Binary Assembly of PbS and Au Nanocrystals: Patchy PbS Surface

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Binary Assembly of PbS and Au Nanocrystals: Patchy PbS Surface Ligand Coverage Stabilizes the CuAu Superlattice Michael A. Boles, and Dmitri V. Talapin ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.9b00006 • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 24, 2019

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Binary Assembly of PbS and Au Nanocrystals: Patchy PbS Surface Ligand Coverage Stabilizes the CuAu Superlattice

Michael A. Boles and Dmitri V. Talapin* Department of Chemistry and James Franck Institute University of Chicago, Chicago, Illinois 60637

E-mail: [email protected]

Abstract Self-assembly of two sizes of nearly-spherical colloidal nanocrystals (NCs) capped with hydrocarbon surface ligands has been shown to produce more than twenty distinct phases of binary nanocrystal superlattices (BNSLs). Such structural diversity, in striking contrast to binary systems of micron-sized colloidal beads, cannot be rationalized by models assuming entropy-driven crystallization of simple spheres. In this work, we show that the PbS ligand binding equilibrium controls the relative stability of two closely related BNSL structures featuring alternating layers of PbS and Au NCs. At intermediate size ratio, as-prepared PbS NCs assemble with Au NCs into CuAu BNSLs featuring orientational coherence of PbS NCs across the lattice. Measurement of interparticle separations within CuAu and modeling of the structure reveals PbS inorganic cores are nearly in contact through (100) NC surfaces in the square tiling of the CuAu basal plane. On the other hand, AlB2 BNSLs with PbS NCs packed in random orientations were found to be the dominant self-assembly product when the same binary NC solution was evaporated in the presence of added oleic acid (OAH). Solution nuclear magnetic resonance (NMR) titration experiments confirmed that added OAH binds to PbS NCs, implicating ligand surface coverage as an important factor influencing the relative stability of CuAu and AlB2 BNSLs at the experimental size ratio. From these results, we conclude that as-prepared PbS NCs feature sparsely-covered (100) surfaces and thus effectively flat patches along NC x-, y-, and z-directions. Such anisotropic PbS-PbS interactions can be efficiently screened by restoring effectively spherical NC shape via addition of 1 ACS Paragon Plus Environment

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OAH to the binary assembly solution. Our findings underscore the important contribution of NC surfaces to superlattice phase stability and offer a strategy for targeted BNSL assembly. Keywords colloidal nanocrystal, surface ligands, lead chalcogenide, self-assembly, and binary superlattice

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Colloidal nanocrystals (NCs) have become an important materials class, promising new insights into fundamental science of crystal growth, surface chemistry, and self-organization.1 Such particles are often prepared in the presence of organic surfactants by decomposition of molecular precursors in hot organic solvent.2 Using this approach, it is possible to obtain size- and shape-uniform crystalline inorganic particles sterically protected by a shell of hydrocarbon chains. For example, reacting lead oleate with a chalcogen source at elevated temperatures affords lead chalcogenide (e.g., PbS, PbSe) NCs,3 a semiconductor material with size-tunable bandgap across the visible-infrared spectrum and promise in applications such as solution-processed optoelectronic devices including transistors,4 solar cells,5 and photodetectors.6 An ensemble of NCs can be coaxed to adopt an ordered arrangement, or superlattice by, for instance, evaporation of carrier solvent or slow destabilization with nonsolvent.7 In the case of self-assembly by solvent evaporation, ordering takes place at the late stages of solvent drying when particles find themselves in crowded solution. To a first approximation, this process can be understood as an example of entropy-driven crystallization, predicted theoretically8 and observed experimentally using monodisperse colloidal beads.9 According to this model, at high volume fraction, a collection of particles will adopt the arrangement that maximizes the space available to them for translational motion.10 Such arguments lead to the prediction that the stable superlattice phase is the one that maximizes packing density (φ) for a given shape. Indeed, the dense packing hypothesis explains the relatively simple phase diagram of colloidal beads, which assemble into face-centered cubic (fcc) and hexagonal close-packed (hcp) arrangements (φ ~ 0.74) of monodisperse spheres and NaCl, AlB2, and NaZn13 packings (φ > 0.74) of two sizes of spheres. On the other hand, a complete understanding of the phase behavior of hydrocarbon-capped NCs remains elusive, exemplified by several intriguing puzzles including the structural diversity of single-component11,12 and binary13,14 NC arrays, stability of shape alloys,15 and origins of quasicrystalline ordering.16,17 One important aspect of self-assembly not accounted for in the hard particle crystallization model is the interaction between NC surfaces. Beyond controlling colloidal stability, reactivity, and optical properties,18 surfaces may play an important role in stabilizing the superlattice phases which appear to be poor candidates from a space-filling perspective. For example, spherical NCs grafted with sufficiently long hydrocarbon surface ligands often assemble, like spherical micelles 3 ACS Paragon Plus Environment

