LETTER pubs.acs.org/JPCL
How to Predict the Growth Mechanism of Supracrystals from Gold Nanocrystals N. Goubet,†,‡ J. Richardi,†,‡ P. A. Albouy,§ and M. P. Pileni*,†,‡ †
Universite Pierre et Marie Curie and ‡Centre National de la Recherche Scientifique, UMR 7070, LM2N, 4 Place Jussieu, 75005 Paris, France § Laboratoire de Physique des Solides Universite Paris-Sud 91405 Orsay, France
bS Supporting Information ABSTRACT: Here we report the influence of the nanocrystal size and the solvent on the growth of supracrystal made of gold nanocrystals. These parameters may determine the final morphology of nanocrystals assemblies with either a layer-by-layer growth or a process of nucleation in solution. Experiments supported by simulations demonstrate that supracrystal nucleation is mainly driven by solvent-mediated interactions and not solely by the van der Waals attraction between nanocrystal cores, as widely assumed in the literature. SECTION: Nanoparticles and Nanostructures
P
eriodic arrangements of mesoscopic architectures are one of the next steps to detect new chemical and physical properties. There is a high potentiality of these novel artificial tailored materials for both fundamental research1-8 and applications ranging from magnetic storage to optical devices.9 A good definition of the size and shape of nanocrystals (NCs) is a prerequisite for their arrangement on a Bravais lattice (called “supracrystal”) during their self-assembly, but which crystalline structure is finally reached may be influenced by such parameters as the temperature, solvents, coating agents, and so on.1,7,10-18 Recently, new intrinsic properties related to the existence of such a long-range translational order were pointed out.2-5,7,8 Whereas various types of mesoscopic materials have been produced, there is, however, no general understanding of which parameters control the supracrystal growth. Here we show how the NC size, coating agent, and its solvation may determine the final morphology of NC assemblies with either a layer-by-layer growth or a process of nucleation and growth in solution. Experiments supported by simulations here demonstrate that supracrystal nucleation is mainly driven by solvent-mediated interactions and not solely by the van der Waals attraction between NC cores, as widely assumed in the literature.14,15 This is due to small differences in the solvent-ligand and ligand-ligand interactions existing even in a nonpolar medium. r 2011 American Chemical Society
The method used here for NC synthesis allows a control of their size with a narrow size distribution, which is a prerequisite for this study. In this way, four batches of spherical Au NCs with diameters of 4.3, 5.1, 5.8, and 7.1 nm are obtained. (See the Experimental and Theoretical Section and Supporting Information.) They are denoted Au4, Au5, Au6, and Au7, respectively. The NCs are coated with dodecanethiol and dispersed in various solvents. Let us consider toluene as the first solvent used. At the end of the evaporation, the SEM images show a drastic change in the film morphology with the NC size (Figure 1). Uniform films covering most of the substrate with an average thickness of ∼1 μm are observed for Au4 and Au5 NCs (Figure 1a,b). In contrast, individual supracrystals with welldefined shapes and sizes ranging from 1 to 10 μm are obtained using Au6 and Au7 NCs (Figure 1c,d). The supracrystals have well-defined shapes (hexagonal or triangular), whereas some of them display five-fold symmetry or a polycrystal-shape, as described previously.12,17,19 To better understand the structural differences between both organizations, small-angle X-ray diffraction (SAXRD) is used. (See the Supporting Information.) The SAXRD patterns obtained for Au4 and Au5 NC films Received: January 3, 2011 Accepted: January 27, 2011 Published: February 09, 2011 417
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Figure 1. Nanocrystal’s size effect on the mesoscopic structure of its supracystals. The nanocrystals are dispersed in toluene and then deposited on a silicon substrate, with (a) (Au4), (b) (Au5), (c) (Au6), and (d) (Au7). The morphology depends on the nanocrystal’s size: for (Au4) and (Au5), the material is a film, and for (Au6) and (Au7), some crystalline shapes are observed. The corresponding small-angle X-ray diffraction patterns obtained in a grazing incidence geometry are inset; the white arrow corresponds to the direction in the surface plane, and the black one is perpendicular to it.
