Order–Order Transition from Ordered Bicontinuous Double Diamond

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Order−Order Transition from Ordered Bicontinuous Double Diamond to Hexagonally Packed Cylinders in Stereoregular Diblock Copolymer/Homopolymer Blends Che-Yi Chu,*,† Rou-Yuan Pei,‡ and Hsin-Lung Chen*,‡ †

Department of Chemical Engineering, National Chung Hsing University, Taichung 402, Taiwan Department of Chemical Engineering, National Tsing Hua University, Hsin-Chu 30013, Taiwan

Macromolecules Downloaded from pubs.acs.org by UNIV OF LOUISIANA AT LAFAYETTE on 10/17/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: Our previous works have disclosed a thermodynamically stable ordered bicontinuous double diamond (OBDD) structure and the order−order transition (OOT) between OBDD and ordered bicontinuous double gyroid (OBDG) phases in a stereoregular diblock copolymer, syndiotactic polypropylene-block-polystyrene (sPP-b-PS). Here we investigate the effect of blending with a small amount of sPP homopolymer (h-sPP) on the stability of the OBDD phase, where h-sPP formed the dry-brush mixture with the minority sPP block chains in the network microdomains due to their comparable molecular weights. The OBDD structure developed in the blend was found to exist over a broader temperature window than that formed in the neat sPP-b-PS. Nevertheless, the OBDD−OBDG transition displayed by the neat diblock was no longer observed in the blends; instead, the OBDD phase transformed into the hexagonally packed cylinder (HEX) structure on heating, indicating that HEX superseded OBDG upon blending with h-sPP. According to the experimentally observed conservation of the lattice parameter across the OBDD−HEX transition, we propose a possible kinetic pathway through which the OBDD tetrapods may reorganize and merge into a cylinder along the direction of the space diagonal in a unit cell; the cylinders developed from different unit cells subsequently shifted and fused at their ends for reducing the interfacial free energy and the packing frustration of the majority blocks, thereby turning into the hexagonal packing.

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INTRODUCTION The self-assembly of block copolymers is capable of generating a series of long-range ordered nanostructures depending on the composition of the constituent blocks.1 An effective way of tailoring the microphase-separated morphology is through blending a diblock copolymer (A-b-B) with its corresponding homopolymer (h-A), i.e., forming A-b-B/h-A blend, via the swelling of the microdomain formed by the minority A block by h-A.2−5 The ability of h-A to swell the microdomain was found to significantly rely on the parameter rA = Mh‑A/Mb‑A, with Mh‑A and Mb‑A representing the molecular weight of h-A and A block, respectively.2,6 When rA ≪ 1, h-A chains can be uniformly dissolved in A microdomains to swell the junction points at the domain interface; this scenario is called “wet brush”. Under the condition of rA ≅ 1, h-A chains tend to be localized to the middle region of A microdomains to avoid the conformational entropy loss; this type of homopolymer solubilization is called “dry brush”. The interfacial mean curvature and the microdomain morphology do not change with h-A composition under the dry-brush condition, but the domain size may be greatly expanded.6 The concept of applying the dry-brush blending to stabilize the complex structure of diblock copolymers has been reported by Matsen et al.7 In the case of the bicontinuous network © XXXX American Chemical Society

morphology, it was theoretically predicted that adding homopolymer to the tetrapod domains constituting the ordered bicontinuous double diamond (OBDD) structure, in which the degree of polymerization of the added homopolymer was equal to that of the minority block, can suppress the packing frustration of the minority block chains, as evidenced by the reduction in the deviation from the constant mean curvature (CMC) of the interfacial shape.7 This deduction was supported by the self-consistent field theory calculations as the fact that the incorporation of h-A into the network domains formed by the minority A block in A-b-B preferentially filled the space in the center of the node, thereby relieving the packing frustration of A block chains and in turn stabilized the OBDD structure over a very narrow range of composition.7−9 The formation of OBDD structure in the blend of polystyreneblock-polyisoprene (PS-b-PI) and PI homopolymer (h-PI) under the dry-brush condition (rH ≅ 1.28) has been demonstrated recently by Tagaki et al.10,11 The OBDD phase was further found to undergo an order−order transition Received: July 21, 2018 Revised: September 29, 2018

