Log-Rolling Block Copolymer Cylinders - Macromolecules (ACS

Apr 20, 2017 - R.A.R. acknowledges financial support from the National Science Foundation (MRSEC Program) through the Princeton Center for Complex Mat...
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Log-Rolling Block Copolymer Cylinders Ye Chan Kim,†,⊥ Dong Hyup Kim,†,⊥ Se Hun Joo,† Na Kyung Kwon,† Tae Joo Shin,§ Richard A. Register,∥ Sang Kyu Kwak,† and So Youn Kim*,† †

School of Energy and Chemical Engineering and §UNIST Central Research Facilities & School of Natural Science, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulsan 44919, Republic of Korea ∥ Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: Shear is an effective method to create long-range order in micro- or nanostructured soft materials. When simple shear flow is applied, particles or polymer microdomains tend to align in the shear direction to minimize viscous dissipation; thus, transverse alignment (so-called log-rolling) is not typically favored. This is the first study to report the transverse alignment of cylinder-forming coil−coil block copolymers. Poly(styrene-bmethyl methacrylate), PS−PMMA, where the PS blocks form the matrix, can adopt a metastable PMMA hemicylindrical structure when confined in a thin film, and this hemicylindrical structure can orient either along the shear direction or transverse to the shear direction depending on the shearing temperature. A monolayer of PS−PMMA forming full cylinders exhibits logrolling alignment. This unusual log-rolling behavior is explained by the low chain mobility of the cylinder-forming PMMA block at low temperatures, which is the critical quantity determining the direction of shear alignment.

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viscous dissipation and chain mixing24 when shear stress is strong enough to neglect other parameters such as normal stress. Molecular dynamics simulations conducted by Arya and Panagiotopoulos25 predicted log-rolling cylindrical micelles when the micelles couple strongly with the confining surfaces. The authors suggested that chain entanglements, present in the high-molecular-weight BCPs typically employed in experiments, would hinder log-rolling.25 Subsequently, Chremos et al. studied the shear alignment of cylinder-forming BCPs with coarse-grained Langevin dynamics simulations; the authors reported a transition from parallel to log-rolling alignment as segregation strength increased.26 Experimentally, all reported BCPs with simple unstructured, random-coil blocks (“coil−coil” block copolymers) align parallel to the shear direction. In bulk, there are two distinguishable types of parallel alignment, which correspond to having either the (10) or (11) planes of the hexagonal macrolattice lying in the plane of shear;24 in thin films, containing only one or a few layers of cylinders, only the (10) orientation is observed.27 The sole report of transverse cylinder alignment is in a BCP where the matrix block forms a smectic liquid crystal, and in which the mesogens exhibit the homogeneous boundary condition at the cylinder−matrix

INTRODUCTION Self-assembly is of particular interest in soft matter physics, and the nanoscale patterning of soft materials such as polymers or ordered colloids has been widely studied and employed in many applications.1,2 Among the various methods for creating long-range order in materials, shear is universal, effective, and readily approachable. Liquid crystals,3−5 carbon nanotubes,6,7 and nanoparticles8−10 can all be aligned using shear. The alignment of block copolymers (BCPs) using flow fields was first demonstrated by Keller et al.11 Early studies investigated the structural changes in BCPs in bulk under unidirectional or oscillatory shear.12−14 More recently, shear alignment has been applied to BCPs in thin films, successfully creating long-range order. In these experiments, shear was applied to BCP thin films via cross-linked poly(dimethylsiloxane) (PDMS) pads mechanically, 15−17 by thermal expansion18,19 or solvent swelling20,21 of the overlying PDMS pad, or laser heating.1,19,22 Lamellae, cylinders, and spheres all have been reported to align in shear. In principle, two macroscale alignments are possible for cylinder-forming BCPs in thin films, both with the cylinders parallel to the substrate (Figure 1): parallel and transverse. In lamella-forming BCPs, transverse alignment is rarely reported since the domain spacing is disturbed by shear.23 Transversely aligned cylinders, which roll along the shearing direction (“logrolling”, Figure 1b), are thermodynamically unfavorable compared to those with parallel alignment due to the increased © XXXX American Chemical Society