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of dendrimers19 and block copolymers,20 into bcc superlattices despite the lower predicted packing fraction (φ ~ 0.68) than fcc or hcp arrangements.11 Such observations prompted the development of a theory for soft-particle ordering which predicts that the lattice with minimal Voronoi cell surface area, and thus the most spherical partitioning of the space available to each particle, maximizes ligand chain entropy.21,22 This framework offers a potential explanation for the stability of low-density sphere arrangements such as bcc and Frank-Kasper phases.12 Beyond corona softness, chemistry of semiconductor NC surfaces can be complex and play a role in directing their assembly. In the case of PbS, for example, two types of surfaces are typically found: the (100) surface, with a checkerboard arrangement of alternating Pb2+ cations and S2− anions, and the (111) surface, featuring a hexagonal arrangement of Pb2+ cations. Each nanocrystal has six (001) and eight (111) facets. Density functional theory (DFT) calculations23 predict that oleic acid (OAH) binds rather weakly to (100) facets as a neutral molecule, with its proton and carbonyl oxygen datively coordinating a surface sulfur and lead atom, respectively. On the other hand, (111) facets are passivated by tightly bound oleate (deprotonated oleic acid, or OA-) ligands together with small inorganic anions (e.g., Cl-, OH-, etc.) typically brought into the synthetic mixture by the lead precursor. Based on reported binding energies, surfactants are approximately one million times more likely to desorb from (100) surfaces. As a result, precipitation and redispersal cycles commonly employed to separate NCs from unreacted precursors after synthesis tend to remove ligands selectively from (100) surfaces. This anisotropic ligand coverage can alter the phase behavior of NC superlattices, encouraging PbS NCs to assemble into orientationally coherent bcc superlattices maximizing ligand van der Waals interaction by placing particles in contact with one another through densely-covered (111) facets.24 In the extreme case, sparselycovered surfaces can facilitate oriented attachment of NCs into single-crystalline wires,25 sheets,26 and buckled, porous structures.27 Furthermore, OAH binding has been shown to induce tensile surface stress on the PbS lattice, creating a permanent electric dipole moment within the otherwise centrosymmetric rocksalt structure.28 Dipole-dipole interactions between such particles destabilize fcc packing, instead favoring the hcp or even simple hexagonal structures which minimize electrostatic energy through adoption of antiferroelectric ordering of NC electric dipole moments within the superlattice.29 All of these cases serve to highlight the important and often subtle role of the surface in driving assembly of counterintuitive structures for even the simple case of nearlyspherical, charge-neutral, hydrocarbon-capped NCs. 4 ACS Paragon Plus Environment

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Evaporating a solution of two sizes of NCs often leads to self-assembly of binary NC superlattices (BNSLs). This process offers a compelling approach to controllably produce ordered solids composed of units with distinct chemical functionality (e.g., semiconductor, magnetic, or plasmonic particles) intermixed for potential use in catalytic,30 electronic,31 and magnetic32 applications. Similar to that of single-component superstructures, BNSL self-assembly has been treated as a process driven by maximization of translational entropy, yielding the densest structure as the equilibrium phase.33 If assembling NCs are approximately spherical, the stability of candidate binary structures can thus be evaluated by calculating the space-filling fraction of spheres packed into the unit cell at a given size ratio, γ = RB/RA, where RA and RB denote the radii of larger and smaller spheres, respectively. For hydrocarbon-capped NCs, the binary size ratio may be calculated using the effective radius, including the contribution of surface ligands to overall particle size, of each component: γeff = Reff,A / Reff,B. In the case of a NC embedded within the interior of a close-packed array, the NC effective radius is well approximated by the optimal packing model (OPM34), which predicts Reff = R(1+3L/R)1/3, where L is the molecular length of surface-bound hydrocarbon chains. On the other hand, in low-coordination lattice sites, the liquidlike hydrocarbon corona may deform to maximize space-filling within the volume available to the particle (the Voronoi cell). Such deformability-induced departure from sphere packing is one important element enabling entropic stabilization of the observed rich set of binary NC phases.35,36 In this work, we demonstrate that variable PbS ligand surface coverage, accessible through facet-dependent binding strength, offers a convenient route to toggle the stability of PbScontaining BNSLs. Using PbS and Au NCs at intermediate size ratio, we observe that CuAu BNSLs are the dominant assembly product, despite low space-filling efficiency predicted using sphere packing models. Detailed transmission electron microscopy (TEM) and wide-angle electron diffraction (WAED) characterization revealed CuAu BNSLs feature orientationallyregistered PbS NCs with (100) surfaces approaching inorganic core-core contact. Importantly, we observe that addition of OAH to the assembly solution dramatically alters the assembly outcome, producing instead AlB2 BNSLs with concomitant loss of PbS orientational registry and restoration of OPM-predicted interparticle separations. Nuclear magnetic resonance (NMR) titration experiments performed on the PbS solution confirm that OAH addition results in rebinding of unsaturated NC surface sites, implicating variable ligand coverage in the selection between CuAu and AlB2 BNSLs. These results allow us to solve the puzzle of the CuAu BNSL, an extremely 5 ACS Paragon Plus Environment

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common binary structure that features orientational coherence of NC atomic planes and only assembles, to the best of our knowledge, far from its predicted maximum sphere packing fraction.