A

DOI: 10.1021/acs.macromol.8b01570 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules (OOT) to the ordered bicontinuous double gyroid (OBDG) structure constituted by the tripod domains upon heating.10 In the case of neat diblock copolymers, OBDD has been believed to be unstable relative to OBDG irrespective of the segregation strength due to lower degree of packing frustration of the minority blocks forming the tripod domains in OBDG than that associated with the tetrapods in OBDD.7 Nevertheless, we have revealed that OBDD could exist as a thermodynamically stable structure in neat stereoregular diblock copolymers, including syndiotactic polypropyleneblock-polystyrene (sPP-b-PS)12,13 and isotactic polypropylene-block-polystyrene (iPP-b-PS).14 Thermally induced OBDD−OBDG transitions were also identified in these systems, showing that OBDD and OBDG represent the stable structure at the lower and higher temperature, respectively, similar to that found for the PS-b-PI/h-PI blend system. The thermodynamic stability of the OBDD structure in the stereoregular diblock copolymers was attributed to the ability of the configurationally regular PP blocks to form helical segments, where the local conformational order and the associations of these segments may decrease the enthalpy of the minority block chains and hence reduce the significance of the entropic penalty associated with their packing frustration.12−14 In this study, we intend to resolve the perturbation of the stabilities of the bicontinuous structures of the stereoregular diblock copolymer exerted by the incorporation of a small amount of the stereoregular homopolymer into the network domain. The OBDD-forming sPP-b-PS was blended with a sPP homopolymer (h-sPP) bearing comparable molecular weight to that of sPP block (rA ≅ 1.03) to satisfy the dry-brush condition. It will be shown that the blends exhibited a broader temperature window of the OBDD phase, consistent with the alleviation of the packing frustration of the sPP block chains in the tetrapod domians by h-sPP. A more striking phenomenon is that the OBDD−OBDG OOT displayed by the neat sPP-bPS no longer occurred in the blends; alternatively, the OBDD phase transformed into the hexagonally packed cylinder (HEX) structure without apparent intervention of OBDG phase in the heating process. Considering that the previous studies of the OOT relevant to the bicontinuous structures involved mainly with OBDG phase, the OBDD−HEX transition observed here represents a new scenario of the OOT between ordered bicontinuous structures and other mesophases for block copolymer systems. On basis of the observation of the conservation of lattice parameters, we propose a possible kinetic pathway for the observed OBDD− HEX transition.

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Table 1. Overall Volume Fraction of the sPP Component in the sPP-b-PS/sPP Blends and the Corresponding Weight Percentage of the Added sPP Homopolymer in the Blends specimen

overall volume fraction of the sPP component (fsPP)

wt % of the added sPP homopolymer (Wh‑sPP)

sPP-b-PS sPP-b-PS/sPP48 sPP-b-PS/sPP52

0.46 0.48 0.52

0 3.4 10.2

and the corresponding weight percentage of the added sPP homopolymer (denoted by Wh‑sPP). Small-Angle X-ray Scattering (SAXS) Measurement. The morphology of the sPP-b-PS/sPP blends was probed by SAXS performed at the Endstation BL23A1 of the National Synchrotron Radiation Research Center (NSRRC), Hsinchu, Taiwan. The energy of the X-ray source and the sample-to-detector distance were 15 keV and 3000 mm, respectively. The scattering signals were collected by a Pilatus-1MF detector of 981 × 1043 pixel resolution. For the temperature-dependent study, the sample was equilibrated at each temperature for 10 min and followed by data acquisition for 5 min. The scattering intensity profile was output as the plot of the scattering intensity (I) versus the magnitude of the scattering vector, q = (4π/λ) sin(θ/2) (θ = scattering angle). The SAXS profiles were corrected for the incident beam intensity, the detector sensitivity, and the background. Transmission Electron Microscopy (TEM) Observation. The real-space morphology of the hexagonally packed cylinders was observed by a JEOL JEM-2100 transmission electron microscope (TEM) operated at 120 kV. The ultrathin sections with a thickness of 60 nm were prepared by a microtome. The ultrathin sections were then picked up onto the copper grids coated with carbon-supporting films and were stained with the vapor of 0.5 wt % RuO4(aq) for 3 min. The PS phase appears as the dark region in the micrograph while the sPP phase corresponds to the bright region.

