DOI: 10.1021/cg100601a
Structural Investigation of Three-Dimensional Self-Assembled PbS Binary Superlattices
2010, Vol. 10 3770–3774
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Davide Altamura,† Michela Corricelli,‡,§ Liberato De Caro,† Antonietta Guagliardi,† Andrea Falqui,^ Alessandro Genovese,^ Andrei Y. Nikulin, M. Lucia Curri,‡,§ Marinella Striccoli,‡,§ and Cinzia Giannini*,† Istituto di Cristallografia (IC-CNR), via Amendola 122/O, 70126 Bari, Italy, ‡IPCF-CNR Bari, c/o Department of Chemistry, Via Orabona 4, I-70126 Bari, Italy, §Department of Chemistry, University of Bari, Via Orabona 4, I-70126 Bari, Italy, ^Fondazione Istituto Italiano di Tecnologia (IIT), via Morego 30, 16163 Genova, Italy, and School of Physics, ARC Centre of Excellence for Coherent X-ray Science, Wellington Road, Monash University, Victoria 3800, Australia )
†
Received May 6, 2010; Revised Manuscript Received June 3, 2010
ABSTRACT: Three-dimensional binary superlattices were obtained by self-assembly of PbS nanocrystals (NCs) of size e4 nm, synthesized by colloidal chemistry routes and characterized by two distinct and narrow size distributions. The resulting binary superstructures have been imaged by small- and wide-angle X-ray diffraction (XRD), and by transmission electron microscopy (TEM). The combined use of such investigation techniques allowed retrieval of crystalline structure, size, and shape of the PbS NCs, along with their spatial arrangement in the 3D architecture. A detailed analysis of the wide-angle XRD data, based on the Debye approach, demonstrated an elongated shape of NCs even smaller than 2 nm and provided a lower limit for the effective NC size, to be compared with results from TEM. The careful interpretation of small-angle XRD data demonstrated the ordered arrangement of NCs perpendicularly to the substrate plane and, together with TEM observations, allowed retrieval of the 3D structure of the assembly. Moreover small-angle XRD is shown to contain peculiar features related to the size distribution of the NCs and the degree of order in the assembly. Such a highly detailed structural analysis, averaged over large volumes of the investigated material, can hardly be obtained even by sophisticated high-resolution TEM.
Introduction In recent years, a variety of superlattices have been made by self-assembly of colloidal nanocrystals (NCs) of different type, size, and surface functionalization.1-4 The interest in superlattice fabrication is mainly due to the enhancement of the nanoparticle properties and to new collective properties arising from the interaction between different nanocrystals.5 Many different applications of self-organized systems are indeed expected, including solar cells, light emitters, and transistors, provided that a precise control of the 2D or 3D assembled structures is achieved.6 As a consequence, suitable characterization techniques are needed to reliably identify the numerous different and relevant features of such materials. The material characterization is here proposed at two hierarchic levels, through the determination of size and shape of the nanocrystalline building blocks and of their spatial arrangement in the superstructure. In particular, small- and wide-angle X-ray diffraction (XRD), and transmission electron microscopy (TEM) are exploited to image structure and morphology of binary superlattices made of self-assembled PbS nanocrystals (NCs) with two distinct size populations (approximately 2 and 4 nm, as derived by TEM analysis). Due to the peculiar features and broad potential range of applications6-12 of lead sulfide NCs, selfassemblies of PbS NCs are indeed extremely valuable systems to be studied for a deep understanding of both geometrical characteristics and final functional properties of self-organized structures. Furthermore, to the best of our knowledge, NC sizes below 3 nm are the smallest reported so far for self-assemblies. *Corresponding author. E-mail:
[email protected]. Phone: 0039080-592-9167. Fax: 0039-080-592-9170. pubs.acs.org/crystal
Published on Web 06/17/2010
