Letter pubs.acs.org/NanoLett
Nanoparticle Clusters with Lennard-Jones Geometries Johann Lacava, Philip Born, and Tobias Kraus* Structure Formation Group, INM Leibniz-Institute for New Materials, Campus D2 2, 66123 Saarbrücken, Germany S Supporting Information *
ABSTRACT: Noble gas and metal atoms form minimum-energy clusters. Here, we present analogous agglomerates of gold nanoparticles formed in oil-in-water emulsions. We exclude interfacial templating and nucleation-andgrowth as formation mechanisms of these supraparticles. Similar to atomic clusters, the supraparticles form when a mobile precursor state can reconfigure until the nanoparticles’ interactions with each other and with the liquid−liquid interface are maximized. This formation mechanism is in striking contrast to that previously reported for microparticle clusters. KEYWORDS: Clusters, emulsions, nanoparticles, self-assembly, Pickering emulsions
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represent crystalline regions in the supraparticles with different orientations. Reflexes at lower q probably represent the increased interparticle spacing at boundaries inside the clusters. Some elements of the supraparticles’ internal structure visible in Figure 1f, in particular “zipper”-like central lines, are reminiscent of the features used for the identification of icosahedral atomic clusters in TEM.16 The supraparticles also exhibit crystalline outer facets that are reminiscent of atomic clusters (Figure 1h). We therefore compared the supraparticles to minimum-energy clusters of particles interacting with Lennard-Jones potentials. Theoretical cluster structures from the Cambridge Cluster Database and other sources17,18 were projected onto their facet planes (see Supporting Information) and compared to the electron micrographs of supraparticles.19 The supraparticles matched the predicted projections (Figure 2). Although our procedure is insufficient to establish a strict bijective mapping, it is extremely unlikely that multiple matches would occur incidentally: the twinning planes, singlecrystal regions, and overgrown layers of the clusters yield tell-tale features in the projections that make the identification robust and reliable. Supraparticles occurred both with icosahedral and decahedral geometries (Figure 2). Note that the cores of many of the larger clusters differ from the structures of all smaller clusters, which excludes a simple nucleation-and-growth mechanism of formation. We therefore assessed whether the supraparticles were templated by the emulsion interfaces. Interfacial energy reduction by particles20,21 and the inward-moving liquid−liquid interface during evaporation22 can both cause interfacial templating. We measured the interfacial tensions between the disperse and continuous phases, hexane and water, in pendant droplet experiments and found (in agreement with Glaser et al.23) a value of 37 mN/m for a Pickering system with
lusters of atoms exhibit geometries that are as characteristic as those of bulk atomic crystals. The atom positions in small clusters deviate from crystalline configurations and maximize nearest-neighbor interactions.1−4 Microparticles readily assemble into clusters inside emulsion templates, too.5−7 Velev et al. assembled latex particles into dense and hollow spheres with limited order by dispersing them in emulsions and fixing the resulting clusters.8,9 Pine and Manoharan created welldefined clusters of microparticles by evaporating Pickering emulsions.10−12 Such emulsion-templated structures are not minimum-energy arrangements but bear witness to their formation mechanism. Emulsion-templated nanoparticle clusters have not been reported yet. It is known that destabilized gold nanoparticles can form agglomerates with crystalline regions and irregular overall morphology (Figure 1a,b).13 Here, we report fully defined clusters of nanoparticles formed in emulsion droplets. Monodispersed gold crystals with core diameters of 6 nm and covered by a dodecanethiol monolayer were dispersed in hexane and the dispersion was emulsified in water using Triton X-100 as surfactant. The oil phase was slowly evaporated until only the nanoparticles remained (Figure 1e). This yielded a stable “second-level” dispersion of supraparticles that were sufficiently robust to be able to dry them and analyze their structures via TEM (Figure 1f). Upon careful evaporation of their dispersion, the supraparticles assembled into hierarchical superlattices (Figure 1f). For comparison, Figure 1b,c shows the TEM and small-angle X-ray scattering images of precipitated polycrystalline agglomerates. The scattering ring at q = 0.93 nm−1 indicates the (111) lattice plane distance of the face-centered cubic (fcc) packing while other rings can be indexed to other lattice planes using Bragg’s law, q = 2π(h2 + k2 + l2)1/2/a (where a is the lattice constant and h, k, and l are the Miller indices).14 The (111) ring also occurs in the scattering from sparse layers of dry supraparticles made from the same nanoparticles (Figure 1g). It is broadened, however, by the distorted lattices in the clusters. Reflexes on the ring and (weaker) at slightly lower q © XXXX American Chemical Society
Received: April 11, 2012 Revised: May 4, 2012
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Figure 1. Nanoparticle clusters created outside and inside of emulsion templates. Addition of an incompatible solvent to a dispersion of alkanethiolstabilized gold nanoparticles (a) yields irregular pieces of densely packed nanoparticle crystals (b) that sediment and exhibit pronounced Bragg peaks in SAXS (c,d). In contrast, emulsion-templated assembly (e) yields supraparticles that exhibit Lennard-Jones cluster-like internal structures as revealed by transmission electron microscopy (f). Their small-angle scattering pattern (g) indicates a regular structure different from the densely packed superlattice (d). The larger the supraparticle, the more crystalline its surfaces appear in scanning electron microscopy (h).
