Entropy-driven segregation of polymer-graftednanoparticles under confinementRen Zhanga, Bongjoon Leeb, Christopher M. Staffordc, Jack F. Douglasc, Andrey V. Dobrynina, Michael R. Bockstallerb,and Alamgir Karima,1

aCollege 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 emergedas a versatile approach to control the interactions and organizationof nanoparticles in polymer nanocomposite materials. Besides theirtechnological significance, polymer-grafted nanoparticle (PGNP) dis-persions have attracted interest as model systems to understand therole of entropy as a driving force for microstructure formation. Forinstance, densely and sparsely grafted nanoparticles show distinctdispersion and assembly behaviors within polymer matrices due tothe entropy variation associated with conformational changes inbrush and matrix chains. Here we demonstrate how this entropychange can be harnessed to drive PGNPs into spatially organizeddomain structures on submicrometer scale within topographicallypatterned thin films. This selective segregation of PGNPs is inducedby the conformational entropy penalty arising from local perturba-tions of grafted and matrix chains under confinement. The efficiencyof this particle segregation process within patterned mesa−trenchfilms can be tuned by changing the relative entropic confinementeffects on grafted and matrix chains. The versatility of topographicpatterning, combined with the compatibility with a wide range ofnanoparticle and polymeric materials, renders SCPINS (soft-confine-ment pattern-induced nanoparticle segregation) an attractive methodfor fabricating nanostructured hybrid films with potential applicationsin nanomaterial-based technologies.

polymer thin film | polymer-grafted nanoparticle | entropy |confinement | topographic pattern

The dispersion and organization of nanoparticles in polymericmatrices 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 theirenhanced miscibility and versatility of assembled structures inpolymeric materials via interacting grafted polymer layers (3, 4).The cloaking of nanoparticles by densely grafted polymer layerswith the same chemical composition as the matrix leads to an“athermal” particle−polymer blend where entropic interactionsdominate the thermodynamics of the system (5). Selective segre-gation of PGNPs at the interface or center of phase-separatedblock copolymer microdomains depends on the interplay betweenconformational and translational entropy of the system (6, 7).Considering the significant contribution of entropy in directednanostructure formation (8, 9), entropic interactions have thepotential to tailor the organization of PGNPs within a chemicallyidentical polymer matrix, which is not achievable by conventionaltechniques (10, 11).The entropic effects can be magnified by confining PGNPs in

thin-film geometries. Under confinement, the conformation of thegrafted chains is altered, and the associated entropic penalty coulddrive directional migration of PGNPs and potentially generate vi-sually ordered microstructures. To illustrate this concept, we in-troduce lateral confinement contrast by topographically patterningthin films of PGNPs in a matrix of the same polymer throughcapillary force lithography (12). By tuning the confinementparameters, soft-confinement pattern-induced nanoparticle

segregation (SCPINS) is achieved, enabling precise localization ofPGNPs within lithographically defined patterned mesa regions.The free energy penalty responsible for this PGNP localizationdepends on the variation of confinement entropy controlled by thegrafted layer thickness, matrix chain length, and confinementlength scale. We validate our observations by direct measurementsof nanoparticle distribution and its time evolution within patternedthin films, combined with theoretical explanations.

Results and DiscussionWe investigate the entropy-driven segregation of PGNPs usingmodel thin films of PGNP/polymer blends with well-controlledmolecular parameters to establish fundamental principles gov-erning this segregation process. In particular, we consider poly-styrene-grafted gold nanoparticles (denoted as AuPS hereafter)embedded in polystyrene (PS) thin film matrices having a seriesof chain lengths. The spherical AuPS particles have an averagecore 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 for10 min at 180 °C, which is significantly higher than the glass tran-sition temperature of PS (Tg,PS ≈ 75 °C to 105 °C), in three dif-ferent ways: with a free air surface (I), confined via conformalcontact with a smooth elastomer (PDMS) capping layer (II), andconfined via a channel-patterned elastomer (PDMS) capping layer(III) (see schematic representations in Fig. 1). In cases I and II, thesmooth 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 alternatingmesas and trenches with a pitch, λ = (752 ± 6) nm, and a step

Significance

Functional polymer nanocomposite thin films demand precisecontrol over the spatial organization of nanoparticles on micro-scales and nanoscales. We demonstrate that conformationalchain entropy can be used as a driving force to direct nanoparticleredistribution in blend systems where the enthalpic interactionsare negligible. Tunable segregation of polymer-grafted nano-particles is achieved within topographically patterned polymericthin films by varying the relative confinement entropy of chainsgrafted to nanoparticles versus matrix chains. We identify keyfactors governing this confinement-induced segregation phe-nomenon and demonstrate the applicability of this technique todifferent 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.1To whom correspondence should be addressed. Email: alamgir@uakron.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1613828114/-/DCSupplemental.

