Self-Assembly in Block Copolymer Thin Films upon Solvent Evaporation

Article pubs.acs.org/Macromolecules

Self-Assembly in Block Copolymer Thin Films upon Solvent Evaporation: A Simulation Study Jinlong Hao,† Zhan Wang,† Zheng Wang,† Yuhua Yin,† Run Jiang,† Baohui Li,*,†,‡ and Qiang Wang§ †

School of Physics, Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, Tianjin, 300071, China ‡ Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), Tianjin, 300071, China § Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523-1370, United States ABSTRACT: The self-assembly in cylinder-forming diblock copolymer thin films upon solvent evaporation is studied by lattice Monte Carlo simulations under the assumption that the solvent evaporation starts from the free surface and gradually propagates toward the substrate. The effects of solvent selectivity, surface preference, and solvent evaporation rate on the morphology evolution during solvent evaporation are systematically investigated. It is found that the perpendicular cylinder morphology tends to form under weak surface preference, whereas under strong surface preference this morphology is promoted by the fast solvent evaporation rate and the strong solvent selectivity. The surface preference window for forming perpendicular cylinders with solvent evaporation is found to be wider than with thermal annealing, and especially much wider when the solvent evaporation starts from random (disordered) initial states. A new mechanism of perpendicular cylinder formation is proposed and elucidated. Hexagonally packed short perpendicular cylinders formed in the earlier stage of the solvent evaporation may remain to the dry film when the solvent selectivity for the majority block is strong or the solvent evaporation rate is fast, which results in the enlargement of the surface preference window of perpendicular cylinder morphology. Mix-orientated morphology with one or two layers of parallel cylinders at the top of the film and perpendicular cylinders throughout the remaining film is also predicted, and its formation mechanism is discussed.

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INTRODUCTION Block copolymers (BCPs) have attracted great interest because of their ability to self-assemble into rich nanostructures with potential applications in diverse areas.1,2 One-dimensional confinement, in which BCPs are placed either between two flat parallel solid surfaces or on a substrate with the other surface in direct contact with the atmosphere, has been extensively studied as an efficient method to minimize the structure defects, thus inducing long-range order of the selfassembled structures. In this case, the copolymers form a thin film. BCP thin films with cylinders oriented perpendicular to the substrate (perpendicular cylinders) are especially interesting, as they can potentially be used in nanolithography3,4 and in ultrafiltration membrane5−8 applications. The thermodynamically preferred orientation, however, is often the parallel one, due to the preferential wetting of one block at the free and/or solid surfaces.9−11 Identifying the conditions to tune the orientation of cylinders in BCP films is crucial for their applications. For cylinder-forming asymmetric diblock copolymer films confined between two parallel surfaces, extensive studies over the past two decades indicate that the surface preference for the two blocks and the film thickness can greatly influence the morphology and cylinder orientation in the film.9,12−18 Perpendicular cylinders are observed only when the surfaces have a slight energetic preference for the majority block, which balances their entropic preference for the minority block,16−18 © XXXX American Chemical Society

or when the surfaces are energetically neutral or close to neutral but the film thickness is incommensurate with the characteristic bulk period of the cylindrical phase.17,18 In the remaining large parameter space, parallel cylinders are usually observed, while noncylindrical morphologies, including spheres, perforated lamellae, and lamellae in the interior of the film or near the surfaces, have also been observed due to the strong surface preference for one of the two blocks.15−18 Similar phenomena were also found for cylinder-forming ABA triblock copolymer films.19,20 Experimentally, many approaches, including thermal annealing,21,22 solvent-vapor annealing,1,2,5,10,11,20,23−35 electric fields,36−38 chemically patterned substrates,22,39−41 corrugated substrates,42,43 and graphoepitaxy,23,36,44,45 have been used to control the long-range order and the orientation of the selfassembled nanostructures in BCP films. Among these approaches, solvent-vapor annealing (SVA) has proven to be very promising in achieving the goal. Comprehensive reviews on SVA have been given by Albert et al.46 and Sinturel et al.47 In SVA, as-prepared BCP films are exposed to the vapor of one or more solvents, at temperatures typically well below the bulk glass transition temperature of both blocks to form a swollen and mobile polymer film atop the substrate. With the existence Received: January 27, 2017 Revised: March 13, 2017

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DOI: 10.1021/acs.macromol.7b00200 Macromolecules XXXX, XXX, XXX−XXX

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concentration and concentration gradient at the vapor-polymer surface. When the film is rapidly dried in solvent-free vapor, perpendicular cylinders have the greatest chance to form.54 Using dynamical self-consistent field theory, Fredrickson and co-workers investigated diblock copolymer self-assembly during solvent evaporation.55 They found that perpendicular cylinders tended to form at modest evaporation rates and relatively weak effective segregation strength. They also found that a selective solvent for the majority block can stabilize perpendicular domain orientation.55 Using dissipative particle dynamics, Potemkin and co-workers studied the domain orientation in diblock copolymer films upon SVA.56 They found that perpendicular orientation was promoted by the solvent evaporation, and that formation of well-ordered cylinders by SVA required an initially disordered swollen state. A perpendicular orientation of the cylinders was observed at a high evaporation rate, which was suggested as necessary to create a pronounced gradient of the solvent concentration within the film. Also, certain solvent selectivity for the majority block is necessary.56 In addition, simulations of solvent evaporation have been reported in studies on the SVA of lamellae-forming BCP thin films,57 on the drying process of polymer or binary polymer blend films,58,59 and on the feature orientation improvement by cyclic solvent annealing.60 Solvent evaporation has proven to be a remarkably successful tool for directing the self-assembled nanostructures of BCPs,1,2,10,28,35,47,55,56 yet the mechanisms of how its control parameters affect the nanostructure and its principles governing the structural formation remain poorly understood. Furthermore, the effects of solvent selectivity and solvent evaporation rate on the nanostructure orientation have not been clarified. Although some explanations for the formation of perpendicular cylinders during solvent evaporation have been suggested,1,2,28,35,47,54−56 no consensus has been reached. Here we investigate the self-assembly in cylinder-forming diblock copolymer thin films upon solvent evaporation using lattice Monte Carlo simulations. The effects of solvent selectivity, surface preference, and solvent evaporation rate on the nanostructure orientation in the film are investigated. The surface preference window that can lead to the formation of perpendicular cylinders after solvent evaporation is identified and compared with that obtained from thermal annealing. The mechanisms of controlling the nanostructure orientation in solvent evaporation are elucidated.

