Vertical vs Lateral Macrophase Separation in Thin Films of Block

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Vertical vs Lateral Macrophase Separation in Thin Films of Block Copolymer Mixtures: Computer Simulations and GISAXS Experiments Anatoly V. Berezkin,*,† Florian Jung,† Dorthe Posselt,‡ Detlef M. Smilgies,§ and Christine M. Papadakis*,† †

Physik-Department, Physik weicher Materie, Technische Universität München, James-Franck-Strasse 1, 85748 Garching, Germany IMFUFA, Department of Science and Environment, Roskilde University, P. O. Box 260, 4000 Roskilde, Denmark § Cornell High Energy Synchrotron Source (CHESS), Wilson Laboratory, Cornell University, Ithaca, New York 14853, United States ‡

ABSTRACT: Mixtures of two diblock copolymers of very different lengths may feature both macro- and microphase separation; however, not much is known about the mechanisms of separation in diblock copolymer thin films. In the present work, we study thin films of mixtures of two compositionally symmetric block copolymers, both in the one-phase and in the two-phase state, combining coarse-grained molecular simulations (dissipative particle dynamics, DPD) with scattering experiments (grazing-incidence small-angle X-ray scattering, GISAXS). We reveal that the film thickness and selective adsorption of different blocks to the substrate control the distribution of macrophases within the film as well as the orientation of the lamellae therein. In thick films, the mixtures separate in the vertical direction into three layers: Two layers being rich in short copolymers are formed near the film interfaces, whereas a layer being rich in long copolymers is located in the film core. The lamellar orientation in the layers rich in short copolymers is dictated by the surface selectivity, and this orientation only weakly affects the vertical orientation of lamellae in the film core. This provides the opportunity to control the domain orientation in the copolymer films by mixing block copolymers with low-molecular additives instead of relying on a more complicated chemical modification of the substrate. In thinner films, a lateral phase separation appears. KEYWORDS: block copolymers, copolymer mixtures, thin films, computer simulations, dissipative particle dynamics, scattering methods, GISAXS, phase separation

1. INTRODUCTION

ones determined experimentally for polystyrene-b-polyisoprene23,25 and polystyrene-b-polybutadiene.26 Due to a number of possible applications, macro- and microphase separation in thin films from block copolymer mixtures were discussed in several papers.31−40 Some of these studies addressed mixtures of A−B and C−D diblock copolymers,32,34 where three or four chemically different constituting blocks were combined. In other investigations, compositionally asymmetric mixtures were considered.36 We focus here on the simplest mixture, where both diblock copolymers are compositionally symmetric, and contain only two types of monomers, A and B. Under confinement, phase separation in such a system may occur in the vertical (normal) direction to the substrate,35,38 or in the film plane,37 i.e., in the lateral direction. Zhang et al.35 experimentally observed vertical phase separation in mixtures of two compositionally symmetric polystyrene-b-polybutadiene diblock copolymers with a ratio of

Block copolymer thin films feature an enormous morphological diversity1−5 with the morphology depending on the copolymer composition, block segregation strength, film thickness, wetting of the confining walls by the different blocks, and tension at the free film surface. Therefore, block copolymer thin films have attracted growing interest in recent years for their potential applications in nanolithography,6−10 as functional templates for photovoltaics11−13 and functional arrays,14−18 for the fabrication of nanoporous films19,20 and photonics and polarizers,21 and in molecular biology, biomineralization, colloid science, and supramolecular chemistry.22 Binary mixtures from block copolymers provide even broader structural diversity, as known from experimental23−28 and theoretical29−31 studies in the bulk. By simple mixing of two block copolymers, one can control the domain period, vary the morphologies, and even create new structures. If the components have very different molar masses, the mixture may demix into (macro)phases along with the microphase separation. In bulk mixtures of compositionally symmetric copolymers, the theoretically predicted periods and phase compositions30 were found to agree quantitatively with the © XXXX American Chemical Society

Special Issue: Block Copolymers for Nanotechnology Applications Received: December 23, 2016 Accepted: March 9, 2017

A

DOI: 10.1021/acsami.6b16563 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces short-to-long copolymer lengths of 0.13 at a moderate film thickness of 2.3 times the period of the pure thick lamellae. Due to the selectivity of the free film surface to the polybutadiene block, parallel lamellae were observed in the upper layer which was rich in short copolymers, while the thick lamellae dominated by the long copolymers in the film core were vertical. The same vertical separation was found in recent Monte Carlo simulations of Wang et al.38 Here, in mixtures of two alternating multiblock copolymers, the phase rich in short diblock copolymers formed two layers close to the impenetrable, nonselective walls, while the phase rich in long chains was located between, as also shown in some of our simulations discussed later. However, neither this effect nor the role of the film thickness was discussed.38 Lateral phase separation was observed by Williamson and Nealey37 in an experiment on 60 nm thin films from mixtures of polystyrene-b-poly(methyl methacrylate) diblock copolymers on a nonselective substrate. The ratios of chain lengths were 1/ 9.4 and 1/7.3, and the native periods of long copolymer lamellae were 130 and 102 nm, respectively, thus higher than the film thickness. In summary, phase separation results in complex hierarchically organized structures on different length scales, since the morphology,36 the period,36,37 and the orientation35 in the two phases may be different. However, it is not clear yet which conditions determine the direction of phase separation and the lamellar orientation. In the present paper, we demonstrate that the direction of phase separation is controlled by the film thickness and the substrate selectivity. We find that thin films and nonselective substrates facilitate lateral phase separation, while selective substrates and thicker films stabilize vertical separation. We show that the vertical separation is driven by an entropic effect, concentrating short diblock copolymers near the film interfaces. Vertical separation results in one layer rich in long diblock copolymers that is “sandwiched” between two layers rich in short diblock copolymers, adjacent to each of the two film surfaces. The orientation of the lamellae in the phase rich in short diblock copolymers is mostly dictated by the surface selectivities, but the orientations in different phases are “decoupled” and can be orthogonal to each other. Lateral separation in thin films reduces the interface between the phases compared to the vertical one. We establish these conclusions by combining molecular simulations with grazing-incidence small-angle X-ray scattering (GISAXS). For the experiments, we chose polystyrene-bpoly(2-vinylpyridine) because of its high Flory−Huggins segment−segment interaction parameter. Thin films of different mixing ratios and different film thicknesses were investigated and confirm the morphology results from simulations. This work is structured as follows: We describe the simulation technique, the sample system, the GISAXS experiments and the data analysis. Then, we present results from computer simulations on nonselective and selective substrates with dependence on film thickness. Next, the GISAXS results obtained in dependence on composition and film thickness are described. By systematic variation of the composition of the mixture, the film thickness, and the surface selectivity, we obtain a more systematic picture of the structure formation in the films of binary mixtures of symmetric block copolymers.

