9). All scale bars represent 100 nm. The TEM simulation results are shown at the bottom of their corresponding TEM images. The inset capitals at lower right in TEM simulations express the type of cocontinuous structures, i.e., G; gyroid and D; diamond, whereas the numbers attached represent the plane of the simulated projection.
series of scattering peaks with position ratio of √2, √6, √8, √10, √12, ..., corresponding to (110), (211), (220), (310), and (222), respectively. Azimuthally integrated synchrotron SAXS profiles for eight blend samples are shown in Figure 4, where the sequence of peaks are pointed out by inverted triangles. The relative peak positions and the q values of the primary peaks are listed in Table 3. All the SAXS profiles reveal the higher-ordered diffraction peaks, which can offer clear identification of the morphology. For Blend(8/2) and Blend(7/3), a series of peaks appeared at relating positions at √2, √6, √8,..., as marked by inverted filled triangles, correspond to the representative peak series for TDG, suggesting that both the samples form TDG. However, in the SAXS pattern of Blend(7/3), two peaks
the TDG and TDD networks by using only 2D micrographs. High-resolution scattering data with sufficiently high signal-tonoise ratio are required to offer unambiguous structural information. High-resolution SAXS is a crucial method to probe the difference in space group symmetry; therefore, the SAXS measurements were conducted at two synchrotron radiation sources (PF and SPring-8, Japan) in this study. The diffraction peak positions obtained by SAXS can easily distinguish the difference between TDG (I4132 symmetry) and TDD (Fd3m ̅ symmetry). According to the calculated scattering amplitude by Suzuki et al.20 and Garstecki et al.,48 a TDD structure displays the diffraction peak series of √3, √8, √11, √12, √16, ..., corresponding to (111), (220), (311), (222), and (400), respectively, while a TDG structure exhibits a E
DOI: 10.1021/acs.macromol.7b00403 Macromolecules XXXX, XXX, XXX−XXX
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composed of C networks encased in B shells embedded in A matrix phase, resulting in a pentacontinuous network structure. The lattice constant of a core−shell type network structure is approximately twice as large as that of a conventional tricontinuous network structure because two ABC triblock chains are required to conform a unit cell of the pentacontinuous network. Fddd networks have 3-fold nodes but with orthorhombic space group. A series of the diffraction peaks associated with Fddd are not simple as that for cubic symmetry, as identified in the crystallographic table.52 Consequently, core−shell type network structures and Fddd can be ruled out on the basis of the SAXS results in the present blend series. Here we can notice that the relative intensities of the scattering peaks change from the Blend(6/4) to the Blend(1/9) even though all the samples identified an TDD structure, reflecting that peak intensities are sensitive to the volume fractions (phase thickness). Hence, the calculations of scattering intensities for TDG and TDD were conducted, taking into account the volume fractions.20 Figure 5 compares the experimental SAXS profiles with the calculated intensities. The latters associated with TDG and TDD are expressed by vertical bars. The scattering profiles are
Figure 4. 1D synchrotron SAXS profiles of the blend samples: (a) Blend(8/2), (b) Blend(7/3), (c) Blend(6/4), (d) Blend(5/5), (e) Blend(4/6), (f) Blend(3/7), (g) Blend(2/8), and (h) Blend(1/9). The sequence of peaks are pointed out by inverted triangles. The inverted open triangles on the curve for Blend(7/3) do not obey the relative intensity rule for TDG.
pointed out by inverted open triangles do not match the possible peak series for TDG. These peaks may be associated with the partially observed TDD structure instead. Then we can notice the distinct difference in the observed peak-position ratios between Blend(7/3) and Blend(6/4), interpreting the morphology change. As the relative scattering peak positions obtained for the blends from Blend(6/4) to Blend(1/9) were √3, √8, √11, and √19, which satisfy the extinction rules for the Fd3̅m cubic space group, these materials were assigned as TDD. The structure assignment made by the SAXS patterns is in good agreement with that made on TEM micrographs. The lattice constant, a, for cubic lattices such as gyroid and diamond structures is expressed by the equation ⎛ 2π ⎞ d2 ⎜d = ⎟. The a’s for the Blend(8/2) and a= 2 qhkl ⎠ h + k2 + l 2 ⎝ the Blend(7/3) are estimated to be 95.5 and 101 nm, respectively, using q110 values. The estimated lattice constants from the primary peaks (q111) are 121, 124, 124, 122, 117, and 106 nm for the Blend(6/4) to the Blend(1/9), respectively, which are in good agreement with the real space results (Figure S12). Recently, the other ordered network structures have been reported in ABC triblock terpolymers at an equilibrium state: core−shell type of network structure50,51 and orthorhombic Fddd network.51,52 For example, a core−shell gyroid has two chemically identical interpenetrating networks, suggesting the same symmetry (Ia3̅d) with OBDG, but the networks are
presented as a function of h2 + k 2 + l 2 , where h, k, and l denote the Miller indexes. The exact volume fractions of all samples, listed in Table 2, were employed for the scattering intensity calculation. The calculation was carried out based on the structure identification from Figures 3 and 4. For the Blend(8/2), the relative peak intensities and the peak-position ratios agree well with those of the calculated profiles for TDG, whereas there are several differences between the observed and calculated results in the Blend(7/3). This discrepancy may be due to the coexistence of TDD and TDG. On the other hand, from the Blend(6/4) through the Blend(1/9), the observed peak series and intensities are consistent with those calculated for the TDD structure, although a small discrepancy between them exists. This may be attributed to the calculation condition where the approximate equations of minimal surfaces were employed. The TEM images coupled with the SAXS results provide a solid evidence for the existence of TDD structures in the binary blends of ISP triblock terpolymers with different chain lengths of two end-blocks. However, in general, TDD is not considered as a thermally equilibrium structure because of the high packing frustration and the nonuniform domain interface with nonCMC, whereas TDG is a thermodynamically more stable structure. In order to confirm the stability and reproducibility of the morphology, all blend samples were prepared at least three times in the same way (solvent casting over 2 weeks and