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RESULTS AND DISCUSSION Thermally Induced Phase Transition of sPP-b-PS/hsPP Blends. It is believed that relieving the packing frustration of the minority blocks forming the network domain is the key for stabilizing the OBDD phase relative to the OBDG structure. Accordingly, the strategy of adding homopolymer to fill the space in the center of the tetrapod microdomains (for the case of diblock copolymer/homopolymer blends) or introducing configurational regularity to the minority block (for the case of stereoregular diblock copolymer) may serve as an effective way of alleviating the contribution of such a packing frustration to total free energy, which in turn stabilizes the OBDD structure.7−14 Perceptibly, the blend of stereoregular sPP-b-PS with sPP homopolymer could represent the scenario where the stability of OBDD phase is enhanced under the combination of both effects. In this study, the OBDD-forming sPP-b-PS diblock (fsPP = 0.46) was blended with a small amount of h-sPP to prepare the sPP-b-PS/h-sPP blends with the overall sPP compositions of fsPP = 0.48 and 0.52, as denoted by sPP-b-PS/sPP48 and sPP-bPS/sPP52, respectively (see Table 1). The corresponding weight percentages of h-sPP in sPP microdomains were 3.4% and 10.2%, respectively. Because the molecular weight of h-sPP (= 7000 g/mol) was slightly higher than that of sPP block (= 6800 g/mol), i.e., rA = 1.03, h-sPP and sPP block chains were expected to form a dry-brush mixture in the sPP microdomain, wherein h-sPP chains may lower the degree of packing frustration associated with the nonuniform stretching of the sPP block chains in the network domains. It is noted that if the present sPP-b-PS were blended with the h-sPP with molecular

EXPERIMENTAL SECTION

Materials and Sample Preparation. The sPP-b-PS diblock copolymer (Mn,sPP = 6800 and Mn,PS = 9400, PDI = Mw/Mn = 1.19) and the sPP homopolymer (Mn,sPP = 7000, PDI = Mw/Mn = 1.4) studied here have been characterized by the 1H NMR spectrum and GPC analysis as can be found in the literature.12 The volume fraction of sPP block in the neat sPP-b-PS sample was 0.46 in the melt state. For the film preparation of sPP-b-PS/sPP blends, the diblock copolymer and the homopolymer were thoroughly mixed in xylene solvent at 50 °C, and the solutions were subsequently cast on the Petri dishes. The films were obtained after evaporating most of the solvent quickly on the hot plate at ca. 140 °C (≅ boiling point of xylene). Then, the films were further dried at 100 °C for 1 h and finally in vacuum at 70 °C for 24 h. Table 1 summarizes the overall volume fraction of the sPP component in the blends (denoted by fsPP) B

DOI: 10.1021/acs.macromol.8b01570 Macromolecules XXXX, XXX, XXX−XXX

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Figure 1. Temperature-dependent SAXS profiles of the (a) sPP-b-PS/sPP48 blend and (b) sPP-b-PS/sPP52 blend in a heating cycle.

disrupted and transformed into the one associated with seemingly distorted morphology in the transition region implied that the OOT occurred through disrupting the OBDD structure followed by reordering into hexagonally packed cylinders rather than through a certain epitaxial relationship.15 The HEX structure still persisted on further heating to 205 °C, and it did not transform back to OBDD upon the subsequent cooling (see Figure S1b), implying a high activation barrier associated with HEX-to-OBDD transition due to the lack of epitaxial relationship. We have also performed the temperature-dependent SAXS experiment for the sPP-b-PS/sPP52 blend to examine whether the OBDD-to-HEX transition could still take place with the addition of more h-sPP, and the results are displayed in Figure 1b (the scattering profiles collected at all temperatures are shown in Figure S2). Apparently, the OBDD structure formed at the lower temperatures of this blend also transformed to HEX phase on heating. It is noted that the higher-order peaks associated with the OBDD phase were still clearly observed at 175 °C, while for sPP-b-PS/sPP48 blend the higher-order diffractions were hardly discernible at 170 °C (see Figures S1 and S2). Such a difference attested that the OBDD structure formed at higher h-sPP composition exhibited better thermal stability. The formation of the HEX structure was further evidenced by the TEM micrograph in Figure 2, showing the top view and the side view of the sPP cylindrical microdomains packed in a hexagonal lattice in sPP-b-PS/sPP52 blend. It is noted that although the overall volume fraction of sPP in the blend was as high as 0.52, the sPP component still formed discrete cylindrical domains dispersed in the PS matrix in the HEX structure. This is an indicative of the dry-brush mixing between h-sPP and sPP block chains in the microdomain, as the domain curvature of dry-brush blend is governed mainly by the composition of the diblock molecules instead of the overall composition. It should be noted that the volume fractions of sPP block in the neat sPP-b-PS (= 0.46) and of the sPP component in the sPP-b-PS/h-sPP blends (= 0.48 and 0.52) were close to

