Latent Alignment in Pathway-Dependent Ordering of Block Copolymer

Letter pubs.acs.org/NanoLett

Latent Alignment in Pathway-Dependent Ordering of Block Copolymer Thin Films Pawel W. Majewski and Kevin G. Yager* Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, United States S Supporting Information *

ABSTRACT: Block copolymers spontaneously form well-defined nanoscale morphologies during thermal annealing. Yet, the structures one obtains can be influenced by nonequilibrium effects, including processing history or pathway-dependent assembly. Here, we explore various pathways for ordering of block copolymer thin films, using oven-annealing, as well as newly disclosed methods for rapid photothermal annealing and photothermal shearing. We report the discovery of an efficient pathway for ordering selfassembled films: ultrarapid shearing of as-cast films induces “latent alignment” in the disordered morphology. Subsequent thermal processing can then develop this directly into a uniaxially aligned morphology with low defect density. This deeper understanding of pathway-dependence may have broad implications in self-assembly. KEYWORDS: Block copolymer, self-assembly, nonequilibrium, shear, photothermal

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in BCP materials. Kinetics can be enhanced using solvent annealing,9−12 microwave annealing,13−15 or zone annealing.16,17 Yet even with improved grain sizes, the material may still be far from the theoretical energy-minimum. Application of a field during thermal annealing can break powder symmetry, forcing one grain orientation to dominate. This has been demonstrated with electric,18−21 magnetic,22−26 and shear27−35 fields. Here, we report the surprising discovery of an efficient ordering pathway for BCPs. Specifically, ultrashort time scale photothermal shearingtoo short for good order to develop evidently leaves an “imprint” in the film morphology, allowing it to be rapidly thermally annealed into a monolithically aligned structure. Beyond being practically useful for rapid ordering of BCP thin films, this result uncovers fundamental aspects of block copolymer ordering pathways. More generally, it highlights the crucial importance of understanding ordering pathways in self-assembling systems. Results and Discussion. We have recently developed a new method for thin-film processing: laser zone annealing (LZA).36,37 This involves sweeping a highly focused laser-line across a polymer thin film supported on a Ge-coated substrate (Figure 1). The Ge absorbs the laser light, creating a highly localized thermal zone within the polymer film. The high temperatures and extreme in-plane thermal gradients give rise to enhanced ordering kinetics for block copolymer assembly (>103 improvement compared to oven annealing), due to a

elf-assembly is a powerful paradigm for constructing nanomaterials. The desired structure is encoded within the molecules themselves; energy-minimization then spontaneously gives rise to a well-defined nanoscale structure, replicated throughout the entire material. Yet, it is being increasingly appreciated that self-assembling materials are not purely regulated by this equilibrium criterion. In practice, nonequilibrium and path-dependent effects can play a major role in determining the structures one obtains. Block copolymers (BCPs) are a versatile and well-studied selfassembly strategy, where chemically distinct polymeric blocks are covalently bonded. The strong drive toward phaseseparation is frustrated by the covalent linkage; the compromise involves the formation of well-defined nanostructures, such as spheres on a cubic lattice, hexagonally packed cylinders, or lamellae.1−5 In principle, the enthalpy minimum occurs when the entire material develops into a single, perfect grain of the given morphology, since defects and grain boundaries represent high-energy configurations. At thermodynamic equilibrium, one of course expects a nonzero defect density, owing to their entropic contribution, but for strongly segregating materials, the equilibrium concentration of high-energy defects should be very low. In reality, samples of BCPs are nearly always found to form polygrain structures, with numerous grain boundaries. This is not surprising: as a BCP is thermally annealed, defects annihilate, and grains coarsen; but the time scale for further coarsening continually increases as defect densities decrease. Experimentally, this frequently follows a power law ξ ∼ tα, where ξ is the correlation distance for the morphology (grain size), t is time, and α is an exponent of order 0.2−0.5 for thin films.6−8 Many methods have been developed to improve order © XXXX American Chemical Society

