Entropy-driven segregation of polymer-grafted nanoparticles under confinement Ren Zhanga, Bongjoon Leeb, Christopher M. Staffordc, Jack F. Douglasc, Andrey V. Dobrynina, Michael R. Bockstallerb, and Alamgir Karima,1 a College of Polymer Science and Polymer Engineering, The University of Akron, Akron, OH 44325; bDepartment of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213; and cMaterials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899
Edited by Andrea J. Liu, University of Pennsylvania, Philadelphia, PA, and approved January 27, 2017 (received for review August 18, 2016)
The modification of nanoparticles with polymer ligands has emerged as a versatile approach to control the interactions and organization of nanoparticles in polymer nanocomposite materials. Besides their technological significance, polymer-grafted nanoparticle (PGNP) dispersions have attracted interest as model systems to understand the role of entropy as a driving force for microstructure formation. For instance, densely and sparsely grafted nanoparticles show distinct dispersion and assembly behaviors within polymer matrices due to the entropy variation associated with conformational changes in brush and matrix chains. Here we demonstrate how this entropy change can be harnessed to drive PGNPs into spatially organized domain structures on submicrometer scale within topographically patterned thin films. This selective segregation of PGNPs is induced by the conformational entropy penalty arising from local perturbations of grafted and matrix chains under confinement. The efficiency of this particle segregation process within patterned mesa−trench films can be tuned by changing the relative entropic confinement effects on grafted and matrix chains. The versatility of topographic patterning, combined with the compatibility with a wide range of nanoparticle and polymeric materials, renders SCPINS (soft-confinement pattern-induced nanoparticle segregation) an attractive method for fabricating nanostructured hybrid films with potential applications in nanomaterial-based technologies.
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he dispersion and organization of nanoparticles in polymeric matrices are important to improve the properties of polymer nanocomposite materials (1, 2). Polymer-grafted nanoparticles (PGNPs) have attracted much attention in this regard due to their enhanced miscibility and versatility of assembled structures in polymeric materials via interacting grafted polymer layers (3, 4). The cloaking of nanoparticles by densely grafted polymer layers with the same chemical composition as the matrix leads to an “athermal” particle−polymer blend where entropic interactions dominate the thermodynamics of the system (5). Selective segregation of PGNPs at the interface or center of phase-separated block copolymer microdomains depends on the interplay between conformational and translational entropy of the system (6, 7). Considering the significant contribution of entropy in directed nanostructure formation (8, 9), entropic interactions have the potential to tailor the organization of PGNPs within a chemically identical polymer matrix, which is not achievable by conventional techniques (10, 11). The entropic effects can be magnified by confining PGNPs in thin-film geometries. Under confinement, the conformation of the grafted chains is altered, and the associated entropic penalty could drive directional migration of PGNPs and potentially generate visually ordered microstructures. To illustrate this concept, we introduce lateral confinement contrast by topographically patterning thin films of PGNPs in a matrix of the same polymer through capillary force lithography (12). By tuning the confinement parameters, soft-confinement pattern-induced nanoparticle
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segregation (SCPINS) is achieved, enabling precise localization of PGNPs within lithographically defined patterned mesa regions. The free energy penalty responsible for this PGNP localization depends on the variation of confinement entropy controlled by the grafted layer thickness, matrix chain length, and confinement length scale. We validate our observations by direct measurements of nanoparticle distribution and its time evolution within patterned thin films, combined with theoretical explanations. Results and Discussion We investigate the entropy-driven segregation of PGNPs using model thin films of PGNP/polymer blends with well-controlled molecular parameters to establish fundamental principles governing this segregation process. In particular, we consider polystyrene-grafted gold nanoparticles (denoted as AuPS hereafter) embedded in polystyrene (PS) thin film matrices having a series of chain lengths. The spherical AuPS particles have an average core radius of R0 ≈ 1.2 nm and are densely grafted with PS chains (Mn,PS,grafted = 11.5 kg/mol) with grafting density of σ ≈ 0.7/nm2. To elicit nanoparticle migration, the homogeneous as-cast AuPS/ PS blend films (SI Appendix, Fig. S1) were thermally annealed for 10 min at 180 °C, which is significantly higher than the glass transition temperature of PS (Tg,PS ≈ 75 °C to 105 °C), in three different ways: with a free air surface (I), confined via conformal contact with a smooth elastomer (PDMS) capping layer (II), and confined via a channel-patterned elastomer (PDMS) capping layer (III) (see schematic representations in Fig. 1). In cases I and II, the smooth surface topography of the blend films were unperturbed, whereas, in case III, capillarity induced rapid mold filling (13, 14) and generated patterned topography composed of alternating mesas and trenches with a pitch, λ = (752 ± 6) nm, and a step Significance Functional polymer nanocomposite thin films demand precise control over the spatial organization of nanoparticles on microscales and nanoscales. We demonstrate that conformational chain entropy can be used as a driving force to direct nanoparticle redistribution in blend systems where the enthalpic interactions are negligible. Tunable segregation of polymer-grafted nanoparticles is achieved within topographically patterned polymeric thin films by varying the relative confinement entropy of chains grafted to nanoparticles versus matrix chains. We identify key factors governing this confinement-induced segregation phenomenon and demonstrate the applicability of this technique to different pattern geometries and nanoparticle systems. Author contributions: R.Z. and A.K. designed research; R.Z. and B.L. performed research; R.Z. analyzed data; and R.Z., C.M.S., J.F.D., A.V.D., M.R.B., and A.K. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1
To whom correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1613828114/-/DCSupplemental.