Table 1. Summary of the Au Nanocrystal Properties: Average Size, Size Distribution, Center-Center Distance (D), and Edge-Edge Distance (δ) sample
diameter (nm)
size distribution
D (nm)
(insets in Figure 1c,d) show continuous rings with discontinuous reinforcements and d-spacings pointing to a structure similar to that of an fcc lattice. The rings are attributed to randomly oriented supracrystals, and the reinforcements are attributed to well-developed supracrystals sitting on their larger flat facets. This agrees exactly with the SEM images shown in Figure 1c,d. The sharp reflections on the rings shown in Figure 1d are due to some larger disoriented supracrystals (we can see these crystals in the inset), and the rings correspond to the smaller disoriented supracrystals. The structure may be explained by a homogeneous nucleation for large Au NCs previously observed in various solvents.10,12,14-16,21 To our knowledge, this is the first experimental evidence that the NC sizes tune the supracrystals growth mechanism from a heterogeneous to a homogeneous one. The average interparticle distance, δ, calculated (see the Supporting Information) from the d111 spacing (Table 1) is close to the length of the dodecanethiol all-trans configuration (1.78 nm). Within the experimental error, no evolution of δ with the NC diameter is found. In the case of heterogeneous nucleation, the substrate effect could be important for the growth of supracrystals. We have evaporated the Au4 and Au5 in toluene on HOPG substrate (Figure S2 of the Supporting Information), and the obtained supracrystals films are similar (i.e., the same crystalline structure (fcc) and same internanocrystal distance).
δ (nm)
Au4
4.3
10%
6.3
2.0
Au5
5.1
6%
6.9
1.8
Au6
5.8
8%
7.8
2.0
Au7
7.1
7%
9.3
2.2
(inset in Figure 1a,b) correspond to the diffraction by an uniaxially oriented assembly of supracrystals: the various diffraction spots are readily indexed using an fcc lattice (inset Figure 1a, b; see the Supporting Information), whereas the [111] axis of each supracrystal is perpendicular to the substrate. The width of the spots is resolution-limited (Figure S1A and S1B of the Supporting Information), indicating average supracrystal dimensions of at least a few tenths of a micrometer. Note that higher magnifications of the film surface reveal lines crossing at nearly 60 or 120° (Figure 1a,b) that can be explained as steps associated with screw dislocations in the film. The pattern symmetry clearly indicates that the growth front corresponds to {110} facets. These observations are in agreement with a heterogeneous layerby-layer growth20 for smaller Au4 and Au5 NCs. Instead of discrete diffraction spots, SAXRD patterns for larger Au6 and Au7 NCs 418
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Figure 2. Nanocrystal’s size effect on the mesoscopic structure of its supracystals in hexane. The nanocrystals are dispersed in hexane and then deposited on a silicon substrate, with (a) (Au4), (b) (Au5), (c) (Au6), and (d) (Au7). In hexane, the supracrystals, for any of the used nanocrystal sizes, the materials are in a film configuration. The corresponding small-angle X-ray diffraction patterns obtained in a grazing incidence geometry are inset; the white arrow correspond to the direction in the surface plane, and the black one is perpendicular to it.