Received: April 15, 2015 Revised: June 23, 2015

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Figure 1. Schematic of laser zone annealing (LZA) processing. (a) LZA consists of sweeping a focused laser-line through a thin film supported on a Ge light-absorbing layer. (b) In LZA, the local heating and intense thermal gradients greatly enhance ordering kinetics. The soft-shear (SS) variant of LZA introduces an elastic (PDMS) capping-layer. Differential thermal expansion from the moving thermal gradients creates shear-fields (small arrows), which can align the polymer film morphology. This shearing only occurs along the thermal gradient direction (across the laser-line); the temperature profile is essentially constant along the laser-line (into the page in the diagram). Thus, morphology is aligned along the laser sweep direction. (c) Cylinder-phase block copolymer thin films were studied using GISAXS. Samples were rotated about the film normal to assess orientation in the ϕ-direction. We define ϕ = 0° when the X-ray beam is parallel to the SS-LZA sweep direction.

Figure 2. Observation of latent alignment of block copolymer films. As-cast BCP films (upper left) are disordered and do not exhibit any welldefined scattering peaks in GISAXS. Thermal annealing (via LZA) yields a well-defined morphology (as evidenced by sharp diffraction peaks), but a polygrain structure (upper right). Ultrabrief soft-shearing of a BCP film (SS, lower left) yields a film that still has only a very weak signature of order. Yet, this film evidently exhibits “latent alignment”, since thermal processing generates an exceptionally well-ordered, and uniaxially aligned, BCP morphology (lower right).

to the BCP film (cross-linked polydimethylsiloxane, PDMS) leads to shear-effects within the polymer layer. The shearing arises due to differential thermal expansion of the PDMS, relative to the substrate, within the strong thermal gradients. This SS-LZA method can give rise to a uniaxially aligned BCP morphology, provided the total processing time (where both

combination of annealing and thermophoretic effects. A sample can be processed with LZA repeatedly (multiple sweeps through the laser), to increase the total annealing time. LZA can be viewed as a convenient and rapid annealing protocol, achieving good order after mere seconds. This method can also be combined with “soft-shear”:38,39 adding an elastic cladding B

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Figure 3. Detailed investigation of latent ordering. This matrix of images describes a variety of ordering pathways. The q-axes for the GISAXS images have been omitted for clarity; they are consistent in all cases and identical to those used in Figure 2 (qx −0.075 Å−1 to +0.075 Å−1; qz 0.00 Å−1 to 0.15 Å−1). The processing history for each sample is marked. In the lower-right corner, the angular spread of the morphology, σϕ, (where measured) is noted; “iso” indicates an isotropic in-plane powder. The lower row shows a variety of control experiments: as-cast films do not exhibit any measurable order, while thermal annealing (oven or LZA) generates grains but no preferred alignment. The top row shows that SS-LZA can align the morphology. This good order can be improved with further LZA. The middle row shows that while a film soft-sheared at 1280 μm/s (0.07 s annealing time) does not exhibit measurable order or alignment, further thermal development yields a well-aligned final state.

defective grain-boundaries between them. If a similar as-cast film is soft-sheared (SS) for just 0.07 s (single SS-LZA sweep at 1280 μm/s), the GISAXS pattern appears largely unchanged. Only a very weak peak is observed, indicative of a very poorly developed morphology. Amazingly, however, if this “presheared” film is then subjected to thermal processing (which should not induce any alignment), the film rapidly develops into a well-ordered and uniaxially aligned morphology. Thus, it must be that the presheared film has some form of “latent alignment” induced within it from the ultrarapid shearing. To explore this phenomenon further, we undertook an extensive series of experiments, which probe different pathways for BCP ordering. The results are summarized in Figure 3. The bottom row represents thermal annealing pathways. The as-cast film (lower left) is disordered. Oven annealing gives rise to peaks for both perpendicular (vertical) and parallel (horizontal) cylinder grains. LZA achieves purely parallel orientations, and much larger grain sizes, especially considering the short annealing time (16 sweeps at 80 μm/s corresponds to 19 s annealing). Nevertheless, both of these thermal treatments yield a polygrain structure. The left-column of Figure 3 shows the results of SS-LZA processing of films. Shearing a film at 320 μm/s (0.3 s) generates a well-ordered and well-aligned morphology, consistent with previous shear experiments on BCPs. This state can be further developed by thermal annealing. We observe that additional processing using oven annealing at 200 °C in fact leads to slightly worse order. The inplane orientational spread (reported as the standard deviation, σϕ, from a Gaussian fit of the peak) increases from ∼3° to >14°

