Effect of Grafting Density of Random Copolymer Brushes on

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Effect of Grafting Density of Random Copolymer Brushes on Perpendicular Alignment in PS‑b‑PMMA Thin Films Wooseop Lee,† Sungmin Park,† Yeongsik Kim,† Vaidyanathan Sethuraman,‡ Nathan Rebello,‡ Venkat Ganesan,*,‡ and Du Yeol Ryu*,† †

Department of Chemical and Biomolecular Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Korea Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, United States

‡

S Supporting Information *

ABSTRACT: We modulated the grafting density (σ) of a random copolymer brush of poly(styrene-r-methyl methacrylate) on substrates to probe its effect on the formation of perpendicularly aligned lamellae of polystyrene-b-poly(methyl methacrylate) (PS-b-PMMA). Supported by coarse-grained simulation results, we hypothesized that an increase in σ will allow us to systematically tune the block copolymer interfacial interactions with the substrates from being preferential to one of the blocks to being neutral toward both blocks and will thereby facilitate enhanced regimes of perpendicularly aligned lamellae. We verified such a hypothesis by using a simple grafting-to approach to modify the substrates and characterized the thickness window for perpendicular lamellae as a function of brush thickness (or σ) on the grafted substrates using scanning force microscopy (SFM) images and grazing incidence small-angle X-ray scattering (GISAXS) measurements. The experimental results validated our hypothesis and suggested that the σ of random copolymer brushes can be used as an additional versatile parameter to modulate the interfacial interactions and the resulting alignment of block copolymer films.

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INTRODUCTION Polymer−substrate interfacial energy plays an important role in determining the compatibility at the boundary of different surfaces, and its control has been an important effort in practical applications such as wetting and adhesion behaviors of polymers onto the substrates.1−5 In this regard, a grafting-to approach using end-functionalized random copolymers has emerged as a simple and versatile method to tune the interfacial energy of substrates.6,7 This method has a practical advantage that at least three independent parameters, viz., the molecular weight (Mn),8 chemical composition ( f),9,10 and grafting density (σ)11 of the brush copolymer can be tuned to modulate the interfacial interactions. Lamellar and cylindrical structures of block copolymer (BCP) films with perpendicularly oriented features have emerged as significant interest for photolithography techniques and nanoimprinting.12−22 Unfortunately, such morphologies are often obtained only in substrates where the interfacial interactions with the blocks are approximately balanced (i.e., “neutral” surfaces) so as to mitigate the preference for features aligned parallel to the substrate.20,23−31 In such a context, the use of random copolymer brush of poly(styrene-r-methyl methacrylate) (P(S-r-MMA)), fabricated by a grafting-to approach to exhibit similar surface energies with the polystyrene (PS) and poly(methyl methacrylate) (PMMA) blocks, was shown to successfully induce a perpendicular orientation of microdomains in thin PS-b-PMMA films.6−11,32 Explicitly, in the absence of such a brush surface, the BCP films © XXXX American Chemical Society

resulted in a parallel orientation due to the large difference in surface energies of the two blocks and/or the resulting preferential interaction with one of the blocks.33,34 In contrast, by the use of a random copolymer brush of appropriate composition, the interfacial interactions were rendered balanced to the two components to lead to perpendicularly oriented morphologies. Theoretical calculations based on self-consistent field theory demonstrated that, in addition to the interactions between the brush and the overlaying block copolymer, a self-assembly “templating” effect enabled a accentuation of the interfacial interactions with the brush copolymer, thereby facilitating perpendicularly oriented morphologies over a wide range of brush compositions.28,35,36 Moreover, this microdomain orientation was significantly influenced by an entropic commensurability effect that dictates the thickness-dependent stability between the equilibrium period of BCP (D ∼ lamellar spacing) and film thickness.37−39 While previous works illustrated the influence of the composition of the random copolymer brush in influencing the parametric regimes where perpendicularly oriented morphologies were achieved,9,10,28,36,40 there has been less clarity on the role of the grafting density on such characteristics. In a different study, we probed the morphologies of thin PS-bReceived: January 26, 2017 Revised: June 14, 2017