of solvent, the glass transition temperature of polymers is reduced and the chain mobility is enhanced,1,2,23,48 allowing for rearrangement of microdomains and annihilation of defects,1,25,49 and hence resulting in highly ordered arrays of hexagonally packed microdomains for cylinder-forming BCPs with grain sizes of several microns.1,12 In a solvent-swollen film, the existence of solvent affects several of parameters including the effective interaction between the blocks, the effective film thickness, the effective surface preference, and the effective volume fractions of the blocks. As a result, various morphologies, including lamellae, perforated lamellae, gyroid, cylinders, and spheres, can be obtained.20,50,51 All or some of the morphologies induced by the existence of solvent may be trapped in the system during the solvent evaporation process.11,26,52,53 Therefore, the resulting morphology may be different from that without SVA treatment, such as from thermal annealing. Furthermore, SVA with different solvents may result in different nanostructure orientations; for example, it was found that a neutral solvent leads to the formation of parallel cylinders or perpendicular cylinders with relatively poor ordering, whereas solvents that are slightly selective for the majority block lead to the formation of well-ordered perpendicular cylinders.5,10,11,25−27 Solvent evaporation can also generate more complex morphologies. In their study of polystyrene-blockpolydimethylsiloxane films using SVA, Son et al. observed the morphology of 3−6 periods of parallel cylinders at the free surface and perpendicular cylinders beneath the parallel cylinders.30 The solvent evaporation rate has also been found to influence the nanostructure orientation.1,2,23,28,29 Despite previous extensive studies, some controversies about the details of this influence still exist. In their pioneering work, Kim and Libera28 investigated the morphological development of a cylinder-forming polystyrene−polybutadiene−polystyrene triblock copolymer film as a function of solvent evaporation rate and postevaporation annealing. They found that, with solvent evaporation changing from fast to very slow, the morphology changed from a disordered structure with no long-range order, to a perpendicular cylindrical structure, to a duplex cylindrical morphology with both domains orientated perpendicular and parallel to the substrate, and finally to a fully parallel cylindrical structure. They suggested that the diffusion of solvent to the free surface of the film and the solvent concentration gradient within the film imposed by different solvent evaporation rates were responsible for the different cylinder orientations.28 Subsequent studies1,5,23,29 found similar behavior; that is, rapid evaporation leads to the formation of perpendicular structures. More recent evidence, however, indicated that wellordered parallel cylinders occurred upon instantaneous solvent removal, whereas removing solvent very slowly reoriented cylinders to be perpendicular to the substrate, in a cylinderforming poly(deuterated styrene-b-isoprene-b-deuterated styrene) thin film.2 It should be noted that their film has a parallel cylinder morphology before solvent removal.2 On the theoretical and simulation front, only a few studies have been reported on solvent evaporation of cylinder-forming diblock copolymer films: Phillip et al.54 developed a theory for preparing perpendicular cylinders based on the assumption that the cylinders are oriented as a result of the solvent concentration profile formed during drying (i.e., solvent evaporation). Their results suggested that the key to forming perpendicular cylinders in a drying BCP film is the solvent

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MODEL AND METHODS

Our simulations focus on the self-assembly in cylinder-forming diblock copolymer thin films under solvent evaporation. The model film is composed of diblock copolymers and solvent molecules. Each copolymer chain consists of three A- and nine B-segments, denoted as A3B9. Our simulations are performed on a simple cubic lattice of V = LX × LY × LZ sites. We use the “single-site bond fluctuation” model proposed by Carmesin and Kremer61 and by Larson,62 where the bond length between two adjacent segments on each chain is either 1 or √2 in units of the lattice spacing; each lattice site therefore has 18 nearest neighbors. For simulations of thin films, two impenetrable flat walls are placed at Z = 0 and Z = LZ −1, respectively, while the periodic boundary conditions are applied in the X and Y directions. The wall at Z = 0 represents the substrate (W), while that at Z = LZ −1 represents the vapor (V) or the free surface. The lattice sites in both wall layers cannot be occupied by either chain segments or solvent molecules (S). The polymer chains and solvent molecules are therefore confined in a thin film with an initial (swollen) thickness Δ = LZ − 2. Each segment (A or B), S, or V molecule occupies one lattice site, and multiple occupation of any lattice site is not allowed. For simulations of bulk B