shearing and annealing occur) is sufficiently long. In this paper, we use both LZA and SS-LZA to explore aspects of BCP ordering pathways. We primarily quantify BCP ordering using synchrotron grazing-incidence small-angle X-ray Scattering (GISAXS), measuring thin-films with the X-ray beam aligned with the SS-LZA sweep direction (ϕ = 0°). To measure the inplane alignment of the morphology, we measured GISAXS patterns as a function of sample rotation (ϕ) and plot the background-corrected integrated peak intensity of the brightest peak in the GISAXS pattern. In the course of studying BCP films ordered by LZA and SSLZA, we happened upon a unique and interesting finding, as summarized in Figure 2. We describe results for cylinderforming polystyrene-block-poly(methyl methacrylate) (PS-bPMMA), of total molecular weight 49 kg/mol. As-cast films do not exhibit any well-defined diffraction peaks, because the morphology, during the rapid solvent evaporation of spincoating, has been quenched into a disordered configuration. The BCP architecture, however, defines a preferred length scale, even if the material is barely phase-separated. This appears in scattering data as a weak “correlation hole” peak.40 Processing by LZA induces the formation of well-defined horizontally oriented cylinder phases. For the film thicknesses discussed here (170 nm), the BCP forms ∼6 cylinder layers (due to the intrinsic morphology cylinder-cylinder repeatspacing of L0 ≈ 30 nm). Although this morphology is quite well-developed (correlation length ξ = 660 nm), it is a polygrain structure. That is, the material forms a variety of grains with different orientations, establishing high-energy C

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apparently poor order of this state, further processing yields aligned morphologies. Oven annealing gives rise to a broadly aligned morphology, consistent with the previously described results. LZA processing gives rise to a very well-aligned sample (σϕ < 5°). These results were confirmed by scanning electron microscopy (SEM), as shown in Figure 5, where development by LZA or oven annealing both yield highly aligned BCP morphologies (with LZA producing somewhat better order). The exceptional order of this final state can be quantified using image analysis (Supplementary Figure S2). For the LZA processed sample, the final orientational order parameter is S > 0.99, and the defect density is only ρd ≈ 6 μm−2. By comparison, the SEM of a rapidly sheared film (upper left of Figure 5), appears, at first glance, to be entirely disordered. And yet, the Fourier transform of the image shows weak anisotropy at the q-value of the BCP morphology. This suggests that the weakly phase-separated domains have been distorted, and stretched along the shear direction (Fourier filtering of the image makes this more evident; refer to Supplementary Figure S3). The remarkable conclusion is that rapidly sheared films possess induced alignment, despite lack of a well-defined morphology. This extremely subtle latent alignment can then be developed into a uniaxial morphology using a mode of thermal processing that does not, by itself, induce alignment. In our previous work, we demonstrated that performing LZA at elevated temperatures can, itself, give rise to alignment of the BCP morphology due to the creep-flow of the polymer film. This effect is not expected to play a role for the annealing temperatures presented here; indeed control samples processed using only LZA (matching the conditions used here) do not show any preferential in-plane alignment of the BCP cylinder morphology. Moreover, the fact that isotropic oven annealing of a rapidly sheared film gives rise to an aligned morphology confirms that the initial, rapid SS-LZA step is the origin of the alignment direction. We emphasize that the PDMS pad used for SS-LZA is removed immediately after processing; thus any residual stresses induced in this layer cannot influence subsequent processing steps. On the other hand, it is possible that the extreme processing of SS-LZA generates anisotropic residual stresses in the BCP film itself and that these stresses cannot relax while the film is below Tg. Subsequent thermal processing could then relax these stresses, concomitantly orienting the morphology. To explore these possibilities, we conducted additional control experiments. We found that any preexisting film ordering disrupts the ability of the rapid-shear step to induce latent alignment (Supplementary Figure S6). Furthermore, when a latent-aligned film is thermally treated (above Tg) in order to relax residual stresses, subsequent annealing nevertheless leads to a well-aligned final state (Supplementary Figure S7). While we cannot completely exclude a contribution from residual stress, these control experiments, coupled with our direct measurement of alignment of the disordered postshear film, strongly support our latent alignment hypothesis. The pathways for BCP ordering can be understood in terms of the dominant energetic contributions. The fundamental driving force in BCP assembly is the phase-separation between the chemically incompatible blocks, which is characterized by their Flory−Huggins interaction parameter, χ. This parameter has entropic (χS) and enthalpic (χH) contributions, giving rise to a temperature-dependence:

