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Self-Assembly and Directed Assembly of Polymer Grafted Nanocrystals via Solvent Annealing Jun Chen, Andrea Fasoli, Julia D. Cushen, Lei Wan, and Ricardo Ruiz* HGST, a Western Digital Company, San Jose, California 95135, United States S Supporting Information *

ABSTRACT: Polymer grafted nanocrystals (PGNCs) incarnate a duality of powerful attributes: their inorganic crystal cores hold promise to design nanocrystal solids from superlattice assemblies while their polymeric ligands exhibit the soft colloidal properties of star polymers. From their star polymer analogues, PGNC derive two important, yet sometimes less-exploited attributes: (1) swollen PGNCs are mobile and can be solvent annealed toward thermodynamic equilibrium, and (2) in the semidiluted regime in good solvents, PGNCs display a richer phase diagram compared to that of hard-sphere colloids which can be accessed by controlling the solvent intake during solvent annealing. Here we study the self-assembly of ∼4 nm Fe3O4 nanocrystals capped with polystyrene ligands under solvent annealing. We confirm swelling behavior and even a phase transition to a hexatic phase, in agreement with models for star polymers. We exploit the polymeric properties of the PGNCs to perform directed self-assembly using thinly textured patterns to achieve long-range orientational order of the superstructure. We also demonstrate the use of the superlattice assembly as a lithographic mask for pattern transfer with a full pitch of 9.5 nm.

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INTRODUCTION Nanocrystal superlattices have demonstrated tremendous potential to form artificial solids with tailored optical, electrical, magnetic, or structural properties not found in naturally occurring solids.1−3 However, controlling the assembly and long-range ordering of thin-film nanocrystal superlattices over wafer scale with submonolayer precision has been a major roadblock preventing the full realization of promising nanocrystal-based applications in diverse areas such as lithography, optoelectronics, magnetic recording, and biology, to name a few.4,5 Assembling ordered superlattices of nanocrystals into thin films on a substrate necessitates a controlled deposition method to bring the particles out of the liquid dispersion into a dense, highly ordered array of uniform thickness. Almost invariably, commonly used deposition and assembly methods tend to be kinetically driven under conditions that are far from equilibrium.6,7 Despite remarkable and meaningful progress in self-assembly via drying-mediated entropic crystallization1,6 such as drying-mediated deposition,7 controlled evaporation,8 or assembly at liquid interfaces,9 these methods remain incompatible with large area processing and/or lack the uniformity needed for wafer scale applications, in part precisely because of their kinetically driven nature. By contrast, selfassembly methods in which the system is brought to near thermodynamic equilibrium could be advantageous and more reliable to achieve long-range order with wafer scale uniformity. A good example is that of block copolymer thin films in which an annealing step is performed after film deposition.10 The annealing step drives the system toward thermodynamic © XXXX American Chemical Society

equilibrium, and a fast quenching locks the attained morphology in a glassy state. In this work, we look at the role of polymeric ligands in the self-assembly of solventannealed nanocrystal superlattices and the opportunities afforded when the assemblies are thermodynamically driven instead of kinetically driven. The assembling and processing properties of spherical, neutral nanocrystals are largely dictated by the grafting density and length of the capping ligands used as stabilizers. Ligands generate a “soft” shell interparticle potential11,12 that may screen, partially or totally, core−core attractive interactions (e.g., van der Waals). The degree of softness scales inversely with the number of ligands, f, such that a hard sphere potential is recovered when f → ∞.12 In addition to ligand density, the length of the ligand in relation to the core size plays an important role screening van der Waals and other attractive potentials and hence in determining whether the ligand-capped nanocrystals can be understood solely in terms of soft repulsive potentials.11 An effective screening requires the ligand length to be above a certain value that depends on a number of parameters including core radius, Hamaker constant, and number of ligands per nanocrystal. For this reason, polymer grafted nanocrystals (PGNCs) in general tend to better screen core−core interactions when compared to short-ligand nanocrystals. PGNCs that effectively screen the core are commonly Received: September 5, 2017 Revised: November 16, 2017

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DOI: 10.1021/acs.macromol.7b01921 Macromolecules XXXX, XXX, XXX−XXX

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disperse26,41,42 and binary nanoparticle superlattices.43 Most importantly, the polymeric ligands may offer new opportunities for directed assembly at the nanometer scale that are compatible with large scale processing. While substantial progress in templating nanocrystals has been made with graphoepitaxy,25,44 block copolymer mediated assembly,45,46 or by selective binding,47 those methods are either limited to small areas or incommensurate with superlattice ordering. Instead, as we show here, the entropic conformations of the polymeric chains from a PGNC monolayer on a rigid substrate could be exploited in conjunction with sparse shallow topography to set the orientation of the superlattice over large areas. In this article, we study the self-assembly of monolayer films of PGNCs by solvent annealing. We use the polymeric properties of the PGNCs to spin-coat films over wafer scale with uniform thickness. The star-polymer properties of PGNCs make it possible to solvent anneal the spin-coated films toward thermodynamic equilibrium to induce a phase transition into a well-ordered 2D hexatic phase as a function of particle density and number of ligands. We also exploit the entropic conformation of the soft shell to induce long-range orientational order on the superstructure from sparse, thinly textured nanoimprinted patterns. Finally, we show the lithographic potential of these superlattices by performing a pattern transfer into the substrate reaching 8.25 Teradot/in.2.