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systems, there is no wall and the periodic boundary conditions are applied in all directions. Hereafter, we consider an A, B, or S to be at the free surface if the site right above it is occupied by a V. We denote the distance between the substrate and the average position of the free surface (i.e., the mean height of all the A, B, and S that are at the free surface) as the film thickness Δ, the thickness of a film without any solvent as the dry film thickness Δ0, and the swelling ratio as Δ/Δ0. In our simulations, only pair interactions between species occupying the nearest-neighbor sites are considered. These interactions are calculated by assigning an energy Eij = εij kBTref to each nearestneighbor pair of different species i and j, where {i, j}={A, B, S, W and V}, kB is the Boltzmann constant and Tref is a reference temperature. We set εii = 0, εAB = 1, εAS = 0.3, and εBS = −0.2 or −0.7 corresponding to a weak or strong solvent selectivity for the B segments, respectively. The solvent selectivity is characterized by α = (εAS − εBS)/εAB. For simplicity, it is assumed that the substrate and the vapor molecules have the same preference for A and B segments; that is, we set εBW = εBV = 1.5 and vary εAW = εAV from 1.5 to 3.5, so that both the substrate and the vapor are either neutral for A and B segments or selective for the B-segments. The surface preference is defined as β = (εAV − εBV)/ εAB. For simulations of the thin films with solvent evaporation, the initial swelling ratio is fixed as 2, and the copolymer chains are generated randomly in the simulation box. After the chains are generated, unoccupied lattice sites are assigned as solvent molecules. Before the solvent evaporation starts, two types of initial states are obtained with the following processes: In one case, we equilibrate the film at a quite high temperature TS = 60Tref , referred to as the random initial state. In the other case, we equilibrate the film at the simulation temperature, TS = 3.5Tref , referred to as the spherical initial state since the copolymers form A-spheres in the film. For trial moves, we exchange positions between chain segments and solvent molecules.63 A solvent molecule (or a chain segment) is selected first, then exchange its position with a segment (or a solvent) at one of its 18 nearest neighbors. If the exchange does not create any broken bond, it is allowed. If the exchange creates a single broken bond, the selected solvent molecule continues to exchange with the subsequent segment(s) on the chain until the chain connectivity is recovered. If the exchange creates two broken bonds, it is not allowed. An allowed trial exchange move is further accepted with the Metropolis rule, that is, with the probability of pacc = min[1, exp(−ΔE/kBTS)], where ΔE is the energy difference between the trial and the old configurations.64 For simulations not involving solvent evaporation, including those in the bulk, in the films with thermal annealing, and in the “static” films discussed in part 3 of the Results and Discussion below, we use the simulated annealing, a well-known procedure to obtain the ground state of the system by performing simulations at decreasing temperatures.65−67 For simulations with thermal annealing, the copolymer concentration (the fraction of lattice sites occupied by chain segments out of the total lattice sites) is fixed as 0.85. In the simulation of solvent evaporation, we evaporate randomly selected solvent molecules (i.e., turn them into vapor molecules) that are at the free surface; this corresponds to the limiting case of μ → −∞ with μ being the chemical potential difference between a V and an S molecule in the model of Rabani and co-workers.68,69 It is expected that when a solvent molecule is evaporated, it results in changes of chains and solvent molecules within a few layers from it. We assume that only the A, B and S in an “evaporation zone” are mobile (i.e., can be selected for exchange trial moves), the thickness of which is taken to be δ layers from the average position of the free surface, and increase δ by one layer after every LXLY solvent molecules are evaporated. As microphase-separation occurs in the “evaporation zone”, δ is called the effective film thickness hereafter. While the initial value of δ is taken to be 7 in this work, we have tested other values in the range of 4−10 and obtained similar results. We further select an A, B or S in the ith layer (i = 1,..., δ with increasing order along the Zdirection) of the evaporation zone with a probability of min{1, [0.1 + 0.15(i − 1)]}/Z(δ) for the exchange trial move, where

Z(δ) = ∑i = 1 min{1, [0.1 + 0.15(i − 1)]} is the normalization factor. The solvent evaporation rate (reva) is defined as the number of solvent molecules that are evaporated within the “time” of 5 × 104 Monte Carlo Step (MCS). One MCS is defined as the number of trial moves taken for, on average, all the A, B, and S molecules in the “evaporation zone” to be selected for an exchange trial move. We evaporate one solvent molecule at a time, and the “time” between evaporating two successive solvent molecules is (5 × 104 /reva) MCS. The “evaporation zone” defined here is similar to the “ordered phase zone” (we call it) used by the authors of ref 54 in their study of solvent evaporation of block copolymer thin films. In the “ordered phase zone”, the solvent concentration is lower than the order− disorder transition concentration due to evaporation. They have presumed that nucleation of the ordered morphology begins at the free surface, and once it is complete, the thickness of the “ordered phase zone” lOD increases. Far from the “ordered phase zone”, the solvent concentration keeps the initial value. The difference between their modeling and ours is that they assumed that the region near the free surface is close to a pseudosteady state and that the cylinders are oriented as a result of the solvent concentration profile formed during drying. These assumptions are not used in our modeling. The diblock copolymers under investigation form hexagonally packed cylinders in the bulk as shown in Scheme 1. As illustrated

Scheme 1. Sketch-Map for the Characteristic Distances between Cylinders in a Cylindrical Phase

previously,9,17 there are three characteristic lengths, L1, L2, and L3, shown in Scheme 1. For the ideal hexagonal arrangement, there is only one independent length, namely the bulk period L0, thus L1 = L2 = L0 and L3 = √3L0/2. In simulations on a lattice, two characteristic lengths are independent. The period of the bulk cylindrical phase of the copolymer A3B9 at the copolymer concentration of 0.85 was found to be L1 = 10.67 and L3 = 9.25.70 It is noted that the presence of the selective solvent increases the characteristic lengths. The swelling ratio is about 1.43 when a cylindrical structure forms during the solvent evaporation. The characteristic lengths at this copolymer concentration is found to be L1 = 11.28 and L3 = 9.77 in bulk simulations. In simulations of thin films, the box sizes LX and LY should be commensurate with (i.e., an integer multiple of) the characteristic lengths in the bulk to minimize the finite-size effects. We therefore set LX ≈ 5.0 L1 and LY ≈ 6.0L3 for simulations from a randomly initial state, and LX ≈ 4.0L1, LY ≈ 4.0L3 for simulations from the spherical initial states.

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RESULTS AND DISCUSSION 1. Morphology Evolution during Solvent Evaporation and Orientation Diagrams. In this section, we investigate the morphology evolution in the film during solvent evaporation at a fixed solvent evaporation rate of reva = 1000, starting from a random initial state. For the relatively weak solvent selectivity case of α = 0.5, typical morphology evolution is plotted in Figure 1. It is noted that, when the surface preference for the majority (B-) block is neutral or weak (i.e., 0 C


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Figure 1. Snapshots during solvent evaporation with α = 0.5 and reva = 1000. For each snapshot, both a side view and a top view are shown, and both the swelling ratio Δ/Δ0 and the reduced effective film thickness δ/L3 are given. Only the minority (A-) domains are shown in green with iso-surface plot at A-density of 0.5. The thickness of completely dried films Δ0 is 4.09L3 with L3 = 9.77.

