What Controls Au Nanoparticle Dispersity during Growth? - Nano

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What Controls Au Nanoparticle Dispersity during Growth? Giannis Mpourmpakis,*,†,‡ Stavros Caratzoulas,† and Dionisios G. Vlachos† †

Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 and ‡ Institute of Electronic Structure and Laser, FORTH, Heraklion 71110, Crete, Greece ABSTRACT Nanoparticles are critical in diverse nanotechnological areas. Their physical and chemical properties are essentially determined by their size, shape, and dispersity, but the underlying mechanisms that determine these are generally poorly understood. Herein, we focus on the electronic structure and solvation properties of the Au-thiolate capping agents (AunMBAn) used in the synthesis of gold nanoparticles and whose accepted function is to stump growth. By DFT calculations we show that they exhibit “magic” number, electronic configuration, and stability for n ) 4 and 8. By Molecular Dynamics simulations, we learn that in water-methanol solution the dominant species is the Au4MBA4 complex, in a conformation stabilized by hydrogen bonds. We argue that the solvent has a multifunctional role: the water acts via hydrogen bonding as a “molecular locker” stabilizing particular conformers, while the methanol prevents polymeric growth of the AunMBAn complexes. A plausible growth mechanism conducive to the formation of monodisperse gold nanoparticles is proposed. KEYWORDS Solvent, molecular dynamics, DFT, theory, capping agent, thiolate

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characteristics of cyclic, thiolated Aun(SMe)n clusters (with n ) 2-12) showed that up to n ) 4 they assume a ring conformation, as opposed to crownlike for larger sizes.19 That study was the first theoretical attempt to elucidate the structural motifs of the AunSRn complexes and provided many insights in that respect. Although methyl thiolate is extensively used as a capping agent17,18,20-22 in theoretical studies of the electronic and structural characteristics of thiolate-protected Au NPs, it is too small a molecule compared to those used to synthesize monodisperse Au NPs in the lab. Moreover, computationally costly solvent effects have been absent from the theoretical studies. Gold rings23 and crowns24 with continuous AuI···AuI bonding interactions, of 16 and 36 Au atoms, respectively, have successfully been synthesized. Zhu et al.16 have proposed that the aggregation state of the AuI-SR complexes (R ) CH2CH2Ph) is key to controlling the formation of monodisperse Au25 NPs. Very recently, Ackerson et al.25 obtained virtually monodisperse MBA monolayer-protected Au nanoparticles of 2 and 3 nm diameter by adjusting the solvent conditions. The percentage of methanol in the solvent was found to play a crucial role, affecting both the size and the uniformity of the products. The mechanism though by which the dispersion control takes place in experiments remains elusive, and one of the reasons is that the electronic properties and of Aun(SR)n complexes in their natural environment are not well understood. Herein, we perform high-level density functional theory (DFT) calculations and molecular dynamics (MD) simulations to investigate the stability and growth of small (n ) 1-12) Aun(SR)n complexes with p-mercaptobenzoic acid (MBA) as the thiolate capping agent SR. Our objectives are to understand how the capping agents participate in NP formation

anoparticles (NPs) find numerous applications in technologicallyimportantandhealth-relatedareas.1-3 Gold NPs, in particular, are unique4,5 in their diversity of applications, ranging from excellent catalysts2,6 to effective inhibitors against HIV fusion.7 In a typical synthesis, metal salt (auric gold, AuIII) is reduced to metallic and aurous (AuI) gold, with the latter associating with ligands (e.g., thiolate, phosphine) to form metal-organic complexes. Supramolecular chemistry is expected to play an important role in Au NP formation. The aurophilic AuI···AuI bonds are the result of strong correlations among the electrons in the closed shells of the Au complexes, and because of relativistic effects these bonds are stronger than dispersion forces and comparable in strength to hydrogen bonds.8,9 Only recently was the thiolate binding to Au NPs10,11 elucidated, following structure determination of Au102-thiolate NPs:12 thiolate groups, in so-called capping agents, can stump growth and lead to small NPs, e.g., Au25.13-16 Theoretical work17 on Au25(SR)18 has evidenced a structure consisting of a Au13 core capped with six (MeS)3Au2 complexes, consistent with experiments.13 The aforementioned findings support the “divide and protect” scheme, initially proposed by Hakkinen et al.,18 whereby Au NPs are capped with molecular Au-thiolate rings. The resulting NPs exhibit core-shell structure with a symmetric, stable, metallic core and an outer shell of metal complexed with thiol ligands. However, the precise nature of the shell constituents (e.g., rings) is poorly understood. A theoretical investigation of the structural and electronic