weight much lower than that of the sPP block to form the wetbrush mixture, the resultant blends would probably have formed the lamellar structure, which was not the interest of this study. The microphase-separated morphology of the sPP-b-PS/hsPP blends were probed by the temperature-dependent SAXS experiment. Figure 1a shows the representative temperaturedependent SAXS profiles of sPP-b-PS/sPP48 blend collected in a heating cycle, where each profile was acquired after annealing at each temperature for 10 min followed by data acquisition for 5 min (the scattering profiles collected at all temperatures are shown in Figure S1 of the Supporting Information). When the as-cast blend sample was heated to 160 °C, which was higher than the end of melting of sPP crystallites (= 137 °C),12 the perturbation on the microphaseseparated structure exerted by the crystallization of sPP was excluded; in this case, the SAXS profile showed five diffraction peaks with the position ratio of 1:(3/2)1/2:21/2:31/2:41/2, consistent with that prescribed by the OBDD structure. The scattering peaks broadened significantly when the temperature was raised to 182 °C, indicating the distortion of the OBDD structure. The high-order peak vanished, and the primary peak shifted to lower q upon further heating to 184 °C. In this case, the SAXS profile was characterized by a broad primary peak and a shoulder at 0.36 nm−1. Such a scattering pattern persisted with the primary peak continuing to move to lower q with increasing temperature up to 188 °C. However, the primary peak started to sharpen at 190 °C, and two higherorder peaks were visible. In this case, the scattering peaks exhibited the position ratio of 1:31/2:41/2, which was consistent with the scattering feature of HEX structure. The temperature-dependent SAXS profiles revealed that the OBDD structure originally formed in sPP-b-PS/sPP48 blend underwent a transition to HEX phase on heating. This morphological transformation occurred over a quite narrow temperature range of 184 ≤ T (°C) ≤ 188, and the OBDD structure fully transformed into HEX at 190 °C. The fact that the scattering pattern of the OBDD structure was completely C

DOI: 10.1021/acs.macromol.8b01570 Macromolecules XXXX, XXX, XXX−XXX

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between OBDD and OBDG phases through a coexistence region of these two bicontinuous structures. Contrarily, the OBDD structure formed in the blends transformed into HEX phase on heating without the intervention of the OBDG structure. Moreover, the TOOT of the OBDD-to-HEX transition was found to increase with increasing h-sPP composition. These results demonstrated that the incorporation of h-sPP into the tetrapod domain via dry-brush mixing with the minority sPP block enhanced the stability of OBDD but destabilized OBDG phase, as OBDG was superseded by the HEX structure at high temperature. It has been shown that the packing frustration of the minority blocks in the tripod microdomain constituting the OBDG structure is weaker than that associated with the tetrapod in OBDD; therefore, OBDG is favored over OBDD when the difference in the conformational free energy penalty arising from such a packing frustration dominates the total free energy difference between these two bicontinuous structures. In the case of A-b-B/h-A blend, the stability of OBDD phase may be enhanced, since the incorporation of h-A into the network microdomain via dry-brush mixing with the minority A blocks may alleviate their packing frustration once a sufficient amount of h-A chains is localized into the center of the node. Such a scenario had been observed experimentally by Tagaki et al., who revealed the formation of the OBDD structure in the blends of an OBDG-forming PS-b-PI and h-PI with the molecular weight ratio rH = 1.28. The translational entropy of the homopolymer chains decreases when they are localized in the nodes; as the temperature is sufficiently high, a portion of these chains may escape from the node to distribute over the other part of the domains to attain higher translational entropy. In this case, the packing frustration in the node region may regain the dominance in free energy, such that the OBDD structure transforms into OBDG on heating. In the present sPP-b-PS/h-sPP blends, the OBDD structure was found to transform into HEX phase without the intervention of OBDG phase on heating. The transition of OBDG to HEX upon lowering the segregation strength has been predicted theoretically and observed experimentally for both neat diblock copolymers and diblock copolymer/ homopolymer blends.9 The OBDG-to-HEX transition should be driven entropically, since the packing frustration of the minority blocks vanishes in the cylindrical microdomain possessing constant mean curvature. In a recent study, Tagaki et al., however, revealed an opposite HEX-to-OBDG transition on heating for a blend of a HEX-forming PS-b-PI with h-PI.11 Such an anomalous OOT may be attributed to the enhancement of the degree of mixing between h-PI and PI blocks at the elevated temperatures, where the dry brush turned into wet brush; in this case, the junction separation at the microdomain interface was swelled effectively by the intimate mixing between these two components in the PI domains, creating an effect equivalent to the increase of minority block volume fraction in the corresponding neat diblock copolymer. As a consequence, the cylindrical microdomains transformed into the bicontinuous tripod domains with smaller curvature. The heating-induced OBDD-to-HEX transition observed here was in accord with the conventional phase diagram predicting the transformation of the bicontinuous structure to HEX phase upon lowering the segregation strength, which implied that the degree of mixing between sPP block and h-sPP homopolymer remained largely unperturbed with increasing temperature.

