Double Layer Morphologies from a Silicon-Containing ABA Triblock

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Double Layer Morphologies from a SiliconContaining ABA Triblock Copolymer Sangho Lee, Li-Chen Cheng, Karim Raafat Gadelrab, Konstantinos Ntetsikas, Dimitrios Moschovas, Kevin G. Yager, Apostolos Avgeropoulos, Alfredo Alexander-Katz, and Caroline A Ross ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b02851 • Publication Date (Web): 01 Jun 2018 Downloaded from http://pubs.acs.org on June 1, 2018

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Double Layer Morphologies from a Silicon-Containing ABA Triblock Copolymer Sangho Lee†, Li-Chen Cheng†, Karim R. Gadelrab†, Konstantinos Ntetsikas‡, Dimitrios Moschovas‡, Kevin G. Yager#, Apostolos Avgeropoulos‡, Alfredo Alexander-Katz†, and Caroline A. Ross†* † ‡

Department of Materials Science and Engineering, MIT, Cambridge MA 02139, USA

Department of Materials Science Engineering, University of Ioannina, University CampusDourouti, 45110 Ioannina, Greece

#

Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton NY 11973, USA

*E-mail: [email protected]

ABSTRACT: A combined experimental and self-consistent field theoretical (SCFT) investigation of the phase behavior of poly(stryrene-b-dimethylsiloxane-b-styrene) (PS-bPDMS-b-PS or SDS32) thin films during solvent vapor annealing is presented. The morphology of the triblock copolymer is described as a function of the as-cast film thickness and the ratio of two different solvent vapors, toluene and heptane. SDS32 formed terraced bilayer morphologies even when the film thickness was much lower than the commensurate thickness. The morphology transitioned between bilayer cylinders, bilayer perforated lamellae and bilayer lamellae, including mixed structures such as a perforated lamella on top of a layer of in-plane cylinders, as the heptane fraction during solvent annealing increased. SCFT modeling showed the same morphological trends as a function of the block volume fraction. In comparison with

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diblock PS-b-PDMS with same molecular weight, the SDS32 offers a simple route to produce a diversity of well-ordered bilayer structures with smaller feature sizes, including the formation of bilayer perforated lamellae over a large process window. KEYWORDS: self-assembly, solvent vapor annealing, ABA triblock copolymer, PS-b-PDMSb-PS, thin film, self-consistent field theory.


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The self-assembly of block copolymer (BCP) films has garnered significant interest due to its ability to fabricate periodic nanostructures with a variety of morphologies.1-10 The diversity of possible BCP morphologies has enabled a wide variety of applications including nanoporous membranes for filtration and desalination,11-12 hydrophobic surfaces for self-cleaning films,13 photonic crystals for optical communication systems,14-16 and porous dielectrics for logic devices.17 Patterns with few-nm feature sizes and with long-range order resulting from directed self-assembly (DSA) have enabled the use of BCP films as masks for pattern transfer to produce bit patterned media (BPM),18-20 graphene nanodevices,21-22 and finFETs (fin field effect transistors).23-24 DSA can be accomplished through the use of topographical or chemical templates and has led to patterns with sub-10 nm period and low defect counts.19, 25-27 The morphology of the microdomains in a BCP film is determined by many factors including the volume fraction of each block, film thickness, surface energy, and interfacial interactions,28-30 and can be regulated via the annealing process, substrate chemistry, and topcoat layer.31-35 The morphology also depends fundamentally on the molecular architecture of the polymer, and has been explored most extensively in diblock copolymers which form morphologies that contain spherical, cylindrical, lamellar and gyroidal microdomains. However, with developments in synthetic techniques, there has been an increasing interest in the formation of microdomain patterns from cyclic block copolymers, linear triblock copolymers and terpolymers, miktoarm star copolymers, and bottlebrush copolymers,36-40 among others. These can exhibit a wide variety of morphologies, such as the tiling patterns or core-shell structures formed in linear or star triblock terpolymers. ABA triblock copolymers (where A and B represent the blocks) provide an interesting comparison with AB diblock copolymers because ABA triblock copolymers have been reported 3 ACS Paragon Plus Environment