2. SIMULATION TECHNIQUE 2.1. Dissipative Particle Dynamics. Dissipative particle dynamics (DPD) is a coarse-grained molecular dynamics technique, initially proposed by Hoogerbrugge and Koelman41,42 for the simulation of liquid suspensions and extended to polymer systems by Espanol, Groot, and Warren.43,44 This simulation approach is very popular in the copolymer studies because of the fast relaxation of the modeled systems and its simple mapping onto Flory−Huggins theory.45 In DPD, a single particle represents an extensive fragment of a polymer chain. The particles interact as point-like origins of conservative, dissipative, and random forces, which are pairwise additive. The conservative force includes a “soft” repulsion, responsible for the excluded volume of the molecule, and an attractive force between bonded particles. The amplitude of the repulsion between particles i and j, aij, is proportional to the Flory−Huggins parameter, as discussed later, and the range of repulsive interactions is limited by a certain cutoff radius, rc, that serves as a characteristic length scale. Dissipative and random forces are balanced via the fluctuation−dissipation theorem to keep the temperature of the system constant. The magnitude of these forces is controlled by the amplitude of thermal noise, σ. Since the forces are known, particle motions are governed by Newton’s law that is integrated numerically in small time steps, thus mapping out particle trajectories. DPD chains are Gaussian-like, and neither entanglements nor the glassy state can be reproduced. In the present work, we investigate the equilibrium morphology of the copolymer system, where these limitations are insignificant. Due to the relatively soft interparticle interactions, relaxation of polymeric systems in DPD toward physically meaningful stable morphologies is fast. We used DPD in standard formulation as established by Espanol, Grott, and Warren:43,44 the average density of particles was ρ0 = 3, the repulsion parameter between chemically identical particles was aii = 25, the thermal noise amplitude was σ = 3.0, and the weight function for dissipative and random forces was ω(r) = 1 − r, where r is the distance between particles. The cutoff radius of the conservative force, rc, was used as a characteristic length scale. Beside repulsive forces, bonded particles interact via an attractive spring force, −kr, with the bond constant k = 4. The Newtonian equations of particle motion were solved using the so-called DPD-VV integration scheme46 (modified velocity−Verlet algorithm) with a time step δt = 0.04. 2.2. System. In the simulation box, the bottom layer of the polymer film and the gas above the film were confined by two solid walls, which are impenetrable in the vertical (z) direction, as shown in Figure 1. In the x- and y-directions, periodic boundary conditions were imposed. The box contains three types of particles: particles of types A and B, which constitute the linear diblock copolymer chains (Figure 1), and inert gas particles (G). The short copolymers have NS = 4 beads per chain; i.e., NSA = NSB = 2 beads of type A and B, respectively. The long copolymer has NL = 28 and NLA = NLB = 14. Thus, both copolymers are compositionally symmetric and lamella-forming. The ratio of chain lengths α = NS/NL = 1/7 = 0.143 is close to the experimental value as discussed later. The box size varies from lx × ly × lz = 50 × 50 × 80 rc3 to lx × ly × lz = 115 × 115 × 19 rc3, depending on the film thickness. Usually, the vertical size of the box was lz = h + 10, where h is B


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where T is the absolute temperature and N the degree of polymerization. Thus, at the temperature of the measurements, T = 298 K, χNS = 28.2 and χNL = 194.3. This system can be directly compared to our DPD simulations and to the theoretical bulk phase diagram of Matsen,30 both derived for χNL = 200. Nondoped 0.5 mm thick Si(100) wafers were purchased from SilChem Handelsgesellschaft mbH (Germany). Propylene glycol monomethyl ether acetate (PGMEA; purity ≥ 99.5%) for dissolution and spin-coating of copolymers was purchased from Sigma-Aldrich. Si wafers were cut into squares of 2 × 2 cm2 and cleaned in an acid bath (165 mL of H2SO4 + 85 mL of a 30% aqueous solution of H2O2 + 70 mL of H2O) for 15 min at 80 °C. Then, the wafers were rinsed with water and toluene and were spin-dried. Films of different thicknesses were prepared by spin-coating at 8000 rpm onto the substrate from the block copolymer solutions in PGMEA. The concentrations were in the range from 1 to 6 wt %, resulting in film thicknesses in the range from 40 to 150 nm, as measured by white light interferometry and X-ray reflectometry. To reduce defects in films, the solutions were filtered through a Teflon filter with pore size of 0.2 μm right before spin-coating. To relax defects in the domain structure and to attain equilibrium morphologies, the as-prepared samples were solvent vapor annealed at saturated vapor conditions in a closed chamber for 3 h at 21 °C using a liquid mixture of toluene and dimethylformamide (mixing ratio, 1/1 (v/v)). As demonstrated in a number of experiments,49 rapid film drying tends to orient the domains perpendicularly to the substrate. In the case of mixed films, we slowly opened the lid of the spin-coater to reduce this effect, but it cannot be completely avoided. Since a nonselective surface also facilitates the vertical lamellar orientation, the choice of a nonselective free film surface in our simulations can partially reproduce the effect of film drying, since it leads to similar morphologies. After opening the lid of the chamber, the films were left to dry for several days under ambient conditions. 3.2. Grazing-Incidence Small-Angle X-ray Scattering Experiments. Experiments were carried out at beamline D1 at the Cornell High Energy Synchrotron Source (CHESS) at Cornell University using a wavelength λ = 0.1155 nm (i.e., at an energy of 10.73 keV), a flux of ∼1012 photons/(s·mm2), and a beam cross-section of 0.2 mm × 0.5 mm (H × W). The detector was a CCD camera with a pixel size of 46.9 μm at a sample-to-detector distance of 1845 mm, resulting in a qresolution of 1.414 × 10−3 (nm·pixel)−1 and an accessible range of qy = −0.712 to 0.746 nm−1 and qz = −0.319 to 1.139 nm−1. To protect the detector, the intense reflected beam and the intense scattering in the incident plane were blocked by a rod-shaped beam stop. From the mass densities, the critical angles of total external reflection were expected at αcPS = 0.120° for PS, αcP2VP = 0.113° for P2VP, and αcSi = 0.167° for the Si wafer. For every sample, measurements were done in the surface-sensitive evanescent regime at an incident angle αi = 0.1°, i.e., below all the critical angles, as well as in the dynamic regime at αi = 0.15°, i.e., between the estimated critical angle of the PS-b-P2VP film (αcP = 0.117°) and the substrate (αcSi), to probe the whole internal film structure.50 In the evanescent regime, the wave penetrates the near-surface layer to a depth of about 10 nm,50 so that the specific lateral ordering details of the upper film layer can be probed. In all cases, the exposure time was as short as 0.5 s to prevent beam damage of the samples. 3.3. Analysis of GISAXS Images. The analysis of GISAXS images is discussed in detail in ref 49. Vertical lamellae give rise to vertical Bragg rods (BRs) at characteristic qy values; i.e., the lateral component of the scattering vector, and the lamellar period can be calculated as follows

Figure 1. Schematics of the simulation box.

the film thickness, and the two other dimensions (lx = ly) were chosen such that the system contained lx × ly × lz × ρ0 ≤ 750000 particles, where ρ0 = 3 is the native density of the DPD fluid. The thickness of the copolymer film was varied from 12 rc to 70 rc. In our simulations and experiments, similarly to the theory of Matsen,30 the strong segregation limit (SSL) with the product NLχAB of about 200 was considered. Here, χAB is the Flory− Huggins interaction parameter that is related to the repulsion between particles A and B (aAB) in the DPD simulation via the empirical relationship47 that takes into account a limited chain length, N: χij =

(0.306 ± 0.003)(aij − 25) 1 + 3.9N −0.51

(1)

According to eq 1, we chose the value aAB = 65 that gives NLχAB = 200.1 and NSχAB = 16.75. A strong repulsion between polymer and “gas” with aAG = aBG = 100 served to prevent “evaporation” of the polymer.5 With these parameters, the free film surface is nonselective to chemically different blocks in all the simulations. The substrate selectivity, which affects the lamellar orientation notably, was varied as well: The case of a nonselective substrate with repulsion parameters aWA = aWB = 25 and a substrate strongly selective to block A with aWA = 25 and aWB = 50 were considered, where the subscript “W” means “wall”. The simulations consisted of two steps: simulated thermal annealing and equilibration for 2 × 106 time steps (δt), when aAB grew linearly from 25 to 65, followed by the collection of statistical data during 2 × 106 steps at constant repulsion parameters. At every combination of parameters, we started simulations from three different randomly generated configurations and have found that they give the same results. We also performed preliminary checks on how the box dimensions affect the morphology, because such artifacts are also possible, and found that they have no influence.