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particle-rich and particle-depleted zones. Note that the potential desorption of grafted thiol PS (PS-SH) ligands from Au particle cores would be a gradual transition that depends on ligand type, ligand chain length, and annealing conditions (18). In the current study, relatively short annealing times were chosen to avoid any noteworthy PS ligand desorption, thus preventing nanoparticle aggregation. The integrity of the polymer ligand layer was confirmed by postannealed films studies (details are included in SI Appendix, Fig. S1). To delineate the thermodynamic driving force for the observed segregation of PGNPs under patterned confinement, we reduced the annealing temperature from 180 °C to 120 °C (≈40 °C higher than Tg,PS 3k) to track the kinetics of this particle segregation process. As shown in Fig. 2A, the capillary force-driven moldfilling process was completed within 3 min. However, the diffusion of AuPS particles continued until complete segregation in mesas occurred upon extended annealing for up to 16 h, indicating that the selective particle segregation was a thermodynamically favorable state. The attractive van der Waals interaction between AuPS particles was estimated to be less than ≈0.15 kBT (where kB is the Boltzmann constant and T is the absolute temperature) on the length scale of a few nanometers (4). Because this interaction is negligible due to the protective PS ligand layer, we interpret the local concentration of PGNPs within mesa regions as an entropydriven phenomenon. In particular, we propose that confining PGNPs in ultrathin trenches causes a loss of conformational entropy of tethered chains (ΔSC), thus giving rise to the chemical potential gradient to drive this visual-ordered dense nanoparticle
Fig. 1. Distribution of PGNPs in polymer thin films generated by different annealing methods. Schematic representations for thermally annealing AuPS/PS blend films with free air surface (case I), smooth confinement (case II), and channel-patterned confinement (case III). The corresponding top-view TEM micrographs and 3D AFM height image for 30% AuPS/PS 3k films (h ≈ 80 nm) annealed at 180 °C for 10 min are shown below the schematics. The dark and light strips shown in TEM micrographs for channel-patterned films are imprinted mesas and trenches, respectively. The TEM micrograph for channel-patterned films is digitized to illustrate AuPS distribution while eliminating film thickness differences.
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height, Δh = (119 ± 1) nm, as shown in the 3D atomic force microscopy (AFM) height image in Fig. 1. For AuPS/PS blend films with an initial thickness h ≈ 80 nm, channel-pattern confined annealing generated a modulated film topography characterized with a mesa thickness h1 ≈ 140 nm, and a trench thickness h2 ≈ 20 nm. Note that the blend films utilized in the present study were sufficiently thick to fill the cavity completely, and there was always a residual layer after capillary force lithography process (15). The distributions of AuPS particles in PS matrix were subsequently characterized by top-view transmission electron microscopy (TEM) images. The molecular mass of the PS matrix is 2.8 kg/mol, which is denoted as PS 3k hereafter. In this case, the mass ratio of AuPS particle relative to PS 3k matrix is approximately 30%, corresponding to a particle number concentration lower than the critical overlapping concentration (v*), estimated as v* = 1=ð4=3πR3np Þ, where Rnp is the radius of the AuPS particles including the polymer shell thickness (Rnp ≈ 14 nm) (16). As displayed in Fig. 1, the homogeneous distribution of AuPS particles was maintained in cases I and II, whereas exclusive AuPS segregation in mesas (dark strips in TEM images) was generated in case III. This localized enrichment of AuPS particles was particularly clear in the digitized TEM image in which the film thickness contrast between mesas and trenches was subtracted. A pertinent feature of the selective AuPS segregation is that the formation of particle-rich zones occurs while the blend system maintains overall miscibility due to the wettability of grafted PS layer by matrix PS 3k chains (17), which was discerned from the absence of particle aggregation in both
Fig. 2. Loss of conformational entropy-induced particle segregation under soft-pattern confinement. (A) Top-view TEM micrographs for 30% AuPS/PS 3k films (h ≈ 80 nm) annealed at 120 °C for the time periods indicated. (B) Top-view TEM micrographs for 100% AuPS/PS 3k and 200% AuPS/PS 3k blend films (h ≈ 85 nm) annealed at 180 °C for 1 h. (C) Schematic representations of channel-patterned blend films with alternating mesas and trenches with particle concentration of ρ1 and ρ2, respectively. The zoom-in image shows the confinement thickness, hconfine, within trenches.
pattern formation. The exclusive segregation of PGNPs in mesas was maintained with higher AuPS concentration as shown in 100% AuPS/PS 3k films, where the mass ratio of AuPS to PS matrix is 1:1 (Fig. 2B). With further increase in PGNP loading fraction to 200% by mass (2:1), the exclusive selective segregation was frustrated, resulting in excess AuPS particles squeezing into thin trenches due to their saturation leveled in mesas (19). To validate the above argument, we established the entropy loss of tethered chains on nanoparticles, which are located in the center of a trench. The entropy loss is shown to be a function of the degree of entropic confinement, defined as a ratio of hbrush/ hconfine, which is controlled by the thickness of the grafted (“brush”) polymer layer hbrush and the confinement dimension hconfine = h2/2 − R0 (shown in the schematics in Figs. 1 and 2C). In the brush regime (σ −1/2 < Rg,grafted), the PS 3k molecules can penetrate into the polymer brush layer analogous to a good solvent, resulting in a swollen polymer brush with a thickness hbrush ≈ 12.8 nm (20, 21). The estimated PS brush thickness is consistent with the nearest interparticle distance when closely packed in mesas as determined from TEM images. For AuPS/PS blend films with an initial film thickness h ≈ 80 nm, assuming AuPS particles are located halfway between the trench surfaces, the relative confinement degree is 2464 | www.pnas.org/cgi/doi/10.1073/pnas.1613828114
