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Gyroid Structures in Solvent Annealed PS‑b‑PMMA Films: Controlled Orientation by Substrate Interactions Sungmin Park,† Yeongsik Kim,† Wooseop Lee,† Su-Mi Hur,*,‡ and Du Yeol Ryu*,† †

Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea Department of Polymer Science and Engineering, Chonnam National University, Gwangju 61186, Korea

‡

S Supporting Information *

ABSTRACT: We investigated the orientation of gyroid structures in thin films of high-molecular-weight (HMW) polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA) upon a solvent vapor annealing (SVA) process with tetrahydrofuran nonselective to the PS and PMMA blocks. During the SVA process, the swollen PS-b-PMMA films produced the gyroid structures that were developed through a cylindrical morphology from a poorly ordered structure. The interfacial interactions exerted by the substrates significantly influenced the orientation of cylinders, like the parallel and perpendicular orientations on the selective and neutral substrates, respectively, while the solvent vapor generated perpendicular cylinders at the surface. In the final formation of gyroid structures, we identified the two distinct [211] and [111] planes on the surface throughout the interior of the films, which were directed from cylinders on the selective and neutral substrates, respectively. To provide the insight of the molecular mechanisms taking place during the order−order transition, we further performed coarse-grained simulations of a block copolymer model. Our results based on experiments and simulations suggest a simple route for the directed orientation of well-defined gyroid structures.

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INTRODUCTION Block copolymer (BCP) self-assembly has provided an extensive platform to be a cornerstone of soft nanostructures to accommodate functional and structural morphologies ranging from 10 to 50 nm.1−5 A well-defined gyroid is 3dimensional (3D) periodic structure with a bicontinuous network connectivity, which is promising for potential applications due to the nanoscopic regular array.6−9 The gyroid structure has been used for various application fields such as photonic crystals,10−12 metamaterials,13−15 energy devices,16,17 superconductor,18 electrochromic materials,19,20 and so on. In addition, the structural chirality of gyroid structure induces the optical circular dichroism,15,21 in rapid response to transport properties due to unique interconnectivity.22,23 For these reasons, the application and scalability of gyroid structure has been a challengeable issue to meet the increasing demands for the improved performance in various fields. A gyroid structure achieved from BCP self-assembly is characterized as an unique complex structure, and its structural materialization offers a prospective route to produce uniform arrays adjustaible in periodicity depending on its molecular weight.24 As a matter of fact, the gyroid structure was described to be less stable in the general phase diagram shown in χN as a function of composition in BCP, where χ and N are the Flory− Huggins segmental interaction parameter between the two blocks and the total number of segments, respectively.25 Since a finding of the revised calculation by Fredrickson et al., however, © XXXX American Chemical Society

the gyroid structure has been believed to be stable even in the super strong segregation limit, expanding higher values of χN within specific composition window.26 Aided by this theoretical background, several efforts have been made to achieve a gyroid structure in high-molecular-weight (HMW) BCP self-assembly. Thomas et al. reported photonic crystal property in gyroid structure using HMW polystyrene-b-polyisoprene (PS-b-PI), which was prepared by slow casting over 2 weeks.10 Besides, Ho et al. introduced a solvent vapor annealing (SVA) process with chloroform to generate gyroid structures in low-molecular-weight (LMW) polystyrene-b-poly(L-lactide) (PS-b-PLLA) films, in which the swelling-controlled morphological evolution was studied by solvent evaporation rate.27,28 Ober and co-workers reported the morphological tunability in BCP films including a gyroid structure by controlling the solvent selectivity to the blocks during SVA process.29 Likewise, the SVA process in thin film geometry has been an effective route to achieve a well-defined gyroid structure for further application. Nevertheless, the study on the controlled orientation of a gyroid structure or 3D periodic template has been less reported, while in the bulk BCP, the epitaxial transition of cylinder to gyroid was studied both theoretically and experimentally.30−33 Received: May 2, 2017 Revised: June 16, 2017

