Regulating Multiple Variables To Understand the Nucleation and

Sep 27, 2017 - Integrated small-angle X-ray scattering (SAXS) patterns of assembled superlattices made by drop-casting of the toluene solutions with v...
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Article Cite This: J. Am. Chem. Soc. 2017, 139, 14476-14482

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Regulating Multiple Variables To Understand the Nucleation and Growth and Transformation of PbS Nanocrystal Superlattices Zhongwu Wang,*,† Kaifu Bian,‡ Yasutaka Nagaoka,# Hongyou Fan,‡,§ and Y. Charles Cao# †

Cornell High Energy Synchrotron Source, Cornell University, Ithaca, New York 14853, United States Sandia National Laboratories, Advanced Materials Laboratory, 1001 University Boulevard SE, Albuquerque, New Mexico 87106, United States § Department of Chemical and Nuclear Engineering, Center for Micro-Engineered Materials, University of New Mexico, Albuquerque, New Mexico 87106, United States # Department of Chemistry, University of Florida, Gainesville, Florida 32611, United States ‡

S Supporting Information *

ABSTRACT: Nanocrystals (NCs) can self-assemble into ordered superlattices with collective properties, but the ability for controlling NC assembly remains poorly understandable toward achievement of desired superlattice. This work regulates several key variables of PbS NC assembly (e.g., NC concentration and solubility, solvent type, evaporation rate, seed mediation and thermal treatment), and thoroughly exploits the nucleation and growth as well as subsequent superlattice transformation of NC assembles and underneath mechanisms. PbS NCs in toluene self-assemble into a single face-centered-cubic (fcc) and bodycentered-cubic (bcc) superlattice, respectively, at concentrations ≤17.5 and ≥70 mg/mL, but an intermediate concentration between them causes the coexistence of the two superlattices. Differently, NCs in hexane or chloroform self-assemble into only a single bcc superlattice. Distinct controls of NC assembly in solvent with variable concentrations confirm the NC concentration/solubility mediated nucleation and growth of superlattice, in which an evaporation-induced local gradient of NC concentration causes simultaneous nucleation of the two superlattices. The observation for the dense packing planes of NCs in fast growing fcc rather than bcc reveals the difference of entropic driving forces responsible for the two distinct superlattices. Decelerating the solvent evaporation does not amend the superlattice symmetry, but improves the superlattice crystallinity. In addition to shrinking the superlattice volume, thermal treatment also transforms the bcc to an fcc superlattice at 175 °C. Through a seed-meditated growth, the concentration-dependent superlattice does not change lattice symmetry over the course of continuous growth, whereas the newly nucleated secondary small nuclei through a concentration change have relatively higher surface energy and quickly dissolve in solution, providing additional NC sources for the ripening of the primarily nucleated larger and stable seeds. The observations under multiple controls of assembly parameters not only provide insights into the nucleation and growth as well as transformation of various superlattice polymorphs but also lay foundation for controlled fabrication of desired superlattice with tailored property.

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properties,2,8−10 scientists and engineers have made intensive efforts to exploit and control the self-assembly of NCs into various superlattices.11−16 Progress has been witnessed to improved understanding of NC assembles and associated mechanisms with subsequent application in rational optimization of material properties and feasible discovery of interesting phenomena.17−19 NC assembly involves multiple driving forces, such as van der Waals attraction, steric repulsion, solvent depletion and entropic forces.20−24 Complex interactions of driving forces originate largely from inorganic NCs, surface decorating

INTRODUCTION

Self-assembly of colloidal nanocrystals (NCs) into periodically ordered structures,1 referred to as superlattices, enables creation of a completely new category of condensed matters, which are not only scientifically interesting but also technologically important.2 Synthetic advance of NCs with excellent control of monodispersity in particle size and shape and molecular flexibility on surface decoration allows easy access and versatile use of NCs as designer building blocks to fabricate novel materials with desired superlattices.3,4 Electron interactions between NCs through interfaces at molecular level are modulated in an ordered way so that a wreath of collective properties arise from assembled superlattices.5−7 Upon emergent applications of enhanced or completely new © 2017 American Chemical Society