Figure 2. TEM micrograph of the HEX structure formed in the sPPb-PS/sPP52 blend, obtained after quenching the blend from 190 °C into liquid nitrogen to freeze the morphology formed at 190 °C. The dark region corresponds to the PS phase while the bright region is the sPP phase.

symmetric. According to the classical phase diagrams of the diblock copolymers and diblock copolymer/homopolymer blends (which were calculated by assuming Gaussian statistics for the block chains), lamellar structure should be formed. Thus, the observation of the OBDD structure and the OBDDto-HEX transition for the present sPP-b-PS/h-sPP blends was rather unique. This could be due to the polydispersity effect that may shift the phase boundary17 and the presence of the conformationally ordered (helical) segments in the sPP block and homopolymer chains (which causes the deviation from Gaussian conformation). With the inclusion of our previous results of neat sPP-bPS,12,13 we constructed a morphological diagram in terms of temperature versus fsPP plot for the sPP-b-PS/h-sPP blend, as shown in Figure 3. The neat sPP-b-PS exhibited the OOT

Figure 3. Morphological diagram constructed by the combined results from the neat sPP-b-PS12,13 and the sPP-b-PS/sPP blends, where black, red, and blue symbols represent the OBDD, OBDG, and HEX structures, respectively. The morphologies indicated in the diagram were identified from the SAXS results. The notation of “coexistence” for the neat diblock means the temperature window within which OBDD and OBDG phases coexisted, while the “transition region” marked for the blends indicates that the OBDD phase was disrupted to form an intermediate structure prior to reordering into the HEX phase. D

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Figure 4. Temperature dependence of the domain spacing (d) and the lattice parameter (a) calculated from the primary scattering peak of SAXS profiles in the heating cycle of sPP-b-PS/sPP48 and sPP-b-PS/sPP52 blends.

uous phase and other morphologies was reported by Schulz et al.,16 who revealed an epitaxial relationship for the transformation from HEX to OBDG in a polystyrene-block-poly(2vinylpyridine) diblock copolymer mixture. Förster et al. further identified an epitaxial relationship between OBDG and the metastable hexagonally perforated lamellar (HPL) structure in a PS-b-PI diblock copolymer.18 The metastable HPL was then suggested to appear as an intermediate phase for the ordering of OBDG from the disordered melt,19,20 lamellae,21,22 or HEX.23,24 Afterward, a number of research groups have devoted to investigating the epitaxial relationship or transition mechanism between OBDG and other mesostructures such as lamellae,22,25 HPL,26−28 HEX,18,23−25,27,29−31 and sponge phase32,33 in block copolymers. Matsen et al. proposed a nucleation and growth process that may effectively drive the epitaxial transition between OBDG and HEX based on their SCFT calculations.34 The mechanism of nucleation and growth was supported by the subsequent theoretical35,36 and experimental24,25,27,37 studies. So far, by contrast, the instance concerning the morphological transitions involving OBDD phase is still very limited.10−14 To deduce the kinetic pathway of the OBDD-to-HEX transition, we tried to refer to the mechanism of OBDG-toHEX transition reported previously.34 The epitaxial transition between the OBDG and HEX structures is driven by the nucleation and growth process, with the requirements of not only an orientational match of the two phases but also a match in the domain spacing.34 Suppose if OBDD could transform into HEX in a similar manner, the nucleation may take place at any two neighboring tetrapods situating at the two interpenetrating networks (one presented in blue color and the other one in yellow color in the schematic illustration in Figure S3), where one tetrapod is rightly oriented by an azimuthal angle of 60° to the other along the [111] direction of the OBDD structure. Then, such a set of the two tetrapods could be connected by one emerging rod which is generated in between the tetrapods during the nucleation process. Subsequently, half of the original “dual tetrafunctional pods” (i.e., each blue or yellow unit in Figure S3) and the nodes at these two tetrapods and one emerging rod merge into a long