* Corresponding author, [email protected]. Received for review: 04/22/2010 Published on Web: 08/18/2010 © 2010 American Chemical Society

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FIGURE 1. (a) Binding energy (BE) per Au atom, n, and HOMO-LUMO (HL) gaps of the AunMBAn complexes for n ) 1-12. (b) Structures of the most stable AunMBAn complexes for n ) 4, 8, and 12. (c) Au4MBA4 structure interacting with eight water molecules on the -COOH end-site. Au atoms are illustrated in yellow, sulfurs in cyan, carbons in brown, oxygens in red, and hydrogens in white.

Au8MBA8. So we see, for the first time, that it is not only the metal NPs that exhibit magic number stability but also the capping complexes (AuMBA)n do so too, for n ) 4 and n ) 8. As discussed below, these stable complexes play a key role in the formation of monodisperse NPs. The Au8MBA8 complex is the only one among those studied where the COOH groups interact via hydrogen bonds. Hydrogen bonds between four out of the eight carboxyl groups contribute only 0.23 eV to its total stability. We confirmed the lack of hydrogen bonds and π-π interactions in the smaller complexes by reoptimizing structures up to n ) 6 using larger basis sets (tzvp and def-tzvpp) (see also comment in the Supporting Information). We have also observed that the Au4MBA4 complex may be found in two nearly isoenergetic conformations: the half-shield one (Figure 1b) and the zigzag one (shown in Figure 3S in Supporting Information). That indicates that the MBAs do not interact in small complexes. Hakkinen et al.18 have also observed increased stability for the Au4(SCH3)4 system, but in a zigzag ground state conformation19 with the methyl groups shielding both sides of the metal (see Figure 3S in Supporting Information). We have performed a natural bond orbital population analysis and concluded that a fractional charge transfer takes place from the Au d-orbitals to the p-orbitals of S. That implies a Au(d)-S(p) orbital hybridization, which gives the Au-S bond a polar-covalent character, in accordance with a previous theoretical study19 on Aun(SMe)n complexes. In order for the stable complexes to block NP growth, in solution, they must be “locked” in a conformation where the metal atoms are not fully shielded by the organic moiety.

and block their growth, to investigate the role of the solvent, and thus to shed light on outstanding issues about the mechanism that leads to monodisperse Au102(MBA)44 NPs.12 In the DFT calculations, the systems were fully optimized without symmetry constrains, using different initial structural configurations. We used the ri-bp86 method combined with the sv(p), tzvp, and def-tzvpp basis sets (default ECPs were included for the Au atoms) as implemented in the Turbomole 5.9.0 package.26-31 In the MD simulations, electrostatic and pairwise additive van der Waals interactions between the atoms made up the MD force field. In particular, the Au-Au interactions were modeled with a Morse potential with parameters fitted to binding energies obtained from the DFT calculations of this study (first principle potential development in Supporting Information). The rest of the van der Waals interactions were modeled with Lennard-Jones 6-12 potentials, with OPLS-AA parametrization.32 For the water, we employed the SPC/E model.33 DFT-optimized structures (starting mainly from stable, planar metallic structures plus MBAs) are depicted in Figure 1S of the Supporting Information; their energetic stability is presented in Figure 1a. Complexes of size n ) 4, 8, and 12 are considerably more stable than others, with binding energies per AuMBA equal to 1.71, 1.75, and 1.70 eV, respectively (structures shown in Figure 1b). Furthermore, our calculations reveal that these structures have very stable electronic configurations, too, with HOMO-LUMO gaps of 3.32, 2.97, and 2.86 eV, respectively. Interestingly, the Au12MBA12 relaxation calculations (see Figure 2S in Supporting Information) yielded a structure that is clearly the composite of the two stable complexes Au4MBA4 and © 2010 American Chemical Society

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FIGURE 2. Population probability for different cluster sizes, n, as a function of time: (a) in pure water solution; (b) in 46% v/v methanol-water solution.