Received: November 21, 2016 Revised: April 12, 2017

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Figure 1. Schematic of the alignment modes of cylinder-forming BCPs. The scheme shows two possible alignments of cylinders in thin films: (a) parallel and (b) transverse (i.e., log-rolling). The shearing direction is indicated in each figure. thickness were deposited by spin-coating, with the thickness controlled through the spin speed and solution concentration, and measured using a spectroscopic ellipsometer (J.A. Woollam Co., M-2000V). Films with thickness gradients were prepared by flowcoating; a bead of polymer solution was placed between a blade and the substrate, and the substrate was moved with a programmed acceleration profile.27,51,52 The local thicknesses of the flow-coated samples were measured using small-spot ellipsometry at 632.8 nm (Gaertner Scientific LS116S300). Shear Alignment. Shear alignment using cross-linked PDMS pads was performed on a hot plate under an applied lateral force.15−17,27 PDMS sheets were prepared from Sylgard 184 (Dow Corning) at a 10:1 ratio of base to curing agent and baked at 60 °C for 24 h. PDMS pads with dimensions of 1.2 × 1.2 cm2 were cut from these sheets and pressed against the supported BCP thin film for shear alignment. Shear stress was controlled by tuning the lateral force (Fl) and was calculated based on the area of the PDMS pad (S) as Fl/S. The shear was given for 30 min, and the PDMS pad moved more than 100 μm in 30 min. Plasma Treatment. To obtain clear SEM and AFM images of PS− PMMA 24K−12K, some of the samples were softly etched with oxygen plasma (Harrick Scientific PDC-32G-2 plasma cleaner). The samples were treated for 40−50 s at a high RF power level (18 W) with an oxygen flow rate of 14 sccm under 300 mTorr. Atomic Force Microscopy. Atomic force microscopy (AFM; Veeco Dimension 3000 and 3100) was used in tapping mode with Bruker tips (RTESP), which have a drive frequency of 300 kHz, a spring constant of 40 N/m, a cantilever length of 125 μm, and a tip radius of 8 nm. SEM. Before imaging by SEM (Hitachi S-4800 field emission scanning electron microscope, high vacuum, 10 keV), the BCP thin films were exposed to the saturated vapor from 0.5 wt % ruthenium tetroxide (RuO4) aqueous solution for 30 min to stain the PMMA domains and thereby increase the interdomain contrast. Crosssectional images were obtained by scoring the back side of the wafer using a diamond scribe, perpendicular to the direction of alignment, and fracturing the wafer by flexing. ToF-SIMS. Depth profiles were obtained using ToF-SIMS (ION TOF, Germany), with a 25 keV Bi3+ analysis beam and a 0.25 keV Cs sputtering beam. The raster sizes for analysis and sputtering were 90 and 300 μm, respectively. The target currents of the analysis and sputtering beams were 0.4 pA and 11.0 nA, respectively. The ToFSIMS instrument was operated in the noninterlaced mode, and negative secondary ions were detected to analyze the composition along the out-of-plane direction. All of the samples were cut to 1 × 1 cm2. GI-SAXS. GI-SAXS measurements were performed at the 6D UNIST-PAL beamline of the Pohang Accelerator Laboratory in Korea. The energy of the X-rays was 10.0 keV (wavelength, λ = 1.2398 Å), the incident angle was 0.14°, and the sample-to-detector distance was 3527 mm. Scattering patterns were collected using a 2D CCD detector (MX225-HS, Rayonix L.L.C., USA). Samples were measured with the incident beam parallel to the cylinder alignment direction observed by AFM.

