Shear-Aligned Block Copolymer Monolayers as Seeds To Control the

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Shear-Aligned Block Copolymer Monolayers as Seeds To Control the Orientational Order in Cylinder-Forming Block Copolymer Thin Films Anabella A. Abate,† Giang Thi Vu,‡ Aldo D. Pezzutti,† Nicolás A. García,† Raleigh L. Davis,§ Friederike Schmid,‡ Richard A. Register,§ and Daniel A. Vega*,† †

Instituto de Física del Sur (IFISUR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional del Sur, 8000 Bahía Blanca, Argentina ‡ Institut für Physik, Johannes Gutenberg Universität Mainz, Staudinger Weg 7, D-55099 Mainz, Germany § Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, United States S Supporting Information *

ABSTRACT: We study the dynamics of coarsening of a cylinderforming block copolymer thin film deposited on a prepatterned substrate made of a well-ordered block copolymer monolayer. During thermal annealing the shear-aligned bottom layer drives extinction of the disclinations and promotes a strong orientational correlation, disturbed only by dislocations and undulations along the cylinders of the minority phase. The thin film bilayer system remains stable during annealing, in agreement with self-consistent field theory results that indicate that although the thickness of a stack of two monolayers is not at the optimum thickness condition, it is very close to equilibrium. Phase field simulations indicate that the bottom layer remains undisturbed during annealing and acts as a periodic external field that stabilizes the orientation of those domains that share its orientation. Misoriented cylinders are rapidly reorganized through an instability mechanism that drives the fragmentation of the cylinders. As annealing proceeds, the fragmented cylinders are reconstructed along the direction imposed by the ordered bottom layer. This mechanism removes the disclinations completely while leaving dislocations that can be slowly annihilated during annealing. These results indicate that with appropriate control over a single self-assembling polymeric layer, it should be possible to propagate order in thick block copolymer films and to obtain structures with controlled orientational order.

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INTRODUCTION Block copolymers have gained increasing attention due to their inherent capacity to self-assemble into well-defined periodic nanostructures, a key requirement for many nanofabrication technologies and the miniaturization of electronic devices. As self-assembly is typically low cost, fast, and easily scalable, it is quite attractive for large-scale applications. However, one of the main drawbacks of the self-assembly strategy is the lack of longrange order due to the presence of defects; consequently, significant effort has been devoted to producing well-defined orientational or positional order in thin films for their potential use in nanopatterning applications.1−9 Numerous methods have been developed to impart such order in both the in-plane and out-of-plane directions,4,10,11 including various zone annealing strategies,9,12,13 the use of external fields,3,14−16 and modifying the local or global substrate chemistry or topography.5,17−21 One technique in particular, shear alignment, has been shown to impart strong in-plane alignment to block copolymer thin films.3,22−24 In thin films, the application of shear stress promotes the elimination of defects and preferential orientation © XXXX American Chemical Society

in the direction of applied shear. Angelescu et al. achieved alignment in monolayers of a cylinder-forming block copolymer by placing a smooth, cross-linked poly(dimethylsiloxane) pad in contact with the film and applying a lateral force.3 Given sufficient stress, the cylinders align in the shear direction over the entire area under the pad. This technique has been further shown to align certain cylinder-,25−28 sphere-,29,30 and lamellaeforming16 block copolymers. Up to now, significant effort has been dedicated to controlling quasi-two-dimensional block copolymer thin film systems developing mainly hexagonal or smectic symmetries.26,31 However, the ability of block copolymers to selfassemble into a diversity of three-dimensional (3D) structures with different symmetries suggests that it should be possible to use these systems to obtain templates for 3D nanofabrication.32−42 As the self-assembly of block copolymers in 3D presents similar drawbacks as in 2D, that is, spontaneous selfReceived: April 19, 2016 Revised: September 12, 2016