3. EXPERIMENTAL SECTION 3.1. Materials and Sample Preparation. Symmetric polystyrene-b-poly(2-vinylpyridine) diblock copolymers (PS-b-P2VP) having equal block molar masses of 57 kg/mol for the long copolymer (Đ = 1.05) and 8.2 kg/mol and 8.3 kg/mol respectively (Đ = 1.09) for the short copolymer were purchased from Polymer Source Inc. (Canada). The overall degrees of polymerization are NS = 158 and NL = 1089 for the short and the long copolymers, respectively. The ratio of low and high polymerization degrees is α = NS/NL = 0.145 = 1/6.9. The Flory−Huggins parameter of PS-b-P2VP is48

χ (T )N = N ((63 K)/T − 0.033)

D⊥ =

2πm qy

(3)

where m is the order of the reflection. Parallel lamellae are identified by diffuse Bragg sheets (DBS) appearing at specific qz values and extending along qy. The lamellar period can be extracted from the DBS’s qz component of the scattering vector using the distorted-wave Born approximation (DWBA) that

(2) C


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ACS Applied Materials & Interfaces accounts for the distortion of the scattered intensity in vertical direction due to reflection and refraction at the film boundaries.49,51 DBSs are expected at the positions

qz = kiz +

kcP

2

⎡ 2πm +⎢ ± ⎣ D=

2

kiz − kcP

2

⎤2 ⎥ ⎦

Dmix = DL xL =

(4)

α + x L(1 − α) [α + x L v + 1(1 − α)]1/(v + 1)

,

α(1 − ϕS) ϕS + α(1 − ϕS)

(5)

Here, DL is the lamellar period of the pure long copolymer in the bulk, and v = 2 in the SSL. At ϕS = 1 and 0, eq 5 gives Dmix = DLα2/3 = DS, and Dmix = DL, i.e., the lamellar periods of the pure short and long copolymers, respectively, according to the scaling of the lamellar period in SSL. Figure 2 shows the theoretical phase diagram of Matsen30 that was quantitatively confirmed in bulk experiments.23,25,26 The mixture compositions explored in our experiments are indicated with yellow points. In the two-phase region, ϕS does not affect the lamellar periods, but only the relative volumes of these phases. Moreover, Figure 2 shows that, similarly to polymer/solvent mixtures, the equilibrium concentration of the long copolymers in the phase of short copolymers is usually quite low, while the equilibrium phase of long copolymers contains a notable fraction of the short copolymers. The question arises, how do confinement and selective interfaces affect the distribution of the macrophases rich in short and rich in long copolymers, respectively, and the lamellar orientations? As shown below, the film thickness influences not only the character of the macrophase separation but also the effective segregation strength, χeffNL, which, in thin films, can become so low that the system is brought into the disordered state. 4.2. Vertical vs Lateral Macrophase Separation: Effect of the Film Thickness. Several experimental investigations have demonstrated that macrophase separation in mixed copolymer films can occur along the vertical axis, i.e., along the film normal,35 or within the film plane, i.e., laterally.37 Figure 3 illustrates these types of phase separation. In the case

Here, kiz = k0 sin(αi) is the z-component of the wave vector of the incoming beam, kcP = k0 sin(αcP) is related to the critical angle of the total external reflection of the polymer film (αcP), and k0 = 2π/λ. In eq 4, “plus” stands for the scattering of the beam reflected off the substrate and “minus” for the scattering of the incident beam before reflection off the substrate. For analyzing the 2D GISAXS data, we used horizontal cuts spanning the whole range of qy values and averaged over the qz range from 0.225 to 0.348 nm−1, which covers the Yoneda peaks50 of the components. Vertical cuts over the whole range of qz values were made as close as possible to qy = 0, but outside the “shadow” from the beamstop. The position of these cuts varied slightly from one sample to another, but generally, the scattered intensity was averaged over the qy range from 0.02 to 0.12 nm−1. In all cases, first-order Bragg reflections in both directions were used for the analysis. To determine the peak positions and the lamellar periods, the peaks in the scattering profiles along qy and qz were fitted with a Lorentzian function.

4. RESULTS AND DISCUSSION 4.1. Macrophase Separation on Nonselective Substrate. According to the self-consistent field theory by Matsen,30 mixtures of two compositionally symmetric diblock copolymers in the bulk can form one or two equilibrium phases, as shown in the phase diagram in Figure 2. Depending

Figure 2. Theoretical phase diagram of the mixture of two symmetric diblock copolymers in the bulk for χNL = 200.30 L and DIS indicate lamellar and disordered phases in the one-phase region, respectively, L + L and L + DIS stand for coexistence of phases rich in long and short copolymers. The values of the short-to-long chain length ratio, α = NS/NL, and the volume fraction of short chains in the mixture, ϕS, chosen for our simulations are marked in the graph in blue. The parameters chosen for our experimental GISAXS studies are marked by yellow points. The phase diagram is adapted with permission from ref 30. Copyright 1995 AIP Publishing.

on the degree of asymmetry and the volume fraction of short copolymers, ϕS, these phases may have an ordered lamellar structure (L) or may be disordered (DIS). In the one-phase region, the lamellar period, Dmix, depends on the ratio of chain lengths, α, and the molar fraction of long chains in the mixture, xL, as follows37

Figure 3. Schematics of lateral and vertical macrophase separation of the copolymer mixture (a) and local distribution of monomers and copolymers of different lengths in the macrophases (b). Dashed lines indicate the boundaries between phases rich in short and long chains. Snapshots are taken from our simulations (see Figure 4). D


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ACS Applied Materials & Interfaces of vertical phase separation, the phases form layers, which are parallel to the substrate. When the macrophase separation occurs in the lateral direction, the interfaces between the macrophases are perpendicular to the substrate, and the phases form irregular “grains”, which can be seen in the top view of the film. While we observe lateral phase separation in thin films, also vertical phase separation appears in thicker films, as discussed below. Both types of separation are found in simulations, while the type of separation occurring in our experiments cannot be decided conclusively. Within the phases, microphase separation results in a lamellar structure. Further, we apply the term “phase” or “grain” to the macrophase rich in either short or long chains; the term “domain” is applied to the individual lamella consisting of one type of monomer. According to the theoretical bulk phase diagram,30 the mixture composition ϕS = 2/3, discussed here, is located in the two-phase region for α = 1/7. Our simulations of thin films between nonselective surfaces show that the character of macrophase separation depends on the film thickness, as seen in Figure 4. In thin films, i.e., at h ≤ 24 rc, grains rich in short

density distribution of long (green) copolymers in this phase oscillates, since the short copolymers (yellow), which are dissolved in this phase, adsorb at the lamellar interfaces and reduce there the local concentration of long copolymers. A similar “surface enrichment” was observed in previous simulations, which were based on self-consistent field theory and dynamic density functional theory.29−31 In the thicker films (at h > 24), a vertical macrophase separation takes place; i.e., a phase rich in short copolymers forms thin layers near the substrate and the free film interface, while the long copolymers are concentrated in the film core, as seen from the vertical density distributions of short copolymers, presented in Figure 5a. The transition from one type of

Figure 4. Snapshots from computer simulations. Long/short and A/B polymer distributions in films of different thicknesses (h) on a nonselective surface. Upper rows: domain structure of A and B blocks (shown in blue and magenta, respectively). Bottom rows: distribution of short and long copolymers (shown in yellow and green, respectively). The figure also depicts “kinks” of the lamellar structure in the boundary region, as discussed in the text.

