shape alloys of nanorods and nanospheres from self...

Shape Alloys of Nanorods and Nanospheres from Self-AssemblyXingchen Ye,† Jaime A. Millan,§ Michael Engel,∥ Jun Chen,† Benjamin T. Diroll,† Sharon C. Glotzer,*,§,∥

and Christopher B. Murray*,†,‡

†Department of Chemistry and ‡Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia,Pennsylvania 19104, United States§Department of Materials Science Engineering and ∥Department of Chemical Engineering, University of Michigan, Ann Arbor,Michigan 48109, United States

*S Supporting Information

ABSTRACT: Mixtures of anisotropic nanocrystals promise agreat diversity of superlattices and phase behaviors beyondthose of single-component systems. However, obtaining acolloidal shape alloy in which two different shapes arethermodynamically coassembled into a crystalline superlatticehas remained a challenge. Here we present a jointexperimental−computational investigation of two geometri-cally ubiquitous nanocrystalline building blocksnanorodsand nanospheresthat overcome their natural entropictendency toward macroscopic phase separation and coassem-ble into three intriguing phases over centimeter scales,including an AB2-type binary superlattice. Monte Carlosimulations reveal that, although this shape alloy is entropically stable at high packing fraction, demixing is favored atexperimental densities. Simulations with short-ranged attractive interactions demonstrate that the alloy is stabilized byinteractions induced by ligand stabilizers and/or depletion effects. An asymmetry in the relative interaction strength between rodsand spheres improves the robustness of the self-assembly process.

KEYWORDS: Nanoparticles, Monte Carlo simulation, binary nanocrystal superlattice, electron microscopy, lamellar phase, demixing

Colloidal mixtures of differently sized and shaped nano-crystals (NCs) not only serve as model systems forstudying a variety of processes in condensed matter but alsoprovide a bottom-up approach for the chemical design of NC-based metamaterials with emergent properties. The majority ofexisting works on self-assembly of colloidal NCs into orderedsuperlattices focuses on single- and multicomponent sphericalNCs (nanospheres, NSs)1−5 as well as single-componentnonspherical NCs.6−13 In contrast, assemblies of mixtures ofdistinct shapes have remained largely unexplored and are onlybeginning to be investigated.1,14−18 A simple deviation from thespherical shape is found in cylindrical nanorods (NRs), forwhich an extensive library of compositions exists through recentadvances in NC synthesis.12,19−22 NRs have been coassembledtogether with NSs into planar structures. Sańchez-Iglesias andco-workers14 used Au nanowires as colloidal templates for theoriented assembly of Au NSs as well as short Au NRs. Nagaokaet al.16 explored the coassembly of CdSe/CdS NRs and AuNSs. However, the spatial extent of ordering has been limitedto submicrometer-sized areas and to two dimensions.The mixture of rods and spheres is a well-studied model

system for colloidal matter exhibiting rich and complex phasebehaviors.23−33 In most of these works, rods are rigid polymersand approximated to be thin,23−27,29,32,33 noninteract-ing,27,29,30,33 and parallel.24,28 In a seminal report of binary

mixtures of rod-like fd viruses (6.6 nm diameter, 880 nmcontour length) and polystyrene latex spheres (diameterranging from 22 nm to 1 μm), Adam et al.25,26 observedboth macroscopic (bulk) demixing and microscopic phaseseparation. They discovered intriguing microsegregated struc-tures including the columnar and lamellar phases, which theyconcluded were entropically stabilized. First reported in atheoretical study of hard particles,24 the lamellar phase consistsof smectic layers of parallel rods alternating with thin layers ofspheres. It is also known from simulation studies that assemblyof the lamellar phase can be difficult because it competes withbulk demixing.28

In colloidal systems, excluded-volume effects are oftenaccompanied by enthalpic interactions that can introducefurther complexity into the phase diagram. For example,simulations of hard Gaussian overlap rods and hard spheresresult in macrophase separation,30 but Gay−Berne rods andLennard−Jones spheres can exhibit a lamellar (smectic) phasefor strong rod−sphere interaction.31 Diversity in phasebehavior resulting from the interplay between shape andinteraction anisotropy has also been observed at the nanoscale,

Received: August 22, 2013Revised: September 14, 2013Published: September 17, 2013