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to have a larger processing window and to form smaller feature size for the same molecular weight.41-46 Nealey, Russell, et al. reported the capability of ABA triblock copolymers (TBCPs) with small microdomain spacing to be guided by chemical or topographical templates.43-44 Epps et al. demonstrated the effect of solvent removal rate or localized annealing on the orientation of cylinders in TBCP thin films.45-46 This work focused on lamellar or cylinder-forming TBCPs,41-46 and perforated lamellar, gyroid morphologies or metastable structures in TBCPs have not been investigated. Silicon-containing TBCPs have not been examined in thin film form, although compared to organic TBCPs, such materials are expected to offer advantages in terms of etch selectivity and etch resistance. These etch characteristics simplify pattern transfer into other materials by additive or subtractive methods.47-49 Here, we describe the effects of film thickness and mixed solvent vapor composition on the thin film morphologies of poly(styrene-b-dimethylsiloxane-b-styrene) (PS-b-PDMS-b-PS) with total number average molecular weight Mn = 32 kg/mol, named hereafter as SDS32; see Supplementary Figure S1. Solvent vapor annealing (SVA) using a continuous gas flow system was employed to allow the simultaneous flow of two different solvent vapor species, toluene and heptane, while independently controlling the partial pressure of each solvent.31 Self-consistent field theory (SCFT) calculations show a good agreement with the experimental observations of the morphology and confirm that a double layer of perforated lamellae represents a stable morphology for a TBCP. This work illustrates underlying principles for the phase behavior of SDS32 thin films as well as clarifying the processing conditions which yield particular morphologies.


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RESULTS AND DISCUSSION We first describe the evolution of the morphology in SDS32 films in situ during SVA using grazing-incidence small-angle X-ray scattering (GISAXS). A film with an as-spun thickness of 100 nm was annealed in a mixed solvent vapor consisting of toluene:heptane = 7.5:2.5, i.e. 7.5 sccm of toluene vapor in N2 plus 2.5 sccm of heptane vapor in N2. A similar film was annealed in toluene:heptane = 10:0, i.e. 10 sccm of toluene vapor in N2. The two films formed gyroid (G) and in-plane cylinders (C), respectively (Figure 1). The film annealed at a flow of 7.5:2.5 showed a G morphology at a swelling ratio (SR) of ~ 1.90 (point A1 in the GISAXS data). This converted to C morphology at the maximum SR of 1.98 (A2), with an in-plane period (= cylinder spacing) of 26 nm according to the scattering peak position in the qx direction. The deswelling process consisted of stopping the solvent vapor flow at ~ 30 min and injecting pure nitrogen (5 sccm for 20 min and 200 sccm subsequently) to dry the film. This resulted in the formation of G microdomains as described in the GISAXS profile at A3 in Figure 1(b), and SEM image in Figure 1(c). The dominant final morphology according to the SEM observation is an imperfect G, with small C-like regions visible that may be incompletely converted to G due to the short time of the deswelling which was not sufficient to allow complete rearrangement of the SDS32 microdomains. When the vapor flow was pure toluene, the morphological evolution of SDS32 was similar to that of a PS-b-PDMS diblock copolymer film.50 Initially the film exhibited well defined cylinders with a coexistence of in-plane and out-of-plane orientations at a SR of ~ 1.60 (B1). The cylinders were gradually oriented to in-plane as annealing proceeded and the final structure was an in-plane C structure after the quenching process, observed both in GISAXS and SEM in Figure 1. The in-plane period L0,C increased from 24 nm at a SR of 1.69 (B2) to 27 nm at a SR of 5 ACS Paragon Plus Environment