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DOI: 10.1021/acs.macromol.6b00816 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules organization always leaves defects43 that for most applications should be avoided,44,45 it is important to develop novel strategies to control order and to understand the physics behind the mechanisms that drive toward the equilibrium state. The chief aim of the present work is to investigate the use of well-ordered block copolymer monolayers as seeds to induce order in block copolymer thin films with the same chemical structure. The coupling between aligned and nonaligned layers is studied in a bilayer of a cylinder-forming poly(styrene)poly(n-hexyl methacrylate), PS−PHMA, diblock copolymer. A multistep approach that includes shear alignment, thin film liftoff, and stacking is employed to obtain the bilayer system while atomic force microscopy (AFM) is used to characterize the morphology of the films. The stability of the bilayer block copolymer thin film against the formation of holes and islands is analyzed through self-consistent field theory calculations while the kinetics of ordering and coupling between the aligned and nonaligned layers are studied through a phase field model that emulates the symmetry and initial configurations of the bilayer systems explored through the experimental setup.

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Figure 1. Schematic of the sample preparation method. (a) Shear alignment of a spin-coated monolayer of a cylinder-forming diblock copolymer, (b) spin-coating of the second layer onto a sacrificial layer of PSS, (c) the block copolymer is floated off in water, and (d) the floated film is redeposited onto the shear-aligned pattern.

EXPERIMENTAL SECTION

Polymer Synthesis. The cylinder-forming PS−PHMA 33/78 diblock employed here was synthesized via sequential living anionic polymerization of styrene and n-hexyl methacrylate, in tetrahydrofuran at −78 °C, using 10 equiv of LiCl to sec-butyllithium initiator and had number-average block molar masses of 33 and 78 kg/mol for PS and PHMA, respectively, and diblock dispersity D = 1.06.25 At 150 °C, the PS volume fraction is 0.28, and the segregation strength χN is estimated to be 32.46 As this work requires floating a polymer on a water surface, we employed a sacrificial layer of a water-soluble polymer: poly(4-styrenesulfonic acid), PSS (Sigma-Aldrich), with a weight-average molecular weight of 75 kg/mol. The PSS was obtained as an 18 wt % aqueous solution; the solution was evaporated to near dryness.27 Sample Preparation and Shear Alignment. The samples consisted of a bilayer block copolymer system where the first (bottom) layer is shear-aligned and the second (upper) layer is nonaligned and characterized by having short-range order. The process flow that describes the steps involved in the sample preparation is shown in the four panels of Figure 1: (a) spin-coating onto a silicon wafer and shear alignment of the bottom layer, (b) spin-coating of the second layer onto a sacrificial layer of PSS, (c) liftoff in water of the second layer, and (d) redeposition of the floated film onto the wellordered bottom monolayer. The first monolayer of block copolymer was produced by spincoating a solution of PS−PHMA in toluene (∼1 wt %) onto a silicon wafer (SiliconQuest, with native oxide). For this system the PHMA matrix wets both substrate and air interfaces.46 The silicon wafer was prewashed with toluene and dried under flowing nitrogen prior to use. After deposition, the thin film was shear-aligned on a hot plate at 150 °C using 10 kPa of pressure and 5 kPa of shear stress, applied through a 1 × 1 cm2 cross-linked polydimethylsiloxane (PDMS) pad for 30 min, after which the system was cooled back to room temperature with the applied stress still in place, thus fixing the postshear morphology.27 A schematic of this setup is shown in Figure 1a. For the second layer, a solution of PSS in 2-propanol (∼2 wt %) was spin-coated onto a silicon wafer, and then the PS−PHMA copolymer was deposited over the layer of PSS, as shown in Figure 1b. The film was annealed on a hot plate at 150 °C to stabilize the films and to relax any elastic distortions introduced during the spin-coating procedure. The silicon− PSS−(PS−PHMA) multilayer was introduced into a Petri dish containing deionized water, at an angle of about 45° to the water surface (see ref 27 for more details). As the PSS is a water-soluble polymer, it acts as sacrificial layer that allows the block copolymer thin film to be floated off (Figure 1c). The floating thin film was immediately picked up from below the water surface using the

