Letter pubs.acs.org/JPCL
Formation of Epitaxially Connected Quantum Dot Solids: Nucleation and Coherent Phase Transition Kevin Whitham† and Tobias Hanrath*,‡ †
Department of Materials Science and Engineering, and ‡Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United States S Supporting Information *
ABSTRACT: The formation of epitaxially connected quantum dot solids involves a complex interplay of interfacial assembly, surface chemistry, and irreversibledirected attachment. We describe the basic mechanism in the context of a coherent phase transition with distinct nucleation and propagation steps. The proposed mechanism explains how defects in the preassembled structure influence nucleation and how basic geometric relationships govern the transformation from hexagonal assemblies of isolated dots to interconnected solids with square symmetry. We anticipate that new mechanistic insights will guide future advances in the formation of high-fidelity quantum dot solids with enhanced grain size, interconnectivity, and control over polymorph structures.
subject to ongoing debate. The formation of QDSs at fluid interfaces involves a complex interplay of assembly, desorption of the stabilizing ligands, and directed assembly to form epitaxial interdot bonds. Experimental protocols for the formation of high-quality SLs in which constituent quantum dots are registered to within a single atomic bond length have been established;15,17 however, significant gaps persist in our fundamental understanding of several aspects of the underlying mechanism by which these structures form. Astonishingly, the irreversible attachment of proximate particles through mutually exposed “sticky {100} facets” occurs in a manner that enables the formation of structures with atomic coherence with micrometer-sized grains. A recent in situ X-ray scattering study by Geuchies et al.22 revealed that the formation involves a sequence of transformations from a hexagonal CQD monolayer through a pseudohexagonal intermediate and finally a simple square lattice. However, the basic mechanism by which O(104) irreversible attachments are coordinated to form a long-range superstructure remains an outstanding question. In this Letter, we present the hypothesis that the transformation mechanism can be described as a coherent phase transition with distinct nucleation and propagation steps. Specifically, we postulate that the transformation is nucleated at defects (voids or grain boundaries) in the preassembled SL. Transmission electron microscopy (TEM) snapshots acquired during the transformation process provide several lines of evidence in support of the proposed model. We find that QDS grains are formed at grain boundaries
T
he directed assembly of nanoscale building blocks into complex superstructures is of widespread scientific and technological interest. Scientists and engineers have been intrigued by the prospects of tailoring self-assembly processes to create materials whose properties and function can be tuned through the interaction between constituent particles.1,2 During the past decade, research interest in self-assembly has received a significant boost from the availability of colloidal quantum dot (CQD) building blocks with precisely engineered size, shape, and composition.3,4 Concurrent advances in self-assembly and the growing library of available CQDs have created a fertile opportunity space for bottom-up solution strategies with important implications for a broad spectrum of technologies. Several reviews have captured the exciting prospects of this emerging class of metamaterials5 in fields spanning catalysis,6−8 electronic,9,10 thermoelectric,11,12 magnetic,13 and photovoltaic14 applications. Recent reports of epitaxially connected CQD superlattices (SLs) with long-range atomic coherence15−17 have generated significant interest as a platform for novel, quasi-2D “designer materials”.18 Calculations of such materials with a dimensionality of less than 2 forecast a rich electronic structure (including topological states and Dirac cones) that profoundly differs from the corresponding 2D quantum well.19−21 For clarity, we delineate between individual building blocks as CQDs, their assemblies as colloidal quantum dot assemblies (CQDA), and superstructures of epitaxially connected dots as quantum dot solids (QDSs). Several QDS polymorphs have been demonstrated, primarily simple square and honeycomb SLs,16 which are predicted to exhibit profoundly different electronic properties.20 Moreover, the physicochemical interactions and mechanism guiding the formation of specific polymorphs are © XXXX American Chemical Society