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1.00, i.e. the dry film (B3). However, the interlayer spacing in the out-of-plane direction was slightly reduced from 16 to 15 nm by drying, according to the qz diffraction peak. The distortion factor of the close packed cylinder array, which is defined as (2/√3)(out-of-plane interlayer spacing/in-plane cylinder spacing L0,C) therefore changed from 0.77 to 0.64. We infer that ~ 1 h of annealing time is not sufficient to form ideally packed C (distortion factor = 1) in this experimental setup even at the highest SR = 1.69 (B2). Thinner SDS32 films were spin-coated and solvent-annealed on bare Si substrates with native oxide, forming lamellae, perforated lamellae or cylinders as shown in Figure 2. A thin PDMS layer is preferentially formed at the air/TBCP interface due to the lower surface energy of PDMS vs. PS (γPDMS = 19.9 mN/m, γPS = 40.7 mN/m),51 and a PDMS layer is also expected to be present at the silica substrate. The internal morphology between these two PDMS wetting layers is determined by the film thickness and effective volume fraction of each block. The films typically exhibited islands and holes corresponding to regions with different numbers of layers of microdomains. This occurs when the film thickness is incommensurate with the layer spacing.28 For SDS32 films with as-cast thickness of 73 nm, Figure 3 shows the effect of solvent vapor ratio on the morphology. For this thickness all the samples exhibited two layers of microdomains between the PDMS wetting layers, but their morphology differed for each annealing condition. The PDMS block is preferentially swelled by heptane while PS is preferentially swelled by toluene,31 and therefore the effective volume fraction depends on the solvent vapor composition. At a solvent flow of toluene:heptane = 6:4, i.e. 6 sccm of toluene vapor in N2 plus 4 sccm of heptane vapor in N2, both top and bottom layers were in-plane lamellae of PDMS (L). Figure S2(a) clarifies that both layers are lamellae. It shows a featureless morphology attributed to L


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over the majority of the sample and a fingerprint-like pattern in the transition region where a C morphology is present. At a flow of 7:3 the bottom layer was a hexagonally coordinated perforated lamella (PL) and the top layer also changed to PL when the flow was 7.5:2.5. The inset of Figure 3(c) shows the two-layer PL structure in more detail. The holes in one layer overlay the junctions of the other. Thicker films of ~ 100 – 200 nm as-spun thickness show a 3D interconnected G morphology under the same annealing conditions (Figure S3), and G was also observed in the 100 nm thick film used for the GISAXS experiments. A bulk G morphology has also been observed in other TBCPs.52 Therefore the double layer of PL is assumed to be a non-bulk structure that is stabilized due to the confinement effect in the out-of-plane direction, and it transitions to a G as the film thickness increases. The center to center distance L0,PL between the pores of the PL morphology was 27 nm. As the toluene fraction increases and heptane decreases, C become dominant in the SDS32 films. For a flow of 8:2, Figure 3(d) shows that a well-ordered PL on top of C is formed, in which the holes in the top PL layer are aligned above the cylinders of the bottom layer. A double layer of C morphology is formed when the flow is 9:1 or 10:0 (Figure 3(e), 3(f), and S2(c)). In the 9:1 case the upper layer shows small regions of out-of-plane cylinders within the dominant C morphology, especially at the C junctions, whereas 10:0 solvent flow (pure toluene) produces only in-plane cylinders, as seen in the GISAXS experiment. In Figure S2, the morphology of each layer for different SVA conditions was clarified by imaging after different CF4/O2 etching times. The center to center cylinder spacing of the C was L0,C = 23 nm. To summarize these observations, a morphological transition from L to PL to C occurs as the fraction of toluene increases, and it is possible to capture non-bulk structures in SDS32 films, 7 ACS Paragon Plus Environment

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such as a double layer of PL or a PL layer on top of a C array, by controlling the solvent vapor ratio. Further, the experimental results demonstrate that sub-15 nm features are achieved using a 32 kg/mol TBCP which is smaller than that of a diblock copolymer film with the same molecular weight. From ref 53, a 23 nm cylinder period would be produced from a PS-b-PDMS diblock copolymer of ~ 20.5 kg/mol, and a sub-10 nm cylinder period would be produced from a diblock copolymer of ~ 19 kg/mol. We therefore expect that sub-10 nm cylinders would require a TBCP of ~ 30 kg/mol or less. On the basis of the SEM images, an experimental phase diagram as a function of as-cast film thickness and solvent vapor ratio was obtained, Figure 4(a). The solvent ratio influences the effective volume fraction of the TBCP, due to the selectivity of the solvents. Notably, the SDS32 forms double layer morphologies over a wide range of initial film thickness from 33 nm to 73 nm. No single-layered structures were found even when the as-cast film thickness was below 30 nm. In this case poorly-defined morphologies or only wetting layers are found, shown in Figure S4. Double-layer islands and holes (consisting of only a wetting layer) formed instead of a film of uniform thickness during the solvent vapor annealing, Figure S5. The fraction of islands and holes depends on the initial film thickness, and for the C morphology, a complete bilayer of microdomains occurs at a commensurate thickness equal to twice the interlayer thickness plus L0,C, assuming a PDMS wetting layer is present at both surfaces of the film with thickness ~ L0,C/2.54 Taking the interlayer spacing as √3L0,C/2, the commensurate thickness is ~ 2.73L0,C for an undistorted hexagonal array of in-plane cylinders. This is 63 nm for L0,C = 23 nm, which is in reasonable agreement with the film thicknesses observed to produce a bilayer with few islands and holes. Figure S6 shows that the step height of