Received: July 3, 2017 Published: September 27, 2017 14476

DOI: 10.1021/jacs.7b06908 J. Am. Chem. Soc. 2017, 139, 14476−14482

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uncertainty, we took advantage of large scale fabrication of high quality NCs, and made sufficient PbS NCs in a single batch, which were able to conduct all the assembly experiments with various controls for different purposes. In this work, we employed PbS NCs with an intermediate size of 7.5 nm in diameter as a model system, and delicately controlled variables of NC concentration, solvent type, evaporation rate, seed meditation, growth rate and thermal treatment to study the NC assembly. With such experimental controls of multiple parameters, we thoroughly studied the nucleation, growth and transformation of NC superlattice and associated mechanisms. Using synchrotron-based small/wide-angle X-ray scattering (SAXS/WAXS) and electron microscopic imaging techniques, we examined the NC assembled superlattices, reconstructed the superlattice phase diagrams, and uncovered the resultant mechanisms. Through analyzing the collected data sets and correlating the multiple observations, we eventually delivered the reliable protocols and fundamental rules, which are capable to reproduce the desired superlattices with tailored properties.

molecules and surrounding solvents. As along as NCs change their assembly environments, the driving forces locally and relatively modify their interacting roles and thus make various magnitudes of contributions to the nucleation and growth of NC superlattice.20,23 Upon rebalancing the driving forces and minimizing the total free energy, the superlattices with distinct symmetries are accordingly developed. Aimed at delicate regulation of the interactions, extensive efforts have been made to design a series of typical experiments to exploit the relative contributions of various driving forces to NC assembly toward the formation of various superlattices.2,25−29 However, it still remains largely unknown of how NC assembly proceeds from the initial nucleation of NC superlattice into a typical lattice symmetry, which in turn acts as a small nuclei seed and continues to grow into large superlattice crystal, called as supercrystal. In particular, much concern is focused on whether the seed-embraced superlattice formed at the early nucleation stage prefers a primary stay in its original lattice or undergoes a transformation into another lattice upon continuous growth of the superlattice grain. In the case of superlattices assembled by PbS NCs, extensive studies have been performed to reconstruct the superlattice phase diagram and uncover their underneath mechanisms.25,30−32 To this end, a series of typical experiments have been designed in terms of delicate tuning of particle size, solvent type and NC concentration.25,33,34 Thin film of NC assembly, such as the fast growing film by drop-casting, appears as one of the simplest and quickest assembles, in which experiments reveal the two high-symmetry superlattice polymorphs of face-centered-cubic (fcc) and body-centeredcubic (bcc), and several structurally distorted intermediates.25−36 Based on variable magnitudes of structural distortion, such structural intermediates, which make direct connection of fcc and bcc, are reasonably indexed into several low-symmetry superlattices, such as rhombohedral, tetragonal and orthorhombic. Making linkage of the martensitic transformation pathway discovered in metallic alloys to the NC assembly,37,38 significant clues can be traced and thus used to understand the structural correlations between various superlattice polymorphs.25 Taking into account the core/shell structural feature of individual NCs, the relative variation of length scale between NC inner core and outer surface-coating molecule has been coupled with the developed magnitude of evaporation/dryinginduced surface stress in two-dimensional (2D) superlattice film to interpret their nucleation and growth as well as transformation.27,39,40 Unfortunately, once superlattice grows from thin 2D into large 3D, such mechanisms have difficulty to interpret the nucleation and growth of large 3D superlattices, which even display the same series of superlattice polymorphs as those in 2D thin film. In an examination of previous reports on NC assembly, large majorities of experiments neglect a critical and quantitative control of several significant parameters, such as NC concentration, solvent type, evaporation rate and so on.25−36,38−40 Among various experiments, NCs often display slight difference in particle size, surface ligand and shape. Such differences have already been observed in NCs from batch to batch, which are prepared even by the same group. When NCs are made by different groups, such an issue becomes much serious. As a result, various superlattices are observed from experiments even under similar and/or identical controls. Accordingly, the experimental reproducibility appears to be one of the critical concerns. In order to minimize such an