represented by the soft interparticle potentials derived from the Daoud−Cotton model for star polymers.13,14 In semidilute solutions in good solvents and at PGNC densities above the overlap concentration (i.e., the concentration at which the ligands from neighboring particles start to overlap), a significant portion of the polymeric chain participates in a swelling matrix of overlapping ligands. Such a matrix can be sustained over a large range of concentrations and therefore over a large range of packing fractions leading to a potentially richer superlattice phase diagram compared to particles capped with nonswelling ligands. PGNCs together with star polymers and block copolymer micelles11,15,16 undergo phase transitions into ordered phases as a function of packing density and ligand number. A phase diagram17 has been provided for three-dimensional assemblies, according to which stars with f > 64 will remain crystalline at all densities above a minimum packing density. Controlling the assembly of these ordered phases in PGNC thin films will be the key to unlock many promising applications from nanocrystal superlattices. The fact that these thermodynamically stable superlattice configurations exist in the solvated state (i.e., at finite concentrations in the semidiluted regime) carries two important consequences for practical considerations: First, the phase diagram offers a thermodynamically stable target to achieve superlattices at equilibrium in the solvated state. Second, solvated polymers18 may no longer be glassy and may gain enough mobility to allow the system to “anneal” toward an equilibrium structure. Indeed, solvent annealing is a useful technique to rearrange swollen polymer matrices. In selfassembly of block copolymers, solvent annealing has been particularly useful in systems that require controlled atmospheres or in materials that cannot be thermally annealed.19,20 Examples of solvent annealing also exist in nanocrystal assemblies where exposure to solvent vapor atmospheres has been used to monitor phase transitions21−23 or to improve the ordering in short ligand assemblies24 and PGNCs.25 While much of the earlier reports focused on a practical form of solvent annealing that involves placing a sample near a solvent reservoir either in a closed vessel or in the presence of a counter flow of inert gas, equilibrium conditions may prove hard to control or not be possible at all in such experimental setups. Better control of equilibrium conditions can be achieved when solvent annealing is performed at controlled solvent activities (e.g., in flow chambers where a solvent vapor is delivered through a separate bubbler) as it has been shown for nanocrystals26 and block copolymers.27,28 Polymeric ligands have brought vast and unique opportunities to the assembly, processing, and applications of nanoparticles.29,30 Examples include nanocomposites,31−34 materials for photovoltaics,35 photonics,36 drug delivery agents,37 and even nanoparticle-templated DNA bonds and frameworks.38,39 The dual colloidal and polymeric properties of PGNCs add ease of processing at the macro scale and structural flexibility at the nanometer scale. Polymeric ligands make it possible for PGNC solutions to be processed in the same way as polymer films are. For example, PGNCs have been shown recently to form films of controllable thickness around a monolayer over cm scale via flow front deposition.40 And as it is done in this work, even conventional spin coating can be used to routinely achieve uniform films with submonolayer resolution. At the molecular scale, PGNCs have been used to tune the configuration and interparticle distance in mono-

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EXPERIMENTAL SECTION

The present study comprised two sets of Fe3O4 nanocrystals (NCs) grafted with polystyrene (PS) ligands: a first set with an average core radius r0 = 2.1 nm, PS ligands with a degree of polymerization N = 25, and an average number of ligands per NC, f ≈ 68; and a second set with r0 = 1.95 nm, N = 19, and f ≈ 50. Throughout the article we refer to each set by the number f of ligands per particle, i.e., PGNCs with f ≈ 68 or f ≈ 50. Making PGNCs involves synthesis of the inorganic cores, synthesis of the polymeric ligands, functionalizing the polymeric ligands with a group that binds to the NC core, and performing the ligand exchange. Each of these steps is briefly described below with additional details found in the Supporting Information. Sample preparation, processing, and image analysis used in this work are also briefly described in this section. Nanocrystal Synthesis. Monodisperse Fe3O4 nanocrystals capped with oleic acid were synthesized according to literature methods.48 Additional details can be found in the Supporting Information. Polymer Synthesis and Functionalization. Bromine-terminated polystyrene (PS-Br) was polymerized by activators regenerated by electron transfer atom transfer radical polymerization (ARGET ATRP) according to the literature.49 Additional details are in the Supporting Information. The Br termination in the PS was substituted with pentaethylenehexamine (PEHA) to form PS−PEHA. The substitution was carried out by adding 50× molar excess of PEHA to a PS−Br solution in toluene. The large excess was used to prevent formation of dimers. The solution was allowed to react for 48 h at room temperature and was then precipitated in methanol. The dry powder was redissolved in THF and then reprecipitated in methanol with a total of two more times to remove unreacted PEHA. Ligand Exchange. Ligand exchange to replace the oleic acid ligands for PS−PEHA was carried out following literature protocols.31,42 Additional details are in the Supporting Information. The number of ligands per particle and the size of the NC were estimated from thermogravimetric analysis and transmission electron microscopy measurements (see Figures S1 and S2, Table S1). See the Supporting Information for an additional comment on the polydispersity of f. Sample Preparation and Solvent Annealing. The 65 mm glass disk substrates coated with 6 nm of Pt were used for the undirected assembly experiments. Polished-grade quartz crystal monitors were used as substrates for the solvent mass intake experiments. Samples B