greater than 1 (hbrush/hconfine ≈ 1.4), which results in a loss of conformational entropy of the grafted chains and drives the migration of particles into thicker mesas in exchange for PS 3k chains. Because the PS 3k chain size (Rg,PS ≈ 1.6 nm) (22) is notably smaller than hconfine, there is minimal conformational entropy loss for PS 3k matrix chains when enriched in trenches. Therefore, the formation of channel-patterned nanoparticle domains by selective segregation of AuPS into mesas is entropically favorable (see SI Appendix for details). During the SCPINS process, visually ordered nanoparticle structures are generated, accompanied with an increase in the overall entropy of the system (i.e., order through entropy) (8). Based on the above discussions, the preferential segregation of PGNPs in athermal blends should be influenced by the degree of confinement of (i) brush chains in trenches (hbrush/hconfine), (ii) matrix polymer chains trapped between gold cores and trench walls (2Rg,PS/hconfine), and (iii) matrix polymer chains confined between top and bottom trench walls (2Rg,PS/h2). Variation of the matrix polymer chain size Rg,PS and the initial blend film thickness h, which controls the trench thickness h2, should allow us to tune AuPS segregation in the patterned mesa−trench regions. We therefore systematically varied the molecular mass of the matrix PS chains from 2.8 kg/mol to 360 kg/mol (detailed information is included in SI Appendix, Table S1) and the initial film thickness from 85 nm to 140 nm. Note that uniform distribution of AuPS particles was maintained in all PS matrices upon thermal annealing without patterned confinement (SI Appendix, Figs. S3−S5). The process of SCPINS was induced by channelpattern confined annealing at 180 °C for 1 h, which was sufficient to generate thermodynamically stable structures. As shown in Fig. 3, with increasing PS matrix molecular mass at the same initial film thickness (h ≈ 85 nm), the selective segregation of PGNPs in mesas was progressively suppressed. This changeover could be explained by a more pronounced conformational entropy loss of the matrix polymer chains with increasing chain length via the increase in 2Rg,PS/hconfine and 2Rg,PS/h2. Simultaneously, there was a gradual reduction in entropic confinement of the grafted chains manifested in a decrease of hbrush in the mixture with longer PS chains (as illustrated in schematics in Fig. 3) (23). For instance, the collapsed brush layer thickness resulted in a suppressed confinement degree of hbrush/hconfine ≈ 0.8 in a PS 16k matrix and further reduced to hbrush/hconfine ≈ 0.6 in a PS 360k matrix (24, 25). Separately, more uniform AuPS distribution was generated by increasing initial film thickness h while the matrix molecular mass was constant (Fig. 3). In this case, the entropic confinement effect for AuPS particles was gradually reduced within the trenches, and thus more uniform PGNP distribution was induced. The SCPINS phenomenon was further quantified by the partition coefficient K, adapted by analogy from dilute polymer solutions in geometrically confined spaces (26). The partition coefficient is evaluated by the concentration ratio of AuPS particles, ρ2/ρ1, where ρ1 and ρ2 are particle concentrations in mesas and trenches, respectively (Fig. 2C). Detailed explanations of the evaluation of partition coefficient K are included in SI Appendix. The dependence of K on hbrush/hconfine by varying initial film thickness h in PS matrices with different molecular masses (color sets) is shown in Fig. 4. With marginal entropic confinement (i.e., hbrush/hconfine → 0), the AuPS distributions in all PS matrices are homogeneous (K = 1). Strong confinement (i.e., hbrush/hconfine > 1), in contrast, generates complete AuPS segregation at mesas (K → 0) in low molecular mass PS matrices, as the entropic penalty associated with grafted polymer chains notably outweighs that of matrix chains when located in trenches. The transition between weak and strong confinement regimes is mediated by the relative size of grafted and matrix polymer chains (hbrush/2Rg,PS), where a milder transition was observed in longer PS matrix chains. When the grafted and matrix chains are of comparable size (i.e., hbrush/2Rg,PS ≈ 1), the partition Zhang et al.
coefficient is constant (K = 1) and independent of the confinement degree, indicating an equivalent conformational entropy loss for both components. In a reversal of the above observations, as the molecular mass of matrix PS chains further increases, the AuPS particles become more concentrated in the trenches (K > 1), whereas the matrix polymer chains segregate into the mesas due to more significant entropic penalty under confinement. It should be noted, however, that, in the case of ultrathin trench confinement (i.e., h2 ≈ 2Rg,PS), only partial depletion of matrix PS chains was observed, as the mobility of polymer chains was significantly suppressed beyond practical equilibration times (27). From partition coefficients of the channel-patterned AuPS/PS blend films, the resultant free energy change can be estimated by ΔF = −kBT ln K (28). ΔF represents the free energy change of the system as one individual AuPS particle is relocated from mesa to trench. Because the enthalpic interactions are largely screened, the free energy change corresponds to the overall entropic penalty. For example, in low molecular mass polymer matrices, ΔF accounts for the conformational entropy gain and translational entropy loss when particles are selectively sequestered into mesas. As shown in Fig. 4, when the confinement degree is relatively weak (hbrush/hconfine < 0.9), only marginal free energy change (jΔFj ≤ kBT) is induced. As the confinement becomes moderate (1< hbrush/hconfine < 1.5), a drastic increase in jΔFj is induced in low molecular mass PS matrices, resulting in stronger segregation of AuPS particles in mesas versus in trenches. Scaling relationships for the free energy change of PGNPs in different polymer matrices under various confinement conditions are included in SI Appendix. To further confirm that the selective particle segregation is driven by entropic confinement effect, we study the variation of ΔF in PS 3k matrix (h ≈ 85 nm) under channel-patterned confinement with varied pattern height difference (Δh). The corresponding TEM micrographs are shown in SI Appendix, Fig. S7, where a more uniform AuPS distribution in mesas versus trenches is induced by reducing Δh. Fig. 4, Inset shows that the transition of ΔF by reducing Δh overlaps similarly with that achieved by increasing initial film thickness h. The general observation of confinementinduced segregation of PGNPs confirms that the equilibrium characteristics of the partitioning system (i.e., K, ΔF) depend only on the relative entropic confinement degree (hbrush/hconfine), rather than on the absolute values of individual parameters (26). As a final remark, we extend our study to other athermal PGNP/polymer blend systems and more complex topographic Zhang et al.
patterns to illustrate the generality and versatility of the SCPINS method. Fig. 5A shows selective segregation of PS−g−SiO2 particles (R0 = 7.7 ± 2.1 nm, Mn,PS = 54 kg/mol, σ = 0.57/nm2) in PS
Fig. 4. Dependence of partition coefficient (K) and the resultant free energy change (ΔF/kBT) on the degree of confinement for brush chains (hbrush/ hconfine). The relative dimensions of brush and matrix chains (hbrush/2Rg,PS) are indicated in the plots. The solid curves in the plot of free energy variation are power-law function fittings [ΔF/kBT = a(hbrush/hconfine)b; a and b are constants]. (Inset) The weak confinement regime shown in an expanded scale.
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Fig. 3. Channel-pattern confinement-induced tunable particle segregation by adjusting entropic confinement degrees. Top-view TEM micrographs for 30% AuPS/PS blend films annealed at 180 °C for 1 h in different PS matrices (PS 3k, 16k, and 360k) with varying initial film thicknesses (h ≈ 85 nm, 100 nm, and 140 nm). Schematics for AuPS nanoparticles (left) and particle distributions in channel-patterned films (right) are shown on each side.