≤ β ≤ 0.8), the resulting morphology in the dry film is a cylindrical phase with perpendicular orientation (C⊥), as shown in parts a and b of Figure1, whereas when the surface preference is strong (i.e., β ≥ 0.9), the resulting morphology is a cylindrical phase with parallel orientation (C∥), as shown in Figure 1c. At the early stage of solvent evaporation, a layer of hexagonally packed or deformed spheres form near the free surface. As solvent evaporation progresses, each sphere grows longer in the Z-direction and evolves into a short perpendicular cylinder. The above occurs in both the weak and strong surface preference cases shown in parts b and c of Figure 1. After the short perpendicular cylinders form, the subsequent process depends on the value of β. For 0 < β ≤ 0.8, the morphology evolution is similar to that at β = 0.8 shown in Figure 1b, where the short perpendicular cylinders grow longer until they penetrate the entire film upon further solvent evaporation. For β ≥ 0.9, each short perpendicular cylinder splits into two spheres in the Z-direction, and the film evolves into two layers of spheres. Spheres in the top layer then connect with each other horizontally, and evolve into a layer of parallel cylinders. Those in the second layer evolve into another layer of parallel cylinders subsequently. As solvent evaporation progresses further, the parallel cylinders in the second layer first become undulated, then break into two layers of parallel cylinders. The above process repeats and parallel cylinders form layer by layer. In the neutral surface case (i.e., β = 0), however, an intermediate morphology with one layer of half-cylinders form near the free surface at the early stage of solvent evaporation. Upon further solvent evaporation, the layer of parallel half-cylinders disappears and the C⊥ morphology forms, as shown in Figure 1a. For the stronger solvent selectivity case of α = 1.0, typical morphology evolution during solvent evaporation is shown in Figure 2. It is noted that the β-window for the formation of C⊥ morphology becomes wider (i.e., 0.1 ≤ β ≤ 1.1). Typical C⊥

evolution is shown in Figure 2c, which is similar to that shown in Figure 1b. When β = 0.1, however, the morphology evolution, as shown in Figure 2b, is similar to that shown in Figure 1a, where one layer of half-cylinders form near the free surface at the early stage of solvent evaporation, and finally C⊥ forms in the dry film. Furthermore, it is interesting to notice that, in this stronger solvent selectivity case, the film can evolve into a mix-orientated cylindrical morphology (Cmix) with one or two layers of parallel cylinders at the top of the film and perpendicular cylinders throughout the remaining film when β ≥ 1.2, as shown in parts d and e of Figure 2. At β = 1.2, Cmix forms with only one layer of parallel cylinders at the top of the film, which are connected to the underlying perpendicular cylinders during solvent evaporation until Δ/Δ0 = 1.38. At β = 2.0, Cmix forms with two layers of parallel cylinders. This morphology usually has defects where a few cylinders may change their orientation to parallel near the substrate due to the stronger surface preference. When β ≥ 1.2, short perpendicular cylinders are always observed in the early stage of solvent evaporation, as shown in parts d and e of Figure 2. These short perpendicular cylinders evolve into one layer of parallel cylinders and one layer of spheres with further solvent evaporation. After the formation of the first layer of parallel cylinders, the underlying spheres usually grow into short perpendicular cylinders. In the subsequent evaporation process, however, the perpendicular orientation may or may not remain depending on the surface preference. When β = 1.2−1.5, the short perpendicular cylinders gradually grow longer, and finally penetrate the remaining film. When β = 1.6−2.0, the short perpendicular cylinders connect to each other horizontally, thus evolving into the second layer of parallel cylinders above the shortened perpendicular cylinders, and this process repeats. Therefore, Cmix forms with one or two layers of parallel cylinders near the top of the film and perpendicular cylinders throughout the remaining film as shown in parts d and e of D


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Figure 2. Snapshots during solvent evaporation with α = 1.0 and reva = 1000. For each snapshot, both a side view and a top view are shown, and both Δ/Δ0 and δ/L3 are given. The thickness of completely dried films Δ0, the color scheme and the details of the plots are the same as those in Figure 1.

Figure 2. Their formation process is quite different from that of C∥ in the case of α = 0.5 as shown in Figure 1c. When β = 0, Cmix forms as shown in Figure 2a. In this case, the morphology evolution in the early stage of solvent evaporation is similar to that at β = 0.1. The layer of half-cylinders at the top of the film, however, remains until the end of solvent evaporation. The final Cmix morphology consists of one layer of half-cylinders and one layer of parallel cylinders near the top, and perpendicular cylinders throughout the remaining film. At the boundary between cylinders with different orientations, some parallel cylinders are connected to the underlying perpendicular cylinders. Figure 3 shows the orientation diagrams for solvent evaporated films at α = 0.5 and 1.0. In the weak solvent selectivity case of α = 0.5, the orientation of cylinders changes from perpendicular to parallel with increasing surface preference β. The β-window for forming the C⊥ morphology is 0 ≤ β ≤ 0.8. In the strong solvent selectivity case of α = 1.0, the β-window for the C⊥ morphology is widened to 0.1 ≤ β ≤ 1.1. Many experimental studies have indicated that solvent with a strong selectivity for the majority block could lead to the formation of the C⊥ phase after the solvent annealing, whereas a neutral or a weakly selective solvent led to the formation of

Figure 3. Cylinder orientation diagrams for postevaporated films with reva = 1000, α = 0.5, and α = 1.0.

the C∥ phase.5,10,11,25−27 Using dynamical self-consistent field theory, Fredrickson and co-workers found that a solvent selective for the majority block can stabilize perpendicular domain orientation.55 The work by Potemkin and co-workers using dissipative particle dynamics suggested that a certain solvent preference for the majority block is necessary for the formation of perpendicular cylinders.56 Our simulation results are consistent with these experimental and simulation results. E


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Figure 4. Snapshots during solvent evaporation at different solvent evaporation rates with α = 1.0 and β = 1.2. The color scheme and the details of the plots are the same as those in Figure 1.