A

DOI: 10.1021/acs.macromol.7b00133 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules PMMA films on the grafted substrates with a hydroxyfunctionalized polystyrene (PS-OH) and produced perpendicular lamellae and cylinders in a selected range of σ of PS-OH on the substrates.41 Such a window for perpendicular structure was rationalized by suggesting that by varying σ of a PS homopolymer on a PMMA-selective native oxide layer of Si substrate, the interfacial interactions were rendered similar to the two blocks and thereby led to perpendicularly oriented morphologies. However, such a strategy is limited to a window of grafting densities before which the surface becomes preferential with the PS block and results in parallel morphologies. This work is based on the hypothesis that variations of grafting density of a random copolymer brush can serve as a more direct parameter to influence the interfacial interactions and lead to the formation of perpendicularly oriented morphologies. Indeed, at low grafting densities, we expect the morphologies to be influenced by the interactions with the bare Si surface and result in morphologies characteristic of preferential surfaces (for the common situation of a substrate preferential to one of the components). As a function of film thickness, such a behavior is expected to manifest at small grafting densities as a small window of film thicknesses which are incommensurate with the lamellar period over which perpendicular morphologies are observed. With increase in the grafting density, we expect that the interactions with the brush copolymers to become more relevant and the morphologies to become representative of neutral surfaces. Such a trend is expected to manifest as an expanded window of film thickness over which perpendicular morphologies are observed. In this study, we validate the above hypothesis using both computations and experiments and also seek to examine the grafting density requisite for shielding the surface interactions. At a computational level, we adapt the method of single chain in mean field approach and probe a range of grafting densities and film thicknesses to demonstrate a widening of the window of the perpendicular morphologies with an increase in grafting density. Motivated by such results, in experiments we exploited a simple grafting-to approach using a random copolymer of P(S-r-MMA) to modify the substrates, where the grafting density (σ) that tunes interfacial interactions on the substrates was controlled by varying thermal annealing temperature and/ or time. The effect of σ on the substrates was investigated with respect to the perpendicular orientation in a lamellar-forming PS-b-PMMA. The film thickness range (named as thickness window) for perpendicular lamellae was evaluated as a function of brush thickness (or σ) on the grafted substrates. The experimental results confirmed the qualitative features deduced in the computer simulations and demonstrated that the σ of the random copolymer brush can indeed be used as a versatile control parameter to influence the formation of perpendicularly oriented morphologies.

surface area, S = Lx × Ly, where Lx and Ly represent the box dimensions in the X and Y directions, respectively. The r-CP chains were grafted to the bottom surface. The grafting density, σ, defined as the number of chains per unit area dictated the number of r-CP chains in the system. The intramolecular interactions in both BCP and r-CP chains were modeled through a Hookean potential energy, Hb, of the form Hb =

3 2b2

n

N−1

∑ ∑ [ri(j) − ri(j + 1)]2 i=1 j=1

where ri(j) represents the position vector of the jth monomer in the ith chain. n, N, and b represent the number of chains, degree of polymerization, and the statistical segment length, respectively. The nonbonded interactions were accounted through pseudopotential fields w(r) and π(r) which respectively incorporate the influence of the incompatibility between the A and B segments and the compressibility of the system. The incompatibility fields w(r) are governed by the Flory−Huggins interaction parameter, χN, and the incompressibility fields π(r) are governed by the compressibility parameter, κN. The interaction of the monomers with the bottom surface was modeled using a potential of the form Hw =

⎛ z2 ⎞ λα exp⎜ − 2 ⎟ ds ⎝ 2ds ⎠

where λα represents the interaction parameter of monomer type, α ∈ {A, B}, with the bottom surface and at a distance z from the bottom surface, and ds represents the characteristic length scale over which the potential decays. Without loss of generality, for all the simulations presented in this paper, we have chosen the bottom surface to be preferential to component A. The top surface was assumed to be neutral to both A and B monomers. The entire system was evolved within a Metropolis Monte Carlo framework using random displacement, chain translation, and slithering snake moves. Acceptance criteria for Monte Carlo moves is given by Pacc → min(1, exp(−ΔHb − ΔHw − Δw − Δπ)). Periodic boundary conditions were employed in the X and Y directions. The entire system was equilibrated for 1.0 × 105 moves followed by a production run of 5 × 104 steps at the end of which the average density fields are computed. Subsequently, those density fields which form lamellae perpendicular (vertical lamellae) to the bottom surface are identified as perpendicular alignment cases. Those which form alignments that are perfectly horizontal to the bottom surface are identified as parallel lamellae. Finally, those which are constituted by a mix of both of the above cases are identified as mixed cases. Examples for the morphology cases mentioned above are depicted in Figure 1a−c. Simulations starting from five different random conditions are employed to identify the most favorable case for each film thickness. For some cases, 15 different initial conditions were employed for statistical certainty. In all the cases, the morphology that appears to be in the majority is assigned to that given film thickness. In the event equal numbers of vertical and parallel formations appear, the morphology is assigned as a mixed morphology. To identify thickness windows, the difference in film thickness obtained from the above analyses, over which continuous regimes of perpendicular or mixed lamella are observed (in situations wherein the top view of the mixed lamellae would be identified