Table 3. Observed Relative Peak Positions of Blend Samples
a
sample
q*a [nm−1]
1st
2nd
3rd
4th
5th
6th
7th
Blend(8/2) Blend(7/3) Blend(6/4) Blend(5/5) Blend(4/6) Blend(3/7) Blend(2/8) Blend(1/9)
0.093 0.088 0.090 0.088 0.088 0.089 0.093 0.103
√2 √2 √3 √3 √3 √3 √3 √3
√6 √6 √8 √11 √8 √8 √8 √8
√8
√22 √8 √19 √27 √19 √19 √19 √19
√26 √12 √27 √36 √36 √36 √36 √27
√38 √20 √43 √43 √43
√50
√40 √36
√48 √59
√11 √19 √11 √11 √11 √11
√51 √51 √59
8th
9th
10th
11th
√26 √59 √59 √75
√36
√38
√50
√83
√99
q*: q value of the primary peak. F
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Figure 5. SAXS profiles of the blend samples and the intensity calculation results for each h2 + k 2 + l 2 , where h, k, and l denote the Miller indexes: (a) Blend(8/2), (b) Blend(7/3), (c) Blend(6/4), (d) Blend(5/5), (e) Blend(4/6), (f) Blend(3/7), (g) Blend(2/8), and (h) Blend(1/9). The vertical triangles point out the scattering peak positions. The vertical bars represent the calculated relative peak intensities. The inset capital characters express the type of cocontinuous structure (G: TDG; D: TDD).
thermal annealing at 150 °C for 5 days) as described in the Experimental Section. High reproducibility was confirmed by TEM and SAXS data with the exception of Blend(7/3) and Blend(6/4); those are in the transition region between TDG and TDD. These results ensure that the present blends form TDD as a thermodynamically stable phase. Furthermore, we have confirmed the casting time (5 days, 1 week, over 2 weeks) effect on the morphology of the Blend(3/ 7) under fixed conditions: the same sample amount, 3 wt % THF solution, annealed at 150 °C for 5 days. Shorter solvent casting (5 days, 1 week) led to TDG or coexistent phase of core−shell gyroid and TDG. TDD structure was obtained in the long-cast film over 2 weeks even without thermal annealing. The annealing time dependence of the morphology was also investigated and discussed in the Supporting Information. On the basis of the results presented here, we concluded that longtime solvent casting method provides an effective and productive processing to obtain equilibrium mesostructures for high-molecular-weight block copolymers. So far, rigorous experimental analyses based upon TEM and SAXS measurements identified the TDD structures in this blend system; however, both the measurements cannot provide the information on a tetrahedral connection that gives definitive evidence for a diamond network structure. Consequently, TEM tomography (TEMT) was conducted to obtain the explicit realspace evidence of the diamond network. We carried out the
tomography for the Blend(1/9) with the thickest I interpenetrating domain. Representative TEMT images of the Blend(1/9) are provided in Figure 6, where the microdomains composed of the I component appear bright. Figure 6a reveals triply periodic network and the 3D image agrees well with the (100) plane of a diamond network. Moreover, Figures 6b,c represent the tetrahedral connections, clearly indicating the formation of the TDD structure. Furthermore, the angle between two adjacent tetrapods is close to 109.5°, which is certainly consistent with a model of a diamond structure.8 Hence, the TEMT images also strongly corroborate the existence of the TDD in the present blend system. Here, it is worth discussing about the reason why TDDs were observed in the binary blends of ISP triblock terpolymers with different chain lengths of the two end-blocks. In this blend system, the two periodically interwoven diamond networks of I and P are composed of long and short block chains, and the matrix phase consists of S block chains with almost constant molecular weights. As suggested in our previous works,35−37 the coexistence of long and short block chains within a single domain possibly induces the localization of junction points of copolymers along the domain interface to relieve the conformational entropy loss, resulting in non-CMC surface. Following them, we can represent the possible chain localization at a 4-fold node with four channels diagrammatically as shown in Figure 7. The illustration at the right-hand side in G
DOI: 10.1021/acs.macromol.7b00403 Macromolecules XXXX, XXX, XXX−XXX
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instead. Considering Martinez-Veracoechea’s result, it seems reasonable to suppose that the bidisperse triblock copolymers with large different chain lengths of the two end-blocks can stabilize the TDD structure by localizing the longer chains at the diamond nodes. Furthermore, from the standpoint of the interfacial curvature, the chain localization leads to the stabilization of the interpenetrating diamond network with non-CMC. As mentioned above, a repeating unit in a diamond network domain can be roughly divided into two parts: 4 channels and a node. There is large difference in the interfacial curvature at the channel and node.25 A channel connecting one node and another is apparently thinner than a node, resulting in higher interfacial curvature than that of a node. The existence of short chains within the channels naturally allows curved interface. In this work, the stability of the resulting morphologies has not yet been treated by simulation or theoretical approaches and hence remains to be proved. Nevertheless, this work is pointing further possibilities to create new morphologies from binary triblock terpolymer blend system with “different chain lengths of the two end blocks”. New morphologies are very beneficial for the view of material science.