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the islands is ~ 40 – 50 nm for an etched sample, which is consistent with the expected 1.73L0,C bilayer thickness. SDS32 therefore offers an opportunity to produce various 3D bilayer nanostructures in a single step process. This may be useful in the manufacturing of 3D devices, for example double layers of PL and G may lead to enhanced performance in catalysts,55 electrochromic devices,56 and filtration membranes11 due to their high surface-to-volume ratio and hierarchical porosity. In comparison with the case of a diblock PS-b-PDMS, SDS32 shows a wider process window to form the PL structure of Figure 4(a).31 This result may be due to the smaller variance in swelling ratio over the range of solvent vapor composition of toluene:heptane from 6:4 to 10:0 as described in Figure 4(b). The swelling ratio of SDS32 films changes only from 1.62 to 1.82 while that of diblock PS-b-PDMS varies by more than a factor of 2.31 In particular, the swelling ratio of the SDS32 remains almost constant for vapor fluxes from 6:4 to 7:3 which produce the PL morphology. We used SCFT simulations (discussed in the Methods section) to model the self-assembled morphologies of TBCPs under solvent vapor annealing. SCFT is well suited for predicting the self-assembly of multi-component systems.57 The stability of self-assembled morphologies of TBCP was studied in 3D as a function of film thickness and volume fraction f. The variation in f in the model mimics the effect of solvent selectivity in changing the effective volume fraction of the TBCP. Two representative equilibrium structures, the double layers of PL and C, obtained from both experiment and modeling are presented in Figure 5. All the structures exhibit in-plane microdomain orientation due to the strong attraction to the minority block B at the TBCP-air interface. The bilayer SCFT simulations reproduce the experimental morphologies, and a 9 ACS Paragon Plus Environment

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uniform top wetting layer is present as described in Figure 2. (The simulation does not include the PDMS wetting layer at the substrate-TBCP interface.) The period of the PL and C morphologies is 3.0 Rg and 2.7 Rg respectively, where Rg is the radius of gyration, and their ratio (L0,PL/L0,C = 1.11) is a good match to the experimentally determined ratio (27 nm/23 nm = 1.17) and to 2/√3 = 1.15, the ratio of center-center spacing/row spacing of a hexagonally close packed array. The ratio of L0,PL/L0,C = 2/√3 is expected if the PL is considered to derive from bridging between cylinders of that the spacing between rows of pores corresponds to the cylinder spacing. The combined influence of f and film thickness on the energy of each morphology was examined by seeding different morphologies and evaluating the equilibrium free energy F of the system. Figure 6 shows the magnitude of F as a function of film thickness for different values of f. At f = 0.6, the L structure has lowest energy at a film thickness of ~ 6.7 Rg. Away from the minimum, there is an approximately quadratic increase in F reflecting the effect of strain from the incommensurate film thickness. The PL structure follows the same behavior, with higher magnitude of F. Interestingly, at low film thicknesses (< 6 Rg), the two-layer C becomes stable over a range of f including values far from those where bulk cylinders are the stable morphology. Allowing the seeded 2-layer C structure to relax at large film thicknesses produced a third layer of C that has significantly higher energies compared to L and PL for the same film thickness. Increasing f to 0.62 stabilized the PL compared to L, with an equilibrium film thickness of ~ 6.5 Rg, but at lower film thickness the C structure was lower in energy. This behavior was maintained up to f = 0.66 at which the range of film thicknesses in which PL is stable (6.4 – 6.9 Rg) becomes bounded by stable C with two layers and three layers for smaller and larger film thicknesses, respectively. The region of stability of PL is limited to film thickness ~ 6.5 Rg at f = 0.68, and C is the stable morphology for f = 0.7 across the range of film thicknesses studied. The