In the case of α = 1.0, the film evolves into the Cmix morphologies when β = 0 or β ≥ 1.2. The Cmix morphology was observed in the experiments by Son et al. in their study of polystyrene-block-polydimethylsiloxane films using SVA.30 To the best of our knowledge, we report the first simulation in which the mix-orientated morphologies are predicted for BCP systems with solvent evaporation. 2. Effect of Solvent Evaporation Rate. In this section, we investigate the effect of solvent evaporation rate on the cylinder orientation using the random initial state. Figure 4 shows the morphology evolution with the evaporation rate reva ranging from 200 to 4000, α = 1.0, and β = 1.2. When the solvent evaporation is fast (e.g., reva = 4000 and 2000), the final morphology is C⊥ as shown in Figure 4a. A medium rate (e.g., reva = 1000) results in a Cmix morphology with a layer of parallel cylinders on the top of perpendicular cylinders, as shown in Figure 4b. With a slow evaporation rate (e.g., reva ≤ 500), C∥ forms with four layers of ordered parallel cylinders in the dry film, as shown in Figure 4c. It is noted that, in all the three cases shown in Figure 4, the morphologies occurring in the early stage of solvent evaporation (where short perpendicular cylinders form) are similar to each other and to those shown in Figure 2c−e. The main difference starts to occur at δ/L3 ≈ 1.74, where the short perpendicular cylinders begin to connect to each other near the free surface when reva ≤ 1000. With further solvent evaporation, the connected parts are detached from the rest of the short perpendicular cylinders at δ/L3 ≈ 2.2−2.5 depending on reva, and gradually form one layer of parallel cylinders near the top of the film while the remaining part of the short perpendicular cylinders grow slightly longer. When reva = 333, the above process repeats with further solvent evaporation so that C∥ finally forms, as shown in Figure 4c. When reva = 1000, however, the short perpendicular cylinders beneath the layer of parallel cylinders gradually grow and finally penetrate throughout the film, so that Cmix forms with one layer of parallel cylinders near the top of the film and perpendicular cylinders throughout the remaining film, as shown in Figure 4b.

When reva = 4000 and 2000, the short perpendicular cylinders formed in the early stage of solvent evaporation do not connect to each other at all. With further solvent evaporation, they gradually grow and finally penetrate throughout the film to form C⊥, as shown in Figure 4a. In this case, it is expected that a tendency of forming parallel cylinders also exists, as the surface preference is the same as that in Figure 4c. However, the solvent evaporation is so fast that a large amount of solvent is evaporated before the polymer chains can rearrange from the existing short perpendicular cylinders formed in the earlier stage of solvent evaporation. Hence, the short perpendicular cylinders remain and continue to grow vertically with further evaporation and the C⊥ morphology forms finally in the dry film. Table 1 lists the final morphology at various reva and β for the solvent-evaporated films with α = 1.0. When the solvent Table 1. Dry-Film Morphology after Solvent Evaporation with α = 1.0a reva β

10000

4000

2000

1000

500

333

200

1.0 1.1 1.2 2.0

dis dis dis dis

C⊥ C⊥ C⊥ Cmix

C⊥ C⊥ C⊥ Cmix

C⊥ C⊥ Cmix Cmix

C⊥ Cmix C∥ C∥

C⊥ C∥ C∥ C∥

C∥ C∥ C∥ C∥

a

C⊥ denotes perpendicular cylinders, C∥ for parallel cylinders, Cmix for the mix-orientated morphology, and dis for the morphology with poor ordering.

evaporation rate is too large (e.g., reva = 10000), the ordering of cylinders in the film is poor, and hence the corresponding morphology is referred to as the disordered phase (dis). It is noted that the morphology usually changes from C⊥ to Cmix, and further to C∥ with decreasing solvent evaporation rate at a given β. From Table 1, it is noted that increasing the solvent evaporation rate enlarges the β-window for the formation of F


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Figure 5. Equilibrium states of thin films with α = 1.0. The swelling ratio is set to be 1.67, 1.43, 1.33, and 1.18 for systems with δs /L3 = 0.41−0.61, 0.82−1.02, 1.23, and >1.3, respectively. The color scheme and the details of the plots are the same as those in Figure 1.

Finally, the case of α = 1.0 and β = 0.1 is similar to that of α = 1.0 and β = 0, except that the entropic effect is partially counteracted by the energetic preference of the free surface in this case, so that the orientation of the already formed parallel half-cylinders is rearranged during further evaporation and C⊥ finally forms. For the case of α = 0.5, we can also understand the morphologies in the same way. When β = 1.2, we have βeff = 0.9 after a layer of parallel cylinders form near the free surface; C∥ should therefore form as seen in the phase diagram shown in Figure 3. The case of α = 0.5 and β = 0 is similar to that of α = 1.0 and β = 0, except that the weaker solvent selectivity leads to less selective swelling of the majority block, and the effective volume fraction of the minority block is larger in this case. Thus, the entropic effect is weaker, the orientation of the already formed parallel half-cylinders is rearranged during further evaporation, and C⊥ finally forms. 3. Mechanisms of the Cylinder Orientations. In order to investigate the formation mechanisms of various cylinder orientations, we need to know the equilibrium morphology for the part of the film in the evaporation zone at different stages during solvent evaporation. We therefore perform simulations of “static” films which have approximately the same boundaries and copolymer concentration as the evaporation zone with different surface preference and thicknesses. Each “static” film is assumed to be confined between two solid walls: the top one corresponds to the free surface of the solvent evaporated film and thus consists of vapor molecules, and the bottom one corresponds to the bottom boundary of the evaporation zone and thus consists of sites having the same property as that of the part below the evaporation zone, namely a random mixture of 12.5% A-segments, 37.5% B-segments and 50% solvent molecules. The “static” film thickness (δs) corresponds to the effective film thickness δ in the solvent evaporated film at the specific stage of solvent evaporation. The results at α = 1.0 are shown in Figure 5. It is noted that, for δs/L3 ≤ 0.82 and 0.2 ≤ β ≤ 1.2, hexagonally packed, short perpendicular cylinders always form since δs is not commensuration with L3. For δs/L3 = 1.02