(bp= 110 °C) compared with hexane (bp = 69 °C). The evaporation time is around 8 h as with toluene. A layer-by-layer growth of fcc supracrystals with the very bright SAXRD reflections normal to the substrate, as for hexane, is obtained. From that, it is concluded that the growth mechanism is not related to the solvent evaporation rate. Instead of toluene, hexane and octane, let us consider cumene characterized by a closely related structure as toluene. In this case, the boiling temperature is 152 °C, and the evaporation time is close to 48 h. Homogeneous nucleation of fcc supracrystals appears, as observed with toluene, with a regular crystalline shape and no preferential orientation as confirmed by the SAXRD pattern. At this point of the experiment, two general behaviors of supracrystal growth appear: With alkane as the solvent, only a heterogeneous nucleation takes place, whereas with aromatic ones, a transition to homogeneous nucleation is found with formation of large and well-defined fcc crystals for NCs having a size >5 nm. To understand the influence of both NC size and nature of the solvent on the supracrystal growth mechanism, the evaporation of Au NC solutions is simulated by Brownian dynamics and Monte Carlo methods at a particle level.21 (See the Experimental and Theoretical Section.) The interparticle interaction (Figure 3A) is given by: (i) the van der Waals attraction between the metallic cores, (ii) the free energy of mixing of the thiol ligand22 with the solvent molecules, and (iii) the elastic compression of these ligands.23 Equations used to compute the energy of
The data for Au7 differ from those observed with 7 nm Co (Co7) NCs initially dispersed in hexane,1 where the final mesostructure is fcc films without any individual crystals. To explain this difference in the supracrystal morphology produced with Au7 and Co7 NCs, toluene is replaced by hexane. To avoid kinetic effects due to the fast evaporation of hexane, the evaporation rate is reduced using quasi-saturated conditions during the deposition. Figure 2 shows the formation of thin films for any NC size in hexane displaying the same type of texture as with Au4 and Au5 films grown in toluene. The SAXRD patterns (insets in Figure 2) confirm that similar fcc supracrystals are present. The ring shown in Figure 1a,d and Figure 2b-d cannot be attributed to an amorphous phase. If it is the case, the second order should be broader than the first. In the present case, the second order is thinner compared with the first ring. This ring is attributed to small-disoriented domains which correspond, in fact, to the contribution of two unresolved ring (i.e., the {111} and {200} family plane). No individually grown micrometric supracrystals are observed even at larger particle sizes (Au6 and Au7). The observation by HRSEM on an Au6 film confirms a heterogeneous growth with a layer by layer stacking. Even under quasi-saturated conditions, the hexane evaporation rate remains faster (5 h) than that of the toluene (7 h). To be sure that the change in the supracrystal growth mechanism is not related to the evaporation rate, let us consider octane (bp= 125 °C) having a closer boiling temperature as toluene 419
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Figure 3. Interaction model and Brownian dynamics simulation of gold NC assembly. (A,B) Interaction potential between two gold nanocrystals in different solvents (ligand: dodecanethiol). (A) Dependence on the nanocrystal size: For toluene, an attractive peak between the NCs is found in contrast with hexane. The attractive peak becomes higher with increasing NC size. (B) Dependence on the solvent: For octane and hexane, repulsion is observed, whereas the interaction for cumene depends on the solubility parameter (given in MPa0.5 in the Figure). (C-H) Final configurations of nanocrystal assemblies obtained by Brownian dynamics simulations using the potential of part A under the conditions indicated in the Figure: (C,F) For 4 nm NCs in toluene: no supracrystals are observed before evaporation (C), and a self-assembled film appears after evaporation (F). (D,G) For 7 nm NCs in toluene, supracrystals form by homogeneous nucleation within the solution. (E,H) For 7 nm NCs in hexane, homogeneous nucleation is absent as for 4 nm in toluene.
ranging from 0.5 to 10-5 (particle number: 10 000) are studied. Toluene solutions are considered first. No nucleation for Au4 is observed, even at the higher density (Figure 3C), and a wellordered 3D assembly is ultimately obtained (Figure 3F). The layer-by-layer growth is attributed to the compression of nanoparticles by the solution-air interface at the end of the evaporation process. For Au5, nucleation starts from a density of 4 10-3, in good agreement with the simulations by Khan et al.26 It finishes with the coexistence of spherical supracrystals and free particles. For larger NCs, like Au6 and Au7 (Figure 3D), small aggregates of globular shape form initially. During the evaporation, these nuclei coalesce to form larger assemblies (Figure 3G). They are characterized by a compact crystalline structure with a random sequence of layers. Turning to the case of hexane, the Brownian dynamics simulations indicate no supracrystal nucleation within the solution at any particle size, whereas a wellordered 3D assembly is usually observed at the end of the evaporation (Figure 3E,H). Good agreement between experiments and simulations is thus found for both solvents. Please note that experimental and theoretical studies were also carried out to exclude that the substrate influences the growth mechanisms of supracrystals under the conditions used here. (See the Supporting Information.)