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where certain exotic phases are not accessible by excluded-volume effects alone.7,9,10,13,34 In real NC systems, it is usuallynontrivial to quantify the strength and distance dependence ofnanoscale forces, most of which cannot be measured directly.Moreover, various interactions can compete, including van derWaals, electrostatic, magnetic, molecular surface, and depletioneffects.35 However, in the absence of electrostatic (includingelectric dipole interactions) and magnetic forces, the particlegeometry often dominates,36 and self-assembly of binarysuperlattices is challenging.37 Interactions can then beconsidered as a perturbation.6,9,10,13,38

In the present work, we report the self-assembly of colloidalNRs and NSs into highly ordered three-dimensional (3D)binary nanocrystal superlattices. Using a range of rod−spherecombinations, we demonstrate that both macro- and micro-phase-separated binary phases can be formed over extendedareas (centimeter scale) with individual grains approaching 100μm2. Electron microscopy observations and analyses allow theidentification of bulk demixing (Figure 1a,d) and two binarynanocrystal shape alloys (BNSAs), the lamellar phase (Figure1b,e) and the AB2 BNSA (Figure 1c,f). We further reproduceand analyze the assembly of rod−sphere binary systems inMonte Carlo (MC) simulations by extensively exploring theparameter space spanning particle shape and strength ofinterparticle interactions. Our simulations show that short-ranged attractions play a key role in helping the shapes toovercome their entropic tendency toward demixing byfacilitating and stabilizing the AB2 BNSA.

NCs are synthesized according to previously reportedprocedures (see Supporting Information). We focus on thecombination of Fe3O4 NSs (diameter: 11.0 ± 0.4 nm) andNaYF4 NRs (length: 38.5 ± 1.5 nm, diameter: 19.5 ± 1.0 nm)for AB2 BNSAs. To understand the role of relative size ratiosbetween NRs and NSs, we also explore rod−spherecoassemblies with different-sized NSs including UO2 (7.4nm), Au (5.5 nm), and Pd (4.5 nm), as well as CdSe NRs(length: 17.4 ± 1.5 nm, diameter: 4.9 ± 0.4 nm). Assembly intoordered superlattices is induced at the liquid−air interfacethrough slow evaporation of the solvent hexane.8,13,39 Single-component NCs readily assemble into superlattices expectedfor their shapes. NSs form stacked hexagonal layers as found inthe face-centered cubic or hexagonal close-packed superlattice(Figure S1). When restricted to monolayers, NRs align theirlong axes either parallel (Figure S2a) or perpendicular (FigureS2b) to the liquid−air interface. At higher NR concentrations,they assemble into stacks of hexagonal layers with side-by-sidecontact of parallel NRs within each layer. NRs fromneighboring layers are offset by about half a rod diameter,which maximizes packing density by avoiding unfavorable tip-to-tip contacts.As shown in Figures 2 and S3, BNSAs comprised of

alternating single layers of NRs and NSs are formed withappropriate concentrations of NaYF4 NRs (15 mg/mL) andFe3O4 NSs (∼3 mg/mL). The NRs within the BNSAs exhibitsimultaneous positional and orientational order, as manifestedby the sharp diffraction spots in the wide-angle as well as thesmall-angle electron diffraction patterns (Figure 2b,c). The

Figure 1. Self-assembled superlattices of NSs and NRs. Depending on the aspect ratio of the rods and the size ratio of the rods to the spheres, weobserve three different phases: (a, d) bulk demixing, (b, e) the lamellar phase with disordered (mobile) spheres, and (c, f) the AB2 BNSA with fullpositional order. TEM images (a−c) are accompanied by theoretical reconstructions (d−f). Scale bars: 25 nm.