Received: April 7, 2017 Accepted: May 22, 2017 Published: May 22, 2017 2623
DOI: 10.1021/acs.jpclett.7b00846 J. Phys. Chem. Lett. 2017, 8, 2623−2628
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The Journal of Physical Chemistry Letters
Specifically, we need to consider (i) the solvent evaporation rate, (ii) CQD diffusion from bulk to the interface, (iii) twodimensional nanoparticle (NP) diffusion on the liquid−gas and liquid−liquid interface, and (iv) recession of the vapor−liquid interface. In the case of isolated NP assemblies, these processes can be tailored to yield high-quality (i.e., large grain) monolayer assemblies, as illustrated, for example, by the work of Bigioni et al.36 The phase behavior and structural evolution of 2D SLs of isolated CQDs at the liqud−air interface was beautifully captured by experiment and KTHNY (Kosterlitz−Thouless− Halperin−Nelson−Young) theory in a recent report by Jiang et al.30 Building on previous reports of interfacial self-assembly, we found that an equilibration time of approximately 20 min is required to form high-quality SLs.15,17,31 Physicochemical processes of CQDs assembled at the fluid interface are summarized in Figure 2b. It is important to recognize that surface-bound ligands are in dynamic equilibrium with the surrounding fluid; this equilibrium is dependent on the chemical composition of the inorganic core and the organic shell.32−34 For example, NMR experiments by Hens and Martin have estimated the exchange rate of amine-based ligands to be on the order of 50/s.35 Oleic acid (OA) ligands
of the initial CQDA. We describe the mechanism in the context of an isochoric transformation from the initial assembly and the connected superstructure and discuss implications on the formation of other SLs, for example, the epitaxially connected honeycomb superstructures. The question at the heart of this Letter is the basic mechanism by which the preassembled CQDS transforms into the epitaxially connected QDS. The transformation illustrated in Figure 1 looks ostensibly simple at first sight, but closer
Figure 1. Transformation from (a) the hexagonal assembly of isolated CQDs to (b) a simple square, epitaxially connected QDS. The scale bar in the corresponding TEM images is 50 nm.
inspection reveals that the constituent CQD building blocks need to undergo coordinated changes in position and orientation before they are “locked” in their final lattice site by irreversible attachment with neighboring particles. TEM images taken before and after the transformation show that the interparticle spacing is reduced to the point where proximate particles touch. More specifically, neighboring particles are epitaxially connected through their {100} facets, as described in previous reports.16,17,23,24 Remarkably, the translation, orientation, and irreversible attachment of thousands of CQDs can be coordinated nearly error-free to enable the formation of epitaxially connected QDSs with micrometer grain sizes. Experimentally, the directed assembly and attachment is performed at fluid interfaces. In a typical experiment, the dispersion of CQDs (e.g., in this case, oleate-capped lead salt PbSe CQDs in hexane) is spread across an immiscible liquid subphase (e.g., ethylene glycol, EG). From a practical perspective, earlier studies25−27 of interfacial self-assembly has illustrated two key advantages: (i) uniform CQD layers can be readily formed over large areas (cm2) and (ii) the assembled structures are sufficiently robust to enable their transfer to solid supports (e.g., substrates with contact electrodes). Dong et al.28 demonstrated that these principles can also be applied to assemble more complex binary assemblies. A third advantage that emerged from more recent studies16,17,22,29 is that processing at fluid interfaces is also readily integrated with chemistry treatments to modify the nature of the ligand shell surrounding the particles. Self-assembly of CQDs at fluid interfaces is a process by which the three-dimensional CQD suspension becomes a quasi-two-dimensional (2D) film at the fluid interface.