interface. In these materials, transverse cylinder alignment allows for a constant smectic layer spacing during shear.28 Tang et al.29,30 reported transverse alignment of lameallar domains relative to the flow direction during a zone-casting process, resulting from directional solvent evaporation and consequent microphase separation along the casting direction.29 They further reported that the alignment direction could be changed to perpendicular when one of the blocks crystallizes during zone-casting. In these cases, the orientation is not governed directly by shear, but rather by solvent evaporation or block crystallization during the casting process. While the log-rolling orientation has not been obtained by shearing coil−coil BCPs, log-rolling objects are often observed in other types of soft matter, such as liquid crystals,31 elliptical particles,32 strings of particles,33 and emulsions.34 In these examples, the particles act as rigid objects with high aspect ratio. Although these are intriguing observations, the conditions required to obtain the log-rolling orientation in coil−coil BCPs by shearingif possible at allremain a mystery. This study provides the first demonstration of log-rolling (transversely aligned) coil−coil BCPs via melt shearing, and investigate the shear alignment mechanism. We show that cylinder-forming polystyrene-b-poly(methyl methacrylate) (PS−PMMA) can be aligned parallel or transverse to the shearing direction depending on the shearing conditions. PS− PMMA is a readily synthesized and processable polymer; thus, it has been employed in pioneering studies on nanopatterning35−39 as well as in many applications,40−43 and many studies have characterized its behavior. Intriguingly, cylinder-forming PS−PMMA can form hemicylinders42,44 parallel to the substrate due to the similarity between the surface energies of PS and PMMA at certain temperatures.45−47 PS and PMMA are known to have similar glass transition temperatures (Tg)48,49 and a relatively low polymer interaction parameter (χ), which is only weakly temperature dependent.50

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METHODS

Sample Preparation. All polymers were purchased from Polymer Source, Inc.: BCPs PS−PMMA 64K−35K, 24K−12K, and 26K−68K, with number-average molecular weights (Mn) of 99 000 g/mol (dispersity Đ = 1.09), 35 500 g/mol (Đ = 1.06), and 94 400 g/mol (Đ = 1.18), respectively, and hydroxy-terminated PS homopolymer (Mn = 9000 g/mol, Đ = 1.03). ⟨100⟩ Si wafers (purchased from Silicon Quest International or Waferbiz) were employed as substrates; the wafer surfaces were rinsed with toluene before spin-coating and had a 2.2 nm thick native oxide layer. A PS-preferential substrate was prepared by spin-coating hydroxy-terminated PS homopolymer at 25 nm thickness and annealing for 24 h at 160 °C in a vacuum oven. Ungrafted polymer was removed by repeated rinsing with toluene, yielding a final grafted thickness of 5 nm. BCP films of uniform B

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Figure 2. Metastable film structure of PS−PMMA 64K−35K hemicylinders for a film thickness of 38 nm. (a) AFM height image after 23 h of annealing at 170 °C. (b) Enlarged image of (a). (c) Bicontinuous terrace structure after 60 h of additional annealing; the height trace taken along the horizontal black line is shown as an inset. (d) ToF-SIMS depth profile of the film annealed at 150 °C for 24 h. (e) Structure of the metastable film.