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Macromolecules were spin-coated from toluene solutions with concentrations ranging from 1 to 3 mg/mL at various speeds from 2K to 5K rpm to obtain samples with different film coverage (thickness). Samples were introduced in a custom-made solvent annealing chamber.50 Disk substrates were annealed at a solvent activity a = 0.75, while the QCM substrates were stepped through a range of values to measure the toluene mass intake as a function of activity (additional details on solvent annealing and QCM measurements in the Supporting Information). The 65 mm glass disk substrates coated with 5 nm of SiNx were used for the directed self-assembly experiments. A nanoimprint template51 was used to imprint circumferential stripes on the SiNx-coated disk. The nanoimprint resist stripes (24.5 nm pitch) were trim-etched using CO2 reactive ion etching (58 W, 7 mTorr, 10, 11, and 12 s). Nanocrystals were spin coated on the trimmed resist lines and solvent annealed (additional characterization data of DSA patterns in the Supporting Information). Pattern Transfer. The pattern transfer from the PGNC film to the substrate was done as follows. A first CO2 RIE (90 W, 2 mTorr, 12 s) etch was used to remove the PS ligand on the top of the film and in between the particles. To transfer into the substrate using the nanoparticle cores as a mask, Ar ion beam etching (200 V, 100 mA, 150 W, 0.0004 mTorr, 5°, 20 s) was used. The Fe3O4 nanocrystal residues were removed with a wet etch in 37% HCl for 1 min, then rinsed thoroughly with DI water, and spin dried. Any polymeric residues were removed with a final O2 (10 W of RF1 forward power, 130 W of RF2 forward power, 20 mTorr, 20 s) inductively coupled plasma. Image Analysis. Square SEM images, 1 μm long (2048 × 2048 pixels), were processed with a homemade software routine in Mathematica using an adaptive filter to detect the location of individual particles. An array of delta functions located at the centroids of each particle was Fourier transformed to compute the circularly average structure factor.52 The orientational correlation and the paircorrelation functions were computed from the centroids of the nanocrystals.52−54 Other statistics like nearest-neighbor distance (pitch), number of nearest neighbors, and the bond angles were extracted from a Delaunay Triangulation from the matrix of centroids.55

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RESULTS AND DISCUSSION

Figure 1. (a) Schematic representation of the spin-coating process on a disk substrate resulting in a PGNC film of uniform coverage throughout the film albeit with very limited short-range order. (b) Schematic representation of the solvent annealing chamber whereby the PGNCs gain enough mobility upon swelling to rearrange in an energetically more favorable packing forming a superlattice. Lowmagnification SEM images (c−f) show the film coverage before (left column) and after (right column) solvent annealing. The sample in (c, d) has a nominal coverage slightly below a monolayer while the sample in (e, f) is just above a monolayer. The midgray tone corresponds to monolayer thickness, while the darker portions are double layer thick. The bright spots in (d) correspond to areas of exposed substrate. High-magnification SEM images reveal the ordering before (g) and after solvent annealing (h). After annealing, the PGNCs form a highly ordered hexagonally packed superlattice as confirmed by the structure factor plots in (i) before (blue curve) and after (red curve) solvent annealing. Distinctive (11) and (10) peaks appear after annealing. (j) Histogram of first neighbor distances before (blue curve) and after (red curve) solvent annealing.

Spin Coating and Solvent Annealing. The polymeric properties of PGNCs32,43 arising from the matrix of interpenetrating chains56 provide unprecedented versatility not available to conventional colloids capped with short ligands. For example, as depicted in Figure 1a, a thin film of uniform thickness can be deposited on a full wafer by spin coating in the same way as it is done for regular polymer films. A uniform but disordered film is expected as a result of the fast drying of the film. In Figure 1b, a subsequent solvent annealing step at fixed solvent activity, a, swells the soft polymer coronas, giving the PGNCs enough mobility to rearrange toward an equilibrium assembly. A fast cooperative diffusion is expected to bring the matrix of overlapping chains to a uniform concentration quickly.56 In a thin film, wetting phenomena will also play a role determining the stability of the PGNC film on the substrate.57 Assuming favorable wetting conditions, the swollen film will continue to rearrange on longer time scales dictated by self-diffusion and structural rearrangements56 into a more ordered and more tightly packed film. As a consequence, PGNCs that landed on a second layer after spin coating may find room to diffuse into the first monolayer during solvent annealing as illustrated by the schematics in Figure 1a,b. PGNCs with f = 68 were spin coated onto two disk substrates with two different thickness (coverage) values near monolayer coverage. A low-magnification SEM micrograph of the first, thinner sample after spin coating is shown in Figure 1c. A

uniform gray tone in the SEM micrograph represents a monolayer film and the darker regions correspond to double layer islands as verified by line scans from atomic force microscopy (AFM) shown in the Supporting Information (Figure S3). This terracing structure and its observation in SEM were also reported recently elsewhere.58 After solvent annealing, as shown in Figure 1d, the double layer islands recede to the monolayer as PGNCs pack more efficiently, even C