mixing were developed in the literature using the Flory theory.22 Within this framework, the affinity between the solvent and the coating chains is quantified by the Flory parameter that itself depends on the difference between the Hildebrand solubility parameters for the solvent and the alkyl chains. The latter is approximated by the Hildebrand parameter for the solvent dodecane (1.6 MPa0.5). Hexane, whose Hildebrand parameter (1.49 MPa0.5) is quite close to this value, is thus expected to be a significantly better solvent for the coating than toluene (1.82 MPa0.5).24 This translates into interaction potentials that are repulsive or very weakly attractive for hexane, whereas they are highly attractive for toluene for any NC size (Figure 3A). The result for hexane is in agreement with recent calculations of the mean force potential for gold NC in hexane using atomistic simulations.25 The evaporation process is modeled as a liquid-gas interface that slowly moves down.21 We have controlled the evaporation rate to be sufficiently slow to reliably predict the growth mechanism of supracrystals. (See the Supporting Information). The main role of evaporation is an increase in concentration. Therefore, whenever the concentration exceeds the one needed for the nucleation of aggregates, the formation of supracrystals is observed. Nanoparticle solutions at several reduced densities 420
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The Journal of Physical Chemistry Letters For Au6 nanoparticles, Figure 3B shows, for octane as hexane, that a repulsive potential is calculated. With cumene as solvent, two determinations are found in the literature for the Hildebrand parameter of cumene: 1.75 and 1.81 MPa. This apparently minute difference in solubility parameters strongly affects the interaction potential: it is sufficient to revert from a repulsive to an attractive potential between Au6 nanoparticles. (See Figure 3B.) Experimentally, homogeneous nucleation of wellfaceted supracrystals is observed, indicating that the larger value for the Hildebrand parameter of cumene is probably correct. This clearly shows the model limit. A precise value of the Hildebrand parameter, which is usually given for widely used solvents, is needed to predict the supracrystal growth mechanism. Here it is shown from experiments that the affinity of the solvent for the coating agent is as important a parameter as the NC size to determine the final morphology of supracrystals grown by the evaporation of Au NC solutions. To be predictive, simulations necessarily include a free mixing energy term, as is done here. Good agreement with experimental observations cannot be reached considering the van der Waals attraction alone. Small changes in the Hildebrand solubility parameter strongly impact the interaction potential and are sufficient to switch from an attractive to a repulsive situation, that is, from a homogeneous to a heterogeneous growth. The proposed theory yields rapid information and is not limited to the system studied here because the parameters needed by the model, such as Hildebrand or Hamaker constants, are known for nearly all solvents and NCs experimentally used. Therefore, this approach could be generalized to the overall (organic/inorganic) NCs coated surfactants and alkyl chains and also to spherical polymers and virus and proteins having branches at the periphery. We will develop the present study in a future full paper.
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1.95 eV from ref 29. The energy of mixing and the elastic repulsion between the ligands depend on several factors: the contour length of the ligand (1.774 nm),26 the volume of the solvent molecule (calculated from their molecular weights and densities for toluene and hexane: (1.78 and 2.182) 10-28 m3), the average core surface area covered by one thiol group (21.5 Å2),26 and the Hildebrand solubility parameters of the solvent and the ligand24 (values in 104 Pa0.5: toluene: 1.82, hexane: 1.49, octane: 1.51, cumene: 1.75 and 1.81, dodecane: 1.60 used here for the ligand (see discussion in ref 26)).