Figure 4. Quantification of morphological alignment. (a) A film softsheared (SS) at 320 μm/s (0.3 s annealing) becomes well-aligned. Further annealing in an oven broadens the orientation distribution, while further LZA processing sharpens the distribution. (b) A film sheared at 1280 μm/s (0.07 s annealing) does not exhibit any strong scattering peaks. Yet, further development with LZA yields an aligned final state. Intensity scales are arbitrary, but consistent. Solid lines are Gaussian fits to the data.

(see also Figure 4a). This can be understood in terms of the effect of annealing temperature. The BCP repeat-spacing exhibits a temperature-dependence, with L0 decreasing as temperature increases; at higher temperatures, chains adopt conformations that are less-stretched by the constraints of the morphology.41,42 Thus, the L0 developed during SS-LZA may not match the L0 which is preferred at 200 °C (oven annealing). Indeed, from the GISAXS, we measure L0 = 30.6 ± 0.4 nm for oven annealing (200 °C), whereas LZA yields L0 = 29.4 ± 0.4 nm. Due to this mismatch, the morphology must rearrange during oven annealing, introducing defects, and broadening the orientation distribution. We also note that the BCP segregation strength, χ, is temperature-dependent. For PSb-PMMA, the temperature dependence is relatively weak;43−46 nevertheless, during LZA or SS-LZA processing, the strength of BCP segregation will vary somewhat as T varies. Further processing using LZA, by comparison, avoids this possible conflict, since the SS-LZA and LZA steps will have similar thermal histories. Indeed, we observe that development of SS-aligned films using LZA further improves the order, with GISAXS peaks sharpening (indicating larger ξ), becoming brighter, and higher-order peaks appearing. This can be confirmed by the orientational spread (Figure 4a), where LZA causes σϕ to decrease from 3.3° to 2.6°. We also note that the inherent speed advantage of LZA is leveraged: after only 19 s of annealing, the film order appears to have saturated. The second row of Figure 3 shows a film sheared at 1280 μm/s (0.07 s). In this case, the shear is so rapid that we do not detect the formation of any well-defined order. Only a very weak scattering peak can be seen (especially within the intensity-enhancement afforded by the Yoneda band). Within the available signal-to-noise, we do not detect a strong orientational bias for this weak peak. Remarkably, despite the D

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Figure 5. SEM characterization. Scanning electron microscopy (SEM) provides direct visualization of the latent alignment state. The initial SS sweep direction is left-to-right in these images. The Fourier transforms (FT) of corresponding large-area SEMs help to characterize the observed morphology. The upper row shows how a rapidly sheared film can be processed using LZA into a well-aligned morphology. The lower row shows how isotropic oven annealing can similarly develop a uniaxially aligned morphology. The film morphology immediately after rapid-shear (upper left) is highly disordered. Yet, the morphology is weakly distorted by the shearing, as confirmed by the anisotropy of the FT at the q-value corresponding to the morphology. (500 nm scale bar applies to all images.)