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Figure 6. TEMT images of the TDD structure of the Blend(1/9) stained with OsO4, where the S and P microdomains were made transparent. Inset figure in (a) shows the computer-generated (100) diamond network domain. Box size of (a) is 300 nm × 100 nm × 140 nm. (b) and (c) show enlarged 3D images with the clear tetrahedral connections.
CONCLUSION In this study, we have applied the “bimodal block chain length blend” system to the cocontinuous structure region of ISP triblock terpolymer system. By blending the two ISP triblock terpolymers with different chain lengths of the two end-blocks, TDD structures were obtained covering wide range of compositions. The combination of TEM and SAXS results strongly corroborated the existence of TDDs in the present blends, and furthermore the TEM tomography offered the solid evidence concerning the tetrahedral connection with connecting angle between the two adjacent nodes of approximately 109.5°, which is perfectly consistent with the structural feature of diamond networks. Thus, we presented the first solid evidence for the occurrence of the TDD structure in ABC triblock terpolymer system, although it has long been considered as an unstable phase because of the free energy penalty associated with interfacial and stretching energy. The localization of chemical junctions on the domain interface must be induced due to the chain length difference to release the energetic penalty.
Figure 7. Schematic illustration of possible chain orientation within a 4-fold node.
Figure 7 indicates the 4-fold nodes are mainly filled with long chains, while thin channels connecting a node are occupied by short chains. The localization can release the entropic cost associated with chain stretching for short chains since the long chains can easily reach the center of the nodes. With regard to gyroid for diblock copolymer melts, Martinne-Veracoechea and Escobedo argued the chain segregation in the nodes.53 They theoretically found that bidisperse diblock copolymer melts stabilize the gyroid phase where the node and channels formed by the minority component. In such a system with the minority components with a 2:1 ratio of chain lengths, the longer chains tend to segregate preferentially inside the gyroid nodes to reduce packing frustration, resulting in a wider region of the gyroid phase in the phase map. However, in order to obtain the DD structure, the chain length ratios in the minor components which conform the diamond nodes and channels should be larger than 2 because the thickness ratio of node/channel for the diamond is higher than that for the gyroid. In our present system, much higher chain length ratios, i.e., 6.9 for I and 4.6 for P, were adopted. The ratios must be too high to stabilize the gyroid phase at the middle blend ratios, the ratios being sufficient to fill the diamond nodes with the longer chains
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00403. TEM and SAXS data of ISP-α, ISP-β, and Blend(9/1); additional comparison data of blend samples between TEM and TEM simulation images (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (Y.M.). ORCID
Yusuke Asai: 0000-0002-6506-2910 Present Address
Y.A.: Sumitomo Chemical Co., Ltd., 5-1, Anesaki-Kaigan, Ichihara City, Chiba 299-0195, Japan. H
DOI: 10.1021/acs.macromol.7b00403 Macromolecules XXXX, XXX, XXX−XXX
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was financially supported by Kakenhi (16H02292), from MEXT and JSPS Research Fellowships for Young Scientists (No. 15J04554 for Y.A.); we are grateful for their supports. This work was also supported partly by the Program for Leading Graduate Schools “Integrative Graduate Education and Research in Green Natural Sciences”, MEXT, Japan. We thank N. Horii at SYSTEM IN FRONTIER INC. for his help in TEM tomography. The use of the synchrotron X-ray source was supported by Photon Factory, KEK, in Japan (No. 2014G635) with the experimental assistance of Prof. N. Torikai at Mie University. The SAXS experiments was also conducted at the BL-40B2 at SPring-8, Hyogo Japan (Proposal No. 2016B1073).
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