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Moire ́ fringe patterns arising from the superposition of atomiclattices of parallel NRs further confirm the 3D crystalline orderof the NRs within each layer (Figure 2d). To fully characterizethe structure of the BNSAs, we have performed TEM tiltingexperiments starting from the commonly observed projection(Figure 2e). As shown in Figure 2f, after tiling around thehorizontal axis for about 33°, two partially overlapping Fe3O4NSs appear in the interstitial spaces between four neighboringNaYF4 NRs, suggesting an AB2 stoichiometry between NRs andNSs. Scanning electron microscopy (SEM) is employed toobtain surface structural information and 3D views throughmicrographs recorded with a large depth of focus. SEM imagestaken from the “cracked” regions clearly demonstrate the 3Dnature (estimated to be 10−15 NR layers) as well as details ofthe ordered arrangements of NRs and NSs in the BNSAs(Figure 3a−c). High-magnification SEM images (Figures 3e,fand S4e,g) show that the presence of NSs disrupts the spatialoffset between neighboring NR layers and gives rise to a NR

arrangement different from that in pure NR superlattices(Figure S2a). More importantly, SEM images reveal thatstructural defects including a few missing NSs or NRs, andvoids that are filled by several NSs, occur predominantly on thetop surface of the BNSAs and do not seem to alter the globalpacking symmetry (Figure 3d−g). From this observation weconclude that BNSA crystallization initiates at the liquid−liquid(hexane wetting layer−ethylene glycol) interface. The BNSAsthen grow “upwards” by successive incorporation of NRs andNSs onto the uppermost layer of the crystallites.40 Moreover,high-magnification SEM images show that, in the AB2 BNSAs,NaYF4 NRs that have a roughly hexagonal cross section (FigureS2b) develop a preferred orientation, with one of their sideedges perpendicular to the horizontal liquid−air interface(Figures 3f and S4e−g). This picture is also supported by theappearance of {100} diffraction spots and simultaneousdisappearance of {110} spots in the small-angle electrondiffraction pattern (Figure 2b). The oriented arrangement ofthe NRs maximizes the contact area between neighboring NRs,thereby increasing the packing density.We also study the phase behavior of NaYF4 NRs and 11.0

nm Fe3O4 NSs as a function of both relative and totalconcentrations of the two building blocks. When the particlenumber concentration of NSs is either much smaller (7 mg/mL) than that of NRs (15 mg/mL), bulk phase separation occurs (Figure S5). The AB2BNSAs does not form until the concentration of NSs (2−3.5mg/mL) becomes high enough to form complete single layersthat alternate with single layers of NRs. Interestingly, a furtherincrease in the concentration of NSs (4−5 mg/mL) does notresult in alternating single NR layers with multiple layers ofNSs. In fact, the AB2 BNSAs can coexist with superlattices ofNSs or sphere-rich aggregates until the concentration of NSs(>7 mg/mL) far exceeds that of NRs. In addition, given theoptimal rod-to-sphere concentration ratio for the AB2 BNSAs,the total concentration of NCs also plays an important role. Atlow concentrations (

separates into single-component NR and NS superlattices (datanot shown). In addition to NaYF4 NRs, CdSe NRs (FigureS2e,f) with a smaller diameter (4.9 ± 0.4 nm) and a largeraspect ratio (about 3.6) are also tested for rod−sphereassembly. Given the dimensions of CdSe NRs, dipole−dipoleattraction does not contribute significantly to the interactionsbetween neighboring NRs (see Supporting Information). Withthe combination of CdSe NRs (1 mg/mL) and 7.4 nm UO2NSs, a random mixture predominates when a low concentrationof NSs (∼0.5 mg/mL) is introduced (Figure S8a,b). As thefraction of NSs increases (1−3 mg/mL), stripe-like NR layersbegin to develop, with patches of NSs intercalated between NRlayers (Figure S8c,d). A further increase in the concentration ofNSs (>5 mg/mL) results in macroscopic phase separation(Figure S8e,f). Macroscopic demixing is also observed withsmaller sized NSs such as Au (Figure 3e,f) and Pd (Figure S9).It is worth noting that the phase behavior of rod−sphere

binary mixtures also depends crucially on the geometric detailsof individual NRs. The NaYF4 NRs used for BNSA formationhave a hexagonal cross section that is consistent with theircrystal lattice structure and rounded tips at both ends (FigureS2a,b). However, taking into account the oleic acid ligand shell,they can be well approximated as spherocylinders, i.e., cylinderscapped by hemispherical ends. When NaYF4 NRs of similar sizebut with a rectangular cross section are coassembled with the11 nm Fe3O4 NSs, demixing rather than BNSA formationoccurs (Figure S10). More importantly, we observe that theprocessing history of NC building blocks and the amount ofligands in the NC solutions strongly affect the assembly ofrod−sphere binary mixtures. Starting from the Fe3O4 NSs andNaYF4 NRs that can form the AB2 BNSAs, when additionaloleic acid ligands (10 μmol) is added to the binary NC solution(1 mL) before spreading onto the ethylene glycol surface, bulkdemixing into sphere-rich and rod-rich domains occurs, which