’ ASSOCIATED CONTENT
bS
Supporting Information. NCs synthesis, small-angle x-ray scattering characterization, transmission electronic microscopy analysis, simulation method, and interaction model. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2008-2011) under grant agreement no. 213382. ’ REFERENCES (1) Pileni, M. P. Nanocrystal Self-Assemblies: Fabrication and Collective Properties. J. Phys. Chem. B 2001, 105, 3358–3371. (2) Fudouzi, H.; Xia, Y. Colloidal Crystals with Tunable Colors and Their Use as Photonic Papers. Langmuir 2003, 19, 9653–9660. (3) Kagan, C. R.; Murray, C. B.; Bawendi, M. G. Long-Range Resonance Transfer of Electronic Excitations in Close-Packed CdSe Quantum-Dot Solids. Phys. Rev. B 1996, 54, 8633–8643. (4) Courty, A.; Mermet, A.; Albouy, P.-A.; Duval, E.; Pileni, M.-P. Vibrational Coherence of Self-Organized Silver Nanocrystals in FCC Supra-Crystals. Nat. Mater. 2005, 4, 395–398. (5) Pileni, M. P. Self-assembly of Inorganic Nanocrystals: Fabrication and Collective Intrinsic Properties. Acc. Chem. Res. 2007, 40, 685–693. (6) Talapin, D. V.; Shevchenko, E. V.; Murray, C. B.; Titov, A. V.; Kral, P. Dipole-Dipole Interactions in Nanoparticle Superlattices. Nano Lett. 2007, 7, 1213–1219. (7) Pileni, M. P. Supracrystals of Inorganic Nanocrystals: An Open Challenge for New Physical Properties. Acc. Chem. Res. 2008, 41, 1799– 1809. (8) Tao, A. R.; Ceperley, D. P.; Sinsermsuksakul, P.; Neureuther, A. R.; Yang, P. Self-Organized Silver Nanoparticles for Three-Dimensional Plasmonic Crystals. Nano Lett. 2008, 8, 4033–4038. (9) Nie, Z.; Petukhova, A.; Kumacheva, E. Properties and Emerging Applications of Self-Assembled Structures Made from Inorganic Nanoparticles. Nature Nanotechnol. 2010, 5, 15–25. (10) Prasad, B. L. V.; Sorensen, C. M.; Klabunde, K. J. Gold Nanoparticles Superlattices. Chem. Soc. Rev. 2008, 37, 1871–1883. (11) Bishop, K. J. M.; Wilmer, C. E.; Soh, S.; Grzybowski, B. A. Nanoscale Forces and Their Uses in Self-Assembly. Small 2009, 5, 1600–1630. (12) Stoeva, S. I.; Prasad, B. L. V.; Uma, S.; Stoimenov, P. K.; Zaikovski, V.; Sorensen, C. M.; Klabunde, K. Face-Centered Cubic and Hexagonal Closed-Packed Nanocrystal Superlattices of Gold Nanoparticles Prepared by Different Methods. J. Phys. Chem. B 2003, 107, 7441– 7448.
’ EXPERIMENTAL AND THEORETICAL SECTION NCs Synthesis. The gold NCs capped with 1-dodecanethiol are synthesized by revisiting the method in ref 27. The difference in size is obtained by varying the dodecanethiol concentration and the reduction rate. Additional details are provided in the Supporting Information. Supracrystals Deposition. The NCs characterized by a low size distribution coated with dodecanethiol are dispersed in toluene [(Au)n = 10-2 M]. We deposited 100 μL of the colloidal solution in a beaker containing a silicon substrate at the bottom. The evaporation takes place at ambient pressure and ambient temperature. Structural Analysis. SAXRD experiments are performed with a rotating copper anode generator operated with a small-size focus (0.1 0.1 mm2 in cross-section) at 40 kV and 20 mA. The optics consists of two parabolic multilayer-graded mirrors in K-B geometry. It delivers a well-defined and intense parallel monochromatic beam. Photostimulable phosphor plate is used as detector. The reading of the exposed imaging plate is performed by a scanner (STORM 