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areas thanks to the polymeric nature of the ligands. To evaluate layer coverage uniformity of monolayer films, we measured the first-neighbor particle−particle distance, or pitch. Monolayer regions with more particles per unit area will show a tighter pitch while regions with less particles per unit area will show a more relaxed pitch. Our films were deposited by spin-coating on 65 mm disk substrates as shown in the inset of Figure 2a. The plot in Figure 2a shows measurements of the pitch and its standard deviation (σpitch) at eight locations around the disk taken from 1 μm2 SEM micrographs at a distance of 20 mm

leaving a few holes of exposed substrate (bright spots in Figure 1d). The second, thicker film in Figure 1e shows a correspondingly higher double layer coverage after spin coating (darker percolating network). After solvent annealing, a uniform monolayer packs up to a maximum crowding density, above which excess PGNCs form a second layer (dark regions in Figure 1f). Similar crowding phenomena on monolayer formation and terracing (islands and holes) occur in other structured films such as autophobic lubricants59 or block copolymers.60,61 The degree of ordering before and after solvent annealing is shown in the high-magnification SEM images of Figures 1g and 1h, respectively, and in the structure factor, S(q), plots of Figure 1i (blue curve and red curve, respectively). While the form factor cannot be extracted without a suitable scattering technique, the structure factor of monolayer films can be conveniently obtained from the location of the particle centroids following common techniques.52 Larger size SEM micrographs (1 μm long, 2048 × 2048 pixels) were processed with a custom-made image processing software to locate the centroids of each particle with subpixel resolution.62 A matrix of unitary delta functions located at the centroid coordinates was Fourier transformed to compute the circularly average structure factor S(q) (see the Supporting Information for further details). After spin coating, due to the fast drying of the film, the PGNC assembly shows only short-range correlations displaying a relatively low intensity first-order peak in the structure factor at q1 = 0.748 nm−1 and a broad, shallow second-order peak. After solvent annealing the ordering is greatly improved with the system undergoing a phase transition into a hexatic phase with characteristic (11) and (02) peaks (dashed lines in Figure 1i) and a higher intensity first-order peak at q1 = 0.767 nm−1. The slight shift of q1 toward a higher wavenumber after solvent annealing reflects a tighter and more efficient packing. Assuming a hexagonal lattice in both cases, and using the q1 values, the lattice parameter changed from about 9.7 to about 9.5 nm after solvent annealing. An analysis of first-neighbor distances (histogram in Figure 1j) also shows that the standard deviation got reduced from 17% to 10% of the median value. The improved packing explains the reduction in double layer coverage after solvent annealing as particles from the second layer get incorporated into a more densely packed monolayer. While the assembled structure of the film after solvent annealing still shows defects that may not represent perfect thermodynamic equilibrium, the solvated film certainly evolved toward an equilibrium configuration during annealing. The situation may be analogous to that of annealing block copolymer films63 in which the annealing step is used to drive the system toward equilibrium achieving a pitch and a pitch distribution that are close to equilibrium but in which the film may still have numerous defects that may be kinetically trapped or that would simply take much longer annealing times to heal. Nonetheless, solvent annealing represents a convenient postdeposition self-assembly step that enables wafer scale processing of monolayer and multilayer films. The effective screening of the core by the polymer ligands and the postdeposition solvent annealing enable film thickness (or layer coverage) control with submonolayer resolution and superlattice assemblies over wafer scale. Polymer films with high accuracy thickness control are ubiquitous in various industries from a variety of deposition techniques including spin-coating and dip-coating. Similarly, it is possible to achieve PGNC film thickness (or layer coverage) uniformity over large

Figure 2. Monolayer uniformity around a 65 mm disk substrate. (a) Plot of nanocrystal pitch (green squares) and standard deviation (blue disks) values measured at a distance r = 20 mm from the disk center at various azimuthal angles. Inset: picture of a disk substrate containing a PGNC monolayer. Red dots indicate approximate radius and interval of measurements. (b−e) Low-magnification SEM micrographs at four different azimuthal locations; scale bar = 5 μm. (f−i) Highmagnification SEM micrographs; scale bar = 100 nm. D