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THEORETICAL SECTION We utilized single chain in mean field (SCMF) simulations to study the self-assembly of block copolymers in the presence of grafted copolymers under confinement. Since the details pertaining to SCMF simulations have been reported in a number of earlier works,20,42−45 we present only the most salient features here. The system considered for our simulations consisted of free AB BCP chains and grafted AB random-CP (r-CP) chains confined between two parallel planes a distance Lz apart and B

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equilibrium lamellar spacing D for pure diblock copolymer was found to be 3.6Rg,bcp, where Rg,bcp denotes the radius of gyration of the BCP chain. The height, Lz, was varied between 0 and 6.5Rg,bcp which corresponds to approximately 2 lamellar spacing. The number of grafted chains were calculated from the grafting density, and the number of BCP chains were calculated from the invariant degree of polymerization, N̅ = nRg,bcp3/V, where V represents the volume of the box. We investigated grafting densities in a unit of σRg,graft2 ranging from 0.028 to 3.5, where Rg,graft represents the radius of gyration of the grafted copolymer. In all our simulations, the value of N̅ is set at 50.0. The value of surface interaction parameter λα is chosen to be 2.2 for component A and −2.2 for component B. We note that the parameter λα impacts the relative interplay between the surface interactions and the influence of the random copolymer brush. Explicitly, a large magnitude of λα causes the surface interaction to be dominant for all the heights investigated, rendering the interactions with the two blocks more disparate and thereby promoting parallel lamellae. In contrast, a small magnitude of λα, corresponding to a situation of weak surface interactions, renders the influence of the brush dominant for almost all grafting densities (Figure S1). To rationalize such results, we note that at small λ values the energetic influence of the surface is weak, and only a smaller grafting density of the brush is required to shield such interactions. The above specific value of λα was chosen to provide a balance between the competing interactions and to render the effects of grafting density explicit. Although the quantitative trends are expected to be dependent upon the absolute values of λα, the qualitative trends arising in our results are expected to be retained and are used to compare with the experimental observations.

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RESULTS AND DISCUSSION For film thicknesses commensurate with D and at zero grafting density, predominantly parallel morphologies were observed. Such a behavior is an outcome of the strong preferential interactions of A segments with the bottom surface. With an increase in the film thickness, and at low grafting densities, the substrate−A interactions still dominate and lead to the formation of parallel lamellae over a range of film thickness. However, for window of film thicknesses which are significantly incommensurate with D, the formation of perpendicular lamellae was identified. The latter reflects the influence of the entropic costs involved in accommodating the parallel lamellae in such incommensurate thicknesses. Figure 2 depicts the thickness window range (δ) normalized by D over which the vertical lamellae are found from simulations. With increasing grafting density, we observed an expansion in the thickness window range for the occurrence of perpendicular lamellae. Such a trend reflects the influence of the random copolymer brush in shielding the preferential substrate interactions and instead replacing them by the neutral affinity toward both A and B segments.

Figure 1. 2D density plots for (a) perpendicular, (b) mixed, and (c) horizontal formations from SCMF simulations.

as perpendicular orientation in experiments, we include such a regime also in the identification of the thickness window), is computed. In situations where two windows appear (in some cases), the maximum of the two windows is considered. The degree of polymerization for the matrix and brush chains was chosen based upon the experimental data for which the ratio between the BCP and r-CP MWs was fixed at 5. Accordingly, the simulated system consisted of 40 BCP repeat units per chain and 8 r-CP repeat units. The molar compositions of A segments, fA, in BCP chains and r-CP chains were set to 0.463 and 0.577, respectively, which are in tandem with the experimental measurements. The Flory− Huggins interaction parameter, χN, was chosen to be 25.0, and the compressibility parameter, κN, was chosen to be 50.0. Qualitatively similar results are also obtained for a different interaction parameter (results not shown), χN = 15. The