Fig. 5. Generality and versatility of soft-pattern confinement-induced nanoparticle segregation. (A) Top-view TEM micrograph for channel-patterned 10% PS−g−SiO2/PS 3k blend films (h ≈ 90 nm) upon thermal annealing at 180 °C for 1 h. (B) AFM 3D height image for lattice-patterned 30% AuPS/PS 3k blend films (h ≈ 85 nm) upon thermal annealing at 180 °C for 1 h, and the corresponding TEM micrographs. (C) Top-view TEM micrographs for 30% AuPS/PS 3k blend films (h ≈ 150 nm) annealed with an electric-circuit–like patterned PDMS layer as confinement. (Insets) AFM 3D height images.
3k films (h ≈ 90 nm) upon channel-pattern confined thermal annealing. The TEM image reveals highly selective concentration of PS−g−SiO2 particles in mesas due to the entropic confinement effect (hbrush/hconfine ≈ 3), as well as superlattice formation of particles within mesas. Because this entropy-driven segregation process only relies on the relative confinement of the grafted and matrix polymers, this method is envisioned to be general for different particle systems. Application of this method to form more complex patterned PGNP domain structures is further demonstrated by using confinement with different geometries. The AFM 3D height image in Fig. 5B shows the topography of lattice-patterned 30% AuPS/PS 3k blend films (h ≈ 85 nm, λ ≈ 750 nm) composed of periodic intersecting rhombic mesas (≈145 nm), intermediate channels (≈85 nm), and trenches (≈25 nm), with confinement from weak to strong. The corresponding variation in AuPS distributions is shown in TEM micrographs, where the nanoparticles are uniformly distributed between rhombic mesas and channels with identical concentration (i.e., particle number proportional to local film thickness), while completely depleted from the trenches. Relevant to nanoelectronic and nanoplasmonic applications, we show complete AuPS nanoparticle segregation within thick mesas when confined by an electronic circuit-shaped topographically patterned elastomer capping layer (Fig. 5C; no particles are present in thin trenches). Conclusion In summary, we demonstrate a simple and widely applicable method of SCPINS to produce visual order via spatially organized PGNPs in polymer thin films, driven by an increase in the overall entropy of the system. The architecture of PGNP arrangements can be controlled by the prescribed topographic patterns, whereas the distribution of PGNPs among mesas and trenches is tunable by varying the relative entropic confinement degree (hbrush/hconfine) and relative matrix chain size (hbrush/2Rg,PS). Different from pattern-directed organization of a phase-separated blend system (29), where the ordered structures are transient and depend on the interplay of phase separation length scale and pattern dimension, this entropy-driven patterning method can result in thermodynamically stable structures. Moreover, the interparticle distance can be easily controlled by varying the particle loading or grafted layer thickness. The versatility of the process with respect to particle composition and pattern geometry should render SCPINS an attractive tool for 2466 | www.pnas.org/cgi/doi/10.1073/pnas.1613828114
fabrication of particle nanostructures for electronic, plasmonic, and photonic applications. The application of multiscale patterns, with controlled distribution of trench thickness, should allow for extension of SCPINS to multicomponent particle systems that play an important role in a range of nanomaterial-enabled technologies. Methods PS with different molecular masses were purchased from Polymer Source Inc. and used as obtained (PS 3k, Mn,PS = 2.8 kg/mol, PDI = 1.09; PS 4k, Mn,PS = 4.8 kg/mol, PDI = 1.07; PS 6k, Mn,PS = 6.1 kg/mol, PDI = 1.05; PS 16k, Mn,PS = 16 kg/mol, PDI = 1.03; PS 160k, Mn,PS = 160 kg/mol, PDI = 1.05; PS 360k, Mn,PS = 360 kg/mol, PDI = 1.09; Mn is the number average molecular mass and PDI is the dispersity index). The PS-SH grafted gold nanoparticles (AuPS) were synthesized by phase transfer reduction of [AuCl4] in the presence of thiol ligands (30). The average radius of gold core R0 = 1.2 ± 0.4 nm. The grafted PS molecular mass is Mn,PS,grafted = 11.5 kg/mol, and the grafting density is σ = 0.7/nm2. Upon vacuum oven annealing at 180 °C for 16 h, AuPS nanoparticles experienced subtle size increase to R0 = 1.3 ± 0.5 nm due to the thermal instability of the thiol−Au bond (31). The average radius of SiO2 core is R0 = 7.7 ± 2.1 nm, grafted with PS chains with Mn,PS = 54 kg/mol at grafting density of 0.57/nm2. The PS−g−SiO2 particles were synthesized by surface-initiated atom transfer radical polymerization using previously published procedures (32). PS solutions (3% by mass in toluene) were premixed with appropriate amounts of PGNPs (mass ratio of AuPS to PS is 30% to 200%) and flowcoated into thin films of thickness h ≈ 80 nm to 140 nm on silicon substrates. The film thicknesses were determined by interferometer (F-20 UV Thin Film Analyzer; Filmetrics, Inc.). Cross-linked poly(dimethylsiloxane) (PDMS) elastomer layers (thickness ≈ 0.5 mm, elastomer mass:curing agent mass = 20:1) were made by curing at 120 °C for 6 h on smooth glass slides, commercial digital video discs (pitch λ ≈ 750 nm, height difference Δh ≈ 120 nm), or electronic-circuit-like patterned silicon templates. The smooth or patterned PDMS layers served as confinement during thermal annealing. After annealing for certain time periods, the PDMS layer was removed for characterization. Nanoparticle distributions were characterized with a JEOL JEM-1230 TEM at 200 kV. Specimens for TEM were prepared by precoating a thin layer (≈10 nm) of aqueous poly(4-styrenesulfonic acid) (PSS; SigmaAldrich) solution on the substrates before coating the blend films, annealing the multilayer films, and then floating the films by immersing into distilled water followed by transferring to copper grids. Surface topography of the blend films was imaged using a Dimension Icon AFM (Bruker AXS) in tapping mode. ACKNOWLEDGMENTS. We thank Prof. S. K. Kumar, Prof. Rob Riggleman, Dr. C. C. Han, and Dr. J. Hwang for valuable discussions. Funding was provided by National Science Foundation Grants DMR-1411046 (to A.K.) and DMR-1410845 (to M.R.B.). Certain equipment, instruments, or materials are identified in this paper to adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology nor does it imply the materials are necessarily the best available for the purpose.