is likely caused by the enhanced depletion attractions due to thepresence of extra ligands (Figure S11a,b).41 On the other hand,when the same NSs and NRs are washed (precipitation with anonsolvent followed by redispersion in hexane) once morebefore being mixed for binary assembly, a random mixture isobtained (Figure S11c,d). We believe that excessive washing ofNCs will not only decrease the amount of free ligands in theNC solutions but also remove some that are originally bound tothe NC’s surface. This can effectively decrease the strength ofinteractions between NCs and increase their hard particlecharacter.The self-assembly process and the relative phase stability are

analyzed theoretically by gradually increasing the sophisticationof the model. First, we approximate the NCs as hard (athermal)shapes and search for their densest packings.42,43 The resultsare relevant at high NC concentrations during the final stages ofthe experiment. Next, we perform MC simulations to resolvethe phase behavior at lower density.11 In a third step, weintroduce short-range interactions between the NCs. Finally,we consider an asymmetry in the relative interaction strengthsas expected for chemically distinct NCs or crystallographicallydistinct NC facets.13,16 The rod shape is chosen as a cylinderwith two spherical caps, which is a valid approximation becausethe NR edges are effectively rounded (softened) by thepresence of the ligand shell. Furthermore, the cylinder cross-section does not influence the relative phase stabilitysignificantly, because the contact between rods is identical forall configurations competing for stability. We characterize therod shape by three dimensionless parameters: aspect ratio AR =L/2σ, rod−sphere size ratio γ = D/2σ, and curvature of the capsκ = σ/R. Here, L is the tip-to-tip length, σ the cylinder radius, Rthe radius of curvature of the caps, and D the sphere diameter.The spherocylinder shape is obtained for κ = 1. In thefollowing, we choose a 2:1 mixture of spheres and rods.

Figure 3. SEM images of the rod−sphere BNSAs self-assembled from NaYF4 NRs and 11.0 nm Fe3O4 NSs close to a cracked region. The crackseparates the superlattice (a, magnified in b) almost perpendicular and (c) almost parallel to the hexagonal layers revealing terraces. (d−f) Voids areoften observed on outside surfaces as seen in the TEM and (g) compared with a theoretical reconstruction. Scale bars: (a−c) 100 nm, (d−e) 200nm, (f) 50 nm.

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Starting from the known densest binary sphere packings,44

we construct analogue binary spherocylinder-sphere packingsby elongating the bigger sphere. Finding the densest packing issimple when the big spheres form hexagonal layers. In this case,provided phase separation does not occur, the optimality of apacking in the binary sphere system guarantees the optimalityof an analogue packing in the spherocylinder-sphere system.For AR = 1.97 (NaYF4 NRs) and size ratios close to γ = 0.55,we find the densest packing is indeed realized in the AB2 BNSA(Figure 6a). As the size ratio decreases (Figure 6b),spherocylinder caps in neighboring layers touch for γ ≤0.528, limiting the packing efficiency. In contrast, toward highersize ratio, 0.577 ≈ 1/√3 ≤ γ ≤ 0.6247, neighboring spherestouch, forcing the lattice to expand laterally in-plane, until for γ> 0.6247 a buckled honeycomb lattice with spherocylinders incontact packs more efficiently (Figure S12).45,46 In both cases,the packing density is lowered, crossing the value for demixing.Strikingly, the experimental size ratio γ = 0.57 for the AB2BNSA falls within the region where bulk demixing is disfavored.In agreement with experiment (Figure S10), demixing becomesmore favorable with decreasing curvature of the caps (Figure