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range of f at which PL is stable closely matches the bulk phase diagram for the G phase that spans f ≈ 0.6 to 0.66 for the χN employed in this study.52 Figure 7(a) summarizes which bilayer morphologies form as a function of film thickness and volume fraction. Low film thicknesses exhibit C morphology. The L morphology is stable for f = 0.6 while the PL occupies a triangular region where it replaces L at low f while the region of stability tapers off towards higher f values as C dominates. These results match well with the experiment in that both show a morphological transition from L to PL to C as f increases. The simulation results provide insight on the effect of film thickness on morphology, but the simulation does not allow for solvent evaporation or for relaxation by island and hole formation. The PL phase exhibits hexagonally coordinated holes within its layers. The two layers have a particular relationship with respect to each other, such that a hole in one layer is situated on top of a junction in the other, as seen experimentally. Hence, the top layer is shifted by an offset of

〈11〉 with respect to the bottom layer25 using indices where h and k are two vectors with

included angle 120˚, oriented along the close-packed directions of the pores and with length equal to the pore spacing. Mapping the free energy difference ∆F theoretically by displacing one layer with respect to the other reveals a three-fold symmetric ∆F map with a minimum energy at the same PL offset seen experimentally (Figure 7(b)). However, ∆F is of ~10-4 nkbT in the vicinity of the equilibrium configuration of the two PL layers and has a maximum barrier value of ~ 6×10-3 nkbT (n is the number of chains in the system, kbT is the thermal energy) suggesting that the two PL layers are able to be slightly displaced from their equilibrium position given the shallow energy landscape. In the bilayer C structure, the two layers are offset so that the upper cylinders lie parallel to and in between the lower cylinders resembling the hexagonal configuration.


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We finally comment on the interlayer spacing of the bilayer morphologies as a function of f in Figure 7(c). The spacing was determined by taking a cross-section in the B block density ϕB and measuring the distance between the two density peaks for the equilibrium film thickness (the film thickness at which the energy is minimized). In general there is a continuous decrease in interlayer spacing with increasing f, which occurs because the equilibrium film thickness decreases with increasing f, so the microdomains become thinner and closer together. For the C structure, the interlayer spacing varied nonmonotonically with f, tracking the equilibrium film thickness.


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CONCLUSION SDS32 triblock copolymer films were self-assembled into a variety of morphologies, some of which are not observed in diblock copolymer PS-b-PDMS or in bulk SDS32. Using a continuous flow solvent annealing system, a phase map showing the morphology dependence on the as-cast film thickness and solvent vapor ratio was constructed. Unlike diblock copolymer PS-b-PDMS, the SDS32 preferentially formed a double layer of microdomains even at low film thickness. The films comprised double layers of PDMS microdomains of C, PL, or L, or mixed morphologies of L/PL or PL/C for the lower/upper layers. The transition from L at higher heptane fraction in the vapor to PL then C at higher toluene fraction is consistent with an increase in the effective volume fraction of PS, because PDMS is preferentially swelled by heptane. SCFT simulations supported the evolution from double layer L to PL to C as the volume fraction of the majority phase increased. SCFT also showed that the double layer PL has lowest energy when the holes of one layer overlay the junctions of the other layer, as seen experimentally. The TBCP therefore provides access to unique nanoscale bilayer architectures by controlling the film thickness and solvent vapor annealing conditions. Some of these nanostructures may be useful in diverse applications such as nanofiltration membranes, photonic crystals, and metamaterials.