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Edited by Andrea J. Liu, University of Pennsylvania, Philadelphia, PA, and approved January 27, 2017 (received for review August 18, 2016)
The modification of nanoparticles with polymer ligands has emerged as a versatile approach to control the interactions and organization of nanoparticles in polymer nanocomposite materials. Besides their technological significance, polymer-grafted nanoparticle (PGNP) dispersions have attracted interest as model systems to understand the role of entropy as a driving force for microstructure formation. For instance, densely and sparsely grafted nanoparticles show distinct dispersion and assembly behaviors within polymer matrices due to the entropy variation associated with conformational changes in brush and matrix chains. Here we demonstrate how this entropy change can be harnessed to drive PGNPs into spatially organized domain structures on submicrometer scale within topographically patterned thin films. This selective segregation of PGNPs is induced by the conformational entropy penalty arising from local perturbations of grafted and matrix chains under confinement. The efficiency of this particle segregation process within patterned mesa−trench films can be tuned by changing the relative entropic confinement effects on grafted and matrix chains. The versatility of topographic patterning, combined with the compatibility with a wide range of nanoparticle and polymeric materials, renders SCPINS (soft-confinement pattern-induced nanoparticle segregation) an attractive method for fabricating nanostructured hybrid films with potential applications in nanomaterial-based technologies.
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he dispersion and organization of nanoparticles in polymeric matrices are important to improve the properties of polymer nanocomposite materials (1, 2). Polymer-grafted nanoparticles (PGNPs) have attracted much attention in this regard due to their enhanced miscibility and versatility of assembled structures in polymeric materials via interacting grafted polymer layers (3, 4). The cloaking of nanoparticles by densely grafted polymer layers with the same chemical composition as the matrix leads to an “athermal” particle−polymer blend where entropic interactions dominate the thermodynamics of the system (5). Selective segregation of PGNPs at the interface or center of phase-separated block copolymer microdomains depends on the interplay between conformational and translational entropy of the system (6, 7). Considering the significant contribution of entropy in directed nanostructure formation (8, 9), entropic interactions have the potential to tailor the organization of PGNPs within a chemically identical polymer matrix, which is not achievable by conventional techniques (10, 11). The entropic effects can be magnified by confining PGNPs in thin-film geometries. Under confinement, the conformation of the grafted chains is altered, and the associated entropic penalty could drive directional migration of PGNPs and potentially generate visually ordered microstructures. To illustrate this concept, we introduce lateral confinement contrast by topographically patterning thin films of PGNPs in a matrix of the same polymer through capillary force lithography (12). By tuning the confinement parameters, soft-confinement pattern-induced nanoparticle
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segregation (SCPINS) is achieved, enabling precise localization of PGNPs within lithographically defined patterned mesa regions. The free energy penalty responsible for this PGNP localization depends on the variation of confinement entropy controlled by the grafted layer thickness, matrix chain length, and confinement length scale. We validate our observations by direct measurements of nanoparticle distribution and its time evolution within patterned thin films, combined with theoretical explanations. Results and Discussion We investigate the entropy-driven segregation of PGNPs using model thin films of PGNP/polymer blends with well-controlled molecular parameters to establish fundamental principles governing this segregation process. In particular, we consider polystyrene-grafted gold nanoparticles (denoted as AuPS hereafter) embedded in polystyrene (PS) thin film matrices having a series of chain lengths. The spherical AuPS particles have an average core radius of R0 ≈ 1.2 nm and are densely grafted with PS chains (Mn,PS,grafted = 11.5 kg/mol) with grafting density of σ ≈ 0.7/nm2. To elicit nanoparticle migration, the homogeneous as-cast AuPS/ PS blend films (SI Appendix, Fig. S1) were thermally annealed for 10 min at 180 °C, which is significantly higher than the glass transition temperature of PS (Tg,PS ≈ 75 °C to 105 °C), in three different ways: with a free air surface (I), confined via conformal contact with a smooth elastomer (PDMS) capping layer (II), and confined via a channel-patterned elastomer (PDMS) capping layer (III) (see schematic representations in Fig. 1). In cases I and II, the smooth surface topography of the blend films were unperturbed, whereas, in case III, capillarity induced rapid mold filling (13, 14) and generated patterned topography composed of alternating mesas and trenches with a pitch, λ = (752 ± 6) nm, and a step Significance Functional polymer nanocomposite thin films demand precise control over the spatial organization of nanoparticles on microscales and nanoscales. We demonstrate that conformational chain entropy can be used as a driving force to direct nanoparticle redistribution in blend systems where the enthalpic interactions are negligible. Tunable segregation of polymer-grafted nanoparticles is achieved within topographically patterned polymeric thin films by varying the relative confinement entropy of chains grafted to nanoparticles versus matrix chains. We identify key factors governing this confinement-induced segregation phenomenon and demonstrate the applicability of this technique to different pattern geometries and nanoparticle systems. Author contributions: R.Z. and A.K. designed research; R.Z. and B.L. performed research; R.Z. analyzed data; and R.Z., C.M.S., J.F.D., A.V.D., M.R.B., and A.K. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1
To whom correspondence should be addressed. Email: [email protected].
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1613828114/-/DCSupplemental.