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EXPERIMENTAL SECTION

The previous section presents computer simulation results which provide support to our hypothesis that the thickness window range of formation of perpendicular lamellae can be expanded by the grafting of the random copolymer brushes. Moreover, our results suggest that beyond some critical grafting density the thickness window range is less sensitive to the grafting density, which reflects the regime wherein the bare substrate interactions are essentially shielded, and the C

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(SAXS) in beamline 4C at the Pohang Accelerator Laboratory (PAL), Korea. A hydroxy-functionalized random copolymer (HO-P(S-r-MMA)) was synthesized by nitroxide-mediated, living radical polymerization. The mole fraction of styrene (XS) and Mn were measured to be 0.577 and Mn = 18.9 kg/mol, respectively, with a dispersity (Đ) of 1.21. This composition was turned out to balance the interfacial interactions to orient the lamellar microdomains normal to the substrate.9,10 For such a surface modification, a grafting-to method was used to prepare the P(S-r-MMA) grafted substrates by thermally annealing the films of HO-P(S-r-MMA) on standard Si wafer that contains the native oxide (SiO2) layer (∼2 nm), followed by rinsing with toluene to wash off unreacted polymer chains. Thermal annealing times were varied from 1 min to 3 days at various temperatures of 130, 150, and 170 °C under vacuum, which are well above the glass transition temperature (Tg ∼ 100 °C) of PS homopolymer; this process provided the copolymer brushes anchored onto the substrates, with the average brush thickness (d0) being controlled from 0.8 to 8.0 nm. PS-b-PMMA (93.5 kg/mol) films were spin-coated onto the grafted substrates. To control film thickness, the processes were run typically at 2000−5000 rpm for 1 min using 0.25−1.50 wt % BCP solutions in toluene. Subsequently, a series of BCP films were annealed at 190 °C for 24 h under vacuum to achieve thermal equilibrium. A spectroscopic ellipsometry (SE-MG 1000, Nano-view Co.) was operated at an incidence angle of 69.7° to measure film thicknesses, where a deuterium−tungsten lamp (Hamamatsu Photonics) was used as the light source with photon energy of 1.45−5.00 eV ranging from the ultraviolet to visible ranges. Scanning force microscopy (SFM; Dimension 3100, Digital Instrument Co.) was used to examine the surface morphology of polymer films, which was operated in a tapping mode with the standard silicon nitride probe at 3% offset below their resonance frequencies ranging from 250 to 350 kHz. Both SFM height and phase images were acquired in 2 μm × 2 μm at a scanning rate of 7 μm/s.

Figure 2. Thickness window range for formation of perpendicular lamellae.

interfacial energies arising from the brush constitute the relevant consideration. To validate such predictions, we undertook a parallel, synergistic experimental study of block copolymer morphologies on brush grafted substrates. A lamella-forming PS-b-PMMA was synthesized with styrene and methyl methacrylate monomers by living anionic polymerization. The number-averaged molecular weight (Mn), as characterized by sizeexclusion chromatography (SEC) combined with the multiangle laser light scattering (MALLS), was 93.5 kg/mol with a narrow dispersity (Đ = Mw/Mn) less than 1.04. The volume fraction of PS (ϕps) was determined to be 0.503 (corresponding to the mole fraction of 0.463), which was verified by 1H NMR (Avance II, Bruker Biospin) based on the mass densities of the two components (1.050 and 1.184 g/cm3 for PS and PMMA, respectively). The equilibrium period of PS-b-PMMA was evaluated to be D = 43.0 nm by small-angle X-ray scattering

Figure 3. (a) SFM height images of the grafted substrates with P(S-r-MMA) on a Si substrate. Brush thicknesses (d0) were indicated on the corresponding images, in which the regime of the reduced surface coverage (Σ) was divided based on an empirical criterion at Σ = 5. (b) Grafting density (in units of σRg,graft2) and distance between the grafted chains (dg) as a function of d0, where Rg,graft is the radius of gyration of random copolymer. (c) Surface roughness of the grafted substrates and reduced surface coverage (Σ) as a function of d0. For comparison, the radius of gyration (Rg,graft = 3.7 nm) of random copolymer chains is indicated. D