supported sample of PS−PHMA film already shear-aligned, as described in Figure 1d. Previous results indicates that although the interlayer region may contain some contamination from PSS residuals, their content must be small. By measuring the step height near an edge of the top layer, it was found that the thickness of the top film was consistent with the film thickness measured through ellipsometry prior to water liftoff. The step height near an edge between the bottom and top layers was also imaged through SEM, where it were observed no indications of the presence of any contaminants between layers.27 The stack of the two layers was then thermally treated at different annealing times to explore the coupling between the aligned and nonaligned layers. Imaging and Analysis. Polymer film thicknesses were measured using a PHE101 ellipsometer (Angstrom Advanced Inc.; wavelength = 632.8 nm). The morphology was characterized at room temperature using an atomic force microscope (Innova, Bruker) operated in tapping mode using uncoated Si tips having a cantilever length of 125 μm, spring constant of 40 N/m, and resonant frequency of 60−90 kHz, purchased from NanoWorld. Since the PS cylinders are glassy and the PHMA matrix rubbery at room temperature, phase imaging of the films reveals the underlying structure and orientation of the cylindrical microdomains. All images were taken at 512 × 512 pixel resolution with a scan size of 2−3 μm × 2−3 μm. To improve image quality, the micrographs were flattened and filtered by performing a discrete Fourier transform to remove high- and low-frequency noise and transforming back to real space.

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RESULTS AND DISCUSSION Figure 2 shows tapping-mode atomic force microscopy (AFM) phase images of the bottom and upper layers of the block copolymer stack prior to thermal annealing. In these images the light (PS) and dark (PHMA) regions correspond to the regions of each of the two polymer blocks. It was found that the average repeat spacing (distance between cylindrical domains) for this diblock copolymer is 45 nm, as measured on both layers by AFM,47 and that the cylinders adopt a configuration parallel to their corresponding substrates due to the interfacial energy differences between the chemically dissimilar blocks. The individual layers of the diblock copolymer develop a smectic symmetry characterized by a local orientation specified by a B


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by the diffusion of dislocations. In these systems it was found that the annihilation of complex arrays of disclinations (multipoles) prevails over the annihilation of dipoles of disclinations and that the correlation lengths obtained through the densities of disclinations and dislocations also follow a power law with the same exponent as the orientational correlation length.1,48 Figure 4 shows AFM phase images of the pattern configuration of the upper layer at different annealing times.

Figure 2. (a) AFM phase image of shear-aligned cylinder-forming PS− PHMA 33/78 deposited at monolayer thickness onto a bare silicon wafer, (b) schematic of the bilayer film, where nonaligned cylinders rest on a monolayer of shear-aligned cylinders, and (c) AFM phase image of the second, nonaligned layer. The average intercylinder spacing for the diblock is 45 nm. Image sizes: 1.5 μm × 1.5 μm.

director field.48 In the smectic phase, defects involve distortions in the director field that are typically referred to as disclinations and dislocations.20,48−50 Figure 3 shows the typical topological

Figure 3. Typical topological defects that disrupt order in smectic systems. These defect configurations were obtained through twodimensional simulations with a phase field model. Panels a and b correspond to positive and negative 1/2 disclinations, respectively.48,51 Disclinations involve rotations of the director field about the disclination core and destroy the orientational order. Panel c shows a less energetic defect, known as a dislocation.

defects that appear in block copolymer systems. Although other topological defects are possible, like ±1 disclinations, they are highly energetic and rarely observed in experiments.48,51 Observe in Figure 3 that while disclinations destroy the orientational order, dislocations break the translational order and also introduce small distortions in the director orientation. The left panel of Figure 2 shows the excellent orientational and translational order in the shear-aligned monolayer and the complete absence of disclinations; in agreement with previous results,25−28 here we also found that the shear-aligned patterns exhibit long-range orientational order, disrupted only by a very small density of dislocations and long-wavelength elastic distortions. On the other hand, although the pattern corresponding to the upper layer (see the schematic representation of the experimental setup in the central panel of Figure 2) shows a very strong length scale selectivity imposed by the radius of gyration of the diblock, it exhibits only short-range order and poor connectivity between the PS cylinders of the minority phase. In addition, these patterns are also characterized by the presence of disclinations that destroy the orientational order and by a high density of dislocations. In order to explore the coupling between both layers, the system was annealed under vacuum at 150 °C for different times. As the bottom layer cannot be visualized through tapping mode AFM, here we focus on the pattern configuration of the upper layer. Previously, it has been found that in planar systems with smectic symmetry the orientational correlation length of the domains ξ2 increases according to a power law ξ2 ∼ t1/4.1,48 In this case, the orientational correlation length is controlled by the density of disclinations, whose annihilation rate is mediated