Results and Discussion We used established synthetic procedures to prepare colloidal PbS and Au NCs passivated with oleic acid and dodecanethiol surface ligands, respectively (see Experimental).37,38 Size-selective precipitation afforded monodisperse PbS NCs with diameter of 7.5 nm and Au NCs with diameter of 3.1 nm (Figures S1,S2). Using high-resolution TEM imaging, we found only single-crystalline PbS NCs, while both single-crystalline and multiply-twinned Au NCs were observed (Figure S3). Wide-angle electron diffraction (WAED) patterns collected from separately deposited PbS and Au NC solids revealed a set of atomic reflections indexed to the rocksalt PbS lattice and face-centered cubic Au lattice (Figure S4). We then assembled BNSLs at γeff ≈ 0.47 from 7.5-nm oleate-capped PbS NCs (2Reff ≈ 10.4 nm) and 3.1-nm dodecanethiol-capped Au NCs (2Reff ≈ 4.9 nm) by evaporating the binary solution over tilted TEM grid (see Experimental). CuAu-type BNSL domains several hundred nanometers across were found to cover most of the grid surface (Figure 1a), with some fraction of the Au NCs deposited as phase-separated, close-packed superlattices (Figure S5). On the other hand, when a slight excess of oleic acid was added to the same binary NC solution, AlB2-type BNSLs were found to be the dominant assembly product (Figure 1b). To collect BNSL phase information averaged over a macroscopic sample area, we measured small-angle X-ray scattering (SAXS) patterns from NCs deposited on carbon TEM grids irradiated with 0.3 x 0.3 mm beam of 12 keV x-rays. The scans were repeated 36 times across the sample in raster fashion and superimposed into a composite scattering pattern containing structural information for the entire grid. The SAXS patterns from each sample were indexed to CuAu and AlB2 BNSLs, confirming a significant change in the relative stability of the two structures upon OAH addition (Figure 2). Modeling both CuAu and AlB2 BNSL structures as binary sphere packings, the calculated space-filling efficiencies are 58% and 74%, respectively (Figure S8). On the basis of simple packing arguments,38 the stability of the CuAu binary structure against demixing into separate close-packed (e.g., fcc, φ ≈ 74%) is therefore somewhat surprising. Along these lines, the configurational 6 ACS Paragon Plus Environment

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contribution to system entropy can stabilize binary structures with only slightly lower density (φ > 67%, refs.39,40) than close-packed monodisperse spheres.

Figure 1. Structural characterization of binary phases formed from 7.5-nm PbS and 3.1-nm Au NCs at effective size ratio of 0.47. (a) TEM overview and (upper inset) zoom of (100)-oriented CuAu-type BNSL. Lower inset shows CuAu unit cell, with PbS shown as grey spheres and Au shown as yellow spheres. (b) TEM overview and (upper inset) zoom of (001)-oriented AlB2-type BNSL formed upon addition of oleic acid to the same binary NC solution. Lower inset shows AlB2 unit cell. (c) Small-angle and (d) Wide-angle electron diffractograms collected from single superlattice domain of CuAu structure. (e) Small-angle and (f) Wide-angle electron diffractograms collected from single superlattice domain of AlB2 structure. Note that reflections from PbS NC atomic planes (panel d) appear as a series of arcs rather than continuous rings in the CuAu structure, indicating orientational coherence of PbS NCs in CuAu BNSLs.


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Figure 2. Transmission small-angle x-ray scattering (SAXS) characterization of AlB2 and CuAu BNSL thin films. (a) Rotationally-averaged intensity of x-ray scattering from AlB2-type BNSLs with indexed reflections shown underneath. Upper inset: 2D scattering pattern used to calculate 1D trace. (b) Rotationally-averaged intensity of x-ray scattering from CuAu-type BNSLs with indexed reflections shown underneath. Upper inset: 2D scattering pattern used to calculate 1D trace. In both cases, 2D scattering patterns represent the average of 36 points collected in 6 x 6 grid across the TEM grid surface (~10 mm2 area).

Further structural insights were obtained in TEM by collecting transmitted electrons in the diffraction plane (Figure 1c-f). In particular, the orientation of superstructure lattice planes (hkl)SL with respect to NC atomic lattice planes (hkl)NC can be elucidated by obtaining the electron diffraction (ED) pattern of a single superlattice domain at small- and wide scattering angles.14 Our ED analysis confirmed that PbS NCs are not randomly oriented within the CuAu BNSL, but instead feature (100)NC planes normal to the (001)SL direction and (111)NC lattice planes normal to the (011)SL direction (Figure 1d). A broad circular ring corresponding to Au (111)NC atomic lattice planes in the same diffractogram indicates that Au NCs are randomly oriented within the CuAu structure. Minor reflections from (200)NC planes oriented perpendicular to the superlattice basal plane indicate a small component of the PbS NCs lie with (100)NC facets in the imaging plane, possibly some of the NCs located at the air-superlattice or superlattice-substrate interface. Fast Fourier transform (FFT) analysis of real-space TEM images of CuAu BNSLs corroborates the ED data suggesting orientational ordering of PbS NCs within CuAu BNSLs (Figure S8). We also observed similar orientational coherence of PbS NCs within Cu3Au BNSLs (Figure S9). For AlB2 BNSLs, on the other hand, only continuous rings were found in the wide-angle diffractogram 8 ACS Paragon Plus Environment