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volume in our PGNCs and tested the applicability of the Daoud−Cotton model by comparing measurements of solvent intake at various activities in PS-homopolymer (61.1 nm thick) and PGNC (136 nm thick) films deposited on polished QCM substrates. The thickness of both films was measured with atomic force microscopy (AFM). Figure 3 shows solvent activity, a, vs film volume fraction, ϕ. The solid line shows the expected values from the Flory−Huggins equation64 (see Supporting Information, eq S6) assuming a ϕ-independent PS−toluene interaction parameter χ = 0.4.65 Film volume fractions were calculated from the film thickness values and from the solvent mass intake measured by QCM converted to volume (see the Supporting Information). The volume fraction of the PS-homopolymer (blue squares) closely follows the expected curve. A fit to the swelling data leaving the film thickness as a fitting parameter yields tPS = 60.8 nm, in excellent agreement (within 0.5%) with the thickness measured by AFM. By contrast, the volume fraction of the PGNC film (red triangles) showed a clear shift away from the PS-homopolymer curve, indicating that it had swollen proportionally less; i.e., at the same activity, the PGNC film had a higher ϕ than the pure PS film. However, according to the Daoud−Cotton model above, not all of the PGNC film is expected to swell with solvent: the volume inside the coat region (r < rct) does not have space to take any solvent molecules. By breaking the PGNC film into a swelling and a nonswelling volume, and using the toluene intake to fit the equivalent thickness of the swelling part only (tswell = 99.2 nm), the swelling portion (yellow triangles) followed the same Flory−Huggins curve as the PS-homopolymer. From the remaining nonswelling volume, we estimate a coat radius rct ≈ 3.2 nm (see the Supporting Information for details) which, being larger than the Fe3O4 core, suggests the core is effectively screened and that the Daoud−Cotton model may be appropriate to represent these PGNCs. Number of Ligands and Phase Transitions. Owing to their colloidal nature, PGNCs are expected to display a disorder-to-order phase transition with increasing particle number density, similarly to hard spheres undergoing a Kirkwood−Alder phase transition;66,67 but contrary to hard sphere colloids, star polymers (and PGNCs that meet the criteria to be regarded as star polymers) will only crystallize if f is above a critical value.15,17,68 Phase transition studies of PGNCs and star polymers are commonly done in threedimensional assemblies, and while multiple studies exist for two-dimensional colloids, not many studies exist on phase transitions in two-dimensional assemblies of PGNCs. Spincoated monolayer films with solvent annealing offer an unprecedented, yet simple access to study two-dimensional colloidal systems. In order to search for a phase transition as a function of the two-dimensional particle number density, ρ, we prepared ten films using PGNCs with f = 68 with various film coverage values (i.e., film thickness) from submonolayer to slightly above a monolayer and solvent annealed them in toluene at an activity of a ≈ 0.75. The circularly averaged structure factor, S(q), was computed as before from 1 μm2 size images, and the plots (offset for clarity) are shown in Figure 4a. Two criteria to identify a phase transition are plotted in the inset of Figure 4a: first, the ratio q2/q1 (solid circles, left axis) where q1 and q2 are the wave vectors of the first and second peaks in S(q)41, respectively, and second, the intensity of the first-order peak, S(q1), according to the Hansen−Verlet rule in 2D53 (inverted triangles, right axis). Representative portions of

from the disk center and separated azimuthally every 45°. Figures 2b−e show low-magnification SEM images at four locations around the disk showing a uniform monolayer coverage. Figures 2f−i show high-magnification SEM images showing the typical superlattice assemblies of the monolayer with multiple grain boundaries. This level of uniformity is accomplished throughout the disk except for an ∼2 mm band around the center hole of the disk and near the outer edge of the disk where the spin-coated film is less uniform. Solvated PGNCs and the Daoud−Cotton Model. The thermodynamic and scaling properties of PGNCs are understood in terms of the Daoud−Cotton model13 originally developed for star polymers and later rewritten to explicitly incorporate nanoparticle cores.14 Star polymers are macromolecular entities consisting of f identical polymeric chains grafted to a common core, each ligand having a degree of polymerization N. The model describes the star as a concentric succession of spherical “blobs” of size ξ(r) ∼ rf1/2 where r is the distance to the center of the core. Within a blob, the polymeric arm adopts the conformation of an isolated, free chain. As a consequence of the radial symmetry of the star, the monomer concentration decreases from the center outward producing three distinct regions in the colloid: a dense core (r < rcr), a nonswelling “coat” (rcr < r < rct), and a swollen soft corona (r > rct). In semidiluted solutions, above the overlap concentration, the soft coronas interpenetrate down to a distance rov forming a polymer matrix of uniformly sized blobs (inset in Figure 3).

Figure 3. Solvent activity vs film volume fraction for a PS homopolymer film (blue squares) and for a PGNC film, calculated using the full, AFM-measured film thickness (red triangles), or by using only the swelling volume of the film (yellow triangles). Both the PS homopolymers and the swelling part of the PGNC film are well fitted by the Flory−Huggins equation with χ = 0.4 (black line). Inset: representation of overlapping PGNCs in the semidiluted regime. The labels indicate the locations of the core, rcr, coat, rct, overlap region, rov, and pitch, Lo. The open circles represent the local blob size ξ(r).