Figure 4. AFM phase image of the second layer after annealing at 150 °C in vacuum for t = 2 h (panel a), 6 h (panel b), 16 h (panel c), and 24 h (panel d). Panels b−d show the AFM phase image (grayscale) overlaid with the orientational color maps associated with the smectic patterns. Color code for both orientational maps indicated in the bottom right corner. The AFM images correspond to different bilayers rather than to a single bilayer annealed and imaged sequentially. Image sizes: 2.0 μm × 2.0 μm.

Observe in the upper left panel of Figure 4 that after a short time of annealing the initial structure of the cylinders shown in Figure 2 is reorganized into a pattern containing both cylinders and dots and that the regions with a dotted structure present no clear evidence of a well-defined symmetry. Note also that in the bilayer system explored here the smectic symmetry could only be fulfilled as a two-dimensional realization of the individual monolayers while the hexagonal packing cannot be fully developed as the film only contains two layers. As annealing proceeds, the interaction between the shearaligned and nonaligned layers drives the complete annihilation of disclinations and promotes the connectivity between cylinders, increasing dramatically the orientational order and the correlation with the bottom pattern. In addition, there is a reduction in the density of dislocations, and much improved orientational and translational order. Note that the mechanism of ordering in this system must be completely different from the one observed in smectics without a guiding field,1,48 as here disclinations are absent. For smectic patterns, the degree of orientational order can be quantified via an orientational order parameter: C


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Macromolecules Υ(r) = exp[2i(θ(r) − θ0)]

(1)

where θ(r) is the local orientation of the stripe pattern (cylinder axis) at a particular position r. Here r is the in-plane position, r = xi + yj, with i and j the basis Cartesian vectors, and θ0 is the shear direction of the bottom layer. The factor of 2 is required for the 2-fold symmetry of the pattern. Note that a value Υ(r) = 1 corresponds to perfect alignment of the pattern (cylinder axes) with the shear direction. The local orientation of the layers θ(r) can be obtained from the AFM phase image through the gradient method described elsewhere.48 Although in our case the orientation of the bottom layer after thermal annealing was not measured, we consider that it remains the same as prior to annealing. This assumption is supported by simulations (see below) and energetic considerations. During annealing the layers are competing with each other to impose a local orientation. Note that any orientational distortion of the bottom layer driven by the nonaligned layer must imply a stretching and eventually breaking of the bottom cylinders. Thus, as the bottom layer is well ordered and closer to equilibrium, its undistorted cylinders are more stable and can drive the alignment of the poorly ordered cylinders in the upper layer. Note that it is possible that the dislocations present in the bottom layer could move during annealing and interact with the upper layer. However, as the density of dislocations in the bottom layer is relatively small (average distance between dislocations ∼200 nm) and its strain field must be partially screened by the upper layer (at least during the early stage of coupling), it can be expected a very slow rate of dislocation annihilation within the time window explored in our experiments. Figure 4 shows the orientational maps corresponding to the upper layer at different annealing times. Note that as annealing proceeds there is a reduction in the density of dislocations that implies an improvement in the degree of orientational order. Through the orientational order parameter we can also define an orientational correlation function g2(r): g2(r ) = ⟨Υ(0)Υ*(r)⟩

Figure 5. Orientational correlation function g2(r) for the initial lower (shear-aligned) and upper (disordered) layers and for the top layer in the bilayer after different annealing times tann (symbols indicated in the figure).