Figure 5. Volume fraction of short copolymers in mixtures of long and short diblock copolymers in films of different thicknesses on nonselective substrate as a function of position (a), and average number density of monomers of short (solid line) and long (dashed line) chains in film of mixed homopolymers of thickness 30 rc, confined by walls in the z-direction (b). In both graphs, the z-axis originates on the substrate and points up toward the film surface, and the overall volume fraction of short chains is ϕS = 2/3. In panel a, the z-axis is normalized by the film thickness, h. Film thicknesses are given in the graph in panel a. The NS and NL values are given in panel b.

copolymers (yellow islands in Figure 4) are formed in the film plane, penetrating the whole film thickness. A similar morphology was observed by Williamson and Nealey37 in an experiment on thin films from mixtures of polystyrene-bpoly(methyl methacrylate) diblock copolymers on a nonselective substrate. These experiments correspond to the film thicknesses h = 4.5 rc and 5.8 rc in our simulations, i.e., far below the film thickness, where vertical separation occurs in our simulations. Our simulations also disclose a nonhomogeneous chain distribution within the phases rich in long chains. As seen from Figure 4 and especially in the right side of Figure 3b, the

separation to the other does not happen abruptly but takes place over a certain range of film thicknesses, as one can conclude from comparing the curves in Figure 5a. We note that we use the term “vertical macrophase separation” even though the vertical domain size is limited by the thickness of the film. We find that vertical macrophase separation originates from an entropic effect: Short chains concentrate near the film interfaces, since longer copolymers lose more conformational entropy at the same distance from the interface. To illustrate E


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relationship R = h/C, where R is the thickness of the phase, always holds, simply because of the constant composition of the equilibrium phases. The simulations above have demonstrated that the type of macrophase separation (lateral or vertical) strongly depends on the film thickness. Below, we introduce the selectivity of the substrate toward one of the copolymer blocks and find that it has an additional strong impact on both the orientation of the lamellae and the direction of macrophase separation. 4.3. Decoupling of Lamellar Orientations on a Selective Substrate. It is well-known52,53 that selective adsorption of one block, e.g., to the substrate, tends to align the lamellae parallel to the interface, while a nonselective substrate facilitates the perpendicular orientation of lamellae. In pure diblock copolymer thin films, selective adsorption at one film interface usually imposes the parallel lamellar orientation throughout the whole film. Domain reorientation is only possible if the selectivity of the substrate is weak and the period of the lamellar structure is incommensurate with the film thickness.52−55 In mixtures of diblock copolymers in the macrophaseseparated state, which are confined between two differently selective surfaces, different lamellar orientations can coexist, as seen in Figure 6 and from our experiments (see later

this effect, homopolymer mixtures of short and long polymers (of the same lengths as the copolymers above) confined in the z-direction between nonselective solid walls were simulated. The resulting density distributions are shown in Figure 5b. The density of short polymers near the interfaces is about 5% higher than in the film core, despite the absence of any selective adsorption. The thickness of this adsorption layer is expected to be proportional to the end-to-end distance of the short polymers. Since macrophase separation is a first-order, i.e., “strong”, transition, even such a small entropy-driven variation in the initial mixture composition near the film surfaces triggers demixing in the normal direction to the substrate. Due to the smaller interfacial area, thermodynamically it would be more favorable to form a two-layer structure instead of the three-layer structure (short−long−short copolymer phases), seen in Figure 4. Therefore, a two-layer structure was assumed in the theoretical model of Spencer and Matsen.40 In contrast, in our simulations, the conversion of three into two layers does not happen, being hampered by slow large-scale mass transfer. The question of whether the lateral macrophase separation may be kinetically hindered was recently discussed by Spencer and Matsen.40 Upon vertical separation, the copolymers are transferred over distances shorter than the film thickness. In contrast, lateral separation requires more distant mass transfer, which was considered to be kinetically impossible or uncompetitive in ref 40. A high surface tension between the macrophases resulting in a large critical nucleus size was also expected by the authors to make lateral separation difficult. However, our simulations and the experimental results of Williamson and Nealey37 show that lateral separation may indeed appear. First, the macrophase separation may proceed via spinodal decomposition that does not restrict the initial dimensions and composition of the grains, making lateral separation practically possible under strongly non-equilibrium conditions. Second, the surface tension between grains can be reduced by the reconstruction of the domain structure in the interfacial region. This reconstruction is seen in Figure 4 at all film thicknesses as a kink of the lamellae at the boundaries of the phases and the formation of onion-like morphologies within the grains. Recent SCFT simulations of Spencer and Matsen showed39 that kinks of lamellae are indeed thermodynamically more favorable than the parallel orientation of lamellae at the interfaces. Our work is the first independent observation of this effect using particle-based molecular simulations. For a rough estimate of the critical film thickness, at which switching from lateral to vertical macrophase separation takes place, one can use geometrical arguments. At the critical film thickness, the interfacial area is the same in both morphologies. In the “sandwiched” structure, a specific interfacial area per unit area of the substrate surface is σ = constant ≈ 2. For the lateral morphology, one can assume that this area scales linearly with the film thickness and is inversely proportional to the size of the grain of the minor phase, R; i.e., σ ∼ h/R. At the transition point, the areas of these interfaces are equal; i.e., h/R = C, where C is a constant, defined by the geometry of the domains and the volume ratio of the phases. This relation means that, below the critical film thickness, the minimal possible lateral grain size, R, is proportional to the film thickness, h. Larger grains are thermodynamically more stable, but their growth is suppressed by the slow diffusion of chains. As a result, in relatively short simulations, the grains keep their minimal size, which is actually smaller in thinner films, as seen in Figure 4. In thick films, where vertical macrophase separation occurs, the

Figure 6. Domain and copolymer distributions in films of different thicknesses (h) on selective surfaces. Upper row: domain structure of A and B blocks (shown with blue and rose, respectively). Bottom row: distribution of short and long copolymers (shown with yellow and green, respectively).

discussion). In the simulations, the substrate repels block A and effectively attracts block B, while the upper free film surface remains nonselective. As a consequence, in the film featuring vertical macrophase separation (at h ≥ 16), the lamellae close to the substrate are parallel, whereas they are perpendicular near the free film surface. In the thick film core, containing thick lamellae, the two orientations are merged via U-shaped bending, i.e., kinks, of the lamellae. We call the weak effect of the lamellar orientation near the film interface on the lamellar orientation in the film core and in the region close to the other film interface “decoupling of domain orientations”. It is related F