According to the Daoud−Cotton model,13 the core and coat regions do not take solvent; only the swelling portions of the soft coronas do. PGNCs may be represented by the Daoud− Cotton model when the polymer ligands are both dense and long enough to form first a nonswelling, concentrated polymer brush coat around the nanocrystal core up to a radius rct and subsequently transitioning to a swollen soft corona for r > rct.14 This Daoud−Cotton behavior is expected in PGNCs when the actual nanocrystal radius, r0, falls below rct of the equivalent star polymer (r0 < rct). We verified the presence of a nonswelling E

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Figure 4. Evolution of the structure factor for PGNCs with f = 68. (a) S(q) plots for nine samples with increasing surface densities. The inset shows the ratio q2/q1 of the wave vectors of the second and first peaks in S(q) (left axis) and the intensity of the first peak, S(q1) (right axis). The phase transition from fluid to hexatic occurs when q2/q1 drops from ∼2 to ∼ √3 and when S(q1) ≈ 5 according to the two-dimensional version of the Hansen−Verlet rule. The SEM images from (b−h) show sample images from seven of the nine samples plotted in (a). The densities are color coded according to the inset plot in (a). The monolayer in (i) has reached its maximum crowding density and the excess amount forms some double-layer islands.

Figure 5. Evolution of the structure factor for PGNCs with f = 50. (a) S(q) plots for eight samples with increasing surface densities. The inset shows the ratio q2/q1 of the wave vectors of the second and first peaks in S(q) (left axis) and the intensity of the first peak, S(q1) (right axis). Neither q2/q1 dropped to ∼√3 nor S(q1) reached ∼5, indicating that a phase transition was absent in this system. The SEM images from (b−i) show sample images from the eight samples plotted in (a). The densities are color coded according to the inset plot in (a). F

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Figure 6. Directed self-assembly (DSA) from thinly textured stripes. (a) Schematic representation showing a nanoimprinted striped pattern. A trimetch step is used to thin the stripes to three different heights, h. PGNCs are spin-coated and solvent annealed on the pattern. (b−d) Monolayer DSA on the imprinted pattern with optimum trim-etch (hopt ∼ 1.2 nm. orange label), underetched (hue ∼ 2.4 nm, blue label), and overetched (hoe ∼ 0.7 nm, green label). Inset in (b): TEM cross section of same sample. (e) AFM height image of the PGNC film on the optimum template, showing minimal modulation from the template and a low rms roughness of 0.43 nm. (f) Pitch histogram of the three DSA samples. Colors are coded according to (b−d); a fourth, black plot, corresponding to the unguided sample of Figure 4h is added for comparison. (g) Bond-angle distribution for the same four samples. The hopt sample has narrow, directional first-neighbor bonds over the entire sample. (h) Orientational correlation function g6. The unguided and the hoe samples show exponential decays characteristic of the lack of a preferred orientation. The other two samples show a high saturation level with the hopt template saturating at ∼0.9. (i) Pair correlation functions with algebraic decays characteristic of quasi-long-range order in the hexatic phase. The longest correlations are observed in the hopt sample.

crystallization. Accordingly, 2D crystallization occurs when the amplitude of the first peak S(q1) exceeds a critical value of about 569 (in 3D the value is 2.85).71 The inverted triangle curve in the inset plot of Figure 4a shows S(q1) > 5 for ρ > 10 × 10−3 nm−2 consistently with the ratio q2/q1 ≈ √3. The inset in Figure 4a includes horizontal dashed lines as guides to the left axis to indicate when the values q2/q1 = √3 and q2/q1 = 2, respectively. There is also a dotted line as a reference to S(q1) = 5 to the right axis. For ρ > 10 × 10−3 nm−2 both criteria are met consistently. The high S(q1) = 10.3 value of the densest monolayer and its well-defined (11) and (20) Bragg peaks afforded by solvent annealing compare favorably to other methods of depositing PGNC monolayers on solid substrates where the assembly is kinetically driven and where reaching the crystallization criteria may be more difficult to achieve.40 By contrast, a corresponding phase transition was absent for films of PGNCs with less ligands per particle (f = 50). Figure 5 depicts the evolution of the films at eight surface densities after solvent annealing. The arrangement and description of Figure 5 are parallel to that of Figure 4. PGNCs with f = 50 did not exhibit a phase transition into an ordered hexatic phase. The second peak in S(q) remained a broad peak with no splitting

SEM micrographs from eight (out of ten) samples of increasing particle densities after solvent annealing are shown in Figures 4b−i. S(q) curves and SEM images are color coded according to the particle surface density shown in the inset plot. The sample of Figure 4i starts to show islands of a double layer which interfered with computing S(q), and thus its corresponding plot is not shown in Figure 4a. At low ρ, the submonolayer film is disordered and portions of the substrate are exposed (bright areas in SEM). As the density increases, the uniformity and coverage improve as reflected on an increased intensity of the first peak in S(q), but the fluidlike disorder remains up to ρ ≈ 7.5 × 10−3 nm−2, with a broad second peak in S(q) where q2/ q1 ≈ 2. At higher densities, the SEM micrographs show ordered domains with hexagonal packing while the second peak in S(q) splits into characteristic (11) and (20) Bragg peaks.52,53 The ratio q2/q1 drops, and a phase transition to a hexatic phase occurs for ρ > 10 × 10−3 nm−2 where q2/q1 ≈ √3. While peak splitting and q2/q1 ≈ √3 are a consequence of the system transitioning to a hexatic phase, it has been pointed out that peak splitting is not a general rule for phase transitions.69 Instead, the two-dimensional version of the Hansen−Verlet rule53,69,70 may be regarded as a more general criterion for 2D G