In the case of such small crystals, high-resolution TEM (HRTEM) imaging is essential to directly determine size, shape, and crystalline structure, with the only drawback remaining intrinsically local. However, to image specimens containing a high NC concentration, even embedded into a matrix through high surfactant concentrations, HRTEM may find severe limitations due to the high scattering power of the surfactant, which covers the nanocrystal signal. Indeed, there is considerable scientific interest in developing new imaging approaches that, while still exploiting laboratory X-ray sources, may allow for nondestructive 3D reconstruction of the shape of nanoparticles sampled over large volumes of material.13 Concerning the structural order of the self-organized architecture, grazing incidence small-angle X-ray scattering (GISAXS) is another very powerful characterization tool, but it is not generally available for fast sample screening, because it usually requires high brilliance sources, such as synchrotron radiation or equivalent alternatives. The integrated approach here presented, based on advanced XRD data analysis, allowed detection of a 3D order in the NC self-assemblies, both in and out of the substrate plane. Specifically, the out of plane order in the assembly is demonstrated by the small-angle XRD pattern analysis, where the superstructure is modeled at a first approximation as a lamellar system consisting of closely packed PbS NCs. Moreover NCs of different size are shown to be arranged on alternating layers. On the other hand, TEM shows that a well-defined in-plane order is present in the lamellar layers of the assembly as well, within hundreds of nanometers size domains. Finally, wideangle XRD analysis shows that NCs have an elongated shape and a smaller size with respect to that deduced by TEM. Overall, a 3D structural image of the material is obtained. r 2010 American Chemical Society
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Figure 1. (a) TEM image; (b) Fourier transform of the sample imaged in panel a; (c) sketch of the proposed hexagonal NC assembly, with the highlighted unit cell.
Experimental Section Chemical Synthesis. The synthesis of PbS NCs, both monodisperse and bimodal in size distribution, has been carried out following a modified literature procedure,14,15 as reported in the Supporting Information. The smaller PbS NCs are sized less than 2 nm, while the larger ones have a size of about 4 nm, as derived by TEM. After the synthesis, PbS NCs capped with oleic acid (OLEA) and trioctylphosphine (TOP) molecules result and are dispersed in toluene. Electron Microscopy. Colloidal NCs have been deposited by drop casting onto TEM carbon-coated copper grids. TEM observations have been carried out by a JEOL JEM 1011 microscope, operating at an accelerating voltage of 100 kV and equipped with a W electron source. The images have been acquired by a Gatan Orius SC1000 CCD camera. X-ray Diffraction. Colloidal NCs were deposited by drop casting both on miscut silicon substrates and TEM grids, in order to allow a direct comparison with the samples investigated by TEM. The superlattice formation was induced by slow solvent evaporation at room temperature and on a horizontally placed substrate. We also verified that superlattices were formed on both silicon and carbon grid substrates, featuring the same diffraction pattern independendently on the substrate. Small- and wide-angle XRD measurements were performed in coupled detector/sample scan mode (2θ/θ scans) on a D8 Discover diffractometer by Bruker, equipped with a G€ obel mirror, using CuKR radiation. A 2D reciprocal space map was also collected in forward scattering (fixed positions of source-sample-detector) by a NONIUS Kappa diffractometer for single-crystal analysis, employing a low noise and high sensitivity CCD.
Results and Discussion Two-Dimensional Packing of the NCs. TEM imaging provides information about in-plane size and spatial arrangement of the nanoparticles. Assemblies of PbS NCs of two different sizes with average diameters of 1.9 ( 0.2 and 4.1 ( 0.2 nm, measured in the plane parallel to the substrate surface (XY plane), are shown in the TEM image reported in Figure 1a. In the following, the two types of differently sized NCs will be referred to as A (small) and B (large) nanoparticles, respectively. Due to the intrinsic features of the 3D structure, a small degree of superposition between the 2D atomic projection of particles constituting different layers cannot be completely ruled out; for this reason, the mean diameters measured by TEM should be considered as the upper values. Images with a large field of view reveal the presence of several domains, hundreds of nanometers wide, in which NCs are arranged according to a well-defined symmetry and “stoichiometry”. Direct and Fourier transformed TEM images of a single domain, reported in Figure 1a,b, respectively, clearly show an in-plane hexagonal arrangement of NCs. In Figure 1c, the hexagonal basal plane is schematically represented. The highlighted region represents the in-plane repetition unit,
Figure 2. Wide-angle X-ray diffraction data and the corresponding simulation; simulations of diffracted intensity from A and B NCs are also separately shown, together with the expected diffraction pattern for a rock-salt cubic PbS powder.