S13a,b). Lattice shear, which is sometimes observed as anintermediate state during assembly simulations (Figure 8d),also does not increase the packing fraction (Figure S13c,d). Forthe remainder of the paper we fix κ = 1 and γ = 0.57.We investigate the entropic stabilization of the AB2 BNSA

with isobaric (NPT) MC simulations. Simulations areinitialized from a disordered fluid in an attempt tospontaneously crystallize the system. Pressure is graduallyincreased following a protocol that was successful for manysystems of hard particles.11 Yet, coassembly is never observedwith the experimental AR = 1.97 (Figure S14a). To enhancethe entropic interactions between the spherocylinders at thesame pressure, we increase the aspect ratio to AR = 2.97.Although spherocylinders now show a stronger preference forlocal alignment (Figure S14b), global order is still not observedon the time scale of our simulations. This inability to assemblethe experimentally observed structure indicates that either thenucleation times are longer than those accessed on (long)simulation or that additional interactions must be included. Todistinguish between those two possibilities, we examine thethermodynamic stability of the AB2 BNSA by performing

Figure 4. Stripes or filament-like assemblies of rod−sphere BNSAs and NR superlattices. (a−d) TEM images of rod−sphere BNSAs self-assembledfrom NaYF4 NRs and 11.0 nm Fe3O4 NSs. The samples shown in a and b are formed with a lower total NC concentration in the spreading solutioncompared to those shown in c and d. (e, f) TEM images of structures self-assembled from CdSe NRs and 5.5 nm Au NSs. The system shows bulkphase separation instead of rod−sphere BNSA formation. Scale bars: (a) 1 μm, (b) 200 nm, (c) 1 μm, (d) 100 nm, (e) 200 nm, (f) 100 nm.

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isochoric (NVT) melting simulations (AR = 1.97) starting fromthe densest packing structure. We observe melting in two steps.At packing fraction 68%, the separation of spherocylinder layersincreases abruptly. Spheres diffuse almost freely betweenadjacent layers as found in the lamellar phase (Figure 6c).Finally, at packing fraction 63%, spheres completely abandonthe interstitial sites, and phase separation occurs (Figure 6d).Two-step melting is also observed for spherocylinders of AR =2.97. Free energy calculations confirm the stability of the AB2BNSA at high packing fractions. We conclude that thecoassembly of rods and spheres into AB2 BNSA is difficult ifnot impossible with entropic interactions alone; it is kineticallyinhibited and competes with macroscopic phase separation.A close inspection of the TEM images reveals configurations

that are not possible with entropic interactions alone. Theseconfigurations are evidence for the presence of additionalenthalpic, attractive interactions during assembly. The followingobservations cannot be explained with hard particles:(i) Assembly of monodisperse NRs with a short aspect ratio.47

(ii) Alignment of NRs at low packing fraction (Figure S2f).(iii) Single layers of NRs that are only loosely coupled to oneanother (Figure S8). (iv) Stripes or filament-like assemblies(Figure 4). The formation of single layers and stripes suggestsanisotropic crystal growth with a higher intralayer growthspeed. Since the NaYF4 NRs and the NSs employed in thiswork do not have appreciable electrostatic charges or dipolemoments,4,13,48 interactions are expected to be induced by vander Waals forces between ligand stabilizers and of short-rangecharacter. Experiments have shown that an anisotropic

distribution of capping ligands can act as “directionalbonds”49 that affect lattice spacing50 and symmetries51 innanocrystal superlattices. Atomistic simulations corroboratethat effective interactions are well-described by a Lennard−Jones-like potential with characteristic well depth comparableto thermal energies, equilibrium separation that allowsinterdigitation of ligands, and interaction range specified byligand properties.52,53 We do not make an attempt to derive aninteraction potential rigorously but merely derive it based onthe simple assumption that the energy is proportional to thecontact area. We thus hypothesize that the interaction can bemodeled by a contact force, which is reasonable both fordepletion and for NCs uniformly covered with ligands (Figure7a). A standard way to treat such a situation theoretically is theDerjaguin approximation.54,55 However, the curvature on thesurface of the NRs is highly nonuniform, and the Derjaguinapproximation is not applicable. Instead, we determine contactforces without approximation and tabulate pair interactions as afunction of NC separation and orientation (Figure S15)assuming a homogeneous distribution of ligands on the NRsand the NSs. Since spheres have the highest curvature, thesphere−sphere interaction is weaker than the rod−sphereinteraction, which in turn is weaker than the rod−rodinteraction. In addition, the rod attracts a sphere (a rod)maximally if the sphere attaches to the side of the rod (the rodsare parallel side-by-side) as shown in Figure S16.We perform NPT MC simulations from a disordered (fluid)