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height, Δh = (119 ± 1) nm, as shown in the 3D atomic forcemicroscopy (AFM) height image in Fig. 1. For AuPS/PS blendfilms with an initial thickness h ≈ 80 nm, channel-pattern confinedannealing generated a modulated film topography characterized witha mesa thickness h1 ≈ 140 nm, and a trench thickness h2 ≈ 20 nm.Note that the blend films utilized in the present study were suf-ficiently thick to fill the cavity completely, and there was always aresidual layer after capillary force lithography process (15).The distributions of AuPS particles in PS matrix were sub-

sequently characterized by top-view transmission electron mi-croscopy (TEM) images. The molecular mass of the PS matrix is2.8 kg/mol, which is denoted as PS 3k hereafter. In this case,the mass ratio of AuPS particle relative to PS 3k matrixis approximately 30%, corresponding to a particle number con-centration lower than the critical overlapping concentration (v*),estimated as v* = 1=ð4=3πR3

npÞ, where Rnp is the radius of theAuPS particles including the polymer shell thickness (Rnp ≈14 nm) (16). As displayed in Fig. 1, the homogeneous distribu-tion of AuPS particles was maintained in cases I and II, whereasexclusive AuPS segregation in mesas (dark strips in TEM im-ages) was generated in case III. This localized enrichment ofAuPS particles was particularly clear in the digitized TEM imagein which the film thickness contrast between mesas and trencheswas subtracted. A pertinent feature of the selective AuPS seg-regation is that the formation of particle-rich zones occurs whilethe blend system maintains overall miscibility due to the wetta-bility of grafted PS layer by matrix PS 3k chains (17), which wasdiscerned from the absence of particle aggregation in both

particle-rich and particle-depleted zones. Note that the potentialdesorption of grafted thiol PS (PS-SH) ligands from Au particlecores would be a gradual transition that depends on ligand type,ligand chain length, and annealing conditions (18). In thecurrent study, relatively short annealing times were chosen toavoid any noteworthy PS ligand desorption, thus preventingnanoparticle aggregation. The integrity of the polymer ligandlayer was confirmed by postannealed films studies (details areincluded in SI Appendix, Fig. S1).To delineate the thermodynamic driving force for the observed

segregation of PGNPs under patterned confinement, we reducedthe annealing temperature from 180 °C to 120 °C (≈40 °C higherthan Tg,PS 3k) to track the kinetics of this particle segregationprocess. As shown in Fig. 2A, the capillary force-driven mold-filling process was completed within 3 min. However, the diffusionof AuPS particles continued until complete segregation in mesasoccurred upon extended annealing for up to 16 h, indicating thatthe selective particle segregation was a thermodynamically favor-able state. The attractive van der Waals interaction between AuPSparticles was estimated to be less than ≈0.15 kBT (where kB is theBoltzmann constant and T is the absolute temperature) on thelength scale of a few nanometers (4). Because this interaction isnegligible due to the protective PS ligand layer, we interpret thelocal concentration of PGNPs within mesa regions as an entropy-driven phenomenon. In particular, we propose that confiningPGNPs in ultrathin trenches causes a loss of conformational en-tropy of tethered chains (ΔSC), thus giving rise to the chemicalpotential 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/PSblend films with free air surface (case I), smooth confinement (case II), and channel-patterned confinement (case III). The corresponding top-view TEM mi-crographs 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 lightstrips shown in TEM micrographs for channel-patterned films are imprinted mesas and trenches, respectively. The TEM micrograph for channel-patternedfilms is digitized to illustrate AuPS distribution while eliminating film thickness differences.