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Macromolecules throughout the entire surface density range. The q2/q1 ratio only went down to about ∼1.9 to increase back to ∼2 at higher densities (possibly due to the onset of a double-layer formation). Similarly, the intensity of the first peak, S(q1), slowly increased to a maximum of 3.8 before receding again without reaching the Hansen−Verlet criterion of ∼5. The SEM images from the denser films show a relatively uniform particle−particle spacing, but without long-range order or a high number of six neighbors. A comparison of pitch evolution, standard deviation, and number of near neighbors for both f = 68 and f = 50 is shown in the Supporting Information (Figures S4 and S5). The lack of a clear phase transition may be attributed to the lower f value according to predictions for star polymers as explained above. While the value of f = 68 for the crystallizing PGNCs that formed a superlattice is above the reported threshold for crystallization with no reentrant melting68 (f > 64) in 3D, we are not aware of a corresponding phase diagram in two dimensions. Other factors such as polydispersity in f32,72−74 and substrate interactions40,57 may play a role and therefore more simulation work in 2D may be needed to establish the conditions for phase transitions of twodimensional PGNC assemblies as a function of f. Directed Self-Assembly and Pattern Transfer. The polymeric nature of PGNCs also makes this type of colloid a particularly good candidate for directed self-assembly (DSA) techniques that exploit entropic chain conformations to achieve long-range orientational order. Among the various DSA techniques used for nanocrystals in general, colloidal epitaxy55,75 and graphoepitaxy44 stand out for their ability to produce superlattice assemblies. However, none of these techniques provide, at once, orientation control at the monolayer over arbitrarily large areas. Colloidal epitaxy relies on an underlayer superlattice (i.e., it needs at least another monolayer underneath) while graphoepitaxy is limited to the size of the trench, and hence it does not work over arbitrarily large areas. In this work, we set out to explore the possibility of artificially printing sparse, periodic potentials to direct the assembly of PGNC monolayers. As shown in Figure 6a, we use thinly textured striped patterns to affect the conformation of the soft coronas, mimicking the subtle modulations typical of colloidal epitaxy,55,75 but without the additional underlayer. In monolayer assembly of PGNCs on a rigid substrate, the polymer chains that fill the interstitial space in between cores and immediately adjacent to the supporting substrate need to stretch relative to the configuration adopted in a 3D bulk superlattice. A thinly textured substrate with modulations commensurate to the superlattice dimensions could take some of the interstitial volume, reducing the amount of stretching that the ligands have to endure to fill the monolayer volume. With the assumption that a commensurate thinly textured pattern would result in energetically favorable configurations, we fabricated sparse, thinly textured patterns as shown in Figure 6a. A nanoimprint template made by block copolymer lithography with circumferential stripes having a full pitch of 24.5 nm was used to imprint a full 65 mm, SiNx-coated, disk.51 Imprinted resist patterns were trimmed and thinned using three etching conditions to produce samples with resist stripes having three different heights, h: an optimum sample hopt ∼ 1.2 nm, an underetched sample hue ∼ 2.4 nm, and an overetched sample, hoe ∼ 0.7 nm, with line widths in the range of ∼2−6 nm (Figure S7). The samples were spin-coated with PGNCs and solvent annealed as before. The pitch of the stripes is nearly commensurate to 3 times the plane spacing of the dense