(83 h) under the same conditions, the film eventually terraced and showed a bicontinuous structure (Figure 2c). The film structure was confirmed by time-of-flight secondary ion mass spectrometry (ToF-SIMS). In the SIMS depth profiles shown in Figure 2d, the depth distributions of PS and PMMA are represented by C6H− and CH3O− ions, respectively.55 The SIMS results revealed the presence of PMMA at the polymer− vacuum interface (film surface) and a wetting layer at the polymer−substrate interface (Figure S9). AFM images (Figure 2b) indicated that the PMMA at the surface was present not as a uniform layer, but as stripes, characteristic of the hemicylindrical structure observed previously.42,44 We also confirmed that hemicylinders formed over a wide range of film thicknesses (25−40 nm) under mild annealing conditions (below 150 °C for a couple of hours; Figure S9), though the hemicylinder structure eventually transitioned to a terraced film comprising a wetting layer at ∼0.5L0 and a fullcylinder structure at ∼1.5L0 (Figure 2c). We further examined the thin-film structure of another diblock, PS−PMMA 24K− 12K, which has PS and PMMA block number-average molecular weights of 24 and 11.5 kg/mol, respectively. This BCP has a PMMA fraction similar to that of PS−PMMA 64K− 35K and, thus, also forms PMMA cylinders. From the annealing and ToF-SIMS experiments (Figures S2 and S9), we confirmed that PS−PMMA 24K−12K also has a thickness (24 nm) at which it forms metastable hemicylinders. We aligned PS−PMMA 64K−35K at 34−38 nm film thickness by applying different shear stresses over an area of 1.2 × 1.2 cm2 with a cross-linked PDMS pad.15 The shearing temperature was 140 °C (Figure 3a) or 150 °C (Figure S6), and shear was applied for 30 min. Surprisingly, as shown in Figure 3a, the hemicylinders aligned transverse to the shear direction (indicated by the arrow in Figure 3). Similarly, the hemicylinders in PS−PMMA 24K−12K aligned transverse to the shear direction at 130 °C (Figure 3b). The higher the applied stress, the greater the extent of alignment. To quantify

Nonequilibrium Molecular Dynamics. Nonequilibrium molecular dynamics (NEMD) simulations were performed using the Langevin thermostat.53 Bead−spring models representing PS (16 beads) and PMMA (8 beads) were constructed by applying WCA and WCA-MM potentials, respectively (see Supporting Information for NEMD). A total of 1179 BCP chains were packed in a box with a thickness of 10 times the bead size (σ). The top and bottom walls were moved in opposite directions at velocities in the range of 0.01−0.2 σ/τ, where τ is the unit of time. NEMD simulations in the canonical ensemble (i.e., constant temperature) were run for 2 × 107 steps with a time step of 0.005τ at a temperature of kBT = ε.

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RESULTS AND DISCUSSION PS−PMMA 64K−35K with PS and PMMA blocks having number-average molecular weights of 64 and 35 kg/mol, respectively, was annealed for 23 h at 170 °C under vacuum to characterize the unsheared film structure. PS−PMMA 64K− 35K exhibits asymmetric wetting behavior on an untreated Si wafer substrate (Figure S1); the equilibrium thicknesses at which uniform films did not terrace were approximately t = (n − 1/2)L0, where t is the film thickness, n is a positive integer, and L0 is the cylinder interlayer spacing.54 For PS−PMMA 64K−35K, the wetting layer thickness was determined to be ∼19 nm and L0 was ∼42 nm. A wetting layer naturally forms when the major block (PS here) is not favored to be at the substrate; the minor block is preferentially attracted to the substrate, forming a layer with a thickness of ∼0.5L0 (Figure 2e). For this reason, films with 0.5 < t/L0 < 1.5 generally terraced into regions with a local thickness of either 0.5L0 or 1.5L0, typically with a micrometer-scale lateral length. However, we observed that films of PS−PMMA 64K−35K at t = 38 nm did not terrace after 23 h of annealing, but instead remained uniform, while films at other thicknesses (t ≠ (n − 1/2)L0) formed islands, holes, or bicontinuous structures (Figure S1). Furthermore, there was an abrupt transition from holes at 36 nm, to a uniform film at 38 nm, to islands at 40 nm (Figure S1). When the film with t = 38 nm was annealed for a longer period C

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Figure 3. AFM height images of (a) PS−PMMA 64K−35K with a thickness of 34 nm sheared at 140 °C and (b) PS−PMMA 24K−12K with a thickness of 23 nm sheared at 130 °C. Arrows indicate the direction of shear; fast Fourier transforms (FFTs) are given in the upper right corners with calculated orientation parameters (S). The AFM images are (a) 2 × 2 μm2 and (b) 1 × 1 μm2. Scale bars are 200 nm.