result is in rough agreement with previous results, where it was found that even in well-ordered defect-free smectics there are undulations of the cylinders which limit ĝ2 below unity,52 in our case the patterns present a lower degree of order. The average degree of order can be quantified through the spatial average of Υ(r).25,52 It was found that even in wellaligned samples Ψ2 = ⟨Υ(r)⟩ is restricted below Ψ2 = 0.999 due to the existence of undulations along the cylinder axis and that Ψ2 decays linearly with the dislocation areal density.25,52 In addition, it was found that the coefficients of the linear relationship between Ψ2 and dislocation density depend on the block copolymer composition.25 In particular, for the block copolymer system studied here it was found that Ψ2 = 0.999 − 0.0016ρ, where ρ is expressed as the number of dislocations per μm2.25 During the annealing of the bilayer system, the pattern configuration of the upper layer couples to the bottom layer, acting as an external field that breaks the rotational symmetry and drives orientational ordering. At long annealing times there is strong orientational order, where the dislocations are the main source of disturbance to the pattern, breaking the translational order and also the local orientation of the cylinders in the neighborhood of the dislocation core (see Figure 3). Observe in Figure 5 the increment in the degree of order after annealing, as seen through g2(r). The pattern configuration of the upper layer reaches Ψ2 ∼ 0.3, Ψ2 ∼ 0.8, and Ψ2 ∼ 0.84 after 6, 16, and 24 h of annealing, respectively. According to the previous findings of Davis et al.,25 in the sample with the longest annealing this value of Ψ2 corresponds to a dislocation density of ∼100 ± 40 dislocations per μm2 (±1 standard deviation), while here we found ∼200 dislocations per μm2 good agreement, especially considering the low defect densities (up to only ∼5 dislocations per μm2) in the films analyzed by Davis.25 Previously, the activation energies of different mechanisms involved in the process of organization of block copolymer thin films have been measured through different order parameters.13,53,54 However, in our case the determination of an effective activation energy in terms of an order parameter is quite difficult since at the intermediate stage of coarsening the symmetry of the upper layer remains ill defined, and the degree of order can be estimated only at those regions where the cylinders are well-defined. Anyway, a rough estimation of the

(2)

where the angular brackets above imply averaging correlation pairs at a given in-plane distance. Figure 5 shows g 2 (r) corresponding to the initial configuration of the upper (nonaligned) and bottom (shearaligned) layers. Observe that g2(r) for the nonaligned layer decays rapidly to zero at a distance of about ten lattice constants (∼400 nm). This poor orientational correlation results from the defects, which destroy the translational and orientational order.1,48 In the absence of external fields, for block copolymer monolayers developing a smectic symmetry, the order can be improved via annealing. However, the lack of a preferential direction leads g2(r) to decay to zero over large distances, since there is no orientational correlation between distant domains. In this case, the correlation length ξ2 can be estimated from the position r where g2(r) decays to e−1 (ξ2 ∼ 120 nm for the image shown in Figure 2c). The situation is different in shear-aligned systems. Although the orientational correlation between domains decays as r increases, in shear-aligned samples g2(r) reaches a plateau ĝ2 = g2(r → L) different from zero due to existence of a preferential direction that induces correlation between distant domains (here L is the characteristic length scale of the image). Figure 5 shows that ĝ2 ∼ 0.95 for the shear-aligned sample. Although this D


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Figure 6. Grand canonical free energy per area in units of kBT/Rg2 vs film thickness in units of Rg for a cylinder-forming diblock copolymer multilayer confined between two surfaces at copolymer chemical potential μ = 2.5kBT. The minima correspond to the stable monolayer state and the metastable bilayer state. Insets show density profiles of the corresponding states. SCFT calculations predict λ ∼ 3.7Rg for the intercylinder spacing in the bulk.

copolymer system. In addition, the kinetics of ordering are studied through a phase field approach with a conserved order parameter (Cahn−Hilliard dynamics).