starting configuration using the precalculated interaction tables.The short-range attractions significantly speed up the kineticsof the assembly process compared to the hard particle case,which permits a summary of the findings in a P−T phasediagram (Figure 7b). Independent of the choice of temperature,increasing pressure always triggers phase separation into anordered rod phase and a fluid sphere phase. The crystallizationof spheres is observed only at substantially lower temperature.We can understand the difference in melting temperatures ofthe rod crystal and the sphere crystal by comparing the groundstate energies per NC. The energy of the sphere crystal, ESS, issignificantly lower than the energy of the rod crystal, ERR =4.7ESS, which in turn is slightly higher than the energy of thebinary AB2 BNSA, ERS = 3.6ESS. While the AB2 BNSA is alsoobserved in the phase diagram, it occurs only in a narrowparameter range at low temperature and very low pressure(Figure 7c). The stability window is too small and inaccessibleto experiments, which are performed at constant temperature.The contact interaction introduces a natural hierarchy of

attraction strengths between different NC species, |ERR| > |ERS|> |ESS|. Such a hierarchy aids the formation of the lamellarphase (and possibly the AB2 BNSA) by disfavoring bulkdemixing.31 However, while the sequence of interactionstrengths is fixed by the particle geometry, their precise valueis highly sensitive to the precise experimental conditions and isnot known to us. For example, variations in the NC curvature,chemical composition, and the crystallographic termination ofNC facets can influence the relative strength of attractionsbetween species.13,35,56−58 We consider these effects byenhancing the rod−sphere interaction energy by a factor ξRS> 1 relative to the other interactions to ξRSERS, which disfavorsdemixing. A factor ξRS < 1 or any other variation of the relativeinteraction strengths does not improve the stability of BNSAs.The P−T phase diagram (Figure 7d) shows a significant

improvement of the stability of the AB2 BNSA already for ξRS =1.4, broadening the temperature and pressure regime where it is

Figure 5. TEM images of BNSAs from NaYF4 NRs and 7.4 nm UO2NSs. (a) Low magnification and (b) high magnification TEM imagesdemonstrate microphase separation with partial positional order(lamellar phase). The spheres between the rods are not ordered.Scale bars: (a) 200 nm, (b) 50 nm.

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found in simulation. This behavior is expected because anincrease of ξRS raises the melting temperature of the AB2 BNSA.For ξRS = 1.6 (Figure 7e), not only is the AB2 BNSA stabilizedfurther, but also the boundaries of its stability range in thephase diagram are altered. Isothermic compression (depictedby a purple line in Figure 7e), which resembles the conditionsduring experiments most closely, can now successfullytransform the fluid to the AB2 BNSA. Only a narrow regimewhere macro-phase separation dominates has to be traversed.In this way, an adjustment of the relative interaction strengthscan open a kinetic pathway for the formation of the AB2 BNSA.We show the different stages of the assembly process in Figure8. The less diffusive spherocylinders initiate the assemblyprocess by aligning parallel. The spheres surround thespherocylinders and fit into the gaps between the spherocy-linder caps. Once the spheres adopt their native openhoneycomb arrangement, they act as a template for the nextlayer of spherocylinders. Note that multiple grain boundariesare present in simulation. This limitation of the crystal size iscaused by periodic boundary conditions as well as the totalsimulation time. Assembly experiments can access significantlylonger equilibration times as evidenced by the high quality ofthe AB2 BNSAs.In conclusion, we have demonstrated binary assemblies of

colloidal NRs and NSs into several unprecedented phasesincluding the 3D long-range ordered AB2 BNSAs. On the basisof experimental observations and simulation results, we have

identified the key elements necessary for successful assembly ofthe AB2 rod−sphere BNSAs: (i) favorable particle geometryasize ratio close to γ = 0.55 and rods with spherical caps allowdense packing and maximize entropic forces, (ii) attractivecontact interactionsthey help to initiate the assembly process,(iii) optimal interaction strengthsvarying the relative strengthof interactions between NCs of different compositions canminimize the width of the demixing zone in the phase diagram.Given the ubiquity of rods and spheres among NC buildingblocks and the added advantage of shape-dependent propertiesoften associated with NRs, we believe that the lamellar phaseand the AB2 BNSAs can be formed with many rod−spherecombinations. Co-assembly of NRs and NSs into orderedarrays opens up new horizons for the chemical design of NC-based mesocale metamaterials exhibiting intriguing physicalproperties.