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Figure 1. Overall scheme and top-view SEM images of 500 nm thick PS-b-PMMA films on the PMMA-selective and neutral substrates during SVA process. Two directions indicate the SVA processes of BCP films prepared on different interfacial interactions on the substrates. The SVA process of BCP films produced different surface morphologies in the final gyroid structures, namely [211] plane on an oxide layer and [111] plane on a neutral substrate. PS-b-PMMA films were prepared by spin-coating onto the substrates typically at 3500 rpm for 60 s using 5−6 wt % BCP solutions in toluene in order to set the film thickness of 0.5 μm. The film thickness was measured by spectroscopic reflectometer (Wonwoo Systems). Two different substrate interactions, like the selective and neutral substrates to the two blocks, were defined: a native oxide layer on a standard Si wafer was set to define a PMMA-selective substrate, and a neutral substrate was prepared using a hydroxyl endfunctionalized poly(styrene-r-methyl methacrylate) (HO-P(S-rMMA)) with a styrene mole fraction (Xs) ∼ 0.64 and Mn = 10 kg/ mol with a dispersity (Đ = Mw/Mn) of 1.30. For the PS-selective substrates, a passivated layer was prepared by removing an oxide layer from a standard Si wafer using a 5% HF solution, and a grafting-to method was used to generate PS-grafted substrate onto the oxide layer using a 10 kg/mol PS-OH.34 The PS-b-PMMA films were exposed to THF (high purity, Aldrich) vapor for the SVA process. The solvent absorption (or swelling) and dewetting times of the swollen PS-bPMMA films were precisely regulated with an optimized temperature gap between the chamber and bottom plate under the condition of s/v = 0.111 cm−1, where s and v indicate the volume of a cylindrical brass chamber and surface area of solvent, respectively.35 The swollen films during SVA process were immediately removed from the sample chamber to set the target periods of annealing times, thus producing the time-dependent morphologies of BCP films. Characterization of BCP Films. Microscopy images of PS-bPMMA film were measured with a field emission scanning electron microscopy (FE-SEM; JSM-6701F, JEOL) under an accelerating voltage of 5.0 kV using a semi-in-lens detector. To enhance the phase contrast between the PS and PMMA blocks, the films were exposed to UV irradiation (λ = 254 nm) under vacuum for 3 h, and they were rinsed thoroughly with acetic acid for 1 h to selectively remove the PMMA block. The BCP films were further cleansed with ethanol and deionized water sequentially; then they were dried in a vacuum oven at room temperature. Grazing-incidence small-angle X-ray scattering (GISAXS) and SAXS experiments were performed at the 9A and 4C beamlines, respectively, at Pohang Accelerator Laboratory (PAL), Korea. The typical operating conditions were set as follows: a wavelength of λ = 1.112 Å, a beam

In this paper, we present results of the formation of the oriented gyroid structures in HMW (Mn > 250 kg/mol) BCP films under different substrate interactions during a SVA process, where the gyroid structures were developed through a cylindrical morphology from a poorly ordered structure. Asymmetric polystyrene-b-poly(methyl methacrylate) (PS-bPMMA) films were applied to the selective and neutral substrates. During the SVA process with a solvent that enhances chain mobility, the high values of χN above 10.5 ensure an ordered state and strong driving force for BCP selfassembly. The final morphology of gyroid structures was significantly influenced by the interfacial interactions from the substrates, resulting in [211] and [111] planes on the selective and neutral substrates, respectively. The entire film structures were characterized by microscopy and grazing incidence X-ray scattering measurements. To provide a rationale of the experimental observations, we explore this morphological transition and the associated orientation during SVA process using diffusive Monte Carlo simulations with the theoretically informed coarse-grained (TICG) model.

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EXPERIMENTAL SECTION

Synthesis and Sample Preparation. An asymmetric (PS-major) PS-b-PMMA was synthesized via sequential living anionic polymerization of styrene (S) and methyl methacrylate (MMA) in tetrahydrofuran (THF) as a solvent using sec-butyllithium (1.4 M, Aldrich) as an initiator. The reaction was performed at −78 °C in the presence of LiCl (high purity, Aldrich) under purified argon environment. The composition and molecular weight in a PS-bPMMA were characterized by size-exclusion chromatography (SEC). The number-averaged molecular weight (Mn) was 278 kg/mol with narrower dispersity (Đ = Mw/Mn) than 1.05. The PS volume fraction (ϕPS) was determined to be 0.660 by 1H nuclear magnetic resonance (1H NMR), based on the mass densities of the two components (1.05 and 1.184 g/cm3 for PS and PMMA, respectively). B

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Figure 2. (a) SEM images of BCP films prepared on (a) an oxide layer and (b) a neutral substrate. The top- and bottom-view SEM images were guided by arrows from the cross-sectional SEM images in the middle. (c) Line intensity profile scanned along 2θf at αf = 0.226° from 2D GISAXS patterns of cylindrical morphologies prepared on different substrates.