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pattern formation. The exclusive segregation of PGNPs in mesaswas maintained with higher AuPS concentration as shown in100% AuPS/PS 3k films, where the mass ratio of AuPS to PSmatrix is 1:1 (Fig. 2B). With further increase in PGNP loadingfraction to 200% by mass (2:1), the exclusive selective segregationwas frustrated, resulting in excess AuPS particles squeezing intothin 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 thecenter of a trench. The entropy loss is shown to be a function ofthe 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 brushregime (σ−1/2 < Rg,grafted), the PS 3kmolecules can penetrate into thepolymer brush layer analogous to a good solvent, resulting in aswollen polymer brush with a thickness hbrush ≈ 12.8 nm (20, 21).The estimated PS brush thickness is consistent with the nearestinterparticle distance when closely packed in mesas as determinedfrom TEM images. For AuPS/PS blend films with an initial filmthickness h ≈ 80 nm, assuming AuPS particles are located halfwaybetween the trench surfaces, the relative confinement degree is

greater than 1 (hbrush/hconfine ≈ 1.4), which results in a loss of con-formational entropy of the grafted chains and drives the migrationof particles into thicker mesas in exchange for PS 3k chains. Be-cause the PS 3k chain size (Rg,PS ≈ 1.6 nm) (22) is notably smallerthan hconfine, there is minimal conformational entropy loss for PS 3kmatrix chains when enriched in trenches. Therefore, the formationof channel-patterned nanoparticle domains by selective segregationof AuPS into mesas is entropically favorable (see SI Appendix fordetails). During the SCPINS process, visually ordered nanoparticlestructures are generated, accompanied with an increase in theoverall 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 ofconfinement of (i) brush chains in trenches (hbrush/hconfine),(ii) matrix polymer chains trapped between gold cores andtrench walls (2Rg,PS/hconfine), and (iii) matrix polymer chainsconfined between top and bottom trench walls (2Rg,PS/h2). Var-iation of the matrix polymer chain size Rg,PS and the initial blendfilm thickness h, which controls the trench thickness h2, shouldallow us to tune AuPS segregation in the patterned mesa−trenchregions. We therefore systematically varied the molecular massof the matrix PS chains from 2.8 kg/mol to 360 kg/mol (detailedinformation is included in SI Appendix, Table S1) and the initialfilm thickness from 85 nm to 140 nm. Note that uniform distri-bution of AuPS particles was maintained in all PS matrices uponthermal annealing without patterned confinement (SI Appendix,Figs. S3−S5). The process of SCPINS was induced by channel-pattern confined annealing at 180 °C for 1 h, which was sufficientto generate thermodynamically stable structures. As shown inFig. 3, with increasing PS matrix molecular mass at the sameinitial film thickness (h ≈ 85 nm), the selective segregation ofPGNPs in mesas was progressively suppressed. This changeovercould be explained by a more pronounced conformational en-tropy loss of the matrix polymer chains with increasing chainlength via the increase in 2Rg,PS/hconfine and 2Rg,PS/h2. Simulta-neously, there was a gradual reduction in entropic confinementof the grafted chains manifested in a decrease of hbrush in themixture with longer PS chains (as illustrated in schematics inFig. 3) (23). For instance, the collapsed brush layer thicknessresulted in a suppressed confinement degree of hbrush/hconfine ≈ 0.8in a PS 16k matrix and further reduced to hbrush/hconfine ≈ 0.6 ina PS 360k matrix (24, 25). Separately, more uniform AuPSdistribution was generated by increasing initial film thicknessh while the matrix molecular mass was constant (Fig. 3). In thiscase, the entropic confinement effect for AuPS particles wasgradually reduced within the trenches, and thus more uniformPGNP distribution was induced.The SCPINS phenomenon was further quantified by the par-

tition coefficient K, adapted by analogy from dilute polymersolutions in geometrically confined spaces (26). The partitioncoefficient is evaluated by the concentration ratio of AuPSparticles, ρ2/ρ1, where ρ1 and ρ2 are particle concentrations inmesas and trenches, respectively (Fig. 2C). Detailed explanationsof the evaluation of partition coefficient K are included in SIAppendix. The dependence of K on hbrush/hconfine by varying initialfilm thickness h in PS matrices with different molecular masses(color sets) is shown in Fig. 4. With marginal entropic confine-ment (i.e., hbrush/hconfine → 0), the AuPS distributions in all PSmatrices are homogeneous (K = 1). Strong confinement (i.e.,hbrush/hconfine > 1), in contrast, generates complete AuPS segre-gation at mesas (K → 0) in low molecular mass PS matrices, asthe entropic penalty associated with grafted polymer chains no-tably outweighs that of matrix chains when located in trenches.The transition between weak and strong confinement regimes ismediated by the relative size of grafted and matrix polymerchains (hbrush/2Rg,PS), where a milder transition was observedin longer PS matrix chains. When the grafted and matrix chainsare of comparable size (i.e., hbrush/2Rg,PS ≈ 1), the partition

Fig. 2. Loss of conformational entropy-induced particle segregation undersoft-pattern confinement. (A) Top-view TEM micrographs for 30% AuPS/PS3k 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 3kblend films (h ≈ 85 nm) annealed at 180 °C for 1 h. (C) Schematic repre-sentations of channel-patterned blend films with alternating mesas andtrenches with particle concentration of ρ1 and ρ2, respectively. The zoom-inimage shows the confinement thickness, hconfine, within trenches.