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particle-rich and particle-depleted zones. Note that the potential desorption of grafted thiol PS (PS-SH) ligands from Au particle cores would be a gradual transition that depends on ligand type, ligand chain length, and annealing conditions (18). In the current study, relatively short annealing times were chosen to avoid any noteworthy PS ligand desorption, thus preventing nanoparticle aggregation. The integrity of the polymer ligand layer was confirmed by postannealed films studies (details are included in SI Appendix, Fig. S1). To delineate the thermodynamic driving force for the observed segregation of PGNPs under patterned confinement, we reduced the annealing temperature from 180 °C to 120 °C (≈40 °C higher than Tg,PS 3k) to track the kinetics of this particle segregation process. As shown in Fig. 2A, the capillary force-driven moldfilling process was completed within 3 min. However, the diffusion of AuPS particles continued until complete segregation in mesas occurred upon extended annealing for up to 16 h, indicating that the selective particle segregation was a thermodynamically favorable state. The attractive van der Waals interaction between AuPS particles was estimated to be less than ≈0.15 kBT (where kB is the Boltzmann constant and T is the absolute temperature) on the length scale of a few nanometers (4). Because this interaction is negligible due to the protective PS ligand layer, we interpret the local concentration of PGNPs within mesa regions as an entropydriven phenomenon. In particular, we propose that confining PGNPs in ultrathin trenches causes a loss of conformational entropy of tethered chains (ΔSC), thus giving rise to the chemical potential gradient to drive this visual-ordered dense nanoparticle
Fig. 1. Distribution of PGNPs in polymer thin films generated by different annealing methods. Schematic representations for thermally annealing AuPS/PS blend films with free air surface (case I), smooth confinement (case II), and channel-patterned confinement (case III). The corresponding top-view TEM micrographs and 3D AFM height image for 30% AuPS/PS 3k films (h ≈ 80 nm) annealed at 180 °C for 10 min are shown below the schematics. The dark and light strips shown in TEM micrographs for channel-patterned films are imprinted mesas and trenches, respectively. The TEM micrograph for channel-patterned films is digitized to illustrate AuPS distribution while eliminating film thickness differences.
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height, Δh = (119 ± 1) nm, as shown in the 3D atomic force microscopy (AFM) height image in Fig. 1. For AuPS/PS blend films with an initial thickness h ≈ 80 nm, channel-pattern confined annealing generated a modulated film topography characterized with a mesa thickness h1 ≈ 140 nm, and a trench thickness h2 ≈ 20 nm. Note that the blend films utilized in the present study were sufficiently thick to fill the cavity completely, and there was always a residual layer after capillary force lithography process (15). The distributions of AuPS particles in PS matrix were subsequently characterized by top-view transmission electron microscopy (TEM) images. The molecular mass of the PS matrix is 2.8 kg/mol, which is denoted as PS 3k hereafter. In this case, the mass ratio of AuPS particle relative to PS 3k matrix is approximately 30%, corresponding to a particle number concentration lower than the critical overlapping concentration (v*), estimated as v* = 1=ð4=3πR3np Þ, where Rnp is the radius of the AuPS particles including the polymer shell thickness (Rnp ≈ 14 nm) (16). As displayed in Fig. 1, the homogeneous distribution of AuPS particles was maintained in cases I and II, whereas exclusive AuPS segregation in mesas (dark strips in TEM images) was generated in case III. This localized enrichment of AuPS particles was particularly clear in the digitized TEM image in which the film thickness contrast between mesas and trenches was subtracted. A pertinent feature of the selective AuPS segregation is that the formation of particle-rich zones occurs while the blend system maintains overall miscibility due to the wettability of grafted PS layer by matrix PS 3k chains (17), which was discerned from the absence of particle aggregation in both
Fig. 2. Loss of conformational entropy-induced particle segregation under soft-pattern confinement. (A) Top-view TEM micrographs for 30% AuPS/PS 3k films (h ≈ 80 nm) annealed at 120 °C for the time periods indicated. (B) Top-view TEM micrographs for 100% AuPS/PS 3k and 200% AuPS/PS 3k blend films (h ≈ 85 nm) annealed at 180 °C for 1 h. (C) Schematic representations of channel-patterned blend films with alternating mesas and trenches with particle concentration of ρ1 and ρ2, respectively. The zoom-in image shows the confinement thickness, hconfine, within trenches.
pattern formation. The exclusive segregation of PGNPs in mesas was maintained with higher AuPS concentration as shown in 100% AuPS/PS 3k films, where the mass ratio of AuPS to PS matrix is 1:1 (Fig. 2B). With further increase in PGNP loading fraction to 200% by mass (2:1), the exclusive selective segregation was frustrated, resulting in excess AuPS particles squeezing into thin trenches due to their saturation leveled in mesas (19). To validate the above argument, we established the entropy loss of tethered chains on nanoparticles, which are located in the center of a trench. The entropy loss is shown to be a function of the degree of entropic confinement, defined as a ratio of hbrush/ hconfine, which is controlled by the thickness of the grafted (“brush”) polymer layer hbrush and the confinement dimension hconfine = h2/2 − R0 (shown in the schematics in Figs. 1 and 2C). In the brush regime (σ −1/2 < Rg,grafted), the PS 3k molecules can penetrate into the polymer brush layer analogous to a good solvent, resulting in a swollen polymer brush with a thickness hbrush ≈ 12.8 nm (20, 21). The estimated PS brush thickness is consistent with the nearest interparticle distance when closely packed in mesas as determined from TEM images. For AuPS/PS blend films with an initial film thickness h ≈ 80 nm, assuming AuPS particles are located halfway between the trench surfaces, the relative confinement degree is 2464 | www.pnas.org/cgi/doi/10.1073/pnas.1613828114