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ACS Applied Materials & Interfaces to an easy reconstruction and kink39 of domains at the interfaces between the phases, resulting in a relatively low interfacial tension of these interfaces and in a loss of long-range correlations in the domain orientation. Decoupling of orientations is potentially important for those applications, where a vertical lamellar orientation in the film core is demanded, despite a pronounced selectivity of the substrate, e.g., in block copolymer nanolithography. In this case, instead of a complex chemical modification of the surface, its effect on the lamellar orientation can be reduced by simple admixing of shorter diblock copolymers to the main (longer) diblock copolymer component to keep the thick lamellae vertical. Comparing Figures 4 and 6, it becomes clear that the effect of the film thickness on the macrophase separation is different on selective and nonselective substrates. The selective substrate facilitates vertical macrophase separation: at h = 16, 20, and 24, the films appear to be vertically separated in Figure 6, while on the nonselective substrates in Figure 4, the phases separate laterally at the same film thicknesses. Moreover, in thin films on selective substrates, no well-defined lamellae appear, but the domains stay disordered (at h = 12 and 16 in Figure 6). The vertical density distribution does not show any order near the free film surface either, as seen in Figure 7. One of the reasons for disordering can be an extremely thin upper layer rich in short chains.

copolymers near the substrate, followed by the macrophase separation. Vertical phase separation is confirmed by the distributions of short copolymers along the film normal shown in Figure 7. Near the substrate (at z ∼ 0), these distributions oscillate between a higher short copolymer particle density in the core of the parallel lamellae and a lower density at the interfaces between the lamellae. A well-defined vertical macrophase separation takes place only up to a moderate film thickness, h ∼ 50. In thicker films, the interface between macrophases strongly oscillates, as seen in Figure 7, and separate grains rich in short copolymers in the phase rich in long copolymers can exist, e.g., at h = 70. We conclude from the simulations that the selectivity of the substrate facilitates vertical macrophase separation in films of mixtures of diblock copolymers. In very thin films, such enforced vertical separation leads to disordering of the phase rich in short copolymers. In thicker films, the lamellar orientations near the film interfaces are governed by their selectivity and do not correlate to each other; i.e., they stay “decoupled”. This offers an opportunity for mixed morphologies which combine orthogonally oriented domains. 4.4. Elevated Miscibility of Short and Long Copolymers upon Confinement. We estimated the relative volume of the phase rich in short copolymers, ΦS, and found the composition of equilibrium phases in films of different thicknesses on selective respective nonselective substrates. The results are presented in Figure 8 together with theoretical

Figure 7. Volume fraction of short copolymers in the mixed film on a selective substrate. z-axis originates on the substrate and points up. The z-scale is normalized to the film thickness, h. Film thicknesses are given in the graph.

The vertical macrophase separation, accompanied by an orthogonal orientation of lamellae in two phases was observed by Zhang et al. at α = 0.13. The native period of lamellae of long copolymers was DL = 82 nm and the film thickness h = 189 nm.35 The latter corresponds to the film thickness h = 20.6 rc in our simulations. In this experiment,35 parallel lamellae appeared in the upper layer being rich in short copolymers (due to the selectivity of the free film surface to the polybutadiene block), while the thick lamellae in the film core were vertical. Our simulations, presented in Figure 6, lead us to assume that the film in ref 35, as well as in our experiment (see below), does not consist of two layers, but rather three layers. The layer rich in short copolymers, located near the substrate, could, however, not be distinguished from the upper layer of the short copolymer phase in the GISAXS maps nor could it be seen in AFM images. From a theoretical point of view, this layer should appear due to the entropy-driven concentration of short

Figure 8. Volume fraction of the phase rich in short copolymers (a) and the equilibrium volume fractions of short chains in the two-phase mixture (b) in dependence on the film thickness (the total volume fraction of short copolymers in the mixture is ϕS = 2/3). Different colors correspond to nonselective and selective substrate, as indicated in panel a.

predictions for the bulk.30 Theory predicts equilibrium compositions of the two phases ϕS* = 0.39 and 0.93, while, in simulations of thin films, the two-phase region is more narrow: ϕ*S = 0.47 and 0.94. Thus, the fraction of short copolymers in the phase rich in long copolymers is higher than in bulk theory,30 and the same effect appears in our experiment (see later text). We attribute this change of the phase diagram to the G


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ACS Applied Materials & Interfaces contribution of the interfacial tension between grains to the free energy of the system. Considering the interfacial tension, one should bear in mind the complex internal morphology of the phases. The simulation snapshots in Figures 4 and 6 show that the domain morphologies are reconstructed at the interface to reduce the interfacial tension. In this case, the theoretical estimate of the interfacial free energy may get complicated. In particular, transitional morphologies with broad interphases between the phases may occur, as seen in Figures 5 and 7. Such morphologies, reducing the interfacial tension, lead to strong thermal fluctuations of the interface, which are clearly seen at h ≥ 30 in Figures 4 and 6, and introduce large-scale defects in thicker films. Figure 8a shows the volume fraction of the phase rich in short chains in the two-phase film, while Figure 8b shows the volume fractions of short chains in the two equilibrium phases of the film. It is seen that, with increasing film thickness, the volume ratio of the phases (Figure 8a) and the phase compositions (Figure 8b) slowly drift toward the bulk values. The selectivity of the substrate only has a weak effect on the phase diagram; it slightly increases the miscibility of the copolymers at h ≤ 24. The observed shift of the phase boundaries reduces the difference between lamellar periods in the coexisting phases. At ϕS = 2/3, the bulk theory30 predicts the ratio of these periods to be D*L ,theor/D*S ,theor = 1.96, while in our thin film simulations at the film thickness h = 70, the periods are DL* = 9.3 and DS* = 5.3 and their ratio is DL*/DS* = 1.75. Summarizing this section, the compositions of the two phases under confinement are closer to each other than in the bulk, and the two-phase region in the phase diagram in the film is smaller. This agrees with previous experimental 37 and theoretical40 results showing an increased miscibility of short and long copolymers upon conf inement. We agree with Spencer and Matsen,40 who attributed this finding to the effect of the interfacial tension between the macrophases on the phase diagram. 4.5. Effect of the Mixture Composition As Seen in Experimental Investigations. Our simulations were compared with and confirmed by experiments on thin films from mixtures of PS-b-P2VP diblock copolymers on a Si substrate. Since the substrate is selective to the P2VP block, the experimental system corresponds to the case of selective adsorption, considered in section 3. In the experiments, we varied the mixture composition but kept the film thickness constant at about 100 nm (which corresponds to h ≅ 20.6 rc in the simulations). The corresponding GISAXS maps, measured in the dynamic regime (at αi = 0.15°) are given in Figure 9a. In addition, GISAXS measurements were carried out on films having film thicknesses ranging from 40 to 150 nm and a fixed mixture composition, ϕS = 2/3: These conditions correspond to the ones in the simulations in Figure 6 at the film thicknesses from h = 8.2 to 30.9 rc. For a detailed analysis of the GISAXS maps, horizontal and vertical cuts (as described in the Experimental Section) are given in Figure 9b,c, respectively. In the vertical cuts in Figure 9c at different mixture compositions (film thickness ∼ 100 nm), DBSs are observed, pointing to parallel lamellae. We attribute this to the P2VP-selective Si substrate, which facilitates the parallel orientation of pure short or long copolymers and also stabilizes parallel lamellae in the mixtures. BRs from vertical

Figure 9. GISAXS maps (a) and horizontal (b) and vertical (c) cuts, as described in the Experimental Section. In panels b and c, the curves are shifted vertically. The corresponding ϕS values are given in the figure. The positions of the BRs (b) and the DBSs (c) are marked with vertical dashes. The values q1(+) and q1(−) correspond to the peak positions expected from eq 4, i.e., the DBWA predictions with “plus” and “minus” signs, respectively.