activation energies associated with the segmental motion of the chain can be determined through the temperature shift factors obtained from the WLF (Williams, Landel, and Ferry) equation.55 From the WLF equation an effective activation energy ΔH for segmental mobility can be determined as ΔH = 2.03RT2c10c20/(c20 + T − T0)2, where T0 is a reference temperature and c01 and c02 phenomenological constants.55 The reordering kinetics in response to the coupling between layers must be dictated by the diffusion of the diblock molecules. In general, this diffusion process depends on a number of parameters, including the friction coefficients of the individual blocks, average molecular weight, composition, architecture, mechanisms of single chain dynamics, symmetry of the phase-separated structure, and degree of segregation between blocks.56 Previously it was found that the temperature dependence of the correlation length of weakly entangled sphere forming and cylinder forming block copolymer thin films can be well described by the WLF equation.43,48 In both systems, the temperature shift factors were found to coincide with those corresponding to the block with the highest glass transition temperature. Here the average number of entanglements per diblock is about 4.5, similar to the values reported by Harrison et al.,43,48 and the films were thermally annealed well above the Tg of both blocks (for PS homopolymer, Tg = 100 °C, while for PHMA homopolymer, Tg = 8 °C). Thus, the PS segmental mobility is expected to be the dominant factor in the segmental mobility. Considering T = 150 °C and the phenomenological constants for PS (T0 = 373 °C, c01 = 13.7 and c02 = 50.0 °C),48 the estimated value for the effective activation energy for the segmental mobility is ΔH ∼ 230 kJ/mol. In order to explore stability and the coupling between layers, in what follows we analyze through self-consistent field theory (SCFT) calculations the free energy of a multilayer diblock

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SCFT CALCULATIONS In order to analyze the stability of the block copolymer thin film system against the formation of holes and islands, we performed self-consistent field theory calculations57,58 to determine the optimum thickness of multilayers of cylinderforming block copolymer systems. We consider a melt of asymmetric AB diblock copolymers confined between two surfaces that preferentially attract the A-segments of the majority block (see Supporting Information for more details). The confined film of thickness h is constrained between two homogeneous surfaces located at z = 0 and z = h. Periodic boundary conditions are imposed in the other directions. We consider the same strength of interaction between the blocks and both surfaces. Although a more systematic study is required in order to explore in detail the effect of the polymer/substrate and polymer/air interfaces, the SCFT calculations considered here allow a rough estimation of the equilibrium configuration for this system. The incompatibility between blocks is characterized by the product χN, of the Flory−Huggins parameter χ and the number of segments N. Here we consider an asymmetric diblock copolymer thin film with χN = 20 and f = 0.7, f being the volume fraction of the A-block. The calculations are done in the grand canonical ensemble; i.e., the chemical potential μ of the copolymers is kept fixed, and their number adjusts to the film thickness. Figure 6 shows an example of a Gibbs free energy landscape as a function of film thickness. Here the value of the chemical potential (μ = 2.5) was chosen slightly below the value where the film becomes macroscopically thick, μ* = 2.56. The minima correspond to the monolayer state, which is globally stable, and the metastable bilayer state. If one increases the chemical E