■ ASSOCIATED CONTENT*S Supporting InformationExperimental, theoretical, and computational methods, estima-tion of dipole−dipole interactions, additional TEM, SEMimages, simulation snapshots, dense packing results, and adescription of the tabulated interaction potentials. This materialis available free of charge via the Internet at http://pubs.acs.org.

Figure 6. Densest packings and MC simulations of hard spheres and hard spherocylinders (AR = 1.97). (a) Comparison of the packing fractions forthe AB2 BNSA and for bulk demixing. The AB2 BNSA is the densest packing close to size ratio γ = 0.56. (b) Toward lower (γ = 0.40) and higher (γ= 0.62) size ratios, the spherocylinders’ caps or the spheres, respectively, touch. This introduces additional packing constraints and reduces thepacking efficiency. (c) Isotensile MC simulations started from the AB2 BNSA show a rapid change in the box aspect ratio Lz/Lx indicative of atransition to the lamellar phase at packing fraction ϕ = 0.68. (d) At ϕ = 0.618, the lamellar phase separates into the rod crystal and a mixed fluid.

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■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected].*E-mail: [email protected] ContributionsX.Y., J.A.M., and M.E. contributed equally to this work.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSX.Y. and C.B.M. acknowledge support from the Office of NavalResearch Multidisciplinary University Research Initiative onoptical metamaterials through award N00014-10-1-0942.J.A.M., M.E., and S.C.G. acknowledge support by the AssistantSecretary of Defense for Research and Engineering, U.S.Department of Defense (N00244-09-1-0062). J.C. acknowl-edges support from the Materials Research Science andEngineering Center program of the National ScienceFoundation (NSF) under award DMR-1120901. C.B.M. isalso grateful to the Richard Perry University Professorship forsupport of his supervisor role. B.T.D.’s work on the synthesis ofsemiconductor nanocrystals was supported in part by the U.S.Department of Energy Office of Basic Energy Sciences,Division of Materials Science and Engineering, under awardNo. DE-SC0002158 and also benefited from the support ofIBM Ph.D. Fellowship Award.

■ REFERENCES(1) Shevchenko, E. V; Talapin, D. V; Kotov, N. A.; O’Brien, S.;Murray, C. B. Nature 2006, 439, 55−59.(2) Bodnarchuk, M. I.; Kovalenko, M. V; Heiss, W.; Talapin, D. V J.Am. Chem. Soc. 2010, 132, 11967−11977.

Figure 7. Phase behavior of the spherocylinder-sphere system from MC simulations. (a) Schematic representation of NSs and NRs with molecularligands. NC interaction is dominated by the attraction of the ligands. Ligand lengths are exaggerated by a factor of about 3 for visualization purposes.(b−e) Reduced pressure PV0/kT vs reduced temperature kT/ESS phase diagrams are shown for different values of the rod−sphere attractionasymmetry ξRS (see text) at (b,c) ξRS = 1.0, (d) ξRS = 1.4, and (e) ξRS = 1.6. The symbols represent simulation data points. The small region ofstability for the AB2 BNSA in b is magnified and shown in c. The purple line in e represents a possible self-assembly pathway for the assembly of theAB2 BNSA from the fluid phase observed in the experiment.

Figure 8. Self-assembly simulation of the AB2 binary spherocylinder-sphere crystal. (a−c) Time evolution of a simulation of 1536 particles(512 spheryclinders and 1024 spheres) at packing fraction ϕ = 0.58and temperature T = 0.519 using ξRS = 1.5. Snapshots are taken duringcrystallization after (a) 0.5 × 106, (b) 1.35 × 106, and (c) 3.3 × 106

MC sweeps. (d, e) A small part of the system cut out from thesimulation demonstrates the local order corresponding to the AB2BNSA. Hexagonal layers of spherocylinders are separated byhoneycomb layers of spheres as visible from the side (d) and fromthe top (e).

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