that is, a hexagonal unit cell with lattice parameter a = 9.0 ( 0.2 nm, in which A and B particles are arranged according to a AB2 stoichiometry. The in-plane distance between a small particle (A) and its neighboring large particle (B) (or between two neighboring B particles) has been evaluated from TEM images and found to be 5.7 ( 0.3 nm. Since no reliable information about the actual shape of the nanoparticles can be retrieved by TEM analysis at such resolution, due to their extremely small size, the specimen was imaged by X-rays in the Fourier space (diffraction). The wide-angle XRD data, illustrated in the next section, provide evidence of nonspherical PbS nanoparticles. Accordingly, A and B particles were represented in Figure 1c by rods instead of spheres. Structure and Morphology of the PbS NCs. In Figure 2, the wide-angle X-ray diffraction data, collected by a superlattice realized from the solution containing a bimodal PbS NC size distribution, are shown together with the corresponding simulation. The experimental pattern was indexed by using the rock-salt cubic structure of PbS. However, discrepancies in terms of relative intensities of the diffraction peaks with respect to the bulk crystalline reference phase can be observed. In fact, the (111) reflection results more intense than the (200) one. In order to explain such a difference, simulations of the intensity of the diffraction signal from PbS NCs were performed for different NC size and shape. In the simulation, NCs have been built up by suitably stacking a few unit cells of rock-salt PbS crystal structure along the crystallographic directions; the diffracted intensity was calculated by using the Debye function.16,17 N X N X IðqÞ ¼ f i f j sinðqrij Þ=qrij ð1Þ i¼1 j¼1
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where q is the scattering vector length, fi (fj) is the scattering factor of the i (j) atom, and rij the distance between them. Such an approach allows the exact calculation of the diffracted intensity from a system consisting of N atoms, irrespective of the periodicity. The simulated diffraction pattern is in good agreement with the experimental result, as comes out from the precise match between the intensity and the width of the diffraction peaks of the calculated and experimental patterns. The simulated curve appears to properly reproduce the experimental diffraction profile only when a rodlike geometry is used to model the nano-objects. Conversely, when NCs are modeled according to an isotropic, spherical shape, a clear discrepancy between simulated and experimental data can be seen as shown in the supporting information. Experimental data and simulation, reported in Figure 2, show a good agreement by assuming rod-shaped nanoparticles, elongated in the (111) direction. Simulations for the two NC populations were summed with a weight factor of 1 or 2 for A or B NCs, respectively, according to the proposed stoichiometry of the superstructure (AB2). Good agreement has been found for a mean NC size of 1.28 nm along the a axis for both populations and of 2.10 and 3.12 nm along the c axis for A (small) and B (large) NPs, respectively. It is worth noting that the NC size, as derived by such an analysis, is underestimated with respect to the actual value, since the full width at half-maximum of the diffraction peak is generally affected by both size and strain contributions. Here, strain was neglected because the actual laboratory data statistics prevented optimization of the pattern simulation taking both size and strain modeling into account. On the other hand, the NP size derived by TEM analysis is an overestimation of the actual size. In fact, although the images are collected in bright field and the contrast can be mainly attributed to the NCs, it has to be pointed out that the preparation of the superlattice requires relatively high NC concentration (with respect to the typical concentration used for TEM investigations). Hence a high content of coordinating molecules surrounding the inorganic NC core is present. The extent of the surfactant contribution along with the packing of the NC in the meso structure, which finally results in the overall projection of the system, typically make more difficult the precise determination of the NC actual size. Wide-angle X-ray diffraction can represent therefore an alternative efficient tool to provide useful and reliable insight on the actual NC size and shape. Structure of the Self-Assembly. In this section, small-angle XRD analyses, which are exploited to investigate the superlattice structural order perpendicularly to the substrate plane, together with the results from TEM analyses, the latter giving information on the superlattice order in the substrate plane, are used to obtain a 3D reconstruction of the superlattice structure. The small-angle X-ray diffraction pattern is reported in Figure 3, featuring equally spaced peaks. These peaks can be indexed as (00l)-type reflections whose repeat distance d can be easily calculated as d = 2π/q1, being q1 the value of q = (4π/λ)sin θ of the first peak18 (which is equal to the spacing Δq between consecutive peaks). The repeat distance was equal to 5.05 ( 0.01 nm, which is close to the in-plane distance between a small NC and its neighboring large NC (or between two neighboring large NCs) as found by the TEM results in Figure 1 (5.7 ( 0.3 nm). A systematic damping of the even-order peaks is easily recognized in the (00l)-reflections. In order to interpret such
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Figure 3. Experimental and simulated small-angle XRD patterns.