superlattice observed in Figure 4h, and a guiding effect was expected. In Figure 6b, the optimum sample (hopt) is shown where the superlattice orients mostly in a single orientation. Larger area images of the DSA pattern are shown in Figures S8 and S9. Figure 6c shows the sample with hue where the trimmed guiding lines are still too thick or too wide. The assembly still orients within the grooves, but the defect density is higher and the excessive width of the stripes shows as dark gaps disrupting the continuity of the pattern, closer to a graphoepitaxy-type guiding. Figure 6d shows the sample with hoe where there is little or no evidence of any guiding effect. It is remarkable that the thinly textured stripes with hopt have little or no impact on the overall topography of the film as revealed by TEM (inset in Figure 6b) and by AFM (Figure 6e) where minimal height modulations are seen on the assembled monolayer. The overall rms surface roughness remained at a low 0.43 nm, demonstrating that DSA akin to colloidal epitaxy, but from the first monolayer, is possible with PGNCs. It is also interesting to note that there may be some latitude in the range of wetting conditions and substrate materials that could support stable monolayer PGNC films as suggested by the films shown in this work on Pt (Figure 2) and textured SiNx (Figure 6) substrates. Further studies would be needed to determine the role of the substrate and the choice of polymer.40,57 Figures 6f−i show analysis results from large (1 μm2) SEM images for the three templates. The curves are color coded according to h. A fourth, black plot corresponding to the undirected superlattice of Figure 4h is added for comparison. The pitch distribution is shown in Figure 6f where the sample with hue shows the broadest pitch distribution as a result of the wider gaps and slightly more confined volume. The bond-angle histograms are shown in the polar plot of Figure 6g where the radial amplitude corresponds to the probability density of a given bond angle. The undirected and hoe samples show no preferred orientation with the hoe sample having only a slightly higher probability at the orientation matching the guiding pattern. The sample with hue shows an overall preferred orientation set by the template, but the peaks are not as sharp or long as those in the better guided sample with hopt. It is also interesting to note that for the guided samples the bond angles at 0° and 180° have larger amplitudes than those at 60° and 120°, reflecting the 1-dimensional nature of the guiding pattern. Lastly, we look at orientational and translational correlations. The orientational correlation,53,54 g6, is plotted in Figure 6h with the unguided and hoe samples displaying an exponential decay. The hue sample starts with a slightly faster decay at short distances to saturate at ∼0.7, indicating a strong influence despite the poor quality of the guiding pattern. The optimum sample shows a slower decay and a higher saturation value as a result of the single orientation of the assembly. The pair correlation function52,53 of Figure 6i shows a similar picture with all samples showing an algebraic decay of the envelope curve as expected for a hexatic phase according to KTHNY theory,76 but with the optimum sample having the longest-lived correlations as a result of the guiding and the ability of the soft coronas to cross-talk across stripe lines. Among all potential applications likely to benefit from the ability to deposit and assemble superlattices over wafer scale via solvent annealing, lithographic patterning77 or texturing with nanocrystals stands to open new opportunities in nanofabrication below 10 nm pitch. In Figure 7 we demonstrate pattern transfer from unguided (Lo = 9.7 nm) and guided (Lo = 9.5 nm) nanoparticles by first removing the polymeric shells H

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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.7b01921. Chemical synthesis of the PGNCs, sample preparation, solvent annealing, solvent swelling measurements, image analysis, preparation of templates for directed selfassembly, pattern transfer, and instrumentation used (PDF)

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AUTHOR INFORMATION

Corresponding Author

*(R.R.) E-mail [email protected]. ORCID

Lei Wan: 0000-0001-6805-2155 Ricardo Ruiz: 0000-0002-1698-4281

Figure 7. Pattern transfer using the PGNCs as an etch mask. (a) Cartoon representation of the etch process: a CO2 reactive ion etch removes the polymer matrix, then an Ar mill step is used to etch into the substrate. Finally an HCl wet etch followed by a dry etch cleans any residues. (b) Transfer to a substrate from an unguided PGNC monolayer at 9.7 nm pitch. (c) Transfer to a substrate from a directed self-assembled PGNC monolayer at 9.5 nm pitch.

Present Addresses

Jun Chen, Indiana University, IN 47405. Andrea Fasoli, IBM Almaden Research Center, San Jose, CA 95120. Author Contributions

Jun Chen and Andrea Fasoli contributed equally. Notes

with CO2 reactive ion etching followed by Ar milling to etch into the substrate using the Fe3O4 nanocrystals as a mask. The Fe3O4 residues are removed in HCl leaving a textured substrate with pillars or bumps ∼1−2 nm high (see the Supporting Information for details).

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS All authors thank J.-M. Beaoujour, D. Braunstein, M. Chan, N. Conley, M. K. Grobis, J. James, B. Terris, Y. Wang, T.-W. Wu, and X. Xu of HGST for technical support and fruitful discussions.

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CONCLUSION In summary, we have studied the self-assembly of monolayers of PGNCs by solvent annealing. PGNCs display dual colloidal and polymeric properties: their hard inorganic cores are capable of forming artificial solids from superlattice assemblies while their polymeric ligands impart star-polymer attributes that are particularly attractive in the solvated state such as the ability to rearrange or “anneal” toward thermodynamic equilibrium and the ability to crystallize according to a phase diagram that depends on the number of ligands and PGNC density. Owing to the dual polymeric and colloidal characteristics of PGNCs, it is possible to prepare uniform films by spin coating and to solvent anneal them to swell the soft coronas and rearrange the particles into well-ordered hexagonal arrays in a thermodynamically driven self-assembly process. The assembly and scaling properties of these particles are explained in light of the models developed for star polymers. In analogy to predictions for star polymers in 3D, we observed a phase transition in 2D from a liquid to a hexatic phase for particles having ∼68 ligands while a phase transition was absent for those having only ∼50 ligands. We used thinly textured striped patterns to direct the assembly of the nanocrystals by affecting the entropic conformations of the ligands in a monolayer film. A single orientation was achieved throughout the sample. We also showed the capability of using these particles as lithographic masks to transfer the pattern into the substrate. The wafer-scale control of these assemblies may pave the way to unlock many of the promising applications of colloidal science and may provide a test bed to study the fundamentals of two-dimensional and multilayer colloidal solids.

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ABBREVIATIONS NC, nanocrystal; PGNC, polymer grafted nanocrystal; PS, polystyrene; PEHA, pentaethylenehexamine; SEM, scanning electron microscopy; TEM, transmission electron microscopy; AFM, atomic force microscopy; QCM, quartz crystal microbalance; RIE, reactive ion etching.

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