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Macromolecules potential, the free energy minima corresponding to multilayers move down relative to the monolayer minimum. However, the bilayer state remains metastable for all μ < μ*. For the monolayer and bilayer systems the optimum intercylinder spacing in lateral direction are respectively λ1 ∼ 3.6Rg and λ2 ∼ 3.7Rg. For this system, the bulk intercylinder spacing is λ ∼ 3.7Rg. Thus, we have λ1/λ ∼ 0.97 for the monolayer and λ2/λ = 1 for the bilayer. These values are in good agreement for those reported by Knoll et al. for a cylinder-forming block copolymer multilayer, where it was found that in thin films the unit cell is stretched perpendicular to the plane of the film, resulting in lateral distances smaller than those in bulk.59 We found that the optimal thickness h for the monolayer correspond to h1L = 3.5Rg, while for the bilayer it becomes h2L = 6.9Rg. Then, for this system we have h2L/h1L ∼ 1.97. This corresponds to the thickness of the block copolymer stacks in the experiments, which is twice the thickness of the individual layers due to the experimental procedure employed here. Consequently, in qualitative agreement with the experimental observations one can expect that a bilayer system with h2L/h1L ∼ 2 should be relatively stable toward the development of holes or islands even during long periods of annealing. We should note that according to the SCF theory, the global equilibrium structure at this copolymer coverage is one where a monolayer film coexists with islands of thick multilayer films. This state is not reached on experimental time scales. However, we expect the second layer to interact with the first layer in the sense that chains interpenetrate and that the cylinders in the second layer accommodate to the local structure of the first layer. The density profiles in the insets in Figure 6 show that the structure of the cylinders changes from squeezed ellipsoids in the monolayer to more circular in the bilayer. (In the bulk, they are fully circular.) Hence, the addition of a second layer slightly changes the structure of the first layer, and this interaction provides a mechanism how a prealigned first layer can help to order the second layer. 3D Simulations. The process of coarsening for diblock copolymer systems can be adequately described by a Cahn− Hilliard model combined with the Ohta−Kawasaki free energy functional60−67 to describe the diblock copolymer bilayer (see Supporting Information for details). This model and similar phase field approaches have been employed to describe a wide diversity of pattern formation phenomena involving competing interactions, including order−order and order−disorder phase transitions, melting, dynamics of coarsening, defect dynamics, and glassy systems.65−71 One of the most important features of this phase field approach is that it is efficient over diffusive time scales and thus allows exploration of the slow dynamics involved in the diffusion and annihilation of topological defects.50,67 Figures 7 and 8 show the coarsening process of a bilayer thin film emulating the experimental system described in Figure 2. Note that at early times the upper layer presents short-range order and a high density of defects but also a strong lengthscale selectivity like the experimental system (see Figure 2c). A comparison of the AFM phase image (Figure 2) and the simulated data indicates good qualitative agreement. To obtain a better comparison with the experimental AFM phase images, rather than considering a level plot through the center of the cylinders, here we integrate the order parameter describing the density fluctuations corresponding to the upper layer along the direction perpendicular to the substrate. In this way, the

Figure 7. Three-dimensional pattern configurations observed through simulations at early (left panel) and late (right panel) times.

Figure 8. Two-dimensional pattern configurations for the upper layer observed through simulations at early (left panel) and late (right panel) annealing times. Observe the similarities of these patterns with those in the experimental system, shown in Figure 2. Note also that after annealing there is a strong orientational coupling with the bottom layer, mainly disrupted by dislocations. During annealing, the bottom layer remains undisturbed.

interfaces are smoothed out, facilitating the comparison with AFM. In agreement with the experiments, as time proceeds the order in the upper layer increases. Observe in Figure 8 the orientational coupling between layers and that order is disrupted only by dislocations while the order of the bottom layer remains undisturbed. The simulations also show that the bottom layer remains undisturbed during annealing, indicating that it cost more energy to disrupt an ordered structure than to move around defects in a disordered structure. By following the evolution of the order parameter during annealing, we identify two different regimes of coarsening during the annealing process. At early times we observe that those cylinders misaligned with respect to the bottom layer suffer an instability that drives their reorientation along the bottom layer’s alignment direction (Figure 9). We found that the reorientation process involves distinct intermediate transformation states, including fragmentation, formation of pearlnecklace-like structures, and reconstruction of the cylinders along the shear direction. The process of reorientation of the cylinders along the direction imposed by the bottom layer is schematized in Figure 10. This process shows features similar to those in the Rayleigh instability72,73 that drives the process of breakage of liquid cylinders due to fluctuations. Rayleigh demonstrated that a liquid cylinder is unstable against sinusoidal perturbations with a wavelength greater than 2πR, where R is the radius of the initial cylinder. Because of minimization of the surface area, a liquid cylinder can break up into spherical drops. However, whereas the Rayleigh instability generally is driven by random fluctuations, here the cylinder undulations are locally driven by the effective field provided by the aligned bottom layer. On the other hand, it is important to emphasize that the phase field F