greater than 1 (hbrush/hconfine ≈ 1.4), which results in a loss of conformational entropy of the grafted chains and drives the migration of particles into thicker mesas in exchange for PS 3k chains. Because the PS 3k chain size (Rg,PS ≈ 1.6 nm) (22) is notably smaller than hconfine, there is minimal conformational entropy loss for PS 3k matrix chains when enriched in trenches. Therefore, the formation of channel-patterned nanoparticle domains by selective segregation of AuPS into mesas is entropically favorable (see SI Appendix for details). During the SCPINS process, visually ordered nanoparticle structures are generated, accompanied with an increase in the overall entropy of the system (i.e., order through entropy) (8). Based on the above discussions, the preferential segregation of PGNPs in athermal blends should be influenced by the degree of confinement of (i) brush chains in trenches (hbrush/hconfine), (ii) matrix polymer chains trapped between gold cores and trench walls (2Rg,PS/hconfine), and (iii) matrix polymer chains confined between top and bottom trench walls (2Rg,PS/h2). Variation of the matrix polymer chain size Rg,PS and the initial blend film thickness h, which controls the trench thickness h2, should allow us to tune AuPS segregation in the patterned mesa−trench regions. We therefore systematically varied the molecular mass of the matrix PS chains from 2.8 kg/mol to 360 kg/mol (detailed information is included in SI Appendix, Table S1) and the initial film thickness from 85 nm to 140 nm. Note that uniform distribution of AuPS particles was maintained in all PS matrices upon thermal annealing without patterned confinement (SI Appendix, Figs. S3−S5). The process of SCPINS was induced by channelpattern confined annealing at 180 °C for 1 h, which was sufficient to generate thermodynamically stable structures. As shown in Fig. 3, with increasing PS matrix molecular mass at the same initial film thickness (h ≈ 85 nm), the selective segregation of PGNPs in mesas was progressively suppressed. This changeover could be explained by a more pronounced conformational entropy loss of the matrix polymer chains with increasing chain length via the increase in 2Rg,PS/hconfine and 2Rg,PS/h2. Simultaneously, there was a gradual reduction in entropic confinement of the grafted chains manifested in a decrease of hbrush in the mixture with longer PS chains (as illustrated in schematics in Fig. 3) (23). For instance, the collapsed brush layer thickness resulted in a suppressed confinement degree of hbrush/hconfine ≈ 0.8 in a PS 16k matrix and further reduced to hbrush/hconfine ≈ 0.6 in a PS 360k matrix (24, 25). Separately, more uniform AuPS distribution was generated by increasing initial film thickness h while the matrix molecular mass was constant (Fig. 3). In this case, the entropic confinement effect for AuPS particles was gradually reduced within the trenches, and thus more uniform PGNP distribution was induced. The SCPINS phenomenon was further quantified by the partition coefficient K, adapted by analogy from dilute polymer solutions in geometrically confined spaces (26). The partition coefficient is evaluated by the concentration ratio of AuPS particles, ρ2/ρ1, where ρ1 and ρ2 are particle concentrations in mesas and trenches, respectively (Fig. 2C). Detailed explanations of the evaluation of partition coefficient K are included in SI Appendix. The dependence of K on hbrush/hconfine by varying initial film thickness h in PS matrices with different molecular masses (color sets) is shown in Fig. 4. With marginal entropic confinement (i.e., hbrush/hconfine → 0), the AuPS distributions in all PS matrices are homogeneous (K = 1). Strong confinement (i.e., hbrush/hconfine > 1), in contrast, generates complete AuPS segregation at mesas (K → 0) in low molecular mass PS matrices, as the entropic penalty associated with grafted polymer chains notably outweighs that of matrix chains when located in trenches. The transition between weak and strong confinement regimes is mediated by the relative size of grafted and matrix polymer chains (hbrush/2Rg,PS), where a milder transition was observed in longer PS matrix chains. When the grafted and matrix chains are of comparable size (i.e., hbrush/2Rg,PS ≈ 1), the partition Zhang et al.
coefficient is constant (K = 1) and independent of the confinement degree, indicating an equivalent conformational entropy loss for both components. In a reversal of the above observations, as the molecular mass of matrix PS chains further increases, the AuPS particles become more concentrated in the trenches (K > 1), whereas the matrix polymer chains segregate into the mesas due to more significant entropic penalty under confinement. It should be noted, however, that, in the case of ultrathin trench confinement (i.e., h2 ≈ 2Rg,PS), only partial depletion of matrix PS chains was observed, as the mobility of polymer chains was significantly suppressed beyond practical equilibration times (27). From partition coefficients of the channel-patterned AuPS/PS blend films, the resultant free energy change can be estimated by ΔF = −kBT ln K (28). ΔF represents the free energy change of the system as one individual AuPS particle is relocated from mesa to trench. Because the enthalpic interactions are largely screened, the free energy change corresponds to the overall entropic penalty. For example, in low molecular mass polymer matrices, ΔF accounts for the conformational entropy gain and translational entropy loss when particles are selectively sequestered into mesas. As shown in Fig. 4, when the confinement degree is relatively weak (hbrush/hconfine < 0.9), only marginal free energy change (jΔFj ≤ kBT) is induced. As the confinement becomes moderate (1< hbrush/hconfine < 1.5), a drastic increase in jΔFj is induced in low molecular mass PS matrices, resulting in stronger segregation of AuPS particles in mesas versus in trenches. Scaling relationships for the free energy change of PGNPs in different polymer matrices under various confinement conditions are included in SI Appendix. To further confirm that the selective particle segregation is driven by entropic confinement effect, we study the variation of ΔF in PS 3k matrix (h ≈ 85 nm) under channel-patterned confinement with varied pattern height difference (Δh). The corresponding TEM micrographs are shown in SI Appendix, Fig. S7, where a more uniform AuPS distribution in mesas versus trenches is induced by reducing Δh. Fig. 4, Inset shows that the transition of ΔF by reducing Δh overlaps similarly with that achieved by increasing initial film thickness h. The general observation of confinementinduced segregation of PGNPs confirms that the equilibrium characteristics of the partitioning system (i.e., K, ΔF) depend only on the relative entropic confinement degree (hbrush/hconfine), rather than on the absolute values of individual parameters (26). As a final remark, we extend our study to other athermal PGNP/polymer blend systems and more complex topographic Zhang et al.
patterns to illustrate the generality and versatility of the SCPINS method. Fig. 5A shows selective segregation of PS−g−SiO2 particles (R0 = 7.7 ± 2.1 nm, Mn,PS = 54 kg/mol, σ = 0.57/nm2) in PS
Fig. 4. Dependence of partition coefficient (K) and the resultant free energy change (ΔF/kBT) on the degree of confinement for brush chains (hbrush/ hconfine). The relative dimensions of brush and matrix chains (hbrush/2Rg,PS) are indicated in the plots. The solid curves in the plot of free energy variation are power-law function fittings [ΔF/kBT = a(hbrush/hconfine)b; a and b are constants]. (Inset) The weak confinement regime shown in an expanded scale.
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Fig. 3. Channel-pattern confinement-induced tunable particle segregation by adjusting entropic confinement degrees. Top-view TEM micrographs for 30% AuPS/PS blend films annealed at 180 °C for 1 h in different PS matrices (PS 3k, 16k, and 360k) with varying initial film thicknesses (h ≈ 85 nm, 100 nm, and 140 nm). Schematics for AuPS nanoparticles (left) and particle distributions in channel-patterned films (right) are shown on each side.