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EXPERIMENTAL SECTION

Synthesis of PbS Nanocrystals (NCs). PbS NCs were synthesized using a slightly modified wet chemistry approach.41 Briefly, 0.45 g of lead oxide was dissolved in 20 mL of oleic acid to form a lead oleate solution, which was heated to 150 °C with continuous stirring under nitrogen-flowing for 1 h. After cooling the solution to 130 °C, a completely dissolved solution of 210 μL of bis(trimethylsilyl)sulfide (TMS) in 10 mL of 1-octadecene (ODE) was rapidly injected into the vigorously stirred lead oleate solution. The solution immediately became brown, indicative of the formation of PbS NCs. After 1 min, the solution was quickly cooled down to 60 °C, and then 2 mL of NH4Cl saturated solution in methanol was added. Upon removal of heat for 10 min, the crude products were washed by a sequential precipitation of ethanol and hexane. After removal of the solvent by nitrogen blowing, the dried PbS NCs were stored in a glass vial for additional use. Nanocrystal (NC) Assembly. A variety of control experiments were designed for self-assembly of PbS NCs into various ordering superlattices. Generally, PbS NCs were dispersed in the three types of solvents, including toluene, hexane and chloroform. Among these, NCs in toluene were used for conducting all various types of assembly experiments, but the two others were used only in the drop-casting assembly. Briefly, the starting toluene solution was prepared with a NC concentration of 140 mg/mL. For easy labeling and better comparison, we define and use “C” as a unit of NC concentration in which 1C equals 17.5 mg/mL. Then, a certain amount of solvent was added into the NC solution to achieve a desired NC concentration. The NC solution was either drop-cast on a substrate or simply retained in a glass vial, allowing the superlattice growth at a slow or rapid fashion of solvent evaporation. The others in hexane and chloroform were chosen for the drop casting examinations only at a reduced but critical concentration range observed in toluene. Three types of substrates were used for the drop-casting assembly, including Kapton tape, silicon wafer and copper grid. For the NC assembly controlled under a slow evaporation environment, several hundred microliters of NC solution was transferred into a small glass vial. After a tight sealing by parafilm, the glass vial remained out of interruption for NC assembly. Additionally, several microliters of NC solution was introduced into a glass capillary with 3 mm in diameter for NC assembly at an intermediate rate of solvent evaporation, and the completion of solvent evaporation normally took about 2−3 days. Synchrotron-Based SAXS and WAXS. Synchrotron-based SAXS and WAXS measurements were performed at the B1 station of CHESS.42,43 A monochromatic X-ray beam with energy of 25.514 keV, equilibrant to a wavelength of 0.485946 Å, was reduced to a small circular beam with 100 μm in diameter for the sample illumination. A large area detector of Mar345 was used to record the X-rays scattered 14477

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Journal of the American Chemical Society from the sample. The sample-to-detector distance and associated detector-sitting parameters were calibrated by the two powder standards of CeO2 and Ag-behenate. The assembled NC superlattice samples were loaded either onto a Kapton tape or into a stainless gasket hole or a glass capillary. Such an assembly was mounted on the stage at the B1 station of CHESS for simultaneous collections of WAXS and SAXS images. Using a free Fit2D package, the collected 2D images were reduced into 1D pattern with plot of intensity against 2θ (deg) or inverse nanometer (nm−1) for structure analysis. Electron Microscopic Imaging. Transmission electron microscopy (TEM) was used to characterize the thin film superlattice, which was loaded onto a carbon-coating copper grid, using a JEOL 200CX and a JEOL 2010F operated at 200 kV. Scanning electron microscopy (SEM) measurements were conducted on assembled superlattice, which was transferred onto a silicon substrate, using a Hitachi S-5200 SEM operated at 10−20 kV.

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Figure 2. Integrated small-angle X-ray scattering (SAXS) patterns of assembled superlattices made by drop-casting of the toluene solutions with various NC concentrations on Kapton tapes (a), in which two typical SAXS patterns were indexed well in (b) body-centered cubic (bcc) and (c) face-centered cubic (fcc) superlattices, respectively, with insets of Miller indexing and unit cell as well as 2D SAXS image. Note: 1C = 17.5 mg/mL.