Figure 4. Temperature-dependent shear alignment of PS−PMMA 64K−35K hemicylinders (thickness = 38 nm) at (a) 140 °C and (b) 180 °C. The ToF-SIMS profile, GI-SAXS 2D pattern, AFM height image with FFT (and orientation parameter), and SEM image are given in each row from left to right. A cross-sectional SEM image is provided in the upper right corner showing the PMMA hemicylinders (an enlarged image is available in Figure S12). Arrows indicate the direction of shear. Unlabeled scale bars are 500 nm. The beam was aligned parallel to the alignment direction in GISAXS measurements. The GI-SAXS 1D line profiles are given in Figure S10c.

the alignment quality, Hermans orientation parameter, S, was

as indicated by the grazing-incidence small-angle X-ray scattering (GI-SAXS) pattern (Figure 4b). PS−PMMA 24K− 12K showed the same trend: the transverse alignment of the hemicylinders gave way to parallel alignment with increasing temperature. However, the transition temperature for PS− PMMA 24K−12K was 150 °C, lower than that for PS−PMMA 64K−35K (see Figure S3). The alignment quality of parallel alignment (S = 0.91) is better than that of transverse alignment (S = −0.40). Because the hemicylinder structure is only metastable, one might ask whether the transverse alignment is transient, with the alignment eventually shifting to be along the shear direction. To show that parallel alignment is not favored under these conditions, after shearing at 140 °C to obtain

3⟨cos2 θ ⟩ − 1 56 . 2

calculated for both films where S is defined as S = Here θ is the azimuthal angle obtained from the FFT images in Figure 3, and ⟨cos2 θ⟩ is calculated as ⟨cos2 θ ⟩ =

90 °

∑I = 0 ° I(θ ) sin θ cos2 θ 90 °

∑I = 0 ° I(θ ) sin θ

. When S has a value of 1, −0.5,

or 0, the cylinders are aligned perfectly parallel, perfectly perpendicular, or randomly to the shearing direction, respectively. These sheared films retained their hemicylindrical structure, as confirmed by ToF-SIMS depth profiles and crosssectional SEM images (Figure 4a). Interestingly, when the shearing temperature was increased to 180 °C, the cylinders aligned parallel to the shear direction, D

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Figure 5. Stepwise annealing results for PS−PMMA 64K−35K hemicylinders (thickness = 35 nm). (a) GI-SAXS 2D images taken every 10 °C from 140 to 190 °C (enlarged 2D data are given in Figure S10a). (b) AFM height images, 2 × 2 μm2, of samples annealed for 30 min at 140 °C (left) and 180 °C (right). Scale bars are 500 nm. (c) GI-SAXS 1D profiles extracted from (a). (d) Intercylinder spacings obtained from GI-SAXS 1D profiles.

wafer (Figure S5). Thus, the observed transverse alignment is not a substrate-specific phenomenon. For PS−PMMA 64K−35K, the bulk Tg values of the PS and PMMA domains reported by the manufacturer are 110 and 124 °C, respectively. The PMMA blocks, which form the cylinders in PS−PMMA 64K−35K, have a high segmental friction factor57 and therefore a low chain mobility at 140 °C, even in bulk. In thin films, Tg can be modulated by polymer−surface and polymer−substrate interactions, with the Tg of PS lower in thin films than in the bulk,49,58 while the Tg in PMMA thin films can either increase or decrease due to substrate interactions.48,49,58−63 Therefore, we expect that this difference in segmental mobility between PS and PMMA will be preserved, or even enhanced, in thin films. We note that the lower-molecular-weight PS−PMMA 24K−12K shows trans-

transversely aligned hemicylinders, a second shear was applied orthogonally at 140 °C. If parallel alignment were favored at steady state, no reorientation should occur during the second shear; however, the hemicylinders rearranged to be transversely aligned with the second shear direction, indicating that transverse alignment is energetically favored under these conditions (Figure S4). Experiments were also performed with a PS-preferential substrate, achieved by grafting 5 nm of hydroxy-terminated PS homopolymer (Mn = 9000 g/mol) to the Si wafer substrate prior to BCP spin-coating. PS−PMMA 64K−35K, 26 nm thick (∼0.5L0), forms hemicylinders on this PS-grafted substrate and shows the same temperature-dependent shear alignment as does a 38 nm thick film on an ungrafted (PMMA-preferential) E