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METHODS Materials and Preparation of BCP Films. Symmetric

linear

PS-b-PDMS-b-PS

(SDS32)

triblock copolymers were synthesized via anionic polymerization in combination with chlorosilane chemistry (Supplementary Information). More details concerning the synthesis of similar samples can be found in ref 58. The number average molecular weight (Mn) for each block of SDS32 was 10.9-10.2-10.9 kg/mol and the polydispersity index (PDI) was 1.06. The volume fraction of PDMS (fPDMS) was 0.35. SDS32 thin films were spin-coated on silicon substrates with native oxide layer from 1 – 2 wt% solutions in cyclohexane. As-cast film thickness (33, 56, and 73 nm) was determined by adjusting the spin speeds (3,000 – 10,000 rpm) and measured values were obtained from a spectral reflectometer (FilMetrics F20-UV). All the solvents used in this study were purchased from Sigma Aldrich. Self-Assembly of BCP Films. SVA was carried out using a continuous flow system where separate streams of nitrogen are bubbled through liquid solvents and the flow of each stream is regulated using a mass flow controller.31 Spin-cast SDS32 films on substrates were placed inside the glass annealing chamber (volume ~ 80 cm3), and mixed solvent vapors of toluene and heptane were introduced into the chamber at flow rates of 10:0, 9:1, 8:2, 7.5:2.5, 7:3, and 6:4, where the numbers represent the flow rate in sccm for toluene:heptane. The total flow rate was fixed at 10 sccm. N2 gas (Airgas, Inc., 99.9997% purity) was distributed into the mass flow controllers (MKS Inc., M100B) with range 0 – 10 sccm. Two of the flow lines were used to deliver toluene and heptane vapors in N2 into the chamber, and a third N2 flow line was available to dilute the vapor pressure. SDS32 films were exposed to a steady flow of mixed solvent vapors for 1 h at ambient temperature. A quartz plate along with a perfluoroelastomer O-ring (Markez Inc., Z1210) was used to tightly seal the chamber. The film thickness was measured using a 14 ACS Paragon Plus Environment

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spectral reflectometer during SVA to calculate the swelling ratio. After the completion of the annealing process, the quartz lid was gently detached from the chamber at room temperature for 10 min to dry the swollen films. Characterization of BCP Films.

To enhance the imaging contrast, the PDMS surface layer

and PS microdomains of the annealed SDS32 thin films were selectively removed by reactive ion etching (RIE, Plasma-Therm 790) treatment with CF4 (5 s, 15 mTorr, 50 W) and O2 (22 s, 6 mTorr, 90 W), respectively. This process yields oxidized PDMS patterns that show the internal morphology of the PDMS microdomains arising from different annealing conditions. After RIE, the etched SDS32 films were imaged using a Zeiss Merlin high-resolution scanning electron microscope (SEM) at 3 kV. GISAXS Measurement. GISAXS experiments were performed at beamline X9 of the National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory. A custom solvent annealing cell was mounted inside the measurement chamber.50 The small cell was airtight and featured two Kapton windows to allow the incident X-ray beam and the scattered X-ray beam to transit. The lid of the cell included a quartz window to allow real-time monitoring of film thickness via UV−vis spectral reflectometry (Filmetrics). The cell also featured an inflow tube and solvent exhaust tube to allow for controlling the atmosphere within the chamber. The inflow tube was connected to a mixer fed by three flow channels: pure nitrogen for controlling the solvent absorption and desorption rate and two solvent bubblers which contained toluene and heptane respectively. In order to obtain sufficient solvent vapor pressure for the vapor ratio of toluene:heptane = 7.5:2.5, 5 mL of toluene:heptane 3:1 volumetric mixture was also added into the custom cell. SDS32 samples were exposed to a vapor flow of toluene:heptane = 7.5:2.5 and 10:0 for 30 min and 1 h respectively and slowly deswelled at room temperature for 20 min 15 ACS Paragon Plus Environment