lamellae appear in the range 0.24 ≤ ϕS ≤ 0.70 in Figure 9b, i.e., in most of the mixtures except those with a high content of short or long copolymers. This means that, in the films from pure copolymers, the parallel orientation is kept throughout the whole film, but, in the mixtures, two different orientations can coexist, as discussed. From the simulations above, we expect that, for these films, vertical separation of phases rich in short and long copolymers takes place. The thin lamellae near the selective substrate are expected to be parallel and the thicker lamellae in the film core to be vertical. The snapshots in Figure 6 at h = 20 also show that the free film surface is expected to have a quite irregular structure. This agrees very well with the results from our GISAXS measurements in evanescent mode, i.e., at αi = 0.1°, and the results from atomic force microscopy (not shown), which do not reveal any pronounced morphology or correlations in the upper layer of the film. While such a film structure is expected from the simulations of the two-phase system at ϕS = 2/3, the experimental results show that the same structure appears in the one-phase region as well. Determining the qz and qy positions of the DBSs and the BRs allows us to find the periods of parallel and vertical lamellae, as presented in Figure 10. The experimentally determined lamellar periods in the pure copolymer films are DL = 47.5 ± 0.9 nm and DS = 13.4 ± 0.4 nm. Their ratio, DL/DS = 3.55, is close to the value expected for the SSL, DL/DS = α−2/3 = 3.66. Addition of short copolymers reduces the overall lamellar period, as seen in Figure 10. At ϕS = 0.24, 0.37, and 0.48, different lamellar orientations coexist, as one can conclude from Debye−Scherrer rings in the GISAXS maps in Figure 9a. This diffuse ring also shows that randomly oriented lamellae are present in the film. While in this onephase region, only one period is expected: the periods of differently oriented lamellae are different; i.e., the parallel lamellae are thinner than the perpendicular ones, as seen from Figure 10. The only way to explain this finding is to assume that, according to simulations, short copolymers are concenH


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Figure 10. Experimentally determined periods and orientations of lamellae for films of a thickness of 100 ± 20 nm in dependence on the volume fraction of short copolymers in the mixture. Periods of parallel and perpendicular lamellae are shown with black circles and blue triangles, respectively. Gray vertical dashed lines mark the theoretical phase boundaries in the bulk from the phase diagram in Figure 2,30 and black vertical dashed lines mark the experimentally estimated boundaries under confinement. The dashed curve is the theoretically predicted lamellar period in the one-phase state, calculated from eq 5 and from the experimentally determined periods of the parallel lamellae in the thin films from pure short and pure long copolymers, respectively.

Figure 11. Periods of lying (black) and standing (blue) lamellae in dependence on film thickness at ϕS = 2/3, as determined using GISAXS.

thinner films is compensated for by the reduction of interdomain interfacial area by an increase of the period. This is not yet the case at a film thickness of 100 nm, studied in detail above.

5. CONCLUSION In this work, we considered the effect of the film thickness, mixture composition, and selectivity of the substrate on the morphology and the character of macrophase separation in thin films of binary mixtures of diblock copolymers. Molecular simulations and GISAXS experiments on mixtures of compositionally symmetric polystyrene-b-poly(2-vinylpyridine) copolymers demonstrated that, in thin films and on nonselective substrates, lateral macrophase separation is favored, while selective substrates and thicker films facilitate vertical macrophase separation. The vertical separation is driven by an entropic effect, concentrating short copolymers near the film interfaces. Such fluctuations of concentrations (about 5%), being amplified by the first-order-type macrophase separation, result in one layer of a phase rich in long copolymers, “sandwiched” between two layers rich in short copolymers, adjacent to the film surfaces. GISAXS experiments, supported by simulations, show that confinement of the two-phase copolymer mixtures affects the phase diagram of the mixtures, increasing the miscibility of short and long copolymers. The selectivity of the substrate or the free film surface to one of the blocks facilitates the vertical macrophase separation in thinner films. We found that the lamellar orientation in the phase rich in short copolymers is mostly dictated by the selectivities of the confining film surfaces, but the orientations in different phases are “decoupled” and can be orthogonal. Decoupling is explained by the unsteadiness of interfacial regions between macrophases, where the domains can easily reconstruct and make a kink to reconcile orthogonal lamellar orientations and to reduce the interfacial tension. In practice, it means that a vertical orientation of the lamellae in the middle of the film can be attained by simple admixing of shorter copolymers as an alternative to a more complex chemical or physical modification of the selective substrate. Despite qualitative agreement between GISAXS experiments and simulations, we also observe some mismatch between expected and observed periods of vertical lamellae, as well as an

trated near the film interfaces, where they form thinner parallel lamellae, and the long copolymers, being concentrated in the film core, form thicker vertical lamellae. The period of the lying lamellae quantitatively follows the theoretical prediction for the bulk, shown by the black dashed curve in Figure 10, while the size of vertical lamellae is notably higher. In the two-phase region, i.e., at ϕS = 0.63, 0.70, and 0.88, the compositions of the two equilibrium phases and the corresponding periods of the lamellar structures therein stay constant, as expected. This allows us to estimate the boundaries between the one- and the two-phase regions in Figure 10. The two-phase region in the thin film geometry is narrower than theoretically predicted for the bulk (Figure 2), and this is in good agreement with the results from simulations (Figure 8). However, the dimensions of the thick standing lamellae in the phase, rich in long copolymers, is higher than expected from theory. The experimentally determined ratio of lamellar periods, DIIL /DIIS = 33.1 nm/14.3 nm = 2.3, is 15% larger than the theoretical prediction, DII,theor /DII,theor = 27.75/14.17 = 1.96. L S In the two-phase region, all thin lamellae are parallel and all thick lamellae are vertical, whereas the fraction of other orientations is negligible. This agrees with our simulations of macrophase separation on a selective substrate (Figure 6). 4.6. Effect of the Film Thickness. Since the direction of macrophase separation was seen to depend strongly on the film thickness, GISAXS investigations of films of different thicknesses were carried out, namely, in the range from 40 to 150 nm, keeping the volume fraction of short chains fixed at ϕS = 2/3. In all cases, we observe thick vertical and thin parallel lamellae, and only a minimal presence of the other orientations. The lamellar periods are summarized in Figure 11. Surprisingly, thinning of the film is accompanied by thickening of the lamellae in both orientations. This can be explained by the fact that the growth of the surface free energy due to contacts with air and the substrate in I


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ACS Applied Materials & Interfaces unexpected increase of lamellar sizes with decreasing film thickness. These interesting effects require more detailed investigations for a full understanding.