It is interesting to note that the primary scattering peak of the OBDD phase moved to lower q with increasing temperature (cf. Figure 1), indicating that the domain spacing swelled in the heating process, as manifested clearly in Figure 4 which plots the domain spacing (d) calculated by d = 2π/qm (qm = the primary peak position) against temperature. The domain spacing of OBDD phase, dD, was found to increase progressively with increasing temperature until it leveled off at ca. 170 °C. The OBDD-to-HEX transition was accompanied by a large increment of dD of ca. 6−8 nm for both blends. The obvious expansion of dD on heating was not observed for the neat sPP-b-PS, and this phenomenon was contrary to the general behavior of block copolymers displaying decrease of domain spacing with increasing temperature because the reduction of interfacial free energy due to the decrease of χ allows the block chains to be more relaxed. Considering that the lattice parameter or the unit cell dimension is given by aD = √2dD and the number of nodes per unit cell Nnode,D is fixed at 2 for the OBDD phase, the number density of node in the blends nnode,D = Nnode,D/aD3 thus decreased with increasing temperature. Because the node is the region in which the h-sPP chains and sPP blocks have the lowest entropy than the other regions in the network domain, the reduction of nnode,D allows the increase of the entropy of the sPP chains. Consequently, we propose that the reduction of nnode,D on heating in the blends was driven by the tendency of the h-sPP chains to gain more translational entropy in the network domains. Nevertheless, the decrease of the nnode,D may result in a greater stretching of the PS block chains in the matrix phase of OBDD phase. When nnode,D was reduced to a threshold degree, the entropic penalty associated with the stretching of PS blocks became dominant, thereby driving the OBDD structure to transform to HEX phase, in which the entropic penalty of both the sPP chains and PS block chains were greatly relaxed. Proposed Mechanism of OBDD-to-HEX Transition. The present study discloses a new type of OOT associated with the bicontinuous structure of block copolymer systems, namely, the OBDD-to-HEX transition. The first observation involving the phase transition between an ordered bicontinE

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Figure 5. Schematic illustration of a possible kinetic pathway of the OBDD-to-HEX transition. The interpenetrating networks of the OBDD tetrapods are marked by the blue and yellow colors, respectively. Each unit cell of the OBDD structure contains two interpenetrating node domains, where one node is situated in the center of the unit cell and the other is equivalent to the total contribution from the one-eighth nodes that are situated at the eight apexes of the unit cell.

temperature;13 equating eq 1 to eq 2 leads to a general relationship among a, Vtp, and RH as

cylinder connecting the two interpenetrating networks. When the above procedure repeatedly occurs along the [111] direction, the “growth process” could proceed along the long axis of the cylinder through disassembling other tetrapod domains followed by growing into a longer one, eventually leading to the cylindrical microdomains packed in hexagonal lattice. According to this picture, the spacing of (111) plane of OBDD is expected to be the same as that of (10) plane of HEX considering the epitaxial relationship, such that these two scattering peaks (i.e., the primary scattering peaks of the OBDD and HEX structures) should situate at the same position across the OOT. However, this scenario was not observed experimentally, indicating that the pathway of OBDD-to-HEX transition observed here did not involve any epitaxial relationship. To elucidate the more plausible kinetic pathway that may efficiently drive the transformation from OBDD to HEX, we began with a geometric analysis to consider the variation in the lattice parameter for the morphological transition from a tetrapod network in a unit cell of OBDD to a cylinder in the unit cell of HEX. Figure 4 shows that the OBDD-to-HEX transition was accompanied by a large increment of domain spacing; however, the change of lattice parameter across the OOT was small (by ca. 1 nm), where the lattice parameters of HEX and OBDD phases were calculated by aH =