features, simulations of the diffraction pattern have been performed, as reported in the following. The (00l)-series of reflections is interpreted as the fingerprint of lamellar layers stacked with a period d = 5.05 ( 0.01 nm along the z-axis (perpendicular to the surface). Long-range order in lamellar systems has been described in the literature by the paracrystalline theory (PT)19,20 and the Caille theory (CT),21,22 the former accounting for stochastic distance fluctuations of ideally flat layers, without any correlation of these fluctuations, the latter accounting for correlations, undulations, and finite size of the lamellar stacks.18 Our experimental data are shown to be well fitted by using the paracrystalline theory, thus verifying the occurrence of a lamellar-type structure, locally forming perfect layers stacked with a very high degree of order. Theoretical and mathematical details are reported as Supporting Information. The correct modeling of the structure depends on how the unit scatterers are defined. The measured XRD pattern is indeed affected by the presence of surfactants that coordinate each nanoparticle and that finally dictate the interparticle distance and also give contribution to the diffracted intensity. However the observed intensity modulation in the small-angle XRD pattern can be accounted by the scattering from the self-assembled NPs, as illustrated in the following. Figure 4 shows the TEM images, collected on three different samples having the same surface chemistry but synthesized with single (Figure 4a,b) or dual size PbS population (Figure 4c) and the corresponding small-angle XRD patterns (Figure 4A). Figure 4a,b correspond to assemblies of monomodal PbS NCs, synthesized and assembled in the same conditions, having comparable average size but a different size distribution. In particular, the sample in Figure 4a is characterized by a larger size distribution with respect to the sample in Figure 4b. Accordingly, larger ordered regions can be recognized in the latter micrograph, because NC selfassembly is known to be inhibited by broad size distributions.5 The comparison among the panels of Figure 4 clearly shows how the 2D order indicated by TEM can be directly related to the lamellar stacking order, which has been investigated by XRD. The lower is the degree of in-plane order (2D assembly, Figure 4a), the smaller is the number of reflections measured in the small-angle XRD pattern (curve a). Conversely, the higher the (out of plane) lamellar packing, indicated by the very high number of reflections measured in curve c of Figure 4A, the higher is the degree of in-plane order (2D assembly) shown in the corresponding TEM image (Figure 4c). Therefore the self-assembly of NCs, which is directly imaged by TEM in the substrate plane, also comes out in an ordered structure in the out-of-plane direction, as detected by XRD. Moreover the intensity modulation with
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Figure 6. Two-dimensional small-angle XRD map collected in forward scattering and registered onto a 2D detector.
Figure 4. (A) Experimental small-angle XRD patterns of monodisperse (curves a, b) and bimodal self-assembled NPs (curve c) and (a, b, c) TEM images of samples for curves a, b, and c, respectively.
Figure 5. Schematic drawing of the mesostructure packing in the XY plane (left view) and along the z-axis (right view).