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(Figure 1f), suggesting that the AlB2 BNSL features both PbS and Au NCs in random orientations within the superlattice. This conclusion is also supported by FFT analysis of AlB2 TEM images (Figure S10). Using the ED data collected in Figure 1, and assuming truncated octahedral PbS NC shape,23 we modeled PbS NCs and their packing arrangement within the CuAu BNSL (Figure S6). Looking down the CuAu (100)SL direction commonly observed in TEM (i.e., Figure 1a), PbS NCs are oriented such that two of six (100)NC faces are parallel to CuAu basal plane (Figure 3a,c). Looking in the plane of the substrate, it can be seen that the other four (100)NC faces participate in PbS-PbS contacts within the superlattice basal plane (Figure 3b,d). From this perspective it also becomes clear that the PbS NCs making contact with the substrate do so through the edge separating (111)NC faces. Such edge-on NC orientation, also observed for bcc superlattices of PbS NCs,41 has been anticipated by molecular dynamics simulations to be the relaxed configuration of NCs passivated with hydrocarbon ligands adsorbed to graphite support.42

Figure 3. Modeling truncated octahedral 7.5-nm PbS NCs and their orientation within the CuAu BNSL. (a) Atomistic model (left) and cartoon sketch (right) of PbS NC with Pb-terminated (111)NC facets and Pb- and S-terminated (100)NC faces viewed along the (110)NC direction. (b) Similar model (left) and sketch (right) of PbS NC viewed along a (100)NC direction. (c) Illustration of the CuAu (100)SL projection imaged in Figure 1a, with orientationally-registered truncated octahedral PbS NCs matching the ED pattern shown in Figure 1d. (d) Illustration of the CuAu (001)SL projection, in the plane of the substrate, showing square packing of PbS NCs within the superlattice basal planes.


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Beyond the orientational registry of PbS NCs within the CuAu BNSL and lack thereof in the AlB2 BNSL, the separation between such particles can also offer important insights into the relative stability of these binary phases. Modeling the structures as packings of simple spheres, at the experimental size ratio (γeff ≈ 0.47) we predict that the A-A (PbS-PbS) contacts are the jamming contacts in both CuAu and AlB2, allowing for expected unit cell dimensions to be expressed in terms of A particle size. For example, within the CuAu A-A contact regime (γeff < 0.73) expected lattice parameters are a = b = 2 2·Reff,A and c = 2Reff,A. Given the PbS effective diameter of 2Reff ≈ 10.4 nm predicted by OPM for R = 3.75 nm and L = 2 nm, such analysis anticipates that a = b ≈ 14.6 nm and c ≈ 10.4 nm. In reasonable agreement with such predictions, the measurement of experimental CuAu lattice dimensions indicates that PbS-PbS center-to-center separation across basal planes is c ≈ 10.3 nm (Figure S11). On the other hand, in striking contrast to the OPM prediction, the measured a = b ≈ 10.6 nm corresponds to PbS-PbS center-to-center separation of ~7.5 nm within the CuAu basal planes. This value is approaching the diameter of the inorganic core, suggesting that the hydrocarbon chains separating (100)NC surfaces within the CuAu basal planes are grafted at low density or perhaps entirely absent from the structure. Indeed, ligand packing calculations have predicted that reduced ligand A-particle grafting density is required to stabilize CuAu at intermediate size ratios.36 For the AlB2 BNSL obtained by assembling the same NCs in the presence of added OAH, however, the experimental superlattice dimensions are wellapproximated by those anticipated using the OPM predictions. Packing of simple spheres within the A-A contact regime of the AlB2 structure (γeff < 0.53) predicts superlattice dimensions of a = b = c ≈ 2Reff,A. We obtained experimental PbS-PbS center-to-center distance of a = b ≈ 10.4 nm within, and c ≈ 10.0 nm across, the superlattice basal planes (Figure S12), indicating that the OPM prediction is in line with the observed PbS-PbS separation within the AlB2 superlattice basal plane but slightly overestimates that measured across the basal planes. From these measurements, we can conclude that PbS NCs approach core-core contact in the CuAu structure but remain wellseparated in the AlB2 BNSL. The interparticle separation measurements presented above suggest the possibility of oriented attachment of PbS NCs within the CuAu basal planes. However, WAED reflections from PbS NC atomic lattice planes (Figure 1d) are arc-shaped, however, with significant intensity over ~60° of the circle. This stands in contrast to the narrower, circular spots observed for crystalline structures formed by oriented attachment of lead chalcogenide NCs.25,27,43,44 In these cases, the use an 10 ACS Paragon Plus Environment