C⊥. That is, the C⊥ morphology is promoted by fast solvent evaporation, consistent with previous experimental1,5,23,28,29 and simulation56 studies. It is also noted that, with decreasing β, the reva value needed to produce the C∥ morphology decreases; that is, the solvent evaporation needs to be slower. Cmix usually occurs between C⊥ and C∥, indicating that it may be a metastable morphology. We can understand the mix-orientated morphology in the following way: In the case of α = 1.0 and β = 1.2, a layer of parallel A-cylinders form near the top of the film in the early stage of solvent evaporation due to the strong surface preference, and under the parallel cylinders there are several lattice layers that contains nearly no A-segments. The bottom of these lattice layers can then be considered as an effective surface for the rest of the film with a surface preference βeff =[c (εAB - εBB)+ (1-c)(εAS - εBS)]/εAB, where c ≈ 0.8 is the copolymer concentration in the “evaporation zone” or the effective surface. When α = 1.0, this gives βeff ≈1.0. As shown in Figure 3 and listed in Table 1, C⊥ should form in a film with β = 1.0, α = 1.0 and reva = 1000, thus leading to the Cmix morphology in this case. For cylinder-forming BCP films, the asymmetry of the copolymer chains causes an entropic attraction that drives the minority block to the confining surfaces.16−18 Thus, in the case where α = 1.0 and β = 0, a layer of parallel half-cylinders form near the top of the film in the early stage of solvent evaporation. However, these parallel half-cylinders are poorly ordered in the early stage of solvent evaporation, as shown in Figure 2a. The short cylinders formed beneath the half-cylinders are also poorly ordered and orient either perpendicular or parallel, so that they connect each other and form a layer of parallel cylinders beneath the half-cylinders. As in the above case of α = 1.0 and β = 1.2, the rest of the film is subjected to an effective surface preference of βeff ≈ 1.0. So with further solvent evaporation the evolution of the part below the layer of parallel cylinders is similar to that of the film with α = 1.0 and β = 1.2; that is, a layer of parallel cylinders forms followed by the growth of the perpendicular cylinders, and the final morphology is Cmix. G


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small enough, the morphology formed during solvent evaporation may be closer to the equilibrium one. From Figure 3, it is obviously that the β-window for the formation of perpendicular cylinders is wider when the solvent selectivity is stronger. As mentioned earlier, the free surface provides an effective attraction to the minority block due to the entropic effect. It can be deduced that, the stronger the solvent selectivity for the majority block, the smaller of the effective volume fraction of the minority block, and hence the stronger the entropic effect. Therefore, for a solvent with stronger selectivity for the majority block, larger surface preference for the majority block is needed to balance the entropic preference for the minority block; the upper boundary of the β-window for forming perpendicular cylinders therefore increases with increasing solvent selectivity. Furthermore, it is deduced that a solvent with a stronger selectivity for the majority block results in a larger free energy barrier to be overcome when the polymer chains rearrange from the already formed perpendicular orientation; a larger β-value is therefore needed for the occurrence of parallel cylinders with increasing solvent selectivity. In previous studies, various speculations about why solvent evaporation promotes perpendicular morphologies have been given. Kim and Libera suggested that the solvent-concentration gradients would be steeper under conditions where solvent is allowed to evaporate quicker. Under such conditions, the cylinders would grow in the direction of the maximum solventconcentration gradient and adopt a perpendicular orientation.28 Potemkin and co-workers assumed that reorientation of domains is driven by the vertical flows of the components, arising upon the solvent evaporation.56 Their speculation is consistent with Kim and Libera’s.28 Kim et al. suggested that, when solvent evaporation is fast, an ordering front is generated by the solvent-concentration gradient and propagates from the free surface through the film.1 Albert et al. and Wu et al. suggested that parallel cylinders may incur more energy penalties when the film is subjected to an ever-changing commensurability condition.2,23 In our simulations, a layer of short perpendicular cylinders always forms near the free surface in the early stage of solvent evaporation, when β > 0.1, and is confirmed as the equilibrium morphology at the corresponding effective film thickness. When solvent evaporation rate is large, this layer of short perpendicular cylinders may gradually grow and finally penetrates the remaining film. By comparing the morphology at different times during solvent evaporation with the corresponding equilibrium structure of the evaporation zone, our work reveals the importance of this layer of short perpendicular cylinders formed in the early stage of solvent evaporation and its templating effect on the final film morphology, different from the previous speculations. 4. Results from Thermal Annealing. We also perform simulations for thermally annealed films. In this case the film is composed of diblock copolymers A3B9, and a certain amount of voids (i.e., S with α = 0), which are confined between two impenetrable walls. In all films the copolymer concentration is fixed at 0.85, and at this polymer concentration, the period of the bulk cylindrical phase was identified as L1 = 10.67 and L3 = 9.25.70 The two walls are identical and their preference for the two blocks is expressed by β. In this case, the film thickness, Δ, has been proven to have significant influence on the resulting morphology orientation.17,18,70 We investigate the morphology orientation as a function of β using a step size of 0.1 and the reduced film thickness, Δ/L3, in the range of 1.29−4.33, and

and 1.23, which are commensurate with the bulk period, C∥ with a diameter similar to that in the bulk is the dominating morphology when β ≥ 0.6. The morphology changes to C⊥ due to the incommensurability between δs and L3 is established again at δs/L3 ≈ 1.5, but changes back to C∥ at δs/L3 = 1.74− 2.25. As mentioned above, when β = 0, the top wall exhibits an effective attraction to the minority block due to the entropic effect,17,18 leading to the formation of a layer of half-cylinders near it. In this case, the two walls are asymmetric since the bottom one energetically prefers the majority block. Hence, the film thickness is commensurate with the bulk period when δs/ L3 is a half-odd integer; as shown in Figure 5, C∥ with a layer of half-cylinders is indeed observed at δs/L3 = 0.61 and δs/L3 ≥ 1.54. When β = 0.1−0.2, although the effective attraction of the top wall for the minority block due to the entropic effect is partially counteracted by the energetic interaction between the wall and the majority block, the commensuration condition is the same as that when β = 0, and hence, the morphologies when β = 0.1−0.2 are close to those when β = 0. By comparing Figures 2 and 4 with Figure 5, it is noted that the short perpendicular cylinders formed in the early stage of solvent evaporation at δ/L3 ≤ 0.82 are consistent with those obtained in Figure 5 at the corresponding effective film thickness, indicating that the short perpendicular cylinders formed during solvent evaporation are equilibrium morphologies. On the other hand, the parallel orientation obtained in Figure 5 at δs/L3 ≈1.0 and 2.0 and 0.2 ≤ β ≤ 1.1 never occurs in Figure 2c, where perpendicular orientation remains until the end of solvent evaporation. This indicates that the already formed morphology in the early stage of the solvent evaporation (i.e., the hexagonally packed short perpendicular cylinders near the top of the film) has a templating effect on the morphology formed subsequently thus driving the film to form a morphology that has the same symmetry. The perpendicular orientation obtained in the dry film at 0.2 ≤ β ≤ 1.1 in Figure 2 is therefore induced by the short perpendicular cylinders formed in the early stage of the solvent evaporation. On the other hand, the surface preference for the majority block has a tendency to drive the film toward the parallel orientation. It is the competition between these two tendencies that determines the cylinder orientation after solvent evaporation. The occurrence of the parallel orientation at the free surface is delayed to β ≈ 1.2 in Figure 2 since the perpendicular orientation is the preferred one in the early stage of the solvent evaporation. Therefore, morphology obtained after solvent evaporation is usually not an equilibrium one but depends on the process. This explains why the morphologies shown in Figure 2 are not always consistent with those occurred in Figure 5 at the corresponding effective thicknesses. There are other factors that can influence the abovementioned two tendencies, such as the solvent evaporation rate and the solvent selectivity. The solvent evaporation rate reva determines the relaxation time of a system. A large reva value implies inadequate relaxation of the system; the morphology or orientation formed in the early stage of solvent evaporation may therefore remain. Whereas a small reva value provides adequate relaxation so that the polymer chains can rearrange and finally overcome the energy barrier needed to change the already formed morphology or orientation; parallel cylinders are therefore observed when β is large, as shown in Figure 4c and listed in Table 1. It is expected that, when the reva value is H