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Figure 4. (a) SFM phase images of PS-b-PMMA thin films prepared on the grafted substrates with various d0 (or σRg,graft2) of 8.0, 4.3, and 2.2 nm, where the horizontal and vertical orders indicate an increase in film thickness and a decrease in d0 (or σRg,graft2), respectively. The film thicknesses were indicated on the corresponding images, in which the thicknesses written in a blue color represented the perpendicular lamellae. (b−f) 2D GISAXS patterns of PS-b-PMMA thin films with thicknesses of 18.8 (b), 20.9 (c), 27.7 (d), 36.6 (e), and 39.1 nm (f), which were prepared on a grafted substrate with d0 = 8.0 nm.

where ρ and d0 are the density of random copolymer and brush thickness measured by ellipsometry, respectively, and NA is Avogadro’s number. The seven different substrates are prepared with the different d0 (or σ) since the other parameters are set in a random copolymer. Figure 3a shows SFM height images of the grafted substrates with P(S-r-MMA) on a Si substrate, where the average brush thicknesses measured by ellipsometry are indicated on the corresponding images. Mushroom-like topology is seen in the loosely grafted substrates up to thickness of 2.2 nm. A contrast inversion in the grafted substrate with thickness of 3.1 nm indicates that the copolymer brush chains are not enough to cover the substrate, leading to some empty or hole regions. When the brush thickness (d0) increases further to a maximum of 8.0 nm, the featureless images display a smooth surface topology. A quantified grafting density in units of σRg,graft2 and distance between the grafted chains (dg) are displayed in Figure 3b as a function of d0, where dg is defined by dg = 2/ σπ and Rg,graft is the radius of gyration in a grafted chain.46 An increase in d0, consistent with σRg,graft2, is inversely proportional to dg, reflecting that a physical change occurs from loosely grafted to densely and highly stretched chains on the substrates. Figure 3c shows the surface roughness of the grafted substrates and reduced surface coverage (Σ) as a function of d0. The root-mean-square surface roughness is assessed from SFM height images using Nanoscope control program, and a dimensionless Σ is calculated by Σ = σπRg,graft2.47−49 With an increase in d0, the surface roughness exhibits a discontinuous decrease to ∼0.2 nm at d0 = 4.3 nm with further values being relatively convergent, although the Σ increases linearly from 1.2 to 12.4. Interestingly, a midpoint displaying a remarkable decrease in surface roughness was estimated to be approximately d0 = 3.7 nm, which corresponds to Rg,graft = 3.7 nm of

The PS microdomains appear dark in contrast to the bright PMMA microdomains due to the viscoelastic contrast between the two phases. The root-mean-square (rms) surface roughness of the grafted substrates is defined by

1 n

n

∑i = 1 yi 2 using the Nanoscope control

program, where n is the number of subdivisions in a selected area and yi is the height deviation from the surface. Grazing-incidence small-angle X-ray scattering (GISAXS) experiments were carried out at the 9A beamline at Pohang Accelerator Laboratory (PAL), Korea. The typical operating conditions were set at a wavelength of 1.12 Å and a sample-to-detector distance of 2.5 m. The incidence angle (αi) was set at 0.140°, which was above the critical angle (0.114°) to probe the entire film structures. 2D GISAXS patterns were recorded using a 2D detector (SX-165, Rayonix) positioned at the end of a vacuum guide tube with an exposure time of 3 s.

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RESULTS AND DISCUSSION A random copolymer of P(S-r-MMA) was used for controlling the experimental grafting density (σ) with the same chain length on a Si substrate, in which the extent of grafting reaction was modulated by controlling the annealing time at several temperatures of 130, 150, and 170 °C under vacuum, well above the glass transition temperature (Tg ∼ 100 °C) of PS homopolymer. The temperature effect can be ascribed by an increase in diffusional mobility of polymer chains at higher temperatures, while the annealing time dependence is attributed to an increase in frequency to have condensation reaction at the interfaces. The σ, corresponding to the number of the grafted chains per unit area (chains/nm2), was calculated by σ=

ρd0NA Mn E

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Figure 5. (a) Thickness window for perpendicular lamellae in PS-b-PMMA thin films prepared on the grafted substrates as a function of d0 (or σRg,graft2 in the top x-axis), which were evaluated by the SFM images and GISAXS measurements. (b) Thickness window range as a function of d0.