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immiscible ethylene glycol subphase encourages fusion of NCs by dissolving OAH molecules that bind weakly to (100) surfaces. Observing broad WAED lobes from PbS atomic reflections, we conclude that necking and large-scale motion of inorganic material across (100) surfaces has not taken place in the CuAu BNSLs presented in this work. On the other hand, assembly of CuAu BNSLs atop an ethylene glycol subphase, and perhaps with the assistance of thermal annealing, may coax PbS NCs to fuse into sheets along the basal plane, reminiscent of B-cluster coalescence within pre-assembled CaB6 BNSLs.45 Based on the orientational registry and near contact of PbS NC cores within the CuAu structure, we hypothesized that OAH coverage on PbS NC surfaces plays an important role in selecting between CuAu and AlB2 BNSLs at the size ratio investigated in this work. Specifically, given the weak binding strength of OAH to lead chalcogenide nonpolar surfaces,23,25–27,46 we can speculate that precipitation and redispersal steps routinely applied after synthesis may result in the release of OAH along PbS NC (100) surfaces as a new population of solvated ligands is established upon redispersal. Such ligand loss may change both entropic and enthalpic components of the selfassembly process. In the general case of isotropic ligand desorption, the effective NC shape may be altered by reducing the ability of the capping layer to screen the faceted inorganic crystallite from its environment. On the other hand, anisotropic ligand desorption will effectively install dimples along the directions of ligand loss. These factors will entropically stabilize superlattice structures not characteristic of the hard sphere phases, including those with low particle coordination numbers and orientational registry.47,48 The enthalpic contribution to NC assembly is also affected by loss of surface ligands. If desorption is uniform across the particle surface, reduced screening of core-core van der Waals interactions will result in stronger interparticle attraction during self-assembly, potentially stabilizing single-component superlattices or binary phases with contacts between sparsely-passivated NCs. On the other hand, if ligand desorption is anisotropic, the enthalpic contribution to NC assembly will contain attractive interactions between bare NC surface patches or between densely-covered facets acting as hydrophobic patches. These enthalpic factors should also stabilize superlattice phases with orientational coherence and reduced particle coordination number. We also evaluated the possibility of the Au component playing a role determining the relative stability of CuAu and AlB2 BNSLs. Icosahedrally-shaped alkanethiolate-capped Au NCs 11 ACS Paragon Plus Environment

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(Figure S3a) are terminated by (111) facets and feature, to a first approximation, ligand sulfurs binding to one third of available threefold sites on the Au surface. Curvature afforded by vertex and edge sites relaxes steric crowding, enabling NC-ligand grafting density on Au to exceed that of extended Au(111) surfaces.49 The strong sulfur-gold interaction (~250 kJ/mol, ref.50) discourages detachment of ligands from the Au NC surface, ensuring that the underlying NC core is screened from its environment by the tightly-held capping layer. In contrast to the 3.1-nm diameter Au NC rendered soft and spherical by strongly-bound, 1.6-nm C12-length ligands, the 7.5-nm PbS component is more susceptible to changes in effective shape imparted by dynamic attachment of weakly-binding OAH ligands to PbS(100) facets. As a result, flat surface interactions and orientational registry between PbS NCs, and resulting stabilization of the CuAu BSNL, can be activated or suppressed by OAH removal or restoration. On the other hand, random orientation of Au NCs in both CuAu and AlB2 BNSLs presented in this work (and, to the best of our knowledge, within all BNSLs reported to date), implies the Au component plays a smaller role than PbS in CuAu vs. AlB2 phase selection. With the suspicion that PbS surface ligand coverage plays an important role in the selection between CuAu and AlB2 structures at γeff ≈ 0.47, we turned to thermogravimetric analysis (TGA) to estimate ligand coverage on the PbS NCs. Approximating the PbS NC surface area as that of a 7.5-nm diameter sphere, the 12% mass loss observed upon heating the dried PbS NC solid (Figure S13) suggests an average surface ligand grafting density of approximately 2.60 nm-2. Assuming a cuboctahedral PbS NC core shape, on the other hand, reduces this estimate to 2.2 nm-2. If Pbterminated (111)NC facets retain strongly-bound oleate ligands at their saturation density of 4 nm2

(ref.23), we can estimate the density of OAH ligands bound to (100)NC surfaces of as-prepared

PbS NCs to be approximately 1.18 nm-2. Taking the saturation density of (100)NC surfaces to be 2.83 nm-2 (OAH carbonyl oxygens bind to every other lead surface atom23), we estimate these facets to be passivated at 42% of maximum OAH coverage for as-prepared PbS NCs. These considerations suggest that the PbS NCs purified by three rounds of washing with ethanol feature (100)NC facets sufficiently protected to prevent oriented attachment, yet bare enough to experience anisotropic excluded volume interactions in the assembly solution. With the PbS (100)NC facet initial surface coverage estimate in place, we then turned to nuclear magnetic resonance (NMR) spectroscopy to approximate ligand coverage during OAH addition to 12 ACS Paragon Plus Environment