Specifically, it is easy to see that the zigzag conformation of Au4MBA4 would keep the Au atoms from interacting with those in the NP, because the MBA molecules are in the way. On the other hand, the half-shield conformation (Figure 1b) would allow interaction with the metal NP. So, an intriguing question arises: which of the two conformations dominates in solution and does water, through hydrogen bonding, have anything to do with it? Indeed, by carrying out DFT calculations with a number of explicit water molecules, we have found that hydrogen bonds between the COOH groups and the solvent stabilize the half-shield conformation of the tetramer. Specifically, by including 12 water molecules in the DFT calculations, we see the formation of an H-bond network of 5.84 eV (waters’ binding energy). The result is the stabilization of the half-shield conformation over the zigzag one by 0.63 eV (at the tzvpp theory level). Upon stabilization, the half-shield conformation of Au4MBA4 interacts weakly with another tetramer via its metallic part, as shown in Figure 4S (Supporting Information). The presence of water molecules12 and water clusters34 interacting via hydrogen bonding with COOH groups, in the interstice of the NPs, has also been observed experimentally. So we see, once again, that solvent effects, manifested with hydrogen bonding interactions with polar groups, play a crucial role during NP growth. Here, we have seen the water act as a “molecular conformation locker” of the Au4MBA4 complex, stabilizing one conformation over another. This is in addition to its already reported role as a structure directing agent in the formation of symmetric metal clusters.35 As noted earlier, these important effects were not captured in previous theoretical calculations on Au NPs, because the water molecules were suppressed. We note, in passing, that hydrogen bonding has also been found to play a critical, shape-determining role in the formation of Ag nanostructures. Interestingly, in the case of silver, it is the protonation state of the capping agentsa citratesthat determines the stabilization mechanism. In its protonated © 2010 American Chemical Society

state, the citrate leads to the formation of Ag nanowires, via hydrogen bond stabilization. When, however, the citrate is deprotonated, an electrostatic stabilization mechanism takes over, resulting in the formation of nanoparticles.36 With the solvent playing such a crucial role, it is essential to investigate the stability of the AunMBAn species in the environment where the growth of the nanoparticles takes place, namely, in solution. To that end, we have also carried out NVT MD simulations in water and in a methanol-water solution mixture, where the NP synthesis actually takes place.12 In pure water, the AuMBA complexes show a polymeric growth behavior, as previously shown for the AuSCH3 complexes by gas-phase DFT calculations.19 In a simulation system with 14 AuMBA and 2244 water molecules, at T ) 300 K and water density 1 g/mL, a 10 ns trajectory shows that the Au atoms want to cluster up as much as possible, with a 13-mer found in the end of the simulation. Visual inspection of the trajectory indicates that cluster formation happens rather incrementally up to the hexamer, although the presence of some intermediate species, e.g., the trimer, is rather fleeting. These observations are also verified by a formal statistical analysis of the trajectory. In Figure 2, panel a, we have graphed the population probability for different cluster sizes n as a function of time. We observe that the dimer, tetramer, and hexamer are the most prominent, intermediate species in the solution. At t ) 3 ns, two hexamers coalesce to form a dodecamer, which shortly thereafter captures a monomer to form a 13-mer. There is no particular reason to believe that the 13-mer is favored over the 14-mersa longer trajectory should eventually yield the latter. The Au-Au pair distribution function (Figure 3, panel a) shows that, on average, each Au atom has about 4.6 tightly bound nearest neighbors at 2.78 Å (the equilibrium separation of the Morse potential modeling the Au-Au interaction) and 3 second-nearest ones at 4.5 Å. The second highest peak in the Au-Au g(r) is almost an order of 3410

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FIGURE 3. Gold-gold pair distribution function (black line, drawn on the left-hand scale) and corresponding coordination numbers (red line, drawn on the right-hand scale): (a) in pure water; (b) in 46% v/v methanol-water mixture.