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during the GISAXS measurement. Swollen films were completely dried by injecting pure nitrogen flow (5 sccm for 20 min and 200 sccm subsequently) to obtain the GISAXS data for the final state, which is identical to the morphology shown in SEM images. More details concerning the GISAXS setup of beamline X9 can be found in ref 50. Self-Consistent Field Theory. Self-consistent field theory (SCFT) simulations are a powerful tool to capture the equilibrium structures of block copolymers. Here, we briefly describe the formalism of SCFT simulations of a symmetric ABA triblock copolymer. We consider a monodispersed melt of n ABA triblock copolymer in a volume V, where each triblock molecule is composed of N segments. The A and B blocks consists of fN and (1-f)N chain segments, respectively. The interaction between the dissimilar blocks is controlled by a Flory-Huggins parameter χ. Within the mean-field approximation, the free energy of the system F is expressed in terms of field variables F 1 = ∫ dr (χNφ A (r )φB (r ) − wA (r )φ A (r ) − wB (r )φB (r ) − p(r )[1 − φ A (r ) − φB (r )]) − ln Q[wA , wB ] , (1) nk BT V where ϕα(r) is the volume fraction of species α at position r. Q[wA,wB] is the partition function of a non-interacting polymer in external fields wα(r). The polymer is assumed to be incompressible, so the constraint ϕA(r)+ ϕB(r)=1 is enforced through a pressure field p(r). The free energy F is compared to the thermal energy kBT. The single chain partition function can be evaluated as follows Q=

1 V

∫

drq ( r ,1) , (2)

where q(r,s) is a restricted chain partition function (propagator) that could be calculated by solving a modified diffusion equation


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∇2 q(r, s) − wA (r )q(r, s), ∂q(r, s)  2 = ∇ q(r, s) − wB (r )q(r, s), ∂s ∇2 q(r, s) − w (r )q(r, s), A 

0≤ s < f /2 f / 2 ≤ s < 1− f / 2 1 − f / 2 ≤ s < 1 , (3)

subjected to the initial condition q(r,0)=1. Since the two ends of the polymer are distinct, a complementary partition function q*(r,s) is defined similarly and satisfies the same modified diffusion equation with an initial condition q*(r,1)=1. Here, we utilize s as a chain contour variable in units of N. All lengths are expressed in units of the unperturbed radius-of-gyration of a polymer, Rg = (Nb2/6)1/2, where b is the statistical segment length which is assumed to be equal for both A and B blocks. The solution to the modified diffusion equation is conducted following the pseudo-spectral method.59 An iterative relaxation of the fields towards their saddle-point values is implemented following.60 By evaluating q(r,s) and its complementary, the segment volume fractions can be determined as follows

φ A (r ) =

2 f /2 dsq(r, s)q* (r, s) ∫ 0 Q

φB ( r ) =

1 1− f / 2 dsq(r, s)q* (r, s) . (4) ∫ f / 2 Q

The numerical implementation of SCFT is conducted in 3D, first on a wide computational lattice of size Nx×Ny = 160×160 pixels and Nz range of 48 to 60 pixels to capture different morphologies that the polymer would self-assemble into. The magnitude of the grid spacing in the x and y directions is kept constant at 0.16 Rg and at 0.12 Rg in the z direction. The volume fraction, f of the majority A block (here representing PS) is varied between 0.60 and 0.68. The degree of incompatibility χN is set to 30 which is higher than at the ODT of this polymer χN ~ 20.52 The set of f and χN values specified would produce lamellar, gyroid, and cylindrical phases 17 ACS Paragon Plus Environment

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in the direction of increasing f for a bulk ABA symmetric triblock copolymer.52 Periodic boundary conditions are applied in all directions. Nonetheless, to capture the effect of thin film confinement between a substrate and a top free surface, a masking method is employed by applying an external pressure field w+ = (wB + wA)/2 = 10 at the top and bottom of the computational cell of thickness 6 pixels each. This creates an excluded area for the polymer to access. The polymer free surface is assumed to be flat and undeformable. To capture the tendency of the PDMS (B block) to migrate to the free surface due to its low surface energy, an exchange field w- = (wB-wA)/2 = 4 is applied at a plane of two pixels thick adjacent to the top excluded zone of the pressure field. This creates an attractive region to the B block at the top surface. The bottom surface is neutral. Fields are randomly initiated with the aim of targeting equilibrium structures in a system of thin films containing only two layer morphologies. These equilibrium structures are then seeded into SCFT calculations with varying Nx and Ny to calculate their equilibrium free energies and construct the phase diagram.