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the NC solution. Over the past decade, solution NMR has proven to be a useful technique in the study of colloidal nanomaterial surfaces,51 offering insights into the chemistry52–55 and thermodynamics56–58 of NC-ligand binding. To probe ligand binding to PbS NCs, we dissolved 30 mg of the dried NC solid into 0.5 mL deuterated toluene and loaded it into an NMR tube. The proton (1H) NMR spectrum of this solution reveals a set of broad resonances contributed by NCbound surface ligands and sharp resonances from residual solvent protons (Figure 4a). Broadening of NMR signals from NC-bound ligands has been attributed to the transversal interproton dipolar relaxation rendered more efficient by the restricted rotational mobility of the ligands when bound to the NC surface.51 As expected for the case of oleic acid capped NCs, the NMR spectrum reveals broad aliphatic (1 < δ < 3 ppm) and vinylic (δ ~ 5.7 ppm) resonances, and sharp methyl (δ ~ 2 ppm) and aryl (δ ~ 7 ppm) solvent resonances. For our analysis of OAH binding to PbS NC surfaces, we focused on the vinyl proton resonance, which is separated from aliphatic and aromatic signals and thus a convenient reporter of ligand binding state.53 The vinyl proton resonance was followed during titration of the as-prepared PbS NC solution with OAH (Figure 4b). After several such additions, the rise of a sharp peak upfield of the broad vinyl resonance was noted, indicating the appearance of free OAH in solution. Monitoring the fraction of ligands contributing to the free oleic acid signal (OAHfree) as a function of the amount added to solution (OAHadded) allows for tracking of ligand binding to the PbS NC surface. In this case, OAHadded was normalized with respect to the quantity of ligands initially present on the NC surface. The corresponding values during the titration are provided on the left side of Table 1. For no ligand-surface interaction, the number of solvated ligands should scale linearly with the quantity added (i.e., OAHfree = OAHadded). Indeed, a control experiment adding OAH into pure toluene solvent confirms this relationship (Figure 4c, open circles; Figure S14). On the other hand, in the presence of PbS NCs, initial ligand additions make a comparatively smaller contribution to free OAH signal (Figure 4c, closed circles). From this we can conclude that OAH addition to the PbS NC solution results in binding of some of the ligands to the NC surface. Moreover, the number of ligands that bind to the PbS NC surface upon OAH addition can be expressed as the difference OAHadded - OAHfree. In the case of strongly-bound OA- (X-type) and weakly-bound OAH (L-type) ligands, adsorption to densely-covered, oleate-passivated (111)NC


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surfaces can be neglected. Added ligands thus bind to the (100)NC surfaces, and the updated (100)NC facet grafting density ρ100 can be estimated as:

{

𝜌100(𝑂𝐴𝐻𝑎𝑑𝑑𝑒𝑑) = 𝜌𝑜,100 1 +

}

1 (𝑂𝐴𝐻𝑎𝑑𝑑𝑒𝑑 ― 𝑂𝐴𝐻𝑓𝑟𝑒𝑒) 𝑂𝐴𝐻𝑜,100

where initial grafting density (ρo,100) is 1.18 nm-2 and OAHo,100 is the fraction of the PbS corona composed of (100)-bound, protonated oleic acid ligands (34%, see the Supporting Information). Following this logic, we estimate that adding 0.8 molar equivalents of OAH to the PbS NC solution results in an increase in coverage of (100)NC surfaces from ρ100 ~ 1.2 nm-2 to ρ100 ~ 2.5 nm-2 (from θ100 ~ 40% to θ100 ~ 90% of the 2.83 nm-2 saturation value, Figure 4d). The corresponding values are provided on the right side of Table 1.

Figure 4. Monitoring repassivation of PbS (100)NC surfaces during addition of oleic acid into solution. (a) 1H-NMR spectrum of oleic acid capped PbS NCs dispersed in 0.5 mL d8-toluene. Inset: OAH molecular structure showing protons giving rise to NMR resonances. (b) Zoom of 14 ACS Paragon Plus Environment

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vinyl proton resonance during titration of PbS NC solution with OAH. Addition of excess ligand leads to increasing intensity of the (sharper, upfield) signal from a population of free OAH in solution. (c) Monitoring free ligand signal as a function of added OAH for the PbS NC solution (closed circles) and the control experiment of solvent without nanocrystals (open circles). The dashed y = x trace indicates expected free ligand population in the absence of NC-ligand interaction. (d) Estimated OAH grafting density and corresponding saturation of PbS(100) surfaces as a function of added OAH. The dashed trace shows the Langmuir fit, and the inset shows extracted adsorption coefficient Kads and binding energy ∆Eads. See Supporting Information for details.

Table 1. Molar ratios of added and free ligands, OAH concentration in solution, (100)NC grafting density ρ and surface saturation θ during titration of PbS NC solution with excess OAH. See Supporting Information for details regarding NMR vinyl signal deconvolution, grafting density, and surface saturation calculations. OAHadded (eq.)

OAHfree (eq.)

[OAH] (10-3 M)

𝝆100 (nm-2)

θ100 (a.u.)