FIGURE 4. The distinct van Hove correlation function, Gd(r,t)/G, for the Au atoms at different times: (a) in pure water; (b) in 46% v/v methanol-water solution. At t ) 0, the correlator reduces to the pair distribution function, g(r).

magnitude lower than the main one but still of large amplitude, indicating an overall tight cluster. This is not surprising, as the Morse potential’s well depth is 4.8 kcal/mol (∼8kT at T ) 300). A very different picture emerges from the simulation of the system in the methanolic solution, the environment where, in fact, the nanoparticle synthesis takes place. In a simulation system with 8 AuMBA, 1894 methanol, and 4912 water molecules, a 20-ns trajectory, at T ) 300 K, shows that the tetramer is the more stable species. The single, highamplitude peak in the Au-Au pair distribution function (Figure 3, panel b), which upon integration measures three nearest neighbors per Au atom, does not equivocate about the presence of two, well-separated tetramerssalbeit in a tetrahedral geometry rather than the planar predicted by the gas-phase DFT calculations. The population probability for the various species as a function of time is shown in Figure 1, panel b. The first tetramer is formed early on, at t ≈ 1.5 ns. Here, the trimer lingers for quite a while before the second tetramer forms ∼6 ns later. We should comment that it would be rather impossible for the single-site interaction model employed for our molecular mechanics force field to capture the exact geometry of the Au4MBA4 cluster, since the DFT-predicted, planar geometry is the result of orbital hybridization, as we have already analyzed. That, however, should not detract from the fact that the tetramer is found to be the most stable species in the methanolic solution. But more importantly, the MD simulations clearly show that, in the methanolic solution, the tetramer assumes the half-shield conformation (see Figure 5S in Supporting Information), exactly as predicted by our gas-phase DFT calculations with a number of explicit water molecules. (See also Comment 2, and MD trajectory snapshot in Figure 5S of Supporting Information). In both solutions, we have not found any significant hydrogen bonding among the MBA carboxyl groups. On the other hand, the anticipated hydrogen bonding between the © 2010 American Chemical Society

carboxyl groups and the water molecules is present, in agreement with the DFT results. Analysis of the relevant pair distribution functions (see Figure 6S in Supporting Information) shows that, on average, each COOH participates in 2.6 H-bonds with water molecules. We also find that there is practically no association between the COOH and the methanol molecules. The alcohol, however, associates with the aromatic ring of MBAsa very short ranged correlation via the carbon-carbon interaction. These findings make a great deal of sense. The mercaptobenzoic acid is insoluble in water, so this accounts for the extended aggregation that we observed in pure water solvent. We believe that in this case the aggregation is not so much driven by the considerable Au-Au attraction as by the fact that the MBA molecules want to “fall out” of solution. On the other hand, the MBA is soluble in alcohol and the solvation of the tetramer in the methanolic solution appears to be thermodynamically more favorable than the solvation of a larger cluster. These differences in the solvation of the AuMBA complex and its oligomers are manifested in the relaxation dynamics of the Au atoms. We have analyzed the Au atoms’ density fluctuations by calculating the corresponding incoherent (or self) and coherent (or distinct) van Hove correlation function G(r b,t)37 (see the Supporting Information for an interpretation of the van Hove function). In Figure 4, we graph the distinct van Hove correlation function, Gd(r,t), for the Au atoms, in pure water (panel a) and in the water-methanol mixture (panel b), for different times t. In the pure water simulation, we can clearly see vestiges of the nearest-neighbor shell even at t ) 10 ps, which means that the identity of the first neighbors is not completely lost with time. This short-range order in the arrangement of an Au atom and its neighbors reveals a certain degree of permanencesreminiscent of the 3411

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FIGURE 5. Au NP growth mechanistic scheme: (a) formation of a stable Au4MBA4 complex; (b) Aun NP growth and stabilization upon interaction with the Au4MBA4 complexes.

permanent correlation existing in solidssand here is a manifestation of the insolubility of the species that form in pure water. In stark contrast, in the methanolic solution, the particles very quickly lose their identity and the density disturbance caused by an Au atom results in high-amplitude fluctuations in the region 0 < r < 1. Such relaxation dynamics imply that in the methanolic solution the AuMBA complex (and its stable tetramers) is very mobile and in true solution. We should mention that the solubility of both the MBA and the Au metal can be affected by the presence of Na+ (counterions) in solution when the cations interact with the AuMBA complexes. All the aforementioned results enlighten a unique NP growth mechanism, presented in Figure 5. Initially, two parallel processes take place in solution (paths a and b). In path a, the metal cation of the salt associates with negatively charged MBAs forming AuMBAs, whose self-assembly leads to Au4MBA4 complexes. Water molecules stabilize the half-shield conformation of Au4MBA4 (Figure 1c) via hydrogen bonds, whereas the presence of methanol prevents the aggregation of AuMBAs and the formation of complexes larger than the tetramer. In path b, metal cation, which is being reduced via a reducing agent, leads to symmetric Aun NPs. During metal NP growth via monomer (Au) addition, water prevents the formation of asymmetric clusters,35 and metal NPs of magic size (which show increased stability) have a longer lifetime in solution. As a result, metal NPs and Au4MBA4 complexes of magic number stability dominate in solution. Then metal NPs and Au4MBA4 complexes associate and the latter block further NP growth. Monomeric Au atoms and AuMBAs may also © 2010 American Chemical Society

associate with NPs. The overall, very plausible reaction that explains the monodispersity of Au102(MBA)44 NPs is