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Figure 6. Temperature- and shear stress-dependent alignment in PS−PMMA 24K−12K full cylinders at 35 nm thickness. A shear stress of 30 kPa was applied at (a) 120, (b) 130, (c) 140, (d) 150, (e) 160, and (f) 170 °C for 90 min. In (d), the shear stress was varied from 10 to 30 kPa as indicated. The shear direction (white arrow) was vertical in all cases. 2D FFTs are shown as insets with calculated orientation parameters; all SEM image scales are 1 × 1 μm2, and the scale bar indicates 200 nm.

due to the much weaker dependence50 of χ on T; nonetheless, d still decreases slightly as T is increased.65 The results of Figure 5 clearly show that the microdomain structure in these films is not at equilibrium, particularly at temperatures below 170 °Canother reflection of low chain mobility. AFM also confirms the apparent increase of d with T: films annealed at 180 °C (vs 140 °C) for 30 mina somewhat different thermal history than that employed for GI-SAXS showed an increase of 9 nm in d. When shear was applied at 180 °C (parallel alignment), the d-spacing was not significantly different from that of the annealed but unsheared film. However, the d-spacing after shearing at 140 °C (transverse alignment) was 13 nm larger than that for the unsheared sample at 140 °C, indicating that the process of shearing imparts sufficient mobility to the chains for the domain spacing to change. However, the low mobility of the PMMA blocks adversely affects the alignment quality in specimens exhibiting transverse alignment, which is generally poorer than in specimens exhibiting parallel alignment (compare Figures 4a and 4b). To further probe the influence of PMMA block mobility, the temperature dependence of shear alignment was also examined in a third BCP, PS−PMMA 26K−68K, in which PMMA is the major block (Figure S8). In this case, no alignment was observed after shearing at 150 °C, due to the low mobility of the PMMA matrix; at 190 °C, where both the PS and PMMA blocks have sufficient mobility, the cylinders aligned in the shear direction, with the high degree of orientation typically observed for parallel alignment.

verse alignment only at temperatures lower than where PS− PMMA 64K−35K shows transverse alignment (Figure 3). Indeed, the bulk Tg values obtained from the manufacturer for PS−PMMA 24K−12K are 99 °C for the PS domains and 107 °C for the PMMA domains, which are 11 and 17 °C lower than the values for PS−PMMA 64K−35K, respectively. The combination of lower Tg and shorter block length thus allows PS−PMMA 24K−12K to transition to parallel alignment at a lower temperature than PS−PMMA 64K−35K. We performed stepwise annealing experiments with PS− PMMA 64K−35K at the hemicylinder thickness, where temperature was increased from 140 to 190 °C and GI-SAXS measurements were conducted every 10 °C. Each targeted temperature was reached in 1 min and held for 30 min before each measurement. Figure 5c shows the GI-SAXS 1D profiles extracted from the GI-SAXS 2D images in Figure 5a. As temperature increased, the domain spacing calculated from the peak position also increased. As mentioned above, the 64K− 35K film formed metastable hemicylinders at 170 °C but terraced rapidly at 190 °C; thus, the reduced peak heights at temperatures above 160 °C were attributed to the macroscopic terracing of the films. We also found similar results for PS− PMMA 24K−12K (see Figure S11). Domain spacing (d) commonly decreases with increasing temperature, as usually the Flory−Huggins parameter χ is inversely related to temperature (T). For example, Hashimoto et al.64 reported that the lamellar domain spacing in neat PS-b-polyisoprene scales as d ∼ (1/ T)1/3. For PS−PMMA, the change of d with T is much weaker, F