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(10) Ross, C. A.; Berggren, K. K.; Cheng, J. Y.; Jung, Y. S.; Chang, J. B. Three-Dimensional Nanofabrication by Block Copolymer SelfAssembly. Adv. Mater. 2014, 26, 4386−4396. (11) Li, F.; Yager, K. G.; Dawson, N. M.; Yang, J. H.; Malloy, K. J.; Qin, Y. Complementary Hydrogen Bonding and Block Copolymer Self-Assembly in Cooperation toward Stable Solar Cells with Tunable Morphologies. Macromolecules 2013, 46, 9021−9031. (12) Basche, T.; Bottin, A.; Li, C.; Müllen, K.; Kim, J. H.; Sohn, B. H.; Prabhakaran, P.; Lee, K. S. Energy and Charge Transfer in Nanoscale Hybrid Materials. Macromol. Rapid Commun. 2015, 36, 1026−1046. (13) Roth, S. V.; Santoro, G.; Risch, J. F. H.; Yu, S.; Schwartzkopf, M.; Boese, T.; Dohrmann, R.; Zhang, P.; Besner, B.; Bremer, P.; Rukser, D.; Rubhausen, M. A.; Terrill, N. J.; Staniec, P. A.; Yao, Y.; Metwalli, E.; Müller-Buschbaum, P. Patterned Diblock Co-Polymer Thin Films as Templates for Advanced Anisotropic Metal Nanostructures. ACS Appl. Mater. Interfaces 2015, 7, 12470−12477. (14) Wu, N. L. Y.; Zhang, X.; Murphy, J. N.; Chai, J.; Harris, K. D.; Buriak, J. M. Density Doubling of Block Copolymer Templated Features. Nano Lett. 2012, 12, 264−268. (15) Liu, Z.; Huang, H.; He, T. Large-Area 2D Gold Nanorod Arrays Assembled on Block Copolymer Templates. Small 2013, 9, 505−510. (16) Xiao, S. G.; Yang, X. M.; Hwu, J. J.; Lee, K. Y.; Kuo, D. A Facile Route to Regular and Nonregular Dot Arrays by Integrating Nanoimprint Lithography with Sphere-Forming Block Copolymer Directed Self-Assembly. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 361−367. (17) Onses, M. S. Fabrication of Nanopatterned Poly(ethylene glycol) Brushes by Molecular Transfer Printing from Poly(styrene-bmethyl methacrylate) Films to Generate Arrays of Au Nanoparticles. Langmuir 2015, 31, 1225−1230. (18) Bigall, N. C.; Nandan, B.; Gowd, E. B.; Horechyy, A.; Eychmuller, A. High-Resolution Metal Nanopatterning by Means of Switchable Block Copolymer Templates. ACS Appl. Mater. Interfaces 2015, 7, 12559−12569. (19) Sarkar, K.; Schaffer, C. J.; Gonzalez, D. M.; Naumann, A.; Perlich, J.; Müller-Buschbaum, P. Tuning the Pore Size of ZnO NanoGrids via Time-Dependent Solvent Annealing. J. Mater. Chem. A 2014, 2, 6945−6951. (20) Pietsch, T.; Müller-Buschbaum, P.; Mahltig, B.; Fahmi, A. Nanoporous Thin Films and Binary Nanoparticle Superlattices Created by Directed Self-Assembly of Block Copolymer Hybrid Materials. ACS Appl. Mater. Interfaces 2015, 7, 12440−12449. (21) Shin, D. O.; Mun, J. H.; Hwang, G. T.; Yoon, J. M.; Kim, J. Y.; Yun, J. M.; Yang, Y. B.; Oh, Y.; Lee, J. Y.; Shin, J.; Lee, K. J.; Park, S.; Kim, J. U.; Kim, S. O. Multicomponent Nanopatterns by Directed Block Copolymer Self-Assembly. ACS Nano 2013, 7, 8899−8907. (22) Shi, A.-C.; Li, B. Self-Assembly of Diblock Copolymers under Confinement. Soft Matter 2013, 9, 1398−1413. (23) Hashimoto, T.; Yamasaki, K.; Koizumi, S.; Hasegawa, H. Ordered Structure in Blends of Block Copolymers. 1. Miscibility Criterion for Lamellar Block Copolymers. Macromolecules 1993, 26, 2895−2904. (24) Koizumi, S.; Hasegawa, H.; Hashimoto, T. Ordered Structure in Blends of Block Copolymers. 3. Self-Assembly in Blends of Sphere- or Cylinder-Forming Copolymers. Macromolecules 1994, 27, 4371−4381. (25) Kane, L.; Satkowski, M. M.; Smith, S. D.; Spontak, R. J. Phase Behavior and Morphological Characteristics of Compositionally Symmetric Diblock Copolymer Blends. Macromolecules 1996, 29, 8862−8870. (26) Papadakis, C. M.; Mortensen, K.; Posselt, D. Phase behavior of binary blends of symmetric polystyrene-polybutadiene diblock copolymers studied using SANS. Eur. Phys. J. B 1998, 4, 325−332. (27) Yamaguchi, D.; Hashimoto, T. A Phase Diagram for the Binary Blends of Nearly Symmetric Diblock Copolymers. 1. Parameter Space of Molecular Weight Ratio and Blend Composition. Macromolecules 2001, 34, 6495−6505. (28) Yamaguchi, D.; Hasegawa, H.; Hashimoto, T. A Phase Diagram for the Binary Blends of Nearly Symmetric Diblock Copolymers. 2.

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (A.V.B.). *E-mail: [email protected] (C.M.P.). ORCID

Anatoly V. Berezkin: 0000-0002-8916-1702 Christine M. Papadakis: 0000-0002-7098-3458 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Justus Oberhausen for help with the initial computer simulations. The financial support from Deutsche Forschungsgemeinschaft (Project PA 771/10-2, A.V.B. and C.M.P.) in the framework of the Memorandum of Understanding on Cooperation between DFG and RFBR is gratefully acknowledged. D.P. thanks DANSCATT (Danish Centre for the Use of Synchrotron X-ray and Neutron Facilities) for financial support. This work is based upon research conducted at the Cornell High Energy Synchrotron Source (CHESS), which is supported by the National Science Foundation and the National Institutes of Health/National Institute of General Medical Sciences under NSF Award DMR-1332208. We thank CHESS for providing beamtime and excellent equipment. A.V.B. acknowledges the Supercomputing Center of Moscow State University for access to supercomputers Lomonosov and Chebyshev, where the simulations were performed.

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REFERENCES

(1) Sevink, G. J. A.; Zvelindovsky, A. V. Confined Sphere-Forming Block Copolymers: Phase Behavior and the Role of Chain Architecture. Macromolecules 2009, 42, 8500−8512. (2) Tan, H.; Song, Q.; Niu, X.; Wang, Z.; Gao, W.; Yan, D. SphereForming Diblock Copolymers in Slit Confinement: A Dynamic Density Functional Theory Study. J. Chem. Phys. 2009, 130, 214901. (3) Yu, B.; Li, B.; Jin, Q.; Ding, D.; Shi, A.-C. Confined Self-Assembly of Cylinder-Forming Diblock Copolymers: Effects of Confining Geometries. Soft Matter 2011, 7, 10227−10240. (4) Li, W.; Liu, M.; Qiu, F.; Shi, A.-C. Phase Diagram of Diblock Copolymers Confined in Thin Films. J. Phys. Chem. B 2013, 117, 5280−5288. (5) Berezkin, A. V.; Papadakis, C. M.; Potemkin, I. I. Vertical Domain Orientation in Cylinder-Forming Diblock Copolymer Films upon Solvent Vapor Annealing. Macromolecules 2016, 49, 415−424. (6) Park, W. I.; Kim, K.; Jang, H. I.; Jeong, J. W.; Kim, J. M.; Choi, J.; Park, J. H.; Jung, Y. S. Directed Self-Assembly with Sub-100 Degrees Celsius Processing Temperature, Sub-10 Nanometer Resolution, and Sub-1 minute Assembly Time. Small 2012, 8, 3762−3768. (7) Salaun, M.; Zelsmann, M.; Archambault, S.; Borah, D.; Kehagias, N.; Simao, C.; Lorret, O.; Shaw, M. T.; Sotomayor Torres, C. M.; Morris, M. A. Fabrication of Highly Ordered Sub-20 nm Silicon Nanopillars by Block Copolymer Lithography Combined with Resist Design. J. Mater. Chem. C 2013, 1, 3544−3550. (8) Luo, M.; Epps, T. H. Directed Block Copolymer Thin Film SelfAssembly: Emerging Trends in Nanopattern Fabrication. Macromolecules 2013, 46, 7567−7579. (9) Park, W. I.; Tong, S.; Liu, Y. Z.; Jung, I. W.; Roelofs, A.; Hong, S. Tunable and Rapid Self-Assembly of Block Copolymers using Mixed Solvent Vapors. Nanoscale 2014, 6, 15216−15221. J