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coefficient is constant (K = 1) and independent of the confine-ment degree, indicating an equivalent conformational entropyloss for both components. In a reversal of the above observa-tions, as the molecular mass of matrix PS chains further in-creases, the AuPS particles become more concentrated in thetrenches (K > 1), whereas the matrix polymer chains segregateinto the mesas due to more significant entropic penalty underconfinement. It should be noted, however, that, in the case ofultrathin trench confinement (i.e., h2 ≈ 2Rg,PS), only partial de-pletion of matrix PS chains was observed, as the mobility ofpolymer chains was significantly suppressed beyond practicalequilibration times (27).From partition coefficients of the channel-patterned AuPS/PS

blend films, the resultant free energy change can be estimated byΔF = −kBT ln K (28). ΔF represents the free energy change ofthe system as one individual AuPS particle is relocated frommesa to trench. Because the enthalpic interactions are largelyscreened, the free energy change corresponds to the overallentropic penalty. For example, in low molecular mass polymermatrices, ΔF accounts for the conformational entropy gain andtranslational entropy loss when particles are selectively seques-tered into mesas. As shown in Fig. 4, when the confinementdegree is relatively weak (hbrush/hconfine < 0.9), only marginal freeenergy change (jΔFj ≤ kBT) is induced. As the confinementbecomes moderate (1< hbrush/hconfine < 1.5), a drastic increase injΔFj is induced in low molecular mass PS matrices, resultingin stronger segregation of AuPS particles in mesas versus intrenches. Scaling relationships for the free energy change ofPGNPs in different polymer matrices under various confine-ment conditions are included in SI Appendix. To further con-firm that the selective particle segregation is driven by entropicconfinement effect, we study the variation of ΔF in PS 3kmatrix (h ≈ 85 nm) under channel-patterned confinement withvaried pattern height difference (Δh). The corresponding TEMmicrographs are shown in SI Appendix, Fig. S7, where a moreuniform AuPS distribution in mesas versus trenches is inducedby reducing Δh. Fig. 4, Inset shows that the transition of ΔF byreducing Δh overlaps similarly with that achieved by increasinginitial film thickness h. The general observation of confinement-induced segregation of PGNPs confirms that the equilibriumcharacteristics of the partitioning system (i.e., K, ΔF) depend onlyon the relative entropic confinement degree (hbrush/hconfine), ratherthan 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

patterns to illustrate the generality and versatility of the SCPINSmethod. Fig. 5A shows selective segregation of PS−g−SiO2 par-ticles (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 en-ergy 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 variationare power-law function fittings [ΔF/kBT = a(hbrush/hconfine)

b; a and b are con-stants]. (Inset) The weak confinement regime shown in an expanded scale.

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 PSmatrices (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.

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3k films (h ≈ 90 nm) upon channel-pattern confined thermalannealing. The TEM image reveals highly selective concentrationof PS−g−SiO2 particles in mesas due to the entropic confinementeffect (hbrush/hconfine ≈ 3), as well as superlattice formation ofparticles within mesas. Because this entropy-driven segregationprocess only relies on the relative confinement of the grafted andmatrix polymers, this method is envisioned to be general fordifferent particle systems. Application of this method to formmore complex patterned PGNP domain structures is furtherdemonstrated by using confinement with different geometries.The AFM 3D height image in Fig. 5B shows the topography oflattice-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 corre-sponding variation in AuPS distributions is shown in TEMmicrographs, where the nanoparticles are uniformly distrib-uted between rhombic mesas and channels with identicalconcentration (i.e., particle number proportional to local filmthickness), while completely depleted from the trenches.Relevant to nanoelectronic and nanoplasmonic applications,we show complete AuPS nanoparticle segregation within thickmesas when confined by an electronic circuit-shaped topographicallypatterned elastomer capping layer (Fig. 5C; no particles are presentin thin trenches).