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dislocations of Burgers vector b= pn, where p is the domain spacing and n is the layer normal. Simulations with the Cahn−Hilliard model indicate that the number of dislocations Nd exhibits a power law dependence on time with a small exponent (Nd ∼ t−0.27±0.2; see also Supporting Information (Figure S1)), consistent with previous findings for monolayers of cylinder forming diblock copolymers48 but involving a completely different mechanism of ordering. Here the ordering process proceeds via the diffusion and annihilation of pairs of dislocations with opposite Burgers vectors, which requires the motion of dislocations through two distinctive mechanisms: climb and glide.34,74−77 Climb is the displacement of the dislocation along the direction of the smectic pattern, perpendicular to the Burgers vector, while glide involves diffusion in the parallel direction. Owing to the smectic pattern, the energy of the dislocation oscillates as a function of its position so that it can move by glide only if the forces overcome the periodic Peierls potential generated by the periodic array of cylinders. In addition to the in-plane Peierls potential, there is also a periodic potential emerging from the bottom layer. It can be expected that this potential also affects the dislocation dynamics during glide. We note also that the potential provided by the bottom layer may also affect the dynamics of climb. Because of its oscillatory nature and the natural commensurability with the bottom layer, the dislocations in the upper layer may be under compressional and dilatational fields that affect the climb dynamics. Note that when a pattern has an optimal wavenumber, in the absence of external fields a dislocation does not move. However, if the wavenumber of the pattern does not coincide with the preferred one due to the compressional and dilatational fields produced by the shear-aligned layer, the dislocation may climb in order to add or remove the extra cylinder associated with a dislocation.

Figure 9. Pattern configurations for the upper layer observed through simulations as seen at short annealing times. The cylinders misaligned with regard to the ordered bottom layer suffer an instability (inset) that drives their fragmentation and reconstruction along the shearalignment direction of the bottom layer (indicated with a red arrow).

Figure 10. Schematic illustration of the transformation pathway from cylindrical domains of the minority phase to pearl-necklace-like domains. The fragmentation and reconstruction of the cylinders allow reorientation of these domains along the direction imposed by the bottom layer.

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CONCLUSIONS In summary, well-ordered monolayer films of cylinder-forming block copolymers can be employed as seeds to induce order in self-assembling block copolymer systems, resembling the process of grapho- or chemo-epitaxy employed to obtain patterns with a low density of topological defects. This process can facilitate the fabrication of well-ordered 3D structures over large areas, and it is a potential complement to conventional grapho- or chemo-epitaxy techniques. The application of this method is not restricted to the production of bilayers, as it would be possible to use well-ordered block copolymers to induce order or to produce new symmetries in systems with different degrees of complexity, including multilayers or stacks of block copolymers with different chemical architectures.

simulations employed here do not consider the molecular details of the block copolymer system. Although the simulations can capture the instability driven by the surface energy of the fluid cylinder, in block copolymer systems there are other effects that add complexity to the process, like the stretching energy of the blocks. This mechanism of pattern organization observed in the simulations is in good agreement with the experimental observations at short and intermediate annealing times. Observe in Figure 4 that after a short time of annealing the upper layer presents features similar to those shown in Figure 9. Note also that after annealing the initial structure of the cylinders shown in Figure 2 is reorganized into a pattern containing both cylinders and dots and that the regions with a dotted structure present no clear evidence of a well- defined symmetry, as expected for the proposed mechanism. In Figure 4 observe also that for intermediate annealing times the pattern presents a multiplicity of dislocations and different elastic distortions but disclinations are absent as in the simulated data. Simulations indicate that once the cylinders are reorganized along the preferential direction imposed by the bottom layer, the long-time process of coarsening occurs via the diffusion and annihilation of dislocations (see also the movies showing the dislocation dynamics in the Supporting Information). Figure 8 also shows the late configuration of the upper layer. Note the qualitative agreement with the experimental pattern configuration shown in Figure 4, disrupted only by the presence of

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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.6b00816. Self-consistent field theory calculations, Cahn−Hilliard dynamic simulations and dislocation dynamics (Figure S1) (PDF) 3D simulation data showing the coupling among aligned and nonaligned layers (AVI) 2D simulation data showing the coupling among aligned and nonaligned layers (AVI) G


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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (D.A.V.). Present Address

N.A.G.: ISC-CNR and Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, 00185, Roma, Italy. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the financial support from the National Science Foundation MRSEC Program through the Princeton Center for Complex Materials (DMR-1420541), Universidad Nacional del Sur, the National Research Council of Argentina (CONICET), and the Deutsche Forschungsgemeinschaft (DFG, Germany). N.A.G. acknowledges support from MIUR Futuro in Ricerca ANISOFT project (RBFR125H0M)

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