Forum Article

ACS Applied Materials & Interfaces Parameter Space of Temperature and Blend Composition. Macromolecules 2001, 34, 6506−6518. (29) Shi, A.-C.; Noolandi, J. Effects of Short Diblocks at Interfaces of Strongly Segregated Long Diblocks. Macromolecules 1994, 27, 2936− 2944. (30) Matsen, M. W. Immiscibility of Large and Small Symmetric Diblock Copolymers. J. Chem. Phys. 1995, 103, 3268−3271. (31) Morita, H.; Kawakatsu, T.; Doi, M.; Yamaguchi, D.; Takenaka, M.; Hashimoto, T. Competition between Micro- and Macrophase Separations in a Binary Mixture of Block Copolymers. A Dynamic Density Functional Study. Macromolecules 2002, 35, 7473−7480. (32) Pan, J.-X.; Zhang, J.-J.; Wang, B.-F.; Wu, H.-S.; Sun, M.-N. Phase Behaviors in a Binary Mixture of Diblock Copolymers Confined between Two Parallel Walls. Chin. Phys. B 2013, 22, 026401. (33) Park, S.-B.; Zin, W.-C. Selective Control over the Lamellar Thickness of one Domain in Thin Binary Blends of Block Copolymer Films. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1393−1399. (34) Rao, J.; Ma, H.; Baettig, J.; Woo, S.; Stuparu, M. C.; Bang, J.; Khan, A. Self-Assembly of an Interacting Binary Blend of Diblock Copolymers in Thin Films: A Potential Route to Porous Materials with Reactive Nanochannel Chemistry. Soft Matter 2014, 10, 5755− 5762. (35) Zhang, J.; Posselt, D.; Smilgies, D.-M.; Perlich, J.; Kyriakos, K.; Jaksch, S.; Papadakis, C. M. Complex Macrophase-Separated Nanostructure Induced by Microphase Separation in Binary Blends of Lamellar Diblock Copolymer Thin Films. Macromol. Rapid Commun. 2014, 35, 1622−1629. (36) Yager, K. G.; Lai, E.; Black, C. T. Self-Assembled Phases of Block Copolymer Blend Thin Films. ACS Nano 2014, 8, 10582− 10588. (37) Williamson, L. D.; Nealey, P. F. Macrophase Separation of Blends of Diblock Copolymers in Thin Films. Macromolecules 2015, 48, 3997−4003. (38) Wang, Z.; Shao, J.; Pan, H.; Feng, X.; Chen, P.; Xia, R.; Wu, X.; Qian, J. Monte Carlo Simulations of the Phase Separation of a Copolymer Blend in a Thin Film. ChemPhysChem 2015, 16, 567−571. (39) Spencer, R. K. W.; Matsen, M. W. Boundary Tension Between Coexisting Phases of a Block Copolymer Blend. Macromolecules 2015, 48, 2840−2848. (40) Spencer, R. K. W.; Matsen, M. W. Confinement Effects on The Miscibility of Block Copolymer Blends. Eur. Phys. J. E: Soft Matter Biol. Phys. 2016, 39, 43. (41) Hoogerbrugge, P. J.; Koelman, J. M. V. A. Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics. Europhys. Lett. 1992, 19, 155−160. (42) Koelman, J. M. V. A.; Hoogerbrugge, P. J. Dynamic Simulations of Hard-Sphere Suspensions under Steady Shear. Europhys. Lett. 1993, 21, 363−368. (43) Espanol, P.; Warren, P. B. Statistical Mechanics of Dissipative Particle Dynamics. Europhys. Lett. 1995, 30, 191−196. (44) Groot, R. D.; Warren, P. B. Dissipative Particle Dynamics: Bridging the Gap between Atomistic and Mesoscopic Simulation. J. Chem. Phys. 1997, 107, 4423−4435. (45) Jamali, S.; Boromand, A.; Khani, S.; Wagner, J.; Yamanoi, M.; Maia, J. Generalized Mapping of Multi-Body Dissipative Particle Dynamics onto Fluid Compressibility and the Flory-Huggins Theory. J. Chem. Phys. 2015, 142, 164902. (46) Besold, G.; Vattulainen, I.; Karttunen, M.; Polson, J. M. Towards Better Integrators for Dissipative Particle Dynamics Simulations. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, R7611−7614. (47) Horsch, M. A.; Zhang, Z.; Iacovella, C. R.; Glotzer, S. C. Hydrodynamics and Microphase Ordering in Block Copolymers: Are Hydrodynamics Required for Ordered Phases with Periodicity in More Than One Dimension. J. Chem. Phys. 2004, 121, 11455−11462. (48) Dai, K. H.; Kramer, E. J. Determining the TemperatureDependent Flory Interaction Parameter for Strongly Immiscible Polymers from Block Copolymer Segregation Measurements. Polymer 1994, 35, 157−161.

(49) Posselt, D.; Zhang, J.; Smilgies, D.-M.; Berezkin, A. V.; Potemkin, I. I.; Papadakis, C. M. Restructuring in Block Copolymer Thin Films: In-Situ GISAXS Investigations during Solvent Vapor Annealing. Prog. Polym. Sci. 2017, 66, 80−115. (50) Tolan, M. X-Ray Scattering from Soft-Matter Thin Films; Springer-Verlag: Berlin, Heidelberg, 1999. (51) Busch, P.; Rauscher, M.; Smilgies, D.-M.; Posselt, D.; Papadakis, C. M. Grazing-Incidence Small-Angle X-Ray Scattering from Thin Polymer Films with Lamellar Structures − The Scattering Cross Section in the Distorted-Wave Born Approximation. J. Appl. Crystallogr. 2006, 39, 433−442. (52) Kikuchi, M.; Binder, K. Microphase Separation in Thin Films of the Symmetric Diblock-Copolymer Melt. J. Chem. Phys. 1994, 101, 3367−3377. (53) Meng, D.; Wang, Q. Complex Morphologies in Thin Films of Symmetric Diblock Copolymers as Stable and Unstable Phases. Soft Matter 2010, 6, 5891−5906. (54) Walton, D. G.; Kellogg, G. J.; Mayes, A. M.; Lambooy, P.; Russell, T. P. A Free Energy Model for Confined Diblock Copolymers. Macromolecules 1994, 27, 6225−6228. (55) Geisinger, T.; Müller, M.; Binder, K. Symmetric Diblock Copolymers in Thin Films. I. Phase Stability in Self-Consistent Field Calculations and Monte Carlo Simulations. J. Chem. Phys. 1999, 111, 5241−5250.

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Vertical vs Lateral Macrophase Separation in Thin Films of Block

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