ConclusionIn summary, we demonstrate a simple and widely applicablemethod of SCPINS to produce visual order via spatially organizedPGNPs in polymer thin films, driven by an increase in the overallentropy of the system. The architecture of PGNP arrangementscan be controlled by the prescribed topographic patterns, whereasthe distribution of PGNPs among mesas and trenches is tunable byvarying the relative entropic confinement degree (hbrush/hconfine)and relative matrix chain size (hbrush/2Rg,PS). Different from pat-tern-directed organization of a phase-separated blend system (29),where the ordered structures are transient and depend on the in-terplay of phase separation length scale and pattern dimension, thisentropy-driven patterning method can result in thermodynamicallystable structures. Moreover, the interparticle distance can be easilycontrolled by varying the particle loading or grafted layer thickness.The versatility of the process with respect to particle compositionand pattern geometry should render SCPINS an attractive tool for

fabrication of particle nanostructures for electronic, plasmonic, andphotonic applications. The application of multiscale patterns, withcontrolled distribution of trench thickness, should allow for ex-tension of SCPINS to multicomponent particle systems that play animportant role in a range of nanomaterial-enabled technologies.

MethodsPS 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 massand PDI is the dispersity index). The PS-SH grafted gold nanoparticles(AuPS) were synthesized by phase transfer reduction of [AuCl4] in the presence ofthiol ligands (30). The average radius of gold core R0= 1.2± 0.4 nm. The grafted PSmolecularmass isMn,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 experiencedsubtle size increase to R0 = 1.3 ± 0.5 nm due to the thermal instability of thethiol−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 atomtransfer radical polymerization using previously published procedures (32).PS solutions (3% by mass in toluene) were premixed with appropriateamounts of PGNPs (mass ratio of AuPS to PS is 30% to 200%) and flow-coated into thin films of thickness h ≈ 80 nm to 140 nm on silicon sub-strates. The film thicknesses were determined by interferometer (F-20 UVThin 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 °Cfor 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 tem-plates. The smooth or patterned PDMS layers served as confinement duringthermal annealing. After annealing for certain time periods, the PDMS layer wasremoved for characterization. Nanoparticle distributions were characterized witha JEOL JEM-1230 TEM at 200 kV. Specimens for TEM were prepared by pre-coating a thin layer (≈10 nm) of aqueous poly(4-styrenesulfonic acid) (PSS; Sigma-Aldrich) solution on the substrates before coating the blend films, annealing themultilayer films, and then floating the films by immersing into distilled waterfollowed by transferring to copper grids. Surface topography of the blend filmswas 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 byNational Science Foundation Grants DMR-1411046 (to A.K.) and DMR-1410845 (toM.R.B.). Certain equipment, instruments, or materials are identified in this paperto adequately specify the experimental details. Such identification does not implyrecommendation by the National Institute of Standards and Technology nor doesit imply the materials are necessarily the best available for the purpose.

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 blendfilms (h ≈ 150 nm) annealed with an electric-circuit–like patterned PDMS layer as confinement. (Insets) AFM 3D height images.

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1. Balazs AC, Emrick T, Russell TP (2006) Nanoparticle polymer composites: Where twosmall worlds meet. Science 314(5802):1107–1110.

2. Kumar SK, Krishnamoorti R (2010) Nanocomposites: Structure, phase behavior, andproperties. Annu Rev Chem Biomol Eng 1:37–58.

3. Akcora P, et al. (2009) Anisotropic self-assembly of spherical polymer-grafted nano-particles. Nat Mater 8(4):354–359.

4. Kumar SK, Jouault N, Benicewicz B, Neely T (2013) Nanocomposites with polymergrafted nanoparticles. Macromolecules 46(9):3199–3214.

5. Harton SE, Kumar SK (2008) Mean-field theoretical analysis of brush-coated nanoparticledispersion in polymer matrices. J Polym Sci, B, Polym Phys 46(4):351–358.

6. Bockstaller MR, Lapetnikov Y, Margel S, Thomas EL (2003) Size-selective organizationof enthalpic compatibilized nanocrystals in ternary block copolymer/particle mixtures.J Am Chem Soc 125(18):5276–5277.

7. Thompson RB, Ginzburg VV, Matsen MW, Balazs AC (2001) Predicting the mesophasesof copolymer-nanoparticle composites. Science 292(5526):2469–2472.