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ACKNOWLEDGMENTS This work was supported by NSF DMR-1606911. Shared experimental facilities of CMSE, an NSF MRSEC under award DMR-1419807, were used. This research used resources of the Center for Functional Nanomaterials, and the National Synchrotron Light Source II, which are U.S. DOE Office of Science Facilities, at Brookhaven National Laboratory under Contract No. DE-SC0012704.

ASSOCIATED CONTENT Supporting Information Additional information on triblock copolymer synthesis and characterization data, SEM images showing morphologies of bilayer, bulk, film thickness below 30 nm, and island and hole, and AFM images showing step height between islands and holes.


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Figure 1. (a) Swelling ratios of PS-b-PDMS-b-PS films with as-spun thickness of 100 nm in a mixed solvent vapor flow of toluene:heptane = 7.5:2.5 (black) and 10:0 (red). (b) GISAXS patterns showing the morphological evolution for the solvent vapor ratios considered in (a); panels above (labelled as A) and below (labelled as B) represent GISAXS data for the vapor flow of 7.5:2.5 and 10:0, respectively. Each scattering profile corresponds to the stage marked on the swelling ratio curves in (a). (c) SEM images of oxidized PDMS nanopatterns for the respective solvent annealing conditions. All the scale bars in the main images are 100 nm and in the insets are 50 nm.


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Figure 2. Schematic illustration of the internal morphology in PS-b-PDMS-b-PS thin film as a function of the volume fraction of PS block. L, PL, and C represent lamellae, perforated lamellae, and cylinders, respectively. The structures in the lower panel are obtained from SCFT simulations, where blue represents the PDMS block and each layer is presented at a different size for clarity.


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Figure 3. SEM images of oxidized PDMS nanopatterns at initial film thickness of 73 nm as a function of the solvent vapor flow of toluene:heptane of (a) 6 sccm:4 sccm, (b) 7:3, (c) 7.5:2.5, (d) 8:2, (e) 9:1, and (f) 10:0, so that the total flow rate is 10 sccm. All the scale bars in the main images are 100 nm and in the insets are 50 nm.


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Figure 4. (a) Experimental phase diagram of PS-b-PDMS-b-PS thin films as a function of ascast film thickness (33, 56, and 73 nm) and solvent vapor flow of toluene and heptane, where the total flow rate is fixed to 10 sccm. The left and right colored squares in each data point correspond to the morphologies of the top and bottom layers. Lamellae, perforated lamellae, and cylinders are represented by L (blue square), PL (red square), and C (yellow square), respectively. (b) Swelling ratios of PS-b-PDMS-b-PS films for different flow rates of toluene and heptane at an initial film thickness of 73 nm.


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Figure 5. A comparison of structures obtained from experiments (left) and SCFT simulations (right): double layer of (a) perforated lamellae and (b) cylinders (top view). The upper cylinders in the simulation image are shown wider than the lower ones. The period of each morphology is indicated.


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Figure 6. Free energy curves as a function of film thickness for the structures obtained from SCFT simulations when the volume fraction of the A block (corresponding to the PS block) is (a) 0.60, (b) 0.62, (c) 0.64, (d) 0.66, and (e) 0.68. Double and triple layers of cylinders are distinguished by 2C (solid line) and 3C (dotted line), respectively.


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Figure 7. (a) Phase diagram of ABA triblock copolymer thin films as a function of film thickness and volume fraction of the A block (corresponding to the PS block) from SCFT simulations. Bilayer lamellae, perforated lamellae, and cylinders are represented by L (blue), PL 32 ACS Paragon Plus Environment

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(red), and C (yellow), respectively. (b) Free energy difference (∆F) map for the bilayer PL obtained by displacing one layer with respect to the other (right). The value of zero in ∆F indicates the most stable structure as indicated in the schematic illustration (left). The blue and yellow colored circles correspond to the holes in the top and bottom layers. (c) Interlayer spacing of bilayer structures as a function of volume fraction of A. Lamellae, perforated lamellae, and cylinders are represented by L (blue circle), PL (red square), and C (yellow triangle), respectively. The inset of (c) defines the interlayer spacing.


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Double Layer Morphologies from a Silicon-Containing ABA Triblock

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