χ (T ) = χS +

χH T

to describe the energy penalty inherent to states where phaseseparation has not occurred (e.g., spin-cast). That is, W → 0 represents segregation of the two blocks, minimizing energy, while large W represents a state where the two blocks are mixed. Another contribution to the total energy of the morphology comes from the morphological defects (dislocations, disclinations, etc.), which have a size of ∼L0. In addition to point-defects, the grain boundaries are also defective; both incur energy penalties. In a theoretical study, Kim et al. quantified the thermodynamic and kinetic aspects of defectivity.50 Each defect incurs an energy penalty of order 10−150 kBT. Elimination of a single defect involves a pathway with 1−4 energy barriers, of height ∼1−20 kBT. Overall, this suggests that the extrinsic energy with respect to number-ofdefects is roughly linear, with a succession of energy barriers superimposed. Herein, we quantify order using the orientational correlation length, ξ, which has an inverse relationship to

(1)

PS-b-PMMA has a relatively weak temperature-dependence:44 χS = 0.028, χH = 3.9. The interfacial width in BCP phases, W, is regulated by this segregation strength. Specifically:47−49 a W= 6χ (2) where a is the polymer statistical segment length. From this, we can write χH T= 2 (a /6W 2 − χS ) (3) Equation 3 describes the temperature require to thermally broaden the BCP interfaces to a breadth W. We can thus postulate an energetic term of a similar form (multiplied by kB), E

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Nano Letters defect density, ρd ∼ 2/(L0ξ). We can sum the two energy contributions to yield a total energy for the morphology, E. This is plotted schematically in Figure 6 (where we have used arbitrary choices of scaling-values in order to highlight the structure of the energy landscape).

Viewed within the energy landscape, this excellent order is inescapable once latent alignment is induced: the strong driving force of phase-separation rapidly drives the system toward highly ordered part of the landscape. The rapid shearing is thus crucial in that this latent alignment must be induced before substantial phase-separation has taken place. It is thus important to emphasize that reversing the order of processing steps (e.g., LZA followed by ultrarapid SS-LZA) does not yield the same final state. More generally, any preexisting morphological order makes the film unresponsive to the latent alignment effect (Supplementary Figure S6), since assembly is hindered by numerous energy barriers. In other words, the assembly is strongly path-dependent. We can exploit this pathway-based understanding to efficiently order other BCP materials. Figure 7 shows thin

Figure 6. Proposed explanation for latent alignment effect. The central graph represents an energy surface for block copolymer ordering. The form of the graph is based on the equations given in the main text; nevertheless, it should be regarded as schematic only, as scaling values have been selected to highlight features of interest. Ordering proceeds along two axes: phase-separation of the two chemical components of the BCP (characterized by interfacial width W) and ordering of the material through defect annihilation and thus growth of the correlation length (ξ). Different processing pathways are sketched. Conventional oven annealing induces rapid phase-separation, with subsequent graingrowth kinetically hindered by numerous energy-barriers (left). Rapid preshearing of a film, on the other hand, establishes long-range orientational correlations (large ξ), before phase-separation completes; subsequent thermal annealing inevitably generates an aligned morphology (right).

Block copolymer assembly proceeds along two axes: phaseseparation of the two block components, and ordering of the morphology. Different pathways through this space are possible. In conventional oven annealing (and LZA), the disordered as-cast film is thermally excited, conferring to the polymer the mobility required to rearrange and relax from the highly nonequilibrium configurations that result from spincoating. The system naturally proceeds along the steepest trajectory of the energy-landscape, which induces rapid phaseseparation, and the formation of a large collection of very small grains. As this polygrain sample anneals, defects annihilate, grains coarsen, and order improves. Yet the film is now following a trajectory mired by an interminable succession of energy barriers. These barriers slow the ordering process. Moreover, as film defect density decreases, it requires everlonger time scales for sufficient defect diffusion to lead to further annihilations. Experimentally, many BCP systems, even after hours or days of oven annealing, only exhibit grain sizes of microns or smaller. Figure 6 shows the alternative two-step pathway described herein. The as-cast film, subjected to a very short, but very intense, shear-field, is essentially driven toward the large-ξ part of the energy-space. Although the morphology has yet to develop, ξ can be thought of as the orientational correlation among stretched disordered domains. This state thus exhibits alignment but weak morphological orderwe refer to this as “latent alignment”. Thermal annealing from this state rapidly generates a uniaxially aligned morphology, and thus exceptionally large grain sizes with very low defect density.