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size of 0.030 × 0.290 mm2, a sample-to-detector distance of 6.48 m, and an optimal exposure time of 10 s. The incidence angle (αi) was varied from 0.080° to 0.140°, which are below and above the critical angle (0.113°) to probe the surface and entire film structures, respectively. 2D GISAXS patterns were recorded by a 2D detector (SX-165, Rayonix) positioned at the end of a vacuum guide tube. Model and Simulation Approach. The theoretically informed coarse-grained (TICG) model was used to investigate the transition behavior from cylinder to gyroid in the swollen BCP films. TICG represents polymer chains by a bead−spring model, whereas the intermolecular interactions are given by a functional of the density fields. To compute such densities, a particle-to-mesh approach was used, in which a grid was introduced such that density fields were computed locally. Thus, the Hamiltonian of the system consists of bonded and nonbonded terms which adopt particle- and field-based representations, respectively. Nonbonded Hamiltonian is expressed as the spatial integral of quadratic terms of density fields, proportional to the segregation strength represented by the Flory−Huggins parameter χABN. It also contains the penalty of density deviation from the average value proportional to the inverse of the imcompressibility κN. Simulation of diblock copolymer melts of ϕPS = 0.641, N = 64, χN = 25, κN = 100, and N̅ = 60 was conducted in film geometry, where N and N̅ are the numbers of beads per chain and interdigitation, respectively. The interactions between polymer segments and substrate/surface were modeled with an exponetially decaying potential as a function of distance z, and the interaction strength of these polymer−surface interactions could be tuned with the parameter ΛN. Explicitly, the Hamiltonian is expressed as follows:

H 3 = 2 kBT 2b +

∑ bi 2 + ∫ i

dr

V

kN (1 − ϕA − ϕB)2 + 2

RESULTS AND DISCUSSION We used an asymmetric (ϕPS = 0.660) PS-b-PMMA in the super strong segregation limit, χN ≫ 100, since a desired orientation of nanoscopic arrays in thin films and transitions were less influenced by the fluctuation effects. Thus, we hypothesized that the surface and/or interfacial properties from the substrates would be the main factor to orient microdomains in an ordered state of BCP films. For this reason, a HMW (278 kg/mol) PS-b-PMMA was applied to a PMMA-selective oxide layer (standard Si wafer) and a neutral substrate using BCP solutions in toluene. The ordering and microdomain orientation in BCP films were investigated when the BCP films prepared on these two substrates were subjected to the SVA process with THF. Figure 1 shows overall scheme and top-view SEM images of the as-cast and solvent-annealed PS-b-PMMA films that were set to approximately 500 nm on the large-area (2 × 2 cm2) PMMA-selective and neutral substrates. The brighter and darker phases correspond to the PS and PMMA blocks, respectively, as the contrast was enhanced by the PMMA removal process. An as-cast film displayed a poorly ordered (or kinetically frozen) structure due to the fast evaporation of solvent on spin-casting, but the time-dependent morphologies of the solvent-annealed BCP films exhibited structural development from the as-cast morphology to hexagonally ordered dots to long-range ordered gyroid structures. During SVA process, the solvent vapor permeates into the BCP films and elevates chain mobility; then the swelling of BCP films saturates at quasi-equilibrium between the solvent absorption and evaporation with further increasing annealing time. Several transient morphologies can be obtained when the rapid evaporation of solvent effectively immobilizes the film structure for a given period of annealing times. At the initial stages (35 min) of SVA process, hexagonally ordered dots (confirmed as cylinders later) were observed in BCP films on both PMMA-selective (top images) and neutral (bottom images) substrates. The BCP

N̅ ⎧ ⎨χNϕA ϕB Re 3 ⎩ ⎪

⎪

∑ K

⎛ − z 2 ⎞⎫ ΛK N exp⎜ 2 ⎟⎬ ds ⎝ 2ds ⎠⎭ ⎪

⎪

where b is the average bond length and bi is the bond length ith beads. Diffusive Monte Carlo simulations with single bead displacements were conducted to capture the time evolution of morphologies.36,37 C