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Macromolecules

not commensurate with the bulk period. At each film thickness, the maximum β-value is smaller and the β-window for the formation of C⊥ morphology is narrower than the corresponding values obtained with solvent evaporation as shown in Figure 3. A comparison between the results obtained with solvent evaporation and those with thermal annealing clearly indicates that solvent evaporation promotes the formation of perpendicular cylinders. 5. Results from Spherical Initial States. Some experimental studies10,11 have indicated that the formation of cylinders may involve an order−order transition; that is, cylinders form from the coalescence of spheres in the solvent evaporation process. In the present work, simulations of the self-assembly in block copolymer thin films upon solvent evaporation with initial spherical states are also carried out. The simulations are performed with the following two steps. In the first step, the film with a swelling ratio of 2.0 is equilibrated at the simulation temperature. The obtained initial morphology is spheres in several layers. Figure 7 shows typical spherical initial states with α = 1.0 and Δ0/L3 = 2.15 (a, b) and 2.35 (c, d). The spheres form an approximately hexagonally packed structure in each layer and exhibit either an ABC-type (i.e., FCC, Figure 7, parts a and b) or an ABA-type (Figure 7, parts c and d) approximately close packed structure three-dimensionally. In the second step, simulations of solvent evaporation are carried out starting from the spherical structure obtained in the first step. Parts a and b of Figure 8 show two typical sequences of morphology evolution during solvent evaporation from spherical initial states, which lead to the formation of final C⊥ and C∥ morphologies, respectively. Both cases have the same solvent selectivity of α = 1.0, the same initial swelling ratio of 2.0, the same reduced dry film thickness of Δ0/L3 = 2.35, but different surface preference of β = 0.9 and β = 1.1. Since the initial state is in an approximately close packed structure as shown in parts c and d of Figure 7, the line connecting the closest spheres in adjacent layers are not along the Z-axis direction but form an angle close to 35° with it. In the early stage of solvent evaporation, the spheres in the top layer move down and each becomes in contact with a sphere in the second layer, which then merge into a short cylinder. Note that this always occurs regardless of the β value and the film thickness, and that the orientation of these short cylinders usually deviates slightly from being perpendicular to the substrate. With solvent

the results are shown in Figure 6. It is noted that in this case the β-window for obtaining the C⊥ morphology oscillates with film

Figure 6. Morphology and orientation diagram for thermally annealed films as a function of the reduced film thickness and the surface preference. The boundaries of the β-window for the C⊥ morphology are marked with a pair of red solid circles at each given Δ/L3 value, while other morphologies including C∥, undulated cylinder, perforated lamellae and a morphology composed of both perforated lamellae and parallel cylinders form outside the window, and their boundaries are marked by hallow symbols. Typical C⊥ and C∥ morphologies (in side view) and other morphologies (in aerial view) are also shown.

thickness almost periodically. The maximum β-value for the formation of C⊥ morphology is usually 0.5 when the reduced film thickness is close to an integer (that is, the film thickness is nearly commensurate with the bulk period), while it is usually 0.6 when the reduced film thickness is close to a half-integer with only one exception of 0.7 at Δ/L3 ≈ 2.5. The minimum βvalue for the formation of C⊥ morphology is usually 0.2 when the reduced film thickness is close to an integer, while it is usually 0 or 0.1 when the reduced film thickness is close to a half-integer with only one exception of −0.1 at Δ/L3 ≈ 1.5. The β-window for the formation of C⊥ morphology narrows for thicker films. This is because there are more layers of cylinders in the parallel structure in thicker films. Hence the chain stretching or compression is smaller when the film thickness is

Figure 7. Typical spherical initial states for film with α = 1.0. Side views of an approximate (a) ABCA-type and (c) ABABA-type close packed structure when Δ0/L3 = 2.15 and 2.35, respectively. (b and (d Different slices at the given Z/L3 values in structures shown in parts a and c, respectively. I


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Figure 8. Snapshots of films during solvent evaporation starting from spherical initial states, where α = 1.0, reva = 1000, the reduced dry film thickness Δ0/L3 = 2.35 with L3 = 9.77, and (a) β = 0.9 and (b) β = 1.1. Side views of the film morphology are shown, except for the morphology atΔ/Δ0 = 1.09, where the top views are shown. The color scheme and the details of the plots are the same as those in Figure 1.