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Macromolecules A PS−PMMA 64K−35K thickness-gradient film, with thickness ranging from 20 to 60 nm, was prepared via flow coating, and shear was applied at 150 °C for 30 min perpendicular to the thickness gradient. Figure S6 presents postshear AFM images at various thicknesses; transversely aligned BCPs were observed for film thicknesses ranging from 25 to 40 nm, where metastable hemicylinders are formed, whereas no alignment was observed at other thicknesses. In all of the transversely aligned films, PMMA hemicylinders were present at the polymer/PDMS interface, as confirmed by ToFSIMS (Figure 4a and Figures S9b,c,g). To achieve transverse alignment in films containing a layer of full PMMA cylinders (vs hemicylinders), higher shear stresses were required. Figure 6 shows SEM images of a 35 nm film of PS−PMMA 24K−12K, containing a layer of full PMMA cylinders, after 90 min of shearing at various temperatures and stresses. While 10 kPa of shear stress is insufficient to produce discernible alignment, 30 kPa yields transverse alignment, observed over the whole range of shearing temperatures employed (120−170 °C). A transition to parallel alignment is expected to occur at sufficiently high temperatures (evidently >170 °C), while this transition occurred at 150 °C in the same polymer at the hemicylinder film thickness of 23 nm (Figure S3). For the higher-molecular-weight PS−PMMA 64K−35K, the alignment quality was poorer, but partial transverse alignment was observed at 170 °C and 30 kPa (Figure S7e). The transition appeared to be abrupt; no intermediate alignment (e.g., absence of preferred orientation) was found at temperatures between those yielding transverse and parallel alignments. We also summarize the shear alignment directions obtained from all experiments in Figure 7.

transition from log-rolling to parallel alignment as segregation strength is reduced; however, for PS−PMMA, χ depends only weakly on temperature,50 so changes in segregation strength cannot be the source of the temperature-dependent alignment transition observed here. Nonetheless, since simulations have observed both parallel and transverse alignment, we employed Langevin dynamics (see NEMD in Methods) to simulate the confined BCPs under shear flow and to observe the behavior of the chains in the two alignment modes. Details of the NEMD simulation method are given in the Supporting Information. Figure 8a (see also Supporting Information Movie 1) shows parallel alignment with respect to the shear direction at Φ = 1.0.

Figure 8. NEMD simulation snapshots of the (a) parallel and (b) transverse alignments. The black arrow represents the shear direction, vw is the velocity of the wall, and gray and yellow beads represent PS (S) and PMMA (M) segments, respectively. The polymer model is shown at the top of the figure. Average velocity profiles of the yellow (M) beads across the thin films (thickness of 10σ and vw of 0.05σ/τ) for (c) parallel and (d) perpendicular alignment. Note that ε is an energy parameter that sets the scale of the short-ranged repulsion.

Figure 7. Summary of shear alignment transitions of PS−PMMA thin films with temperature. Red circles, blue triangles, and green squares represent transverse (log-rolling), parallel alignment, and no alignment, respectively. Solid shapes represent confirmed structures, whereas transparent shapes represent expected structures under conditions not explored experimentally.

Note that Φ represents the segregation strength, which is correlated with the depth of the potential well. When the two walls slide in opposite directions, the polymer chains in the upper half of each cylinder and the polymer chains in the lower half of the cylinder experience the same force but in opposite directions. Figures 8c and 8d show the velocity profiles as functions of segregation strength for parallel and log-rolling alignments, respectively. The dilemma for cylinders oriented along the shear direction is that they experience a significant velocity difference between their upper and lower halves. Therefore, there is continuous interchain mixing inside the

As mentioned in the Introduction, block copolymer domains tend to orient along the shear direction to minimize viscous dissipation and chain mixing between dissimilar blocks.66 However, in the present case, we believe that the observed log-rolling or transverse alignment is actually favored at temperatures modestly above the Tg of the cylinder-forming PMMA block. In a recent simulation study using Langevin dynamics, Chremos and Panagiotopoulos26 predicted a G