Figure 2. Comparison of transmission electron micrographs to projections and three-dimensional renderings of clusters theoretically predicted for particles with Lennard-Jones potentials (see text). In each box, n indicates the number of particles in the predicted cluster. We observed supraparticles having an icosahedral core with a Mackay overlayer (“IC”), an icosahedral core with an anti-Mackay overlayer (“FC”), complete Marks decahedra (“MD”) and such having an icosahedral core with a Mackay overlayer and a central vacancy (“IC*”).1,2,15
above the critical micelle concentration.24 It is therefore energetically unfavorable for the nanoparticles to segregate to the interface.
nanoparticles at the interface, considerably below the native interfacial energy of 53 mN/m, but above the interfacial tension of 3 mN/m in the presence of Triton-X 100 at concentrations B
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In a drying droplet, the liquid−liquid interface moves inward and collects particles, while diffusion will redistribute them throughout the volume. The Peclet number compares these effects22 Pe =
R2 Dτ
(1)
where R is the radius of the droplet, D is the diffusion coefficient of the particles in the liquid, and τ is the time required for a droplet to evaporate. If Pe ≫ 1, particles cannot diffuse to the remaining volume and will accumulate at the droplet interface. In a typical assembly process, we have an evaporation time τ = 240 min, R = 1180 nm (the radius directly after emulsification), and the nanoparticles’ diffusion constant (from DLS) is D = 2.3 × 10−10 m2/s. This corresponds to Pe = 4.2 × 10−7, which indicates a homogeneous particle distribution inside the droplets. Above results suggest that interfacial templating is not the source of order in supraparticles. Free energy minimization is another mechanism that could drive structure formation by maximizing next neighbors and particle−water distances. The short interaction lengths of van der Waals forces would then imply assembly at low particle−particle and particle−interface distances. To check this hypothesis we used in situ surface plasmon spectroscopy and small-angle X-ray scattering to detect at which stage agglomerates form. Samples were removed from the evaporating emulsions at regular intervals and characterized by UV−vis spectroscopy. The surface plasmon resonance (SPR) of the gold nanoparticles depends on the average particle distances; UV−vis spectra therefore indicate the local concentration of particles. The large droplets in freshly prepared emulsion scatter light efficiently and cause an overall weak transmission (Figure 3, inset). As the droplets evaporate, transmission increases. After 80 min of evaporation time, the surface plasmon peak is clearly visible at λ = 516 nm. It slowly shifts until a drastic change to 520 nm occurs in the last 30 min. Concurrent DLS measurements show that the average droplet size decreases continuously. Each point in Figure 3a indicates the mean and standard deviation of the droplet sizes observed in three evaporation experiments. We estimated the average number of nanoparticles per supraparticle from the final size and calculated the theoretical evolution of the SPR peak using the effective medium approximation (EMT),25,26 assuming homogeneously distributed particles (see Supporting Information for the detailed algorithm). The expected SPR shift at different stages of evaporation is indicated by the continuous line in Figure 3. The predictions agree with the experimental observation until the EMT approximation breaks down for the closely packed supraparticles (for a hydrodynamic droplet radius from DLS Rh < 200 nm). Spectroscopic evidence therefore suggests that supraparticle assembly does not occur by early nucleation and subsequent growth but in a late stage of evaporation where particles and interfaces strongly interact. Small-angle X-ray scattering (SAXS) can distinguish a particle shell at the liquid−liquid interface from compact clusters. We performed an assembly experiment by evaporating the particle-containing dispersion in a nitrogen stream directly at a synchrotron and took samples for scattering measurements at fixed intervals. Figure 3c shows the time-dependent scattering during the evaporation process. Persistently strong oscillations of the structure factor in the high q region (q > 0.5 nm−1) indicate the presence of nanoparticles with a narrow
Figure 3. Analysis of the cluster formation mechanism by UV−vis spectroscopy and SAXS. Samples were taken from the evaporating emulsion and analyzed for the position of the particles’ surface plasmon peak (a). It is shifted only toward the end of the evaporation process when the droplet size decreases rapidly, while a core−shell geometry (in the absence of surfactants) leads to an immediate strong shift (inset, dotted line). The continuous line in the graph indicates the shift predicted for homogeneously distributed particles. Small-angle X-ray scattering was also performed on samples at regular intervals. At all times, the evolution of the scattering intensity clearly differs from that expected for a core−shell arrangement (b, inset). The cluster model (inset) fits the evolution well. A secondary peak in the structure factor (c) occurs toward the end of the evaporation and indicates increasingly dense, interacting particles.