Au58 + 11Au4MBA4 f Au102MBA44

since all reactants and products exhibit high electronic and structural stability with long lifetimes in solution (Au58,38 Au102MBA44,10-12,39 Au4MBA4 (present study)). In the case of Au102(MBA)44, the NPs follow the 58-electron shell closing: each Au atom of the 102 contributes one valence electron (5d106s1), where 44 of them bind sulfur atoms and the remaining 58 fill up the shell.10,12 This electronic stability was also recently confirmed theoretically by a large HOMOLUMO gap.11 Very interestingly, a theoretical study on the Au102MBA44 NP39 revealed that the complex can be described as a D5h Au79 metallic core, with a protective Au23(MBA)44, Au-thiolate layer. This Au-thiolate layer is organized in such a way that the surface of the Au79 metal core is chemically fully passivated, with a shell giving a large HOMO-LUMO gap to the whole structure. It becomes apparent that in the last stage of the NP formation, structure relaxation is driven by electronic factors, such as electron shell closures and creation of large HOMO-LUMO gaps. The NP symmetry together with the Au-S bond orientations determine the final electron density distribution and consequently the electronic characteristics of the NP. As a result the NP surface can reorganize forming RS-Au-SR “staple” motifs20,21 in a way that the whole system minimizes its total energy. Putting our results and those by Walter et al.39 together, it is possible that NP formation takes place by 3412

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(2) (3)

aggregation of the very stable Au58 with 11 Au4MBA4 units and by subsequent surface relaxation that results in an Au79 metallic core surrounded by a Au23(MBA)44 protective shield. In summary, the present theoretical work has revealed magic numbers in the complexation of the Au-SR intermediates and unraveled a mechanism that is conducive to the formation of monodisperse NPs.12,16,25 In this mechanism, the roles of the solvent and of the functional groups of the capping agent are intertwined. By using first-principle calculations, we showed that the AunMBAn complexes exhibit “magic” number stability for n ) 4 and 8, with very stable electronic configurations. By Molecular Dynamics simulations, we revealed that in water-methanol solution the dominant species, among those exhibiting “magic” stability, is only the Au4MBA4 complex, in a conformation stabilized by hydrogen bonds. The pivotal role of the solvent was elucidated: the water acts as a “molecular locker”, while the methanol prevents polymeric growth of the AunMBAn complexes. Our predictions are supported by experimental findings, namely, the reported importance of the aggregation state of these complexes in controlling NP dispersity,16 the structural determination of the monodisperse Au102 NPs,12 and the effect of solvent on synthesizing virtually monodisperse Au NPs.25 Moreover, it is worth noting the resemblance between our Au-thiolate structures and the synthesized AuI···AuI bonded, rings and crowns,23,24 even though the latter’s architecture is driven by ligand design. In Au102,12 NPs were stabilized with 44 MBAs (a number likely to arise from the association of 11 Au4MBA4 units on the A58 NP surface). Our work clearly indicates that in order to control NP dispersity, experimental efforts should focus on designing stable (“magic”) Au-SR complexes via supramolecular chemistry and by “tuning” the effects of solvent on these complexes. Building blocks of core-shell structures and their self-assembly may be a much more frequently occurring mechanism in nanomaterials synthesis than previously thought.3

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Acknowledgment. This research was supported by a Marie Curie International Outgoing Fellowship to G.M. within the seventh European Community Framework Programme and by the Department of Energy (DE-FG02-05ER257022). Authors would like to thank Dr. E. Roussakis from the Department of Biochemistry and Biophysics, University of Pennsylvania for fruitful conversations.

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Supporting Information Available. Computational details, DFT optimized structures and interaction potentials, MD snapshot, analysis of the Van Hove correlation function, and atom-pair distribution functions. This material is available free of charge via the Internet at http://pubs.acs.org.

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