0

0

8.6

1.18

0.42

0.20

0.03

13.6

1.77

0.63

0.40

0.15

18.6

2.05

0.72

0.60

0.22

23.6

2.50

0.88

0.80

0.43

28.6

2.46

0.87

Using the relationship between ligand surface coverage θ100 and concentration [OAH] we also estimated the adsorption constant of OAH binding to PbS (100) surfaces. Binding of ligands to NC surfaces has been treated using the Langmuir adsorption isotherm,56–58 which relates the fractional surface coverage θ to the concentration of free adsorbate [L] in solution with an adsorption coefficient K according to the expression: 𝜃=

𝐾[𝐿] 1 + 𝐾[𝐿]

Neglecting strongly-bound OA- (X-type) ligands, we can rewrite this expression to consider only OAH binding to (100)NC surfaces:


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𝜃𝑂𝐴𝐻 𝑜𝑛 𝑃𝑏𝑆(100) =

𝐾𝑎𝑑𝑠,𝑂𝐴𝐻[𝑂𝐴𝐻] 1 + 𝐾𝑎𝑑𝑠,𝑂𝐴𝐻[𝑂𝐴𝐻]

Fitting our data to this expression allowed us to estimate the adsorption constant of OAH on PbS (100) surfaces as Kads ≈ 178 M-1 (Figure 4d), in line with the values obtained for other L-type ligands binding to semiconductor NC surfaces (e.g., amine-capped CdSe, ref.58). This value can be related to the energy of adsorption according to the expression ∆𝐸𝑎𝑑𝑠 = 𝑘𝐵𝑇 ∙ 𝑙𝑛(𝐾𝑎𝑑𝑠) which produces a binding energy estimate of 0.13 eV, in reasonable agreement with the DFTobtained value of 0.16 eV.23 From these NMR data we can thus conclude that OAH addition to assembly solution containing PbS NCs results in rebinding of sparsely-passivated (100) surfaces. Conclusions Combining BNSL structural analysis and modeling (Figures 1-3) with the investigation of OAH binding to PbS NCs in solution (Figure 4) we can propose a mechanism for the role of OAH addition in selecting between CuAu and AlB2 BNSLs at the experimental size ratio. As-prepared PbS NCs, precipitated three times from hexane/ethanol solution, feature (100) surfaces with fewer than half of the available sites retaining a weakly-binding OAH ligand. These particles, when combined in solution with Au NCs and condensed by solvent evaporation, self-assemble into a binary structure with anisotropic PbS-PbS interactions reflected in the orientational coherence and narrow surface separation such particles across the structure (Figure 5, left). On the other hand, OAH addition rebinds many of the bare surface sites on PbS (100)NC facets, restoring nearly spherical effective particle shape (Figure 5, top). Reflecting such changes to PbS NC effective shape, evaporation of the same binary solution in the presence of added OAH produces the AlB2 BNSL with randomly-oriented PbS NCs (Figure 5, right) separated by ligand bilayers with effective thickness matching the OPM prediction. We observed that addition of 0.2 molar equivalents of OAH yielded CuAu and AlB2 in approximately equal proportion, while 0.4 molar equivalents (1 µL of 10 mM OAH to assembly solution containing ~0.1 mg PbS NCs) was sufficient to result in nearly complete conversion of CuAu to the AlB2-type structure. From this we conclude that the CuAu-to-AlB2 transition occurs at approximately 1.8 nm-2 OAH grafting density (~60% occupation of available sites) on PbS (100)NC surfaces. 16 ACS Paragon Plus Environment

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Figure 5. Sketch of proposed re-passivation of PbS {100}NC facets upon addition of excess OAH (top) and resulting influence on stable binary phase (bottom) when cocrystallized with Au NCs at intermediate effective size ratio.

Along these lines, a similar set of experiments by Gang and coworkers59 revealed that addition of excess dodecanethiol surface ligands to a solution of cubic Pd NCs enabled the effective particle shape to be tuned from cubic to quasi-spherical, with resulting superlattice structure following the densest packing of either shape. Such observations indicate that the CuAu BNSL may be a denser structure than sphere packing models suggest. For this system, simple space-filling calculations employing revised assumptions about A-particle shape may reveal that the CuAu BNSL is indeed a dense (i.e., φ > 0.74) structure and thus stabilized by translational entropy. It should be noted that changes to the underlying shape of the NC inorganic lattice may occur upon addition of surface-binding species. For instance, Vanmaekelbergh and coworkers recently demonstrated60 that addition of lead oleate to a solution of well-washed PbSe NCs results in a change in the relative areas of NC surface facets: (111) PbSe facets are extended at the expense of (110) facets, while (100) facets remain. As a result, the NC shape changes from truncated cube to truncated octahedron. In this report, we evaluate the phase behavior of PbS NCs without 17 ACS Paragon Plus Environment