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Figure 3. (a) Swelling ratios of 500 nm thick PS (216 kg/mol) and PMMA (106 kg/mol) films during SVA process at 10 °C. The measured thickness (t) was normalized by the initial film thickness (t0). (b) A possible pathway from cylinder to gyroid during SVA process on the phase diagram of BCP self-assembly.26

films at the intermediate stages (80 min) revealed the mixed morphologies of hexagonally arranged dots and less-developed gyroid structures. After long or enough annealing at quasiequilibrium, very intriguingly, the SVA process of BCP films produced different surface morphologies in the final gyroid structures, namely [211] plane on an oxide layer and [111] plane on a neutral substrate; these were discernible even in the mixed morphologies at the intermediate stages of SVA process. Hence, the orientations of gyroid structures were directed by the selective and neutral substrates during SVA process, although perpendicular cylinders were observed consistently on both substrates at the initial stages of SVA process. Figures 2a and 2b show SEM images of BCP films prepared on an oxide layer and a neutral substrate at the initial stages (35 min) of SVA process, respectively, where the top- and bottomview SEM images were guided by arrows from the crosssectional SEM images in the middle. In the cases of bottomview SEM images, the opposite sides were taken and measured after peeling the films from the substrates using a 5% HF solution. Above all, hexagonally ordered dots at both surfaces, as shown in the top-view SEM images, were proved to be hexagonally packed cylinders that were oriented normal to the surface. The same perpendicular cylinders were observed at both surfaces regardless of the bottom substrate properties because the solvent vapor during SVA process makes the swollen films favorable with perpendicular cylinders due to a nonselective environment to both blocks. In other words, it was not likely to form a parallel orientation of microdomains because of high energy barrier for generating island/holes nucleation and commensurability.28,38 In the case of BCP films prepared on a (PMMA-selective) oxide layer, however, this perpendicular orientation dissipates rapidly with distance from the surface to the bottom, leading to the parallel (in major) orientation of cylinders, as shown in the cross-sectional and bottom-view SEM image of Figure 2a. In contrast, perpendicular cylinders formed at the surface predominantly maintain in the interior of the films and to the bottom of the neutral substrate due to the balanced interfacial interactions, as shown in Figure 2b. The two different orientations of cylinders indicated that the substrate interactions are more influential to

orient cylinders, and they compete or cooperate with a neutral effect of solvent vapor from the surface. The film structures were complementally analyzed by GISAXS. In the scattering geometry, αf and 2θf are the exit angles of the X-ray beam along the out-of-plane scattering normal to the sample surface and along the in-plane scattering parallel to the sample surface, respectively, where q = (4π/λ) sin θf is the scattering vector. Incidence angle (αi) was set at 0.140° above the critical angle (0.113°) for PS-b-PMMA films to trace the entire thickness. For more information, the line intensity was scanned along 2θf at αf = 0.226° from 2D GISAXS patterns of cylindrical morphologies prepared on different substrates, as shown in Figure 2c. For BCP film prepared on a neutral substrate, the in-plane scattering peaks arising from multiple-order Bragg rods could be indexed with the scattering vector ratios of q/q* = 1:√3:√4:√7, confirming perpendicularly oriented cylinders. Whereas for the intensity profiles of BCP film prepared on an oxide layer, the peak ratios were less distinct and the full width at half-maximum (fwhm) of primary peak was broader due to randomly oriented cylinders. In order to understand how the solvent-annealed PS-bPMMA films undergo a pathway through cylinder to gyroid, we speculated volumetric change between the two components during SVA process. To model PS-b-PMMA (177 kg/mol-b101 kg/mol) in this study, the molecular weights of PS and PMMA homopolymers were similarly selected to be 216 and 106 kg/mol, respectively, for the solvent absorption experiments. Figure 3a shows the swelling ratios of 500 nm thick PS and PMMA films as a function of annealing time with THF, measured by in situ reflectometer. Experimental condition was set at 10 °C during solvent absorption experiments to suppress dewetting the substrates, and the measured thickness (t) was normalized by the initial film thickness (t0). Interestingly, the initial slope of swelling ratio for PS film was measured to be larger than that for PMMA film, indicating that the solvent absorption rate of PS film was faster at an initial stage of SVA process. The difference (approximately 2.5 times in the slopes) at this stage presumably induced an asymmetric swelling between the two blocks, in which the PMMA-rich cylinders were formed in PS-rich matrix due to an increase in volume D