between the equilibrium period of BCP (D = 43.0 nm) and film thicknesses, as denoted with different color codes. Grazing incidence small-angle X-ray scattering (GISAXS) was measured to confirm the thickness window for perpendicular lamellae out of the mixed morphologies. In the scattering geometry, αf and 2θf are the exit angles of the X-ray beam along the out-of-plane scattering normal to the sample surface, and along the in-plane scattering normal to the incidence plane (or parallel to the sample surface), respectively. An incidence angle (αi) was applied at 0.140°, which is above the critical angle (0.114°) for PS-b-PMMA films to probe the film morphology across the entire thickness. Here, q = (4π/λ) sin θf is the in-plane component of scattering vector, where λ and θ are the wavelength of X-ray and scattering angle, respectively. Figures 4b−f show a 2D GISAXS patterns of PS-b-PMMA thin films prepared on a grafted substrate with d0 = 8.0 nm. For all the GISAXS patterns, Bragg rods of the primary peaks are identified at 2θf = ±0.150° (q* = 0.146 nm−1) along out-ofplane scattering direction, indicating a consistent interlamellar spacing (D) of 43.0 nm by D = 2π/q*. With an increase in the film thickness, the higher order peaks in in-plane scattering direction along the horizon of αf = 0.132° become evident with the scattering vector ratios of q/q* = 1:(2):3, characteristic of lamellar microdomains due to volumetric symmetry between the two blocks. Unlike typical scattering patterns of the BCP films within the thickness window, however, the strong out-ofplane scatterings along the beamstop are observed in the mixed morphologies of 18.8 and 39.1 nm thick BCP films (marked as the arrows in the patterns), which are caused by the surface roughness arising from the hole or island formations rather than parallel lamellae. Likewise, the thickness window for perpendicular lamellae can be verified with the GISAXS measurements. The thickness range of perpendicular lamellae becomes narrower when the d0 decreases to 2.2 nm along the vertical orders (or the σRg,graft2 decreases to 1.095), as marked by the blue colors of film thicknesses in the second and third rows of SFM images. Intriguingly, the dot structures are identified in very thin BCP films on the grafted substrate with d0 = 4.3 nm, as shown in film thicknesses below 17.1 nm, similarly observed in 15.8 nm thick BCP film on the grafted substrate with d0 = 2.2 nm. As the d0 (or σRg,graft2) decreases, the interfacial

random copolymer chains. In addition, the value of Σ at d0 = 3.7 nm is calculated to be 5.8, and this value may be associated with an empirical criterion by Brittain et al. (at Σ = 5) and Chen et al. (at Σ ∼ 6), above which the grafted chains become stretched out of the substrates.48,50 Such a trend reflects that the highly stretched chains on the substrates are achieved above Σ = 5, where we observe the minimum surface roughness, as also guided in Figure 3a by the range of Σ. The PS-b-PMMA films were spin-coated onto the grafted substrates with different d0 (or σ), and the film thicknesses were controlled to illustrate thickness-dependent structures and orientation of lamellae. Subsequently, a series of BCP films were annealed at 190 °C for 24 h under vacuum to achieve thermal equilibrium. Figure 4a displays SFM phase images of thin PS-b-PMMA films prepared on the grafted substrates with various d0 (or σRg,graft2) of 8.0, 4.3, and 2.2 nm, where the horizontal and vertical orders indicate an increase in film thickness and a decrease in d0 (or σRg,graft2), respectively. Along a densely grafted substrate with d0 = 8.0 nm (σRg,graft2 = 3.945) in the first row, the 15.4 and 18.8 nm thick BCP films exhibit some islands of perpendicular lamellae due to an insufficient surface coverage and the featureless smooth areas that correspond to the PS blocks. The top PS layers are attributed to single layer of parallel lamella due to slightly lower surface energy of the PS blocks, which overcomes an entropic loss to form perpendicular orientation. When the film thickness of BCP layer on a substrate increases from 20.9 to 36.6 nm, however, the film structures are developed to typical short and long stripe patterns of perpendicular lamellae predominantly due to the balanced interfacial interactions from the grafted substrates. This thickness regime with a consistent morphology is hereafter referred to as a thickness window for perpendicular lamellae. Further increase in film thickness to 39.1 nm produces again a mixed morphology consisting of perpendicular lamellae and some holes formed by the PS layers arising from parallel lamellae. Above this thickness, the parallel orientation of lamellar microdomains may become favorable because the interfacial interactions from the substrates dissipate with film thickness and the chain deformation dissipated over many layers relieves the entropic penalty for forming perpendicular orientation. Therefore, the film thickness dependence on perpendicular lamellae indicates a commensurability effect F