820 Molecular Dynamics). JEOL 5510-lv and Carl Zeiss SUPRA scanning electron microscopes were used to image the supracrystal morphology. Simulation Method and Interaction Model: The motion of the NCs is described by Langevin equations integrated using an algorithm proposed by Allen in ref 28. The explicit formulas and details for the interaction model are given in the Supporting Information. The van der Waals attraction between the NCs is determined by the effective Hamaker constant of gold taken as 421
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(13) Whetten, R. L.; Shafigullin, M. N.; Khoury, J. T.; Schaaff, T. G.; Vezmar, I.; Alvarez, M. M.; Wilkinson, A. Crystal Structures of Molecular Gold Nanocrystal Arrays. Acc. Chem. Res. 1999, 32, 397–406. (14) Sigman, M. B.; Saunders, A. E., Jr.; Korgel, B. A. Metal Nanocrystal Superlattice Nucleation and Growth. Langmuir 2004, 20, 978–983. (15) Abecassis, B.; Testard, F.; Spalla, O. Gold Nanoparticle Superlattice Crystallization Probed In Situ. Phys. Rev. Lett. 2008, 100, 1–4. (16) Yan, H.; Cingarapu, S.; Klabunde, K. J.; Chakrabarti, A.; Sorensen, C. M. Nucleation of Gold Nanoparticle Superclusters from Solution. Phys. Rev. Lett. 2009, 102, 1–4. (17) Compton, O. C.; Osterloh, F. E. Evolution of Size and Shape in the Colloidal Crystallization of Gold Nanoparticles. J. Am. Chem. Soc. 2007, 129, 7793–7798. (18) Park, S. Y.; Lytton-Jean, A. K. R.; Lee, B.; Weigand, S.; Schatz, G. C.; Mirkin, C. A. DNA-Programmable Nanoparticle Crystallization. Nature 2008, 451, 553–556. (19) Rupich, S. M.; Shevchenko, E. V.; Bodnarchuk, M. I.; Lee, B.; Talapin, D. V. Size-Dependent Multiple Twinning in Nanocrystal Superlattices. J. Am. Chem. Soc. 2010, 132, 289–296. (20) Bauser, E. Atomic Mechanisms in Semiconductor Liquid-Phase Epitaxy. In Handbook of Crystal Growth 3b: Thin Films and Epitaxy; Hurle, D. T. J., Ed.; Elsevier: Amsterdam, 1994; p 880. (21) Lalatonne, Y.; Richardi, J.; Pileni, M. P. Van der Waals Versus Dipolar Forces Controlling Mesoscopic Organizations of Magnetic Nanocrystals. Nat. Mater. 2004, 3, 121–125. (22) Smitham, J. B.; Evans, R.; Napper, D. H. Analytical Theories of the Steric Stabilization of Colloidal Dispersions. J. Chem. Soc., Faraday Trans. 1 1975, 71, 285–297. (23) Evans, R.; Smitham, J. B.; Napper, D. H. Theoretical Prediction of the Elastic Contribution to Steric Stabilization. Colloid Polym. Sci. 1977, 255, 161. (24) Barton, A. F. M. CRC Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press, Inc.: Boca Raton, FL, 1983. (25) Schapotschnikow, P.; Pool, R.; Vlugt, T. J. H. Molecular Simulations of Interacting Nanocrystals. Nano Lett. 2008, 8, 2930–2934. (26) Khan, S. J.; Pierce, F.; Sorensen, C. M.; Chakrabarti, A. SelfAssembly of Ligated Gold Nanoparticles: Phenomenological Modeling and Computer Simulations. Langmuir 2009, 25, 13861–13868. (27) Zheng, N.; Fan, J.; Stucky, G. D. One-Step One-Phase Synthesis of Monodisperse Noble-Metallic Nanoparticles and Their Colloidal Crystals. J. Am. Chem. Soc. 2006, 128, 6550–6551. (28) Allen, M. P. Brownian Dynamics Simulation of Chemical Reaction in Solution. Mol. Phys. 1980, 40, 1073–1079. (29) Ohara, P. C.; Leff, D. V.; Heath, J. R.; Gelbart, W. M. Crystallization of Opals from Polydisperse Nanoparticles. Phys. Rev. Lett. 1995, 75, 3466–3469.
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