Figure 2. Physicochemical processes at the fluid interface play a critical role in the irreversible attachment of proximate CQDs. (a) Schematic illustration of how the introduction of the chemical trigger (CT) (e.g., ethylene diamine) leads to the formation and desorption of metal chelation complexes that in turn render the deprotected CQD surface “sticky” to fuse with a proximate particle. (b) Illustration of two particles at a fluid interface forming an epitaxial interdot bond. (c) Oblique view of the assembly at the fluid interface illustrating interfacial transport of a CT to the reactive site and a product from the reactive site. Mass transport near defects (i.e., voids in the SL) is enhanced. 2624
DOI: 10.1021/acs.jpclett.7b00846 J. Phys. Chem. Lett. 2017, 8, 2623−2628
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that that irreversible attachment between O(104) CQDs either uniformly (in space and time) or stochastically seems highly unlikely to lead to the formation of micrometer-sized singlegrain structures observed in experiments.15−17 An alternative hypothesis, proposed in this Letter, is that the transformation proceeds by a coherent phase transformation defined by distinct nucleation and growth steps. Analogous to solid-state phase transformation in atomic crystals,36 we expect that defects (e.g., voids or grain boundaries in the preassembled lattice) play a critical role in nucleation events. We propose that the nucleation is enhanced by two effects, a kinetic effect of mass transport and a thermodynamic effect of the energy change associated with rotation and translation of the CQD. Vis-à-vis the interfacial transport processes discussed above (Figure 2c), we argue that transport to and from the CQD surface is enhanced near defects because the local environment is less “crowded” by CQDs and their surface-bound ligands in the interstitial volume of the preassembled film. From a thermodynamic perspective, a CQD near a defect would be easier to change from a “bound” state to a “free” state. Interdot “binding” here refers to ligand−ligand interactions between proximate CQDs; particles near the defect will have fewer than eight interacting nearest neighbors. Direct experimental validation of how the phase transformation nucleates and grows is complicated by the fact that in situ TEM characterization is limited to particles in a thin homogeneous liquid37,38 or on the surface of a film.39,40 Probing the nucleation via in situ GISAXS is challenging because the large sampling volume (defined by the intersection of the beam with the sample) precludes the spatial isolation of a single nucleation event. To study how defects in the preassembled SL influence the nucleation of the CQDA-toQDS transformation, we analyzed TEM images of sample films prepared midway through the transformation. Figure 3 illustrates low- and high-magnification images of a polycrystalline, multilayered assembly. We previously showed that the epitaxially connected films can be formed at thicknesses up to 10 layers.17,41 In the discussion below, we focus on multilayer assemblies. TEM snapshots of similar transformations in monolayer films are provided in the Supporting Information. For clarity, we differentiate between the crystallographic orientation of the SL and the atomic lattice (AL) of the constituent particles. The preassembled CQDA exhibits a bodycentered cubic (BCC) symmetry with the {110}SL and {110}AL planes oriented parallel to the plane of the interface (see the Supporting Information). The epitaxially connected QDS is a simple cubic (SC) structure in which {100}SL and {100}AL align parallel to the interface. Analysis of the phase transformation from a “polycrystalline” SL supports the proposed nucleation and growth mechanism. In Figure 3b, three unconnected SL grains are separated by two connected SL grains. Each unconnected SL grain has a unique orientation, thus creating grain boundaries at their intersections. It is clear that the connected SL grains are located at the boundaries where the unconnected grains intersected. The transformation of an unconnected SL to a connected SL propagates in a crystallographic direction. The interface between unconnected and connected phases is shown in Figure 3d. The {110}SL plane is the boundary between the preassembled BCC CQDA and the connected SC QDS. Quantitative analysis of the lattice constants (a) reveals a ratio of aCQDA/aQDS = 1.27. The underlying relationship between lattice constants of the CQDA and the QDS can be described