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pertinently, it can be seen that both experiments and simulations predict that a grafting density of σRg2 ≈ 2.0 suffices to shield the native substrate−polymer interactions and ensure perpendicularly oriented lamellae. Even though the different chain lengths of random copolymer (r-CP) brushes have been studied to achieve the surface neutrality of a grafted substrate, no information on a generalized grafting effect was available. This guideline, which is independent of molecular weight of r-CP, provides a criterion for a minimum grafting effect of random copolymers onto the substrates in order to maximize the thickness window of BCP.

interactions from the loosely grafted substrates become more PMMA-favorable, while the PS blocks are repelled out of the substrates; this volumetric imbalance on the surface due to an underlying PMMA layer generates the spherical PMMA microdomains surrounded by the matrix of PS blocks.51,52 For clarity, the coexistence with parallel lamellae and/or dot structures is treated as a mixed morphology. Figure 5a shows the thickness window for perpendicular lamellae in thin PS-b-PMMA films prepared on the grafted substrates as a function of d0 (or σRg,graft2 in the top x-axis), which were evaluated by the SFM images and GISAXS measurements. The upper and lower limits in thickness ranges including each d0 are defined as the medians of transition thicknesses deviated from perpendicular lamellae at a selected d0. The similar upper boundaries are associated with a commensurability effect as the film thicknesses approach the equilibrium period of BCP (D = 43.0 nm). This effect is evident on such a grafted substrate that is PMMA-favorable, as in the BCP films prepared on a grafted substrate with d0 = 0.8 nm only to display a narrow thickness range close to D. Above the upper boundaries, the parallel lamellae become entropically more favorable in competition. As the d0 on the grafted substrates increases, the lower boundaries broaden initially to d0 = 6.0 nm and remain relatively unchanged up to d0 = 8.0 nm (σRg,graft2 = 3.945), as plotted in Figure 5b. An increase in d0 corresponds to an increase in the enthalpic effect by the balanced interfacial interactions from the substrates to hold perpendicular lamellae. However, the surface neutrality of a grafted substrate with d0 = 6.0 nm is not less than that with the maximum d0 = 8.0 nm, which suggests the existence of a threshold σ to ensure a consistent thickness range of perpendicular lamellae. In very thin BCP films below the lower boundaries, nevertheless, the mixed morphologies include the short-range ordered PMMAdot structures and hole/island structures of microdomains due to an insufficient surface coverage of the BCP films. Comparison between Experimental and Simulation. As noted earlier, a quantitative comparison between the experiments and simulations requires knowledge of the surface interaction energies of the A and B components. Despite this shortcoming, in Figure 6 we overlay the experimental and theoretical results to demonstrate broad agreement between the qualitative trends and indicate a broadening of the thickness window with increasing grafting densities. Perhaps more

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CONCLUSION In summary, in this work, we presented both computational and experimental results illustrating the influence of the grafting density of random copolymer brushes on the formation of perpendicular lamella morphologies. We hypothesized and validated through our results that an increase in the grafting density would lead to an expansion in the thickness window for the formation of perpendicular lamellae. We observed that beyond a critical value the thickness window was less sensitive to the brush grafting density. Such a result illustrates that by a minimal extent of surface grafting of random copolymer brushes may suffice to neutralize the substrate−polymer interactions and pave the way for realizing perpendicular morphologies as may be desired in applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00133. Figure S1 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (V.G.). *E-mail: [email protected] (D.Y.R.). ORCID

Venkat Ganesan: 0000-0003-3899-5843 Du Yeol Ryu: 0000-0002-0929-7934 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.G. acknowledges funding in part by grants from the Robert A. Welch Foundation (Grant F1599), the National Science Foundation (DMR-1306844), and King Abdullah University of Science and Technology (OSR-2016-CRG5-2993-1). Acknowledgment is also made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research (56715-ND9). D.Y.R. acknowledges funding by the NRF grants (2017R1A2A2A05001048, 2017R1A4A1014569) and funding (20163030013960) from the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE), Korea.

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Figure 6. Comparison of experimental results with the simulations. Thickness window range for formation of perpendicular lamellae is given as a function of σRg,graft2.

REFERENCES

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