size distribution that agree with reference measurements (particle radius r = 3.55 ± 0.33 nm), while no oscillations are visible at lower q < 0.1 nm−1. A Pickering phase would cause oscillations in the low q-range even for droplets broadly distributed in size, a signature that we did not observe in any of our evaporation experiments. Instead, a peak appeared toward the end of the process at around 0.6 nm−1 that shifted to increasing qc upon further evaporation (Figure 3d). We attribute this peak to the formation of nanoparticle clusters with decreasing particle−particle distances, where the center-tocenter distance between particles dc is roughly related to the peaks’ positions as dc ≈ 2π/qc. These mobile clusters represent a precursor state with initial distances of dc ≈ 10.5 nm, corresponding to a ligand layer spacing of approximately 2 nm. As the droplets shrink, the particles are compressed until the C
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for their support of the SAXS studies, Stephan Förster for useful discussions and Eduard Arzt for his continuing support of this project. This work was supported by funding of the Deutsche Forschungsgemeinschaft and beam time granted by the ESRF.
maximum possible ligand interdigitation is reached and they lose their individual mobility, which leads to a peak around qc ≈ 0.88 nm−1 that corresponds to a particle spacing of 7.1 nm, slightly below the value of dc ≈ 7.7 nm observed in TEM images of dry supraparticles. A particle clustering model27 also fits our scattering data and suggests correlation lengths that coincide with the droplet diameters and volume fractions that are in line with particles homogeneously distributed in the available volume (see Supporting Information for the fitting parameters’ values). In summary, we showed that nanoparticles in emulsion droplets arrange into regular supraparticles by free energy minimization. This is in contrast to the process that Manoharan et al. reported for microparticles in emulsions, which are confined to the liquid−liquid interfaces and collapse into clusters when the liquid evaporates. The structure of our supraparticles is governed by the interparticle potential of metal nanoparticles that resemble Lennard-Jones potentials13,28 and the influence of the liquid−liquid interface. In contrast to destabilized nanoparticles with strongly attractive potentials that quickly agglomerate in a nucleation-and-growth mechanism, the particles in the emulsion droplets retain their mobility as the attraction between the particles increases. They have time to find their energetically optimal position in the increasingly dense, nonagglomerated mobile precursor state before they are finally quenched when their ligand shells interdigitate. The liquid− liquid interface gently pushes the particles into a dense geometry, thus funneling the particles into their minimum-energy positions while avoiding secondary minima such as multiple twinned fcc crystals. We did not study whether this process depends on the exact energetic state of the specific cluster geometry. It would be interesting to see whether those supraparticles containing “magic” numbers of particles are more stable than others, as it is the case for atomic clusters. Technologically, supraparticles are interesting because they are fully defined by the number of nanoparticles involved. The process used here is general and compatible with all moderately attractive nanoparticles, for example, semiconductor quantum dots. To create fluorescent suparparticles, for example, one would measure the diffusion constant of the desired quantum dots, analyze their tendency to segregate to the interface, and choose appropriate evaporation parameters and surfactants.
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ASSOCIATED CONTENT
S Supporting Information *
Sample preparation and characterization techniques, overview micrographs showing larger numbers of supraparticles, the projections used to identify Lennard-Jones geometries, and the algorithms used to analyze surface plasmon and SAXS spectra. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +49-681-9300-389. Fax: +49-681-9300-279. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Ahmed-Amine Ouali for contact angle measurements, Michael Sztucki and his colleagues at the ESRF D
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