bound to the surface of CQDs will thus gradually detach and dissolve into the EG subphase. If stabilizing ligands are lost during the initial assembly stage, deprotected particles can irreversibly attach upon close approach, which significantly disrupts the particle mobility required to form high-quality (i.e., long-range) defect-free SLs. Fortunately, premature interdot attachment can be prevented by adding a small amount of OA into the EG subphase;17,29 this modification eliminates ligand desorption and thereby affords the assembling CQDs sufficient time to find their equilibrium lattice site in the SL. Temporally decoupling the assembly and attachment into two sequential steps simplifies the processing challenges and transfers the high degree of order in the preassembled CQDA to the final structure. Once the stable SL is formed, the interparticle attachment can be deliberately induced by introducing a chemical trigger (CT) to displace the native oleate (X-type) ligand. One method for chemical displacement of the X-type ligands is to introduce L-type (neutral electron donor) ligands. The L-type ligand coordinates with a surface metal atom (M) bound to two carboxylates (X) to displace L− MX2 from the surface (Figure 2). Anderson et al.33 classified the equilibrium constants for the displacement reaction 2L + NC−MX2 ⇆ L−MX2 + NC−L of various L-type ligands. Small alkyl amines and diamines most readily displaced ligands from lead and cadmium chalcogenide CQDs, while fewer ligands were displaced by larger diamines, alcohols, trialkyl amines, and trialkyl phosphines. A recent study by Walravens et al.29 reported that the ligand displacement potency of the CT (parametrized by pKb of the amine) plays a critical role in transformation of the structure. Interfacial transport processes associated with the formation of these surface complexes and the particle attachment are likely to play a critical role. As illustrated in Figure 2, the competing dynamics of several concurrent processes must be considered, specifically, (i) CT diffusion through the bulk EG subphase, (ii) CT diffusion through the CQD film, (iii) formation and detachment of the interfacial metal chelation complex (CT−Pb(OA)2), (iv) diffusion of the CT−Pb(OA)2 complex from the film into the subphase complex, and (v) irreversible formation of epitaxial bonds between mutually exposed {100} facets of neighboring particles. The {100} facets are stoichiometric and likely coordinated by lead oleate. As schematically illustrated in Figure 2a, the ligand displacement likely involves the formation of the metal chelation complex (CT−Pb(OA)2). In light of the fast ligand exchange rates discussed above,35 the overall process is unlikely to be limited by the formation and detachment of the CT−Pb(OA)2. Instead, we expect rate-limiting steps to be defined by interfacial transport of the CT to, or metal chelation complex from, the site of interdot attachment. Having laid out the interplay of interfacial physicochemical and transport processes involved in the CQDA-to-QDS transformation, we now turn our attention to the underlying mechanism. The elementary transformation mechanism must describe not only the translation, rotation, and oriented attachment of the constituent particles but also how this transition is initiated in the first place. In the context of the propagation of oriented attachment through the film, is it important to note that a single “incorrect” attachment could significantly disrupt the long-range order of the QDS. One hypothesis is that the entire film uniformly transforms from a hexagonal assembly to a square assembly followed by interparticle attachment. A challenge for this hypothesis is 2625
DOI: 10.1021/acs.jpclett.7b00846 J. Phys. Chem. Lett. 2017, 8, 2623−2628
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schematically in Figure 4. In the first stage, CQDs assemble at the fluid interface in a hexatic arrangement without preferred orientational ordering of the AL of the constituent particles. The density of ligands on the surface of the polyhedral CQD decreases from left to right in Figure 4. The effect of reduced ligand coverage upon lowering the inter-CQD spacing is most pronounced in the first stage of the process. The progressive displacement of ligands from the CQD surface reduces the inter-CQD separation, which has significant implications on the nature of the inter-CQD interactions. Whereas CQDs with a well-solvated ligand shell of CQDs in the initial hexatic assembly can be described as “soft spheres”,42 reduced ligand coverage and concomitant shorter interparticle separations introduce nonisotropic interactions due to the facet-specific ligand coverage and shape of the particle. In the second stage, the hexatic arrangement is transformed into a rhombic arrangement in which constituent CQDs are oriented with {110}AL parallel to the fluid interface. This hexatic-to-rhombic transformation is the 2D analogue of the FCC−BCC Bain transition previously reported in 3D PbSe CQDA.42,43 The rhombic lattice shown in Figure 4 is the 2D analogue of the 3D BCC lattice shown in Figure 3. The oleate binding energy is facet-specific and increases in the order {100}AL < {110}AL < {111}AL.44 Consequently, the deprotection of specific CQD facets proceeds in this order, as is