8. Frenkel D (2015) Order through entropy. Nat Mater 14(1):9–12.9. Glotzer SC, Solomon MJ (2007) Anisotropy of building blocks and their assembly into

complex structures. Nat Mater 6(8):557–562.10. Nepal D, et al. (2012) Control over position, orientation, and spacing of arrays of gold

nanorods using chemically nanopatterned surfaces and tailored particle-particle-surface interactions. ACS Nano 6(6):5693–5701.

11. Karim A, et al. (1998) Phase separation of ultrathin polymer-blend films on pat-terned substrates. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 57(6):R6273–R6276.

12. Xia Y, Whitesides GM (1998) Soft lithography. Annu Rev Mater Sci 28(1):153–184.13. Suh KY, Kim YS, Lee HH (2001) Capillary force lithography. Adv Mater 13(18):1386–1389.14. Singh G, Yager KG, Berry B, Kim H-C, Karim A (2012) Dynamic thermal field-induced

gradient soft-shear for highly oriented block copolymer thin films. ACS Nano 6(11):10335–10342.

15. Suh KY, Lee HH (2002) Capillary force lithography: Large-area patterning, self-organization,and anisotropic dewetting. Adv Funct Mater 12(6-7):405–413.

16. Teraoka I (2002) Polymer Solutions: An Introduction to Physical Properties (Wiley,New York).

17. Meli L, Arceo A, Green PF (2009) Control of the entropic interactions and phase behaviorof athermal nanoparticle/homopolymer thin film mixtures. Soft Matter 5(3):533–537.

18. Jia X, et al. (2010) Effect of matrix molecular weight on the coarsening mechanism ofpolymer-grafted gold nanocrystals. Langmuir 26(14):12190–12197.

19. Teraoka I, Langley KH, Karasz FE (1993) Diffusion of polystyrene in controlled poreglasses: Transition from the dilute to the semidilute regime. Macromolecules 26(2):287–297.

20. Ohno K, Morinaga T, Takeno S, Tsujii Y, Fukuda T (2007) Suspensions of silica particlesgrafted with concentrated polymer brush: Effects of graft chain length on brush layerthickness and colloidal crystallization. Macromolecules 40(25):9143–9150.

21. Choi J, Dong H, Matyjaszewski K, Bockstaller MR (2010) Flexible particle array struc-tures by controlling polymer graft architecture. J Am Chem Soc 132(36):12537–12539.

22. Terao K, Mays JW (2004) On-line measurement of molecular weight and radius ofgyration of polystyrene in a good solvent and in a theta solvent measured with a two-angle light scattering detector. Eur Polym J 40(8):1623–1627.

23. Green PF (2011) The structure of chain end-grafted nanoparticle/homopolymernanocomposites. Soft Matter 7(18):7914–7926.

24. Choi J, et al. (2012) Toughening fragile matter: Mechanical properties of particlesolids assembled from polymer-grafted hybrid particles synthesized by ATRP. SoftMatter 8(15):4072–4082.

25. Robbes A-S, et al. (2012) Polymer-grafted magnetic nanoparticles in nanocomposites:Curvature effects, conformation of grafted chain, and bimodal nanotriggering offiller organization by combination of chain grafting andmagnetic field.Macromolecules45(22):9220–9231.

26. Casassa EF (1967) Equilibrium distribution of flexible polymer chains between amacroscopic solution phase and small voids. J Polym Sci B 5(9):773–778.

27. Jiang Z, et al. (2007) Evidence for viscoelastic effects in surface capillary waves ofmolten polymer films. Phys Rev Lett 98(22):227801.

28. Teraoka I (1996) Polymer solutions in confining geometries. Prog Polym Sci 21(1):89–149.

29. Zhang R, et al. (2016) Pattern-directed phase separation of polymer-grafted nano-particles in a homopolymer matrix. Macromolecules 49(10):3965–3974.

30. Brust M, Walker M, Bethell D, Schiffrin DJ, Whyman R (1994) Synthesis of thiol-derivatisedgold nanoparticles in a two-phase liquid-liquid system. J Chem Soc Chem Commun (7):801–802.

31. Zhang R, et al. (2013) Nanoparticle-driven orientation transition and soft-shear align-ment in diblock copolymer films via dynamic thermal gradient field. Macromol RapidCommun 34(20):1642–1647.

32. Hui CM, et al. (2014) Surface-initiated polymerization as an enabling tool formultifunctional (nano-)engineered hybrid materials. Chem Mater 26(1):745–762.

Zhang et al. PNAS | March 7, 2017 | vol. 114 | no. 10 | 2467

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