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Figure 4. SEM images of BCP films prepared on (a) an oxide layer and (b) a neutral substrate, representing [211] and [111] planes of gyroid structures, respectively. The top- and bottom-view SEM images were guided by arrows from the cross-sectional SEM images in the middle. (c) 2D GISAXS patterns of gyroid structures developed on an oxide layer (left) and a neutral substrate (right). The characteristic peaks of {211} were indexed (left).

on the diagram by the original values of χeff and Φ of PS-bPMMA before SVA process, while the as-cast film displayed a kinetically frozen structure. As a high value (154.8) of χeffN decreases remarkably to 42 during SVA process (for 100 min), a pathway undergoes the formation of cylinders due to an asymmetric swelling between the two blocks at an initial stage of SVA process, as indicated by an arrow line. Then, the swollen BCP film recovers into nearly symmetric swelling at the intermediate stage, leading to an irreversible transition from cylinder to gyroid. It should be noted that the χeffN evaluated during SVA process remains at an ordered state in the strong segregation limit (SSL; where χeffN ≫ 10.5).45 Figures 4a and 4b show top-view, cross-sectional, and bottom-view SEM images of BCP films prepared on an oxide layer and a neutral substrate at the final stages (100 min) of SVA process, representing [211] and [111] planes of gyroid structures, respectively. The same planes of gyroid structures were observed at both top- and bottom-view images depending on the substrates, namely [211] plane on an oxide layer and [111] plane on a neutral substrate. The inclined feature at an angle of 45° from the substrate, as shown in cross-sectional SEM images, is characteristic of [211] plane, while the perpendicular feature corresponds to [111] plane. A significant difference between two planes of gyroid structures was identified in 2D GISAXS patterns of gyroid structures developed on an oxide layer (left) and a neutral substrate (right), as shown in Figure 4c, which were measured at αi = 0.140° for the interior films as well as surfaces structures. The characteristic peaks of {211} were indexed (left), while the simple patterns of [111] plane were elongated along out-ofplane scattering due to the destructive interference effects caused by lattice symmetries. It should be pointed out that the [111] plane of gyroid structure has been even less reported than [211] plane usually formed on most of surfaces (substrates) because the [211]

fraction of PS-rich phase. With further annealing with solvent vapor, more asymmetric composition with solvent became recovered to the similar swelling ratios of PS (2.38) and PMMA (2.29) films at 50 min and longer annealing times, thereby producing the gyroid structures due to the inherent composition of BCP. Flory−Huggins segmental interaction parameter (χP−S) between polymer and solvent can be described by χP − S =

Vs (δS − δ P)2 + 0.34 RT

where Vs, R, and T are the molar volume of solvent, ideal gas constant, and temperature, respectively.39 The χP−S values between polymer and THF were calculated to be 0.340 and 0.346 for PS and PMMA, respectively, using solubility parameters (δ) of PS (18.68), PMMA (19.02), and THF (18.60) according to the literatures.40−42 Little difference in χP−S was consistent with an equilibrium neutral property of THF to both blocks at the final stages of SVA process, but the diffusion rate of THF to the PS block was faster at the initial stages of SVA process. Therefore, the morphological transition in solvent-annealed PS-b-PMMA films would be a consequence of a delicate change in solvent diffusion and selectivity to the PS and PMMA blocks rather than strong solvent selectivity. On the basis of the solvent absorption behavior of homopolymers, we propose a possible pathway from the ascast morphology to cylinder to gyroid on the phase diagram during SVA process, as displayed in Figure 3b. Effective interaction parameter (χeff) during SVA process was evaluated by χeff = χΦ considering the screening effects of solvent molecules into the interfaces between the two blocks, where χ = 0.0425 + 4.046/T from a recent report.43 Here, the volume fraction (Φ) of BCP was calculated with Φ = t 0 /t, corresponding to the inverse of swelling ratio (t/t0) due to the dilution approximation.44 The starting point was deducible E

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Figure 5. 2D GISAXS patterns of gyroid structures for PS-b-PMMA films on (a) a passivated layer and (b) a PS-grafted substrate. Green and blue circles in these patterns correspond to {211} indexes of gyroid structures. Both insets show top-view SEM images displaying [211] planes of gyroid structures.