Fig. 5. Generality and versatility of soft-pattern confinement-induced nanoparticle segregation. (A) Top-view TEM micrograph for channel-patterned 10% PS−g−SiO2/PS 3k blend films (h ≈ 90 nm) upon thermal annealing at 180 °C for 1 h. (B) AFM 3D height image for lattice-patterned 30% AuPS/PS 3k blend films (h ≈ 85 nm) upon thermal annealing at 180 °C for 1 h, and the corresponding TEM micrographs. (C) Top-view TEM micrographs for 30% AuPS/PS 3k blend films (h ≈ 150 nm) annealed with an electric-circuit–like patterned PDMS layer as confinement. (Insets) AFM 3D height images.
3k films (h ≈ 90 nm) upon channel-pattern confined thermal annealing. The TEM image reveals highly selective concentration of PS−g−SiO2 particles in mesas due to the entropic confinement effect (hbrush/hconfine ≈ 3), as well as superlattice formation of particles within mesas. Because this entropy-driven segregation process only relies on the relative confinement of the grafted and matrix polymers, this method is envisioned to be general for different particle systems. Application of this method to form more complex patterned PGNP domain structures is further demonstrated by using confinement with different geometries. The AFM 3D height image in Fig. 5B shows the topography of lattice-patterned 30% AuPS/PS 3k blend films (h ≈ 85 nm, λ ≈ 750 nm) composed of periodic intersecting rhombic mesas (≈145 nm), intermediate channels (≈85 nm), and trenches (≈25 nm), with confinement from weak to strong. The corresponding variation in AuPS distributions is shown in TEM micrographs, where the nanoparticles are uniformly distributed between rhombic mesas and channels with identical concentration (i.e., particle number proportional to local film thickness), while completely depleted from the trenches. Relevant to nanoelectronic and nanoplasmonic applications, we show complete AuPS nanoparticle segregation within thick mesas when confined by an electronic circuit-shaped topographically patterned elastomer capping layer (Fig. 5C; no particles are present in thin trenches). Conclusion In summary, we demonstrate a simple and widely applicable method of SCPINS to produce visual order via spatially organized PGNPs in polymer thin films, driven by an increase in the overall entropy of the system. The architecture of PGNP arrangements can be controlled by the prescribed topographic patterns, whereas the distribution of PGNPs among mesas and trenches is tunable by varying the relative entropic confinement degree (hbrush/hconfine) and relative matrix chain size (hbrush/2Rg,PS). Different from pattern-directed organization of a phase-separated blend system (29), where the ordered structures are transient and depend on the interplay of phase separation length scale and pattern dimension, this entropy-driven patterning method can result in thermodynamically stable structures. Moreover, the interparticle distance can be easily controlled by varying the particle loading or grafted layer thickness. The versatility of the process with respect to particle composition and pattern geometry should render SCPINS an attractive tool for 2466 | www.pnas.org/cgi/doi/10.1073/pnas.1613828114
fabrication of particle nanostructures for electronic, plasmonic, and photonic applications. The application of multiscale patterns, with controlled distribution of trench thickness, should allow for extension of SCPINS to multicomponent particle systems that play an important role in a range of nanomaterial-enabled technologies. Methods PS with different molecular masses were purchased from Polymer Source Inc. and used as obtained (PS 3k, Mn,PS = 2.8 kg/mol, PDI = 1.09; PS 4k, Mn,PS = 4.8 kg/mol, PDI = 1.07; PS 6k, Mn,PS = 6.1 kg/mol, PDI = 1.05; PS 16k, Mn,PS = 16 kg/mol, PDI = 1.03; PS 160k, Mn,PS = 160 kg/mol, PDI = 1.05; PS 360k, Mn,PS = 360 kg/mol, PDI = 1.09; Mn is the number average molecular mass and PDI is the dispersity index). The PS-SH grafted gold nanoparticles (AuPS) were synthesized by phase transfer reduction of [AuCl4] in the presence of thiol ligands (30). The average radius of gold core R0 = 1.2 ± 0.4 nm. The grafted PS molecular mass is Mn,PS,grafted = 11.5 kg/mol, and the grafting density is σ = 0.7/nm2. Upon vacuum oven annealing at 180 °C for 16 h, AuPS nanoparticles experienced subtle size increase to R0 = 1.3 ± 0.5 nm due to the thermal instability of the thiol−Au bond (31). The average radius of SiO2 core is R0 = 7.7 ± 2.1 nm, grafted with PS chains with Mn,PS = 54 kg/mol at grafting density of 0.57/nm2. The PS−g−SiO2 particles were synthesized by surface-initiated atom transfer radical polymerization using previously published procedures (32). PS solutions (3% by mass in toluene) were premixed with appropriate amounts of PGNPs (mass ratio of AuPS to PS is 30% to 200%) and flowcoated into thin films of thickness h ≈ 80 nm to 140 nm on silicon substrates. The film thicknesses were determined by interferometer (F-20 UV Thin Film Analyzer; Filmetrics, Inc.). Cross-linked poly(dimethylsiloxane) (PDMS) elastomer layers (thickness ≈ 0.5 mm, elastomer mass:curing agent mass = 20:1) were made by curing at 120 °C for 6 h on smooth glass slides, commercial digital video discs (pitch λ ≈ 750 nm, height difference Δh ≈ 120 nm), or electronic-circuit-like patterned silicon templates. The smooth or patterned PDMS layers served as confinement during thermal annealing. After annealing for certain time periods, the PDMS layer was removed for characterization. Nanoparticle distributions were characterized with a JEOL JEM-1230 TEM at 200 kV. Specimens for TEM were prepared by precoating a thin layer (≈10 nm) of aqueous poly(4-styrenesulfonic acid) (PSS; SigmaAldrich) solution on the substrates before coating the blend films, annealing the multilayer films, and then floating the films by immersing into distilled water followed by transferring to copper grids. Surface topography of the blend films was imaged using a Dimension Icon AFM (Bruker AXS) in tapping mode. ACKNOWLEDGMENTS. We thank Prof. S. K. Kumar, Prof. Rob Riggleman, Dr. C. C. Han, and Dr. J. Hwang for valuable discussions. Funding was provided by National Science Foundation Grants DMR-1411046 (to A.K.) and DMR-1410845 (to M.R.B.). Certain equipment, instruments, or materials are identified in this paper to adequately specify the experimental details. Such identification does not imply recommendation by the National Institute of Standards and Technology nor does it imply the materials are necessarily the best available for the purpose.
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