damping of even-order diffraction peaks only occurred for assemblies achieved by using bimodal NC populations. The diffracted signal could be ascribed to the arrangement of the differently sized surfactant-capped NCs within the self-assembled domain. The final geometry is strongly influenced by the surfactant, which contributes to the final assembly stabilization. A simple cartoon of the modeled mesostructure unit cell is shown in Figure 5, which combines the in-plane view already derived from the TEM data in the XY plane (Figure 1) with the description along the z-axis. In the z-direction two different scatterers are present, the nanoparticle of type B in the position z = 0 and the nanoparticle of type A at z = 0.5 (at half the unit cell size c). In any case, the surfactant molecules surrounding each nanoobject contribute to define the distance and the arrangement among the A- and B-type nanoparticles. The presence of high-order Bragg peaks in the small-angle XRD pattern, up to an angle of 30 and more, reveals a high stacking order, so we assumed that the disorder influencing the structure factor only consists of dispersion in shape or orientation of the nanoparticles but not of variations of the fractional coordinates along the c-axis (stacking direction). Moreover, assuming the diameter of B-type NPs to be almost twice that of the A ones, as can be inferred from TEM
analysis, the theoretical simulation (eqs s1-s4 of the Supporting Information) is in good agreement with the experimental data, except for the angular range close to the critical angle for total reflection (Figure 3). By comparing the experimental and simulated data (more details are reported in the Supporting Information), a ratio DB/DA =1.9 ( 0.1 was derived, in good agreement with the evaluation of the ratio DB/DA = 2.1 ( 0.2 obtained by TEM characterization. This ratio is overestimated with respect to the value derived from wide-angle XRD analysis (DB/DA =1.5 ( 0.2). However, it is worth emphasizing that wide- and small-angle XRD do not explore exactly the same sample. A few drops of solution are enough to collect a significant XRD signal in the small-angle region, while a much thicker sample has to be deposited onto the substrate to collect a significant highangle diffracted signal. Future experiments are planned with synchrotron radiation to collect wide- and small-angle patterns from the same sample prepared with just a few drops of solution. This will allow us to fully relate information from small- and wide-angle diffraction ranges. A deeper insight and a confirmation of the presented results is given by a 2D map of small-angle XRD collected in forward scattering, by using a 2D detector and positioning the sample approximately parallel to the incident beam. The interpretation of the 2D diffraction pattern in Figure 6 is straightforward. Equally spaced signals are clearly visible as small portions of rings, meaning that a spatial order is present at the nanometer scale with a period of 5.05 nm. Moreover, in the light of what was discussed in the previous section, such satellite peaks indicate the self-assembly of a 3D superstructure, which is formed by a nonuniform lamellar stacking, organized in superlattice mosaic blocks; these in turn are not randomly oriented, as in a powder-like sample, but have their c-axes aligned within a small angular range around the normal to the substrate plane. Small-angle diffraction data (from both 1D and 2D scans) show therefore the occurrence of 1D superlattice domains with their axes approximately perpendicular to substrate plane. On the other hand, TEM analysis gives a direct proof of the 2D in plane order occurring in the bimodal population of PbS NCs through self-assembly, thanks to the very small size dispersion in each single population. The domain size of the assembly extends up to some hundreds of nanometers in the case of the highest degree of order. As a consequence, the XRD pattern is in any case representative of the self-assembly as a whole, formed by
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nanoparticles and ligands, and can give useful complementary information to TEM analysis in order to define the 3D character of the assembly.
Altamura et al. data simulation. This material is available free of charge via the Internet at http://pubs.acs.org.
References Conclusions Superlattices made from self-assembly of PbS nanoparticles with bimodal size distribution have been imaged at different hierarchic levels by XRD and conventional TEM. Combination and matching of data analysis of the small-angle and wide-angle XRD measurements provide relevant information about the structural order of the self-assembled superstructure perpendicular to substrate plane, as well as about size, shape, and structure of the constituent building blocks, even when smaller than 2 nm. TEM characterization allowed imaging of the in-plane order of the self-assembly and provided a priori information about nanoparticle size distribution, which was used in XRD data analysis. XRD data are shown to be representative of the degree of order in the assembly. In particular, our study shows that small-angle XRD allows discrimination between superlattices with single and bimodal NC size distribution, because the intensity modulation in the diffraction pattern contains the fingerprint of such different kinds of superlattices, and can be a powerful tool for prompt structural investigations of NCs self-assemblies. The analysis of the wide-angle XRD pattern by means of the Debye approach gives useful insight on size and shape of NCs, giving a lower limit for NC size. Overall the combined XRD and TEM provide a full 3D image of the structure, both at the level of the constituent PbS nanocrystals and at the level of the selfassembled architecture. Acknowledgment. This work has been partially supported by the EC-funded project METACHEM (Grant CP-FP 228762-2). We thank Mr. R. Lassandro and Mr. G. Chita for their valuable technical support. Supporting Information Available: Details of chemical synthesis procedures, simulated XRD pattern for PbS NCs with spherical shape, theoretical and mathematical aspects of small-angle XRD
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