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Macromolecules cylinders when they align along the shear direction. In Movie 1, a few PS chains in the upper (lower) part of the cylinders are colored in black (pink); the chains with different colors move in opposite directions, and chains occasionally change color as they move across the centerplane, indicating that the upper and lower parts of the PMMA cylinders mix. On the other hand, at an increased strength of interchain attraction (i.e., Φ = 1.6) in the cylinders, log-rolling alignment prevails, as shown in Figure 8b (see Movie 1). The velocity profiles in Figures 8c,d show that the velocity gradient is negligible across the cylinders when Φ > 1.6. These results clearly demonstrate that a strong attraction between the cylinder-forming blocks restrains their movement during shear; this lower mobility then favors the log-rolling orientation, as observed experimentally at temperatures modestly above the PMMA block Tg. Thus, the principal effect of increased Φ in the simulations is not its influence on the interblock segregation strength, but its reduction in the cylinder block mobility. In both orientations, significant slip was observed at the walls due to the repulsive nature of the wall− polymer interactions. Simulation results at other segregation strengths and wall velocities are given in Figure S13.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Ph +82 52 217 2558(S.Y.K.). ORCID

Se Hun Joo: 0000-0003-4507-150X Richard A. Register: 0000-0002-5223-4306 Sang Kyu Kwak: 0000-0002-0332-1534 So Youn Kim: 0000-0003-0066-8839 Author Contributions ⊥

Y.C.K. and D.H.K. contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2014R1A1A2056774) and Ministry of Science, ICT and Future Planning (NRF-2016M3A7B4905624). GI-SAXS experiments at PLS-II 6D beamline of the Pohang Accelerator Laboratory were supported in part by UCRF, MSIP and POSTECH. R.A.R. acknowledges financial support from the National Science Foundation (MRSEC Program) through the Princeton Center for Complex Materials (DMR-1420541). S.K.K. acknowledges financial support from KISTI (C17006) and computational support from UNIST-HPC and KISTI (KSC2016-C2-0003). We gratefully acknowledge Dr. Alexandros Chremos for helpful discussions.

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CONCLUSIONS In this study, we reported temperature-dependent shear alignment of cylinder-forming coil−coil BCPs, including the observation of transverse, log-rolling alignment. Under shear, the free energy is minimized when the cylinder axes align parallel to the shear direction, but this orientation requires sufficient mobility of the cylinder-forming blocks. If the mobility is insufficient, log-rolling alignment is favored instead. Notably, this unusual log-rolling alignment was observed for the BCP chemistry (PS−PMMA) which is the most widely used in directed self-assembly for nanofabrication. This implies that understanding the fundamental physics of these copolymers (e.g., mobility of the constituent blocks) can be critical in determining their quality of alignment,67 which has great implications for nanopatterning.

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Movie 1: simulation for parallel and transverse alignment (AVI)

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REFERENCES

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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.6b02516. Film structure of PS−PMMA 64K−35K at various thicknesses; film structure of PS−PMMA 24K−12K at various thicknesses; alignment transition of PS−PMMA 24K−12K hemicylinders with temperature; alignment transition of PS−PMMA 64K−35K hemicylinders with a second shear; transverse alignment of PS−PMMA 64K− 35K on a PS-preferential substrate; shear alignment of PS−PMMA 64K−35K at various thicknessesm; shear alignment of PS−PMMA 64K−35K full cylinders at 57 nm; PS−PMMA 26K−68K cylinders at 36 nm; sheared at different temperatures; ToF-SIMS depth profiling; GISAXS results for PS−PMMA 64K−35K; GI-SAXS results for PS−PMMA 24K−12K; cross-sectional SEM image of PS−PMMA 64K−35K hemicylinders; results of nonequilibrium molecular dynamics simulations at various conditions; nonequilibrium molecular dynamics (NEMD) simulation details (PDF) H

DOI: 10.1021/acs.macromol.6b02516 Macromolecules XXXX, XXX, XXX−XXX

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