evaporation progressing, the orientation of these short cylinders gradually changes to be perpendicular. The formation of a layer of short perpendicular cylinders in this case is similar to that from the random initial states shown in Figure 2c−e. With further solvent evaporation, the short perpendicular cylinders move down and merge with spheres in the third layer. It should be noted that for each cylinder, its closest sphere in the layer below is not right under it as well. The subsequent process depends on the β-value. When β ≤ 0.9, each short cylinder can easily merge with its closest sphere and grow longer, and this process repeats for the remaining layers of spheres, so that the perpendicular cylinders continue to grow and finally penetrate throughout the film. When β > 0.9, however, mismatches between short cylinders and spheres form such that one cylinder can be in contact with more than one spheres or no sphere resulting in cylinders that are tilted in various directions. Because of the strong surface preference, the tilted cylinders, especially those close to the free surface, reorient to form short parallel cylinders, which then grow longer horizontally. With further solvent evaporation, more mismatches between the short cylinders and spheres form. Parallel cylinders thus form layer by layer, as shown in Figure 8b. Figure 9 shows the cylinder orientation diagram for films evaporated from spherical initial states as a function of the reduced dry film thickness Δ0/L3 and β, when α = 1.0. The initial state is composed of 3−7 layers of spheres, depending on the film thickness. It is noted that the minimum β-value for the formation of perpendicular cylinders is always 0.2, independent of the film thickness. It is also noted that the β-window for the formation of C⊥ morphology slightly narrows with increasing Δ0/L3. As explained above, usually a sphere is not right below a formed cylinder, and there is a chance of forming mismatches when the cylinders and spheres merge during solvent evaporation. For larger Δ0/L3, there are more layers of spheres in the initial state, and the chance of forming mismatches is larger. The β-window for forming the C⊥ morphology therefore narrows with increasing Δ0/L3. On the other hand, spheres have to move collectively in order to merge with the cylinders and to avoid the mismatches, during which a higher energy barrier needs to be overcome compared to the case starting from a random initial state. Since the mismatches finally drive the film toward a parallel morphology, the β-window for the formation of C⊥ morphology is narrower than that for films starting from random initial states. Finally, the β-window for the formation of the C⊥ morphology with solvent evaporation is always wider than that in the thermal annealing case,

Figure 9. Cylinder orientation diagram for films after solvent evaporation with reva = 1000, α = 1.0. The initial swelling ratio is 2.0 for all films. The color scheme and the details of the plots are the same as those in Figure 6.

indicating that solvent evaporation promotes the formation of the C⊥ morphology even with the spherical initial states.

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CONCLUSIONS Using lattice Monte Carlo simulations, we have systematically studied the self-assembly in cylinder-forming diblock copolymer films on a flat substrate upon solvent evaporation. It is assumed that the free surface (vapor) and the substrate have the same interactions with the copolymers, and that the solvent evaporation starts from the free surface and gradually propagates toward the substrate. Our treatment of solvent evaporation corresponds to the limiting case of the chemical potential difference between a vapor and a solvent molecule μ → −∞ in the model of Rabani and co-workers.68,69 Two types of initial states are considered, morphology evolutions during solvent evaporation are investigated, and the results are compared with those from thermal annealing. It is found that the perpendicular cylinder (C⊥) morphology is promoted by the solvent evaporation as well as the selectivity of the solvent, and mix-orientated morphologies are predicted. The microscopic mechanisms of the resulting morphology orientations are elucidated. J


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For solvent evaporation starting from a random (disordered) initial state, the effects of solvent selectivity, surface preference (measured by β) and solvent evaporation rate on the morphology orientation are investigated. A stronger solvent selectivity for the majority block results in a wider β-window for the formation of C⊥ morphology due to the increased entropic preference of the free surface for the minority block and the higher energy barrier to be overcome by the copolymer chains in order to rearrange from the already formed morphology orientation. This β-window for the formation of C ⊥ morphology is much wider than that obtained from the thermally annealed films. Mix-orientated cylinders with one or two layers of parallel cylinders at the top of the film and perpendicular cylinders throughout the remaining film are obtained in films with stronger solvent selectivity, and they are consistent with those observed in a recent experimental study.30 The formation of mix-orientated morphology can be understood based on the effective surface preference after one layer of parallel cylinders forms near the free surface during the evaporation. When the solvent evaporation rate changes from fast to slow at relatively strong surface preference, the resulting morphology changes from perpendicular cylinders to mixorientated cylinders and finally to parallel cylinders, indicating that fast solvent evaporation can promote the formation of perpendicular cylinders, and that the mix-orientated structure is an intermediate morphology between the parallel and the perpendicular cylinders. By comparison with the simulation results of “static” films with different thicknesses and approximately the same boundaries and copolymer concentration as the evaporation zone, it is deduced for the first time that the short perpendicular cylinders formed in the early stage of solvent evaporation may remain to the dry film when the solvent evaporation is fast or the solvent selectivity is strong, and hence they have induced the formation of the final perpendicular cylinders. This mechanism is different from those suggested previously.1,2,23,28,56 For the case of solvent evaporation starting from a spherical initial state containing approximately close-packed spheres, the cylinders form by coalescence of spheres layer by layer during solvent evaporation. In this case, the β-window for the formation of C⊥ morphology is smaller than that in the case of random initial states, but is larger than that in the case of thermal annealing. In the early stage of solvent evaporation, spheres in the top two layers can always merge together and form a layer of short perpendicular cylinders, independent of the surface preference and the film thickness. Therefore, it is deduced that the same mechanism as in the case of random initial states exists in this case. However, mismatches often occur when the already formed short cylinders connect to the remaining spheres at large β-values, which drives the film toward a parallel morphology and results in smaller β-window than in the case of random initial states. Because a sphere connects to the already formed cylinders as a whole while only one or several segments can be moved each time in our simulations, this results in a higher energy barrier to be overcome by the copolymer chains in order to rearrange, thus giving a smaller β-window, compared to the case of random initial states.

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Baohui Li: 0000-0002-8403-1220 Qiang Wang: 0000-0001-6456-9288 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (21574071, 21528401, 20925414, and 91227121), by the PCSIRT (IRT1257), and by the 111 Project (B16027). Zhan Wang gratefully acknowledges the supports from the National Science Fund for Talent Training in Basic Sciences under Grant No. J1103208.

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Self-Assembly in Block Copolymer Thin Films upon Solvent Evaporation

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