4 3

Vtp ij aD yz jj zz = 3 jj a zz π RH 2aD k H{ 2

Assuming that the lattice parameter remained almost a unchanged across the OOT, i.e., aD ≈ 1, we have ia y Vtp ≅ πRH 2jjjj D zzzz k 3{

fD =

3

dH and

2 2π RH 3 aH 2

3

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CONCLUSION The effect of blending with a small amount of sPP homopolymer on the stability and phase transition behavior of the OBDD structure displayed by the sPP-b-PS has been revealed in this study. The two sPP-b-PS/h-sPP blends with fsPP = 0.48 and 0.52 were found to exhibit an OOT from OBDD to HEX phase without the intervention of OBDG structure on heating, and the phase transition was characterized by an obvious increment of domain spacing. A kinetic pathway of the OBDD-to-HEX transition was deduced according to an assumption of the conservation of the lattice parameter across the transition. We proposed that the tetrapods in each unit cell may reorganize into one cylinder along the direction of the space diagonal in the unit cell, generating an intermediate structure where the cylinders formed from different unit cells packed in a square lattice.

(1)

where Vtp is the volume of a tetrapod in the unit cell (as schematically illustrated in Figure S4). The number “2” shown in eq 1 accounts for the fact that there are two interpenetrating networks of OBDD in the unit cell. As for the HEX phase, the volume fraction of sPP cylinders is given by fH =

(4)

the length of the space diagonal of the unit cell of the OBDD phase. Consequently, the equality in eq 4, which relates the volume of a tetrapod in the unit cell to the volume of a cylinder, implies that the OBDD-to-HEX transition may take place through a local transformation of the tetrapod in the unit cells to a cylinder, as schematically illustrated in Figure 5. From step (a) to step (b) in Figure 5, the four pods and one node of the tetrapod and the four one-eighth nodes associated with the tetrapod at the apexes in an OBDD unit cell reorganize and merge into one cylinder along the direction of the space diagonal in a unit cell; the cylinders formed through such a structural reorganization pack in a square lattice. To minimize the interfacial free energy of the cylinders and the packing frustration of the majority block chains, the cylindrical micordomains shift and fuse at their ends to pack in the hexagonal lattice, as displayed from step (b) to step (c) in Figure 5.

2Vtp aD3

H

The right-hand side of eq 4 corresponds to the volume of a cylinder with RH in radius and aD in length; aD corresponds to

, respectively. In light of this finding, we aD = √2dD, postulated that the OBDD-to-HEX transition occurred under the conservation of the lattice parameter. The kinetic pathway of the OBDD-to-HEX transition under the condition of constant lattice parameter is illustrated as follows. For the OBDD structure, the volume fraction of sPP microdomains can be calculated by 38,39

(3)

(2)

where RH is the radius of the cylinder. We assume that the volume fraction of the sPP domain did not change upon transition from OBDD to HEX over a narrow range of F

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Macromolecules

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The cylinders then shifted and fused at their ends to reduce the interfacial energy and the packing frustration of the majority block, leading to the hexagonal lattice.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b01570.

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Entire temperature-dependent SAXS profiles of sPP-bPS/sPP blends; schematic illustration of the proposed OBDD-to-HEX transition via a nucleation and growth process; schematic illustration of the volume of OBDD tetrapods (PDF)

AUTHOR INFORMATION

Corresponding Authors

*(C.-Y.C.) E-mail [email protected]. *(H.-L.C.) E-mail [email protected]. ORCID

Che-Yi Chu: 0000-0002-8482-903X Hsin-Lung Chen: 0000-0002-3572-723X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Ministry of Science and Technology (MOST) Taiwan under Grant MOST 102-2221E-007-136-MY3.

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REFERENCES

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DOI: 10.1021/acs.macromol.8b01570 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b01570 Macromolecules XXXX, XXX, XXX−XXX