the [211] plane of gyroid structure at the surface of the BCP films prepared on a PMMA-selective oxide layer did not epitaxially match with perpendicular cylinders initially observed from the surface, leaving a question on the detailed ordering mechanism. As mentioned above, at the initial stages of SVA, perpendicular cylinders were observed at the surface, but the cylinders near the oxide layer were oriented parallel to the substrate because of the selectivity of the bottom substrate with the PMMA block. These results indicated that the [211] and [111] planes of long-range-order gyroid structures were developed epitaxially from the presettled parallel and perpendicular orientations of cylinders in the bottom of the films, respectively. The order-to-order transition from cylinder to gyroid is a first-order phase transition which proceeds via nucleation and growth mechanism.30,46,47 Nucleation is known to be faciliated at a heterogeneous surface, since the heterogeneous nucleation has lower kinetic barrier than the homogeneous nucleation. Thus, it is expected that the gyroid nucleate would be initiated at the interface between perpendicular and parallel cylinders or either at the surface or the bottom substrate. Among these three heterogeneous interfaces, most optimal nucleation site can be chosen to have lowest nucleation barrier height with its optimal nucleate shape and size. Experimentally, only [211] plane of gyroid structure was identified over the selective substrates as an epitaxial relationship with parallel cylinders, suggesting that the nucleation occurs at the bottom substrates. This was also supported by the cross-sectional SEM images of the mixed morphologies at the intermediate stages (80 min) of SVA process (Figure S1), in which perpendicular cylinders remain on the surfaces regardless of the bottom substrate properties while the oriented gyroid structures developed from the bottom substrates proceed to the interior of the films. Consequently, the gyroid structure induced from the bottom parallel cylinders propagates toward the surface that initially consisted of perpendicular cylinders, indicating that the epitaxy is a dominant factor in nucleation step to determine the orientation of gyroid structures, and the growth of the structures occurs directionally toward the surface. In order to investigate the gyroid propagation in the film, we performed simulations using the coarse-grained polymer model

plane could be developed from the parallel cylinders prepared on any non-neutral substrate even under a neutral air/polymer interface. To verify this, the substrate interactions were exchanged from the PMMA-selective (oxide layer) to PSselective substrates. A passivated layer was obtained through removing an oxide layer from a standard Si wafer, and a grafting-to method was used to generate the PS-grafted substrate onto the native oxide layer using a 10 kg/mol PSOH. Figure 5 shows 2D GISAXS patterns of gyroid structures for PS-b-PMMA films prepared on a passivated layer and a PSgrafted substrate, which were measured at αf = 0.140° for the entire film structures. Both GISAXS patterns correspond to {211} indexes, and the inset SEM images are also identical with the top-view [211] plane of gyroid structure. These results were consistent with those observed in BCP film prepared on an oxide layer, confirming that the selective interfacial interactions from the substrates induced the same [211] plane of gyroid structures that were developed from parallel cylinders regardless of the PS- and PMMA-selective substrates. In fact, Ho et al. reported the mixed [211], [111], and [110] planes of gyroid structures in the solvent-annealed PS-b-PLLA films, where the mixed morphology was differently formed at the surface during ordering process by modulating the solvent evaporation rate.28 However, our results should be distinguished from the mixed planes because the directed orientation was consistently achieved in [211] and [111] planes of gyroid structures of the entire films. Let us turn our attention to the order-to-order transition from cylinder to gyroid during the SVA process. Phase transition between two ordered phases has certain optimal crystallographic orientations which have minimum interfacial energy between the ordered phases. It has been known that phase transition from cylinder to gyroid follows an epitaxial relationship between hexagonal cylinder axis and ⟨111⟩ gyroid direction. This epitaxial relationship between the [10] plane of hexagonal cylinder and the [211] plane of gyroid structure was demonstrated both experimentally and theoretically.30 According to this epitaxy, perpendicular cylinders have to transit into the [111] plane of gyroid structure observed from the surfaces. Our results from BCP films prepared on a neutral substrate confirmed this epitaxial relationship between the oriented cylinders and gyroid structures. However, the observation of F

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Figure 6. Morphological evolution predicted in diffusive dynamics Monte Carlo simulations of BCP films developed on (a) a neutral substrate and (b) a selective substrate. Representative densities at 0, 5000, 30 000, 55 000, 255 000, 505 500, 1 005 000, and 1 355 000 time steps of the simulations sequentially. Cross-cut view images were taken from the last steps of morphologies. The simulation was seeded from cylinders arranged perpendicular to the surface, when external fields to nucleate gyroid structures were imposed on the bottom of the films.