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introducing additional lead atoms into the system, suggesting that such extension of leadterminated (111) facets cannot take place. On the other hand, at fixed (111) surface area, the relative areas of (100)- vs. (110) facets may change without electrostatic penalty. While we cannot rule out this possibility, our choice to model the PbS NC shape as a cuboctahedron without (110) facets is supported by DFT calculations23 presenting a surface-energy-minimized PbS NC as one without (110) facets. Beyond entropy, superlattice structures which enable spatial concentration of ligand chains can be stabilized by van der Waals interactions between hydrocarbon chains at the late stages of solvent evaporation. For example, orientational ordering of PbS NCs within bcc superlattices allows each NC to be in contact with its 8 nearest neighbors through densely-covered (111)NC facets, maximizing energetic interactions between chains in the absence of solvent.61 Similarly, the CuAu BNSL places a Au NC in the body-centered site of the tetragonal PbS sublattice and orients PbS NCs such that all (111)NC facets are in contact with the alkanethiolatecapped Au NC (Figure 3c,d). Such orientational arrangement of PbS NCs within the CuAu BNSL thus not only facilitates dense packing through flat surface alignment, but also maximizes van der Waals interactions between NC-bound hydrocarbon chains after solvent evaporation. Accordingly, future simulations of PbS NC assembly may consider treating not only the shape effects associated with patchy ligand coverage but also nonuniform distribution of attractive surface interactions that can result. Furthermore, the assembly pathway recently observed for PbS NCs,41 in which the ensemble of particles moves through disordered dilute state to fcc rotator crystal to bcc registered crystal, may have a binary analog. Interesting future in-situ x-ray scattering experiments could explore whether formation of the orientationally-coherent CuAu BNSL is preceded by a binary rotator crystal at the late stages of solvent evaporation. In conclusion, we have demonstrated that the CuAu BNSL can serve as an illustrative example of the role of NC surfaces in driving self-assembly of unanticipated superlattice structures. Due to differences in ligand binding affinity between PbS (100)- and (111) facets, post-synthetic solvent/nonsolvent purification results in selective removal of passivating chains from (100)NC surfaces. As a result, when mixed with Au NCs at intermediate size ratio, the binary system does not assemble into the expected densest sphere packing AlB2 BNSL but instead the CuAu BNSL which maximizes space-filling efficiency through flat surface alignment and maximizes van der Waals interaction through spatial concentration of hydrophobic ligand chains. Importantly, addition of OAH ligands to the binary assembly solution rebinds the sparsely passivated (100)NC 18 ACS Paragon Plus Environment

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surfaces, restoring spherical effective particle shape and, with it, stability of the AlB2 BNSL. These results underscore the importance of NC surfaces in determining the relative stability of superlattice phases and offer a strategy to target particular BNSL structures.

Methods Au NCs with 3.1-nm diameter were prepared by reducing Au(III) salt in oleylamine and tetralin at 25°C according to ref.37 After two cycles of precipitation and redispersal, oleylamine-capped Au NCs were stirred in a toluene solution of dodecanethiol at 1:1 mass ratio of NCs to displacing ligand for 30 minutes. The resulting dodecanethiol-capped Au NCs were precipitated twice from toluene/ethanol and redispersed in toluene for storage. PbS NCs with 7.5-nm diameter were prepared by reacting bis(trimethylsilyl)sulfide in a stirring solution of lead acetate, oleic acid, and 1-octadecene at 145°C for 20 minutes. After cooling to room temperature, the NCs were separated from unreacted precursors by three cycles of precipitation from hexane/ethanol. PbS NCs were then redispersed in octane for storage. Single-component superlattices of Au or PbS NCs were prepared by drop casting a dilute solution (~5 mg/mL) over a TEM grid resting on filter paper on a hot plate set to 50°C. Binary superlattices were prepared by combining ~0.5 mg Au and ~0.1 mg PbS NCs (5:1 mass ratio corresponds to ~1:1 number ratio) in 20 μL octane and evaporating the solution atop a hotplate set to 50°C over a tilted 2-mL scintillation vial standing at 25° from horizontal.62 Addition of 1 μL of 10 mM solution of OAH in octane was found to be sufficient to result in nearly quantitative conversion of CuAu to AlB2-type BNSLs. TEM investigations were carried out on FEI Technai F30 microscope operating at 300 kV. NMR investigations were carried out using a Bruker Avance III 500 MHz spectrometer. SAXS experiments were performed at Argonne National Lab (ANL) Advanced Photon Source (APS). BNSLs deposited on carbon TEM grids were irradiated with 0.3 x 0.3 mm beam of 12 keV x-rays and collected with CCD area detector. Multiple scans were repeated across the sample in raster fashion and superposed into a composite scattering pattern containing structural information for the entire grid. One-dimensional profiles were subsequently calculated by azimuthal averaging of the composite 2D scattering patterns. 19 ACS Paragon Plus Environment

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Associated content Supporting information TEM images of NCs and NC superlattices, FFT analysis of TEM images, TEM electron diffractograms, TGA data, BNSL modeling, measurement of experimental BNSL lattice parameters, NMR data, superlattice defect structure, and ligand grafting density calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

Author information Corresponding author [email protected]

Acknowledgements We thank Michael Engel (FAU Erlangen-Nuremberg) and Alex Travesset (Iowa State University) for stimulating discussions and Byeongdu Lee (Argonne National Lab) for help with synchrotron SAXS measurements. This work was supported by the MICCoM Center, funded by the Department of Energy, Basic Energy Sciences, Air Force Office of Scientific Research, under Grant FA9550-14-1-0367, National Science Foundation (NSF) under Award No. DMR-1611371, and NSF MRSEC Program under Award No. DMR-14-20703. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DEAC02-06CH11357.


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