schematically illustrated by the left-to-right gradient of the optical density of the ligand coverage on blue {100}AL, green {110}AL, and red {111}AL facets. During the second stage, the interparticle separation in the 2D rhombic or 3D BCC is gradually shortened as the ligand coverage is reduced.43 The transition from the second to third stage of the mechanism illustrated in Figure 4 is defined by the interface coherence criterion (c = 21/3a) (Figure 3e). A basic geometric model (detailed in the Supporting Information) shows that the onset of this criterion is defined by a critical ligand shell thickness. During the third stage of the transformation, the coarse registry of CQDs to their square lattice sites is guided by two factors: (1) the truncated cubic shape of the CQDs and (2) the van der Waals interactions between remaining ligands on {111}AL facets of neighboring particles. Several previous studies have described how patchy ligand coverage influences the anisotropic interaction potential between colloidal particles in an assembly.43,45−50 The final stage in the transformation is defined by the irreversible formation of interparticle bonds. Following the coarse particle registry in stage iii, neighboring particles must now align with atomic precision to enable formation of defectfree epitaxial interdot bonds. Previous studies of similar “oriented attachment” described a mechanistic sequence of particle alignment followed by atomic attachment (interface elimination).37,51 In the specific case of the PbSe QDS shown
Figure 3. TEM images of the coherent CQDA-to-QDS transformation. (a) Low-resolution TEM image of a polycrystalline CQDA. (b) TEM image of three distinct BCC grains with QDSs forming at the grain boundaries. The coloration of the grains in the high-resolution TEM image is related to the coloration in the lowmagnification image. The coloration in part a,b is based on electron diffraction from the atomic lattice and Fast Fourier transform analsyis of the superlattice, respectively. (c,d) Magnified views of the BCC/SC interface illustrating the lattice coherence along the {110}SL planes. (e) Illustration of the coherent interface model in which the SC and BCC lattice constants are related through c = 21/3a.
through a simple geometric model (detailed in the Supporting Information). We note that the experimentally observed ratio of lattice constants stands in good agreement with the ratio of 21/3 = 1.26 that would be expected for an isochoric transformation. As a result of the coherence predicted by the simple isochoric model, the BCC SL can transform into the SC structure with minimal strain or lattice defects. The mechanism of the CQDA-to-QDS transformation can thus be summarized as a four-stage process, illustrated
Figure 4. Schematic illustration the four-stage mechanism of the CQDA-to-QDS transformation. 2626
DOI: 10.1021/acs.jpclett.7b00846 J. Phys. Chem. Lett. 2017, 8, 2623−2628
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The Journal of Physical Chemistry Letters in Figure 4, this process involves a surface reconfiguration39,52 to form interdot bonds to connect mutually exposed {100}AL facets of neighboring CQDs. In summary, we describe the mechanism by which an isolated NP assembly is transformed to an epitaxially connected quantum dot in the context of a coherent solid-state phase transition with distinct nucleation and growth stages. Defects in the preassembled SL provide nucleation sites for the transformation. The transformation propagates along a coherent phase boundary, which can be described by a simple geometric model based on an isochoric transition. The mechanism described in this Letter provides insight into concurrent changes in CQD position and orientation during the transformation. We identified a coherent interface criterion that enables the transformation to proceed with minimal strain or lattice defects. We expect that the transformation along a pathway with minimal strain has important implications on the creation of QDS with extended long-range ordering. We hope that this mechanistic model provides helpful guidance to future advances of controlling transformations in self-assembled structures.
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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/acs.jpclett.7b00846. Additional TEM images of QDS monolayers, structure analysis of CQDA−QDS transitions, grain boundaries in QDS, and a facet-specific ligand coverage model (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Tobias Hanrath: 0000-0001-5782-4666 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported by the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1120296). T.H. and K.W. acknowledge support from NSF-DMR 1056943. We thank Fernando Escobedo for valuable discussions.
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DOI: 10.1021/acs.jpclett.7b00846 J. Phys. Chem. Lett. 2017, 8, 2623−2628