RESULTS AND DISCUSSIONS PbS NCs with surface coating of oleic acid (OA) molecules were synthesized by the previously developed approach.41,44 The synthesized PbS NCs were treated in NH4Cl solution for a partial coating of chlorines on NC surfaces to avoid or weaken a surface oxidation effect.33,45 A typical TEM image (Figure 1a)

concentration equals or is smaller than 1C, NCs self-assemble exclusively into a single fcc superlattice. Increase of NC concentration to 4C or above results in an exclusive formation of single bcc superlattice. When NC concentration falls into the range between 1C and 4C, both bcc and fcc coincidently form and coexist together. Noticeably, the increase of NC concentration dramatically improves the superlattice crystallinity. In the typical range of NC concentrations for the exclusive formation of a single superlattice, the assembled bcc superlattices collected at 4C and above all display great crystalline quality (Figure 2b), but the fcc superlattice collected only under 1C conditions displays the highest crystallinity (Figure 2c). The drop-casting NC assembly involves development of an evaporation-induced gradient of concentration, but careful examination of the NC assembly made at the same concentration reveals a superlattice consistence across the whole sample area (Figures S2−4). The coexistence of the two superlattices at each examined spot indicates a small and local gradient of NC concentration. The observed concentration range of 1C−4C suggests a critical concentration boundary to separate bcc from fcc superlattice, which can be approximately estimated at the intercepting value of 2.5C [e.g., (1C + 4C)/2 = 2.5C)]. Such an estimation allows one to determine the local concentration gradient of 1.5C (e.g., 4C − 2.5C = 2.5C − 1C = 1.5C) across a small length scale. Taking into account the incident X-ray beam size of 100 μm in diameter and the observed powder SAXS feature, the maximum scale for the estimated concentration gradient of 1.5C is about several microns. Such estimations on evaporation-induced concentration gradient and critical boundary for the concentrationdependent fcc/bcc transformation interpret well the exclusive formation of the two single superlattices at concentrations above 4C (bcc) and below 1C (fcc), and their simultaneous nucleation and final coexistence at concentration in the range of 1C−4C. Once the dispersing solvent was replaced with hexane or chloroform, only a single bcc superlattice was observed. Lack of the concentration-mediated superlattice change in the observed critical concentration range of 1C−4C (Figure 3) in toluene indicates the existence of a solvent-related effect on NC

Figure 1. Electron microscopic and X-ray scattering characterizations of the synthesized PbS nanocrystals (NCs): (a) typical transmission electron microscopy (TEM) image; (b) high resolution TEM (HRTEM) image with inset demonstration of single NC along (111) orientation; (c) wide-angle X-ray scattering (WAXS) pattern showing the atomic structure of PbS NCs in (d) a face-centered cubic lattice.

reveals that PbS NCs have an average diameter of 7.5 nm. Individual NCs display a truncate shape with surface terminations of six {100} and eight {111} facets (inset Figure 1b and S1).44 A typical WAXS pattern shows that individual NCs crystallize in a cubic rocksalt-type structure (Fm3m) with a unit cell constant of 5.942 Å (Figure 1c,d). Concentration-Mediated NC Assembly and Its Dependence on Solvent Type and NC Solubility. The toluene solutions with variable concentrations of PbS NCs were drop-cast on Kapton tapes to exploit the concentrationmediated NC assembly. Figure 2a presents several typical SAXS patterns of assembled superlattices controlled at concentrations of NCs in toluene from 0.3C to 8C (1C = 17.5 mg/mL). NC assembly displays a noticeable concentration-mediated nucleation of superlattice, which determines the final symmetry of assembled superlattice. When NC 14478

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an expense of smaller ones dissolving in solutions. To examine whether such a nucleation and growth mechanism undertakes similarly in NC assembly and also examine whether a superlattice transforms to others along with continuous growth of the early nucleated grain, a small amount of NC-dispersed toluene solution was filled into a glass capillary to monitor the developments of superlattice grain and structure symmetry. Upon evaporation of solvent from vertically positioned capillary (Figure 5a), the superlattice started an early nucleation at the

Figure 3. Schematic demonstration on the concentration-mediated superlattice formation of NCs in various dispersing solvents which include toluene, hexane and chloroform.

