Molecular Simulation of Ag Nanoparticle Nucleation from Solution

Letter pubs.acs.org/NanoLett

Molecular Simulation of Ag Nanoparticle Nucleation from Solution: Redox-Reactions Direct the Evolution of Shape and Structure Theodor Milek