with periodicity of both cylinders and gyroid structures. Lx = 8.818 16, Ly = 10.1823, and Lz = 12.470 77 in units of Re, the end-to-end distance of polymer chain. χN = 25 and κN is set to 100. In Figure 6, representative densities at 0, 5000, 30 000, 55 000, 255 000, 505 500, 1 005 000, and 1 355 000 time steps of the simulations are presented to demonstrate the morphological evolution. The gyroid structure developed on a neutral substrate propagate epitaxially toward the surface of the film through the distortion, disconnection, and reconnection of the cylinders, as shown in Figure 6a. These morphological changes at transitions from cylinder to gyroid were consistent with the SCFT analysis by Matsen29 as well as experiments by Jinnai et al.31 A cross-cut vew image at Lz = 4.8 corresponds to the [111] plane of gyroid structure. As shown in Figure 6b, our simulation results also displayed that the gyroid nucleates transitted from parallel cylinders developed on a selective substrate could intergrow throughout the perpendic-

described above, starting from cylinders arranged perpendicular to the surface. When we used the diffusive dynamic simulation that has initialized from cylinders and quenched to a stable gyroid condition, network-like morphologies with high level of defects were obtained. This could be explained by the fact that, in addition to the narrow thermodynamically stable gyroid region, the order-to-order transition such as lamellar to gyroid or cylinder to gyroid often leads the system to be trapped in a metastable structures such as a perforated layer state.46 Considering that these long-lived intermediate nonequilibrium structures would transit into gyroid after enough annealing time, thus instead, the external fields to nucleate gyroid structures were imposed on the bottom of the films in two different directions: one matching with the [111] plane and the other is the [211] plane from the top. A simulation box consisted of periodic boundary conditions in the lateral directions, while in the z-direction a hard wall was imposed for film geometry. The simulation box size was set to match G

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ular domains even though it did not epitaxially matches. The cross-cut vew images at selected Lz correspond to [111] and [211] planes of gyroid structures developed on the neutral and selective substrates. However, the results revealed that the growth speed is slower than the [111] plane. Our study indicated that the origin of the epitaxy was found from the nucleation process while the growth could occur in the upward direction in which epitaxy fails. Hence, the orientation of gyroid structures at the surface could be dominated by modifying the bottom substrate properties, where heterogeneous nucleation occurred as demonstrated in both our experiments and simulations.

Du Yeol Ryu: 0000-0002-0929-7934 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by the NRF grant (2017R1A2A2A05001048, 2017R1A4A1014569), Korea. S.M.H. acknowledges funding from Chonnam National University 2016 and NRF grant (2015R1C1A2A01054713), Korea.

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CONCLUSION We presented the controlled orientation of gyroid structures in asymmetric HMW PS-b-PMMA films, in which the gyroid structures were developed through a cylindrical morphology on the selective and neutral substrates during SVA process with THF nonselective to the PS and PMMA blocks. At an initial stage of SVA process, a pathway undergoes the formation of cylinders due to an asymmetric swelling between the two blocks. The same perpendicular cylinders were observed at both surfaces because the solvent vapor during SVA process provided a nonselective environment to both blocks. In the interior of the films and to the bottom, however, the interfacial interactions exerted by the substrates had an significant effect on the orientation of cylinders, resulting in the parallel (or mixed) and perpendicular orientations of cylinders on the selective and neutral substrates, respectively. Furthermore, the swollen BCP film recovered into nearly symmetric swelling at the intermediate stage, leading to an irreversible transition from cylinder to gyroid. Particularly in the final formation of gyroid structures, the two distinct [211] and [111] planes on the surface throughout the interior of the films were directed from cylinders on the selective and neutral substrates, respectively. Our results also confirmed that the epitaxial growth from cylinder to gyroid was induced from the substrates during SVA process and then propagated toward the surface, not likely from the surface to the interior, leading to the [211] plane on the PS- and PMMAselective substrates and the [111] plane on a neutral substrate. Theoretically, its phase transition behavior and orientation during SVA process were also demonstrated by brute force Monte Carlo simulations with a coarse-grained model. Our results suggest that the large-area controlled [211] or [111] planes of gyroid structures could be achieved over the films by modulating substrate interactions as a feasible approach to directing the orientation of 3D nanostructures for further application.

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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.7b00898.

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REFERENCES

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DOI: 10.1021/acs.macromol.7b00898 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b00898 Macromolecules XXXX, XXX, XXX−XXX