assembly. In comparison with toluene, both hexane and chloroform have a reduced NC solubility, implying the occurrence of NC saturation in the two solvents at a lower concentration. As a result, it is reasonable and understandable to observe only a single bcc in the hexane and chloroform solutions, while NC concentration falls into the same range as those studied in toluene. This also explains well the formation of the bcc superlattice in the air-aging NC solutions, because an oxidization-induced loss of surface ligands takes place, and thus causes significant reduction of NC solubility in solvent.40,44 The solvent evaporation rate plays a significant role in the nucleation and growth of various superlattices, such as grain size and superlattice crystallinity.25,46 To examine whether the solvent evaporation rate does affect the superlattice symmetry, the NC-dispersed toluene solutions with NC concentrations of 4C and 1C were sealed in two separate glass vials for a slow NC assembly. The superlattices collected from the two glass vials have a bcc and fcc structure, respectively, (Figure 4) consistent

Figure 5. Evaporation-induced assembles of PbS NCs dispersed in toluene with concentrations of 4C and 1C, respectively. Insets show the superlattice-growing capillaries and observed assembly features (a) and corresponding SAXS images of NC superlattices assembled from 1C (b and c) and 4C (d and e) solutions. Note: panels b and d present typical SAXS images of NC assembles located at the top gray area, whereas panels c and e show SAXS images of NC assembles located at the bottom dark area inside the capillary tubes. Figure 4. Scanning electron microscopy (SEM) imaging of assembled superlattices made by slow evaporation of toluene dispersing solutions of PbS NCs: (a) face-centered cubic (fcc) superlattice made with 1C solution; and (b) body-centered cubic (bcc) superlattice made with 4C solution. Note: 1C = 17.5 mg/mL.

capillary top. Upon subsequent recess of solvent level, a portion of grains were dried and left on the capillary wall, whereas the others remained suspending in solutions and thus served as a series of superlattice seeds to grow continuously. Eventually, the superlattices on the wall displayed gradual increases of both grain size and thickness from the top to bottom of the capillary, as visualized with a distinct color change from light gray to dark black (Figure 5a). SAXS characterization revealed that the NC superlattices assembled from 1C and 4C solutions in the two separate capillaries have a single fcc and bcc phase, respectively (Figure 5b−e). Such observations indicated that the nucleation and growth of both fcc and bcc superlattices depends largely on the concentrations of the starting NC solutions, but continuous growth of these grains as the primary seeds does not change their original superlattice symmetries. Based on the CNT, it is understandable that the lately nucleated secondary superlattice grains at increased concentrations are relatively smaller and

with the observations in thin films controlled with the two correspondingly identical concentrations under rapid evaporation conditions. Such consistent observations of assembled superlattices exclude the possibility for an evaporation rate induced effect on superlattice symmetry. Therefore, the superlattice symmetry of large 3D assembly is solely determined by a concentration-mediated nucleation of superlattice at the early stage of NC assembly. Seed-Mediated Growth of Superlattice. In the case of atomic crystal, the classical nucleation theory (CNT) suggests the early nucleation of large number of small nuclei seeds.47 Therefore, a fraction of larger nuclei seeds continue to grow at 14479

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Journal of the American Chemical Society have larger surface energy, and the resultant structural instability favors a subsequent dissolving of these secondary small grains, which serve as additional source to support continuous growth of the energy-favored large and primary grains which are early nucleated and still remain suspending in solutions. Fast Drop-Casting Resultant 2D Superlattice. In order to obtain straightforward evidence of how both the fcc and bcc superlattices started a nucleation at the early stage, TEM was employed to make snapshot of the local structures of dropcasting resultant fast NC assembly. Two thin films were prepared by drop-casting the toluene-dispersing 1C and 4C NC solutions onto the two separate TEM copper grids to produce fcc and bcc, respectively (Figure 2a and Figure 6). Typical

Figure 7. SAXS patterns of the two NC-assembled superlattices as a function of temperature: (a) body-centered cubic (bcc), and (b) facecentered cubic (fcc) superlattices. Note: dark squares and red diamonds represent indexed peak positions of fcc and bcc, respectively.