Figure 7. Efficient ordering of PS-b-PMMA BCPs of different molecular weights. The discovered efficient ordering pathway can be applied to various materials. PS-b-PMMA with very high molecular weights (difficult to order with conventional oven annealing) were rapidly ordered (∼20 s).

films (170 nm) of PS-b-PMMA of different molecular weights. High molecular-weight BCPs are frequently difficult to order: the slower chain dynamics and increased entanglements that accompany longer polymer chains serve to significantly arrest the kinetics. Here, by using a single SS-LZA sweep, followed by thermal processing via LZA, we are able to achieve good order in high molecular-weight materials rapidly (∼20 s total annealing). This level of order would be impossible with conventional oven annealing (within a reasonable time frame). In summary, we have demonstrated an aspect of pathwaydependent assembly in block copolymer thin films. Conventional annealing leads to rapid phase-separation, followed by slow grain coarsening due to the kinetics of defect diffusion and annihilation. In contrast, an ultrarapid shearing step can be used to induce latent alignment in a BCP film, even without the formation of a well-defined morphology. This latent order can then be rapidly developed, via thermal annealing, into a uniaxially aligned morphology with exceptionally low defect density. This effect can be understood in terms of the energy landscape, where one bypasses the kinetic barriers of defect F

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Nano Letters annihilation, and instead primes a film to inescapably evolve toward monodomain ordering. This improved understanding of pathway-dependent processing in block copolymer films should have broader implications with respect to understandingand exploitingnonequilibrium effects in self-assembly. Methods. Polymer Films. Substrates were 1 mm thick glass (BK-7 FisherFinest) slides coated with 100 nm of germanium (Ar-plasma sputtered), which acts as a light-absorbing layer. Cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) materials were obtained from Polymer Source, Inc.; we predominantly report results for material with total molecular weight 49.1 kg/mol (31.6−17.5 kg/mol, PDI = 1.06, minority volume fraction f PMMA = 0.33). Films were spin-cast from toluene solutions (∼3% by weight, 1000 rpm) to yield films ∼170 nm thick. Films were dried under vacuum at 60 °C for 4 h to remove residual solvent.51 Samples were diced into 12 × 12 mm2 squares. Oven Annealing. Isotropic thermal treatment was performed in a vacuum-oven; annealing temperatures (±2 °C) were verified independently using a thermocouple at the sample position. Laser Zone Annealing. We have previously reported the laser zone annealing (LZA) setup in detail.36 Briefly, a highpower (3W) green (532 nm) laser (Melles Griot 85 GHS 309) was focused using a lens system into a sharp line at the sample position (20 μm fwhm × ∼20 mm breadth). The laser-light is absorbed by the Ge substrate layer, leading to local heating and thermal gradients. The sample is translated through the laserline; thus a “thermal zone” is effectively swept through the film. Because of the nontrivial thermal history experienced by any given film location (temporally experiencing a spike in temperature, while being exposed to in-plane thermal gradients), we opt to characterize the annealing conditions using the half-height of the thermal spike. The thermal zone has a fwhm of ∼90 μm, a characteristic temperature (at halfmaximum) of THM ≈ 270 °C, and induces thermal gradients of ∇THM ≈ 1500 °C/mm. The annealing temperature can also be adjusted using the Ge thickness, the laser power, and/or the base-plate temperature. The effective annealing time depends on the sweep velocity (and the number of repeated sweeps). Soft-Shear LZA. For soft-shear (SS) experiments, polydimethylsiloxane pads (PDMS, Sylgard 184 with 5:1 mix ratio, vacuum-cured at 80 °C for 24 h) of 0.5 mm thickness were cut to match the size of the substrates and placed on top of the polymer films. The PDMS naturally achieves conformal contact with the BCP top-surface. Samples were then processed using LZA; the soft elastic PDMS cladding undergoes differential thermal expansion (with respect to the rigid glass substrate), generating shear-fields in the polymer thin film. The PDMS pad was removed from the samples immediately following SS-LZA processing. Thus, any modification to the PDMS layer due to SS-LZA sweep (cross-linking, buildup of residual stress, etc.) cannot influence subsequent film processing steps. GISAXS. Grazing-incidence small-angle X-ray scattering (GISAXS) measurements were performed at the X9 undulator beamline of the National Synchrotron Light Source at Brookhaven National Laboratory. Two-dimensional scattering images were collected using a fiber-taper charge-coupled device (MarCCD) or a hybrid pixel-array detector (Dectris Pilatus 1M). Samples were measured under vacuum using an X-ray beam of 13.5 keV (λ = 0.0918 nm). GISAXS data were collected across a range of incidence angles (0.07−0.20°). The data presented in the manuscript are for 0.12° (the structures

implied by GISAXS were not dependent on incident angle). The X-ray beam was focused using a KB mirror system to a spot 150 μm wide × 50 μm tall. Owing to the grazing-incidence geometry, the projected beam size along the beam (24 mm) overilluminates the sample (12 mm). The overall beam footprint is thus 0.15 mm × 12 mm =1.8 mm2. Silver behenate powder was used as a standard for data conversion to q-space. A laser-beam reflected from the sample surface was used to level each sample, with respect to the ϕ-rotation stage, to ensure that the samples remained aligned with the X-ray beam during inplane rotations. This proper alignment was confirmed both by ensuring that the reflected laser-beam was invariant upon rotation, and that the GISAXS patterns (e.g., position of Yoneda band) were similarly stable upon large rotation (±90°). Average grain size was estimated using a Scherrer peak width analysis to compute the in-plane correlation length, after accounting for peak broadening contributions from instrumental and grazing-incidence aspects.52 The instrumental resolution (standard deviation ∼0.0003 Å−1) implies an error to estimates of realspace distances on the order of ±0.4 nm. SEM. Thin film surface morphology of samples was characterized using scanning electron microscopy (SEM). After UV-irradiation and removal of the top layer (∼10 nm) of polymer by brief O2 plasma treatment (Nordson CS-1701, 100 mT, 20 W), samples were imaged using a Hitachi S-4800 SEM. High resolution (2560 × 1920 pixels) images at a magnification of 25 000× were used in the FFT analysis of azimuthal grain orientation. Images were analyzed in order to quantify the quality of morphological ordering and alignment. To estimate the in-plane orientational correlation length (ξ), we use local image gradients to compute an orientation map and then fit the average spatial decay of the orientation correlation to an exponential function.16,17,36 The histogram of orientations was analyzed to compute the Hermans orientational order parameter (S). For this metric, S = 1 indicates perfect uniaxial alignment, and S = 0 indicates a random (isotropic) orientation distribution. The reported measurements average over 3−10 different images. We estimate the areal density of topological defects (ρd), i.e., disclinations or dislocations, by manually identifying these features in representative images, and normalizing by total image area.

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ASSOCIATED CONTENT

S Supporting Information *

Wide-area SEM images of aligned and latent states, including quantification of order, along with images of the stages of alternate ordering pathways, are provided. Graphs of the energetics of BCP ordering are also included. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b01463.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Research carried out at the Center for Functional Nanomaterials, and National Synchrotron Light Source, Brookhaven National Laboratory, which are supported by the U.S. G

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Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-SC0012704.

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DOI: 10.1021/acs.nanolett.5b01463 Nano Lett. XXXX, XXX, XXX−XXX