SAXS patterns of bcc (Figure 7a) and fcc (Figure 7b) superlattices upon increase of temperature from 25 to 200 °C. The two superlattices display a similar temperaturedependent volumetric shrinkage, which is shown by a noticeable shift of SAXS peak positions to large q in Figure 7. The fcc remains stable to the peak temperature of 200 °C (Figure 7b), whereas the bcc starts a thermally driven superlattice transformation to fcc at a temperature of 175 °C (Figure 7a). A thermal energy of 0.5kT is required to catalyze such a bcc-to-fcc superlattice transformation. However, previous study on 3.5 nm PbS NCs revealed a reversed superlattice transformation, in which thermal treatment or long-term aging in air caused an fcc-to-bcc superlattice transformation.25 Basically, individual NC can be treated as a typical core/shell structure, which includes a hard inorganic inner core and a soft surface-decorating organic molecular shell.27 Without additional exchange of surface coating molecule, a smaller NC is indeed reflected only by a decrease of inner hard core without any change of the thickness of soft molecular shell. Therefore, the resultant relative increase of soft molecular shell component in individual NCs dramatically enhances the intermolecular interactions, which overplay the direct intercore interactions to induce a reversed superlattice transformation in small PbS NCs.25 An overall analysis of collected data sets with reasonable correlations of experimental observations under multiple controls allows improved understanding of the superlattice phase diagram and associated nucleation and growth mechanisms. Upon dispersing of NCs in a good solvent such as toluene, if NCs in solvent have a low concentration, the large fraction of space around individual NCs allows surface coating molecular chains to radiate straightly out so that the NC core/ ligand entities act much like a series of hard spheres. Based on the hard sphere packing theory that suggests the formation of close-packing structure (such as fcc), the hard sphere-like PbS NCs in a dilute solution prefer a formation of the fcc superlattice, which not only holds the high packing fraction of 74% but also maximize the positional (configurational/ translational) entropy. Upon increase of NC concentration in solution, NCs are locally jammed so that the shape begins to play a significant role. Therefore, a rational alignment of NCs through their flat surface facets starts to play, and the resultant

Figure 6. Transmission electron microscopy (TEM) characterization of drop-casting resultant assembles of PbS NCs from dilute and concentrated solutions of (a) 0.3C with (111) hexagonal and (110) rectangle planes of fcc and (b) 4C with (100) square planes of bcc, respectively.

TEM images revealed the dominant features of 2D lattices with (111) hexagon and (110) rectangle in fcc film and (100) square in bcc film (Figure 6). In an fcc lattice, (111) and (110) represent the two densest packing planes (Figures 6a and S5), so the observation of these two dense planes indicates that the positional (also called as configurational or translational) entropy plays a governing role in the formation of the fcc superlattice. In the bcc film, the observation of an unexpected less dense (100) square lattice (Figures 6b and S6) rather than the densest packing (110) rectangle suggests different type of driving forces to guide the nucleation and growth of the bcc superlattice. Unlike the close packing fcc lattice that has a high packing fraction of 74%, bcc appears as a typical open structure with a reduced packing fraction of 64%. If only the NC inner cores are counted in calculation, the packing faction of NCs in bcc is dramatically reduced to 33%.48 Previous work observed a highly ordered bcc superlattice made up of Pt3Ni octahedral NCs, which displays coherence of both NC translational and atomically orientational orderings.48 In situ SAXS/WAXS measurements of single supercrystal under elevated temperatures evidently revealed the governing role of the rotational entropy in the formation of bcc superlattice. PbS NC with an intermediate size of 7.5 nm has a truncate surface (Figure 1b), in which eight (111) facets of surface terminating facets make PbS NC to display octahedron-like behaviors (Figure S1). Therefore, it is most likely that the rotational entropy plays a similar role in the nucleation and growth of bcc superlattice in PbS NC system as well.48 Temperature-Dependent Superlattice Transformation. Thermal treatment was made to explore the temperature-induced effect on the structural stability and transformation of NC-assembled superlattice. Figure 7 shows several 14480

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simultaneous nucleation and ultimate coexistence of fcc and bcc within a concentration range of 17.5−70 mg/mL. The early nucleated superlattice grains serve as a series of supercrystal seeds, which remain in original lattice symmetry and continue to grow into a large supercrystal. Replacement of solvent with hexane or chloroform and control of NC concentration within the observed critical range in toluene allow for harvesting only a single bcc superlattice phase. The dependence of superlattice on concentration and solvent type is eventually ascribed to difference of NC solubility between various solvents. In the fast-growing 2D thin film, the local structures are dominated by the (111) hexagon and (110) rectangle in fcc and the (100) square in bcc. Taking into account the dense packing planes in different lattices, the observation of the above 2D lattices indicates that the nucleation and growth of bcc and fcc are governed by the positional and rotational entropic forces, respectively. Thermal treatment does not change the fcc to the peak temperature of 200 °C, but transforms the bcc into an fcc at 175 °C. These experimental observations and structural correlations not only shed lights into the nucleation and growth of various superlattice polymorphs but also provide quantitative definition of experimental tuning parameters to design and fabricate desired superlattices with newly manifested properties.

increase of free space causes an increase of directional entropy.23 In the case of octahedron-like truncate PbS NCs, the reduction of the facet−facet distance is impeded by the large length of individual NCs along the tip direction,48 but an additional contribution can be reasonably made by a free rotation of NC along the tip axis. As a result, the increase of rotational entropy compensates the loss of positional entropy toward the formation of a less-dense bcc superlattice. At the early stage, the two concentration-mediated superlattice polymorphs of fcc and bcc nucleate from the solutions with different starting NC concentrations, which are below and above the critical concentration boundary. However, the evaporation-induced local concentration gradient always results in the coexistence of both bcc and fcc in a certain range of concentrations near the critical boundary. In this typical PbS NC system in toluene, the combination of estimated critical concentration of 2.5C and local gradient of 1.5C allows for the observation of single fcc and bcc at concentration above 4C and below 1C, respectively, and simultaneous nucleation of the superlattices and their coexistence between 1C and 4C. Upon continuous growth, the two superlattices retain no change of lattice symmetry and ripen into large 3D superlattices. During this growing process, the change of NC concentration can also trigger additional nucleation of superlattice. However, unlike the simultaneous nucleation at the early starting stage, the lately nucleated secondary grains are relatively smaller and have much higher surface energy than the early nucleated primary grain. The classical nucleation theory favors their quick dissolving in solution, providing NC sources to the early nucleated large primary grains suspending in solutions to grow continuously. However, at the early growth stage, if thin 2D or small 3D superlattice suffers a uniaxial compressive stress, certain degrees of NC alignment through flat surface facets takes place and accordingly causes a shapemediated variation of superlattice, such as a shape-induced bcc superlattice.39,40,49 For example, the fcc-to-bcc superlattice transformation observed in thin film can be interpreted by an evaporation-induced compression stress normal to the substrate.39 However, while the superlattice is thermally treated, the additional contribution of thermal energy activates NCs and causes an increased ratio of translational (positional or configurational) disordering, which accordingly induces a bccto-fcc superlattice transformation. It is obvious that rational controls of NC concentration and shape allow one to achieve fabrication of desired superlattices by design.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b06908. Additional data sets include figures, 2D SAXS images and integrated 1D SAXS patterns, TEM images and superlattice information (PDF)

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Zhongwu Wang: 0000-0001-9742-5213 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We appreciate technical support from CHESS staff and constructive discussions with several colleagues across Cornell campus. CHESS is supported by the NSF award DMR1332208. This work is partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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CONCLUSIONS We synthesized a large quantity of PbS NCs with an average size of 7.5 nm in a single batch, delicately regulated variables of NC concentration/solubility, solvent type, evaporation rate, seed mediation and thermal treatment, and systematically exploited NC assembly and developed superlattices as well as underneath mechanisms. The NC assembly displays a NC concentration-mediated nucleation and growth of superlattice, in which the resultant superlattice polymorph depends on the concentration of NCs in the starting solutions. As toluene is used as a dispersing solvent, the two single high symmetry superlattices of fcc and bcc nucleate exclusively from the solutions at concentrations ≤17.5 and ≥70 mg/mL, respectively. The critical point for the concentration-induced fcc/bcc superlattice transformation is estimated approximately at 43.75 mg/mL (2.5C), and the evaporation-induced local concentration gradient of 26.25 mg/mL (1.5C) results in a

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REFERENCES

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DOI: 10.1021/jacs.7b06908 J. Am. Chem. Soc. 2017, 139, 14476−14482

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DOI: 10.1021/jacs.7b06908 J. Am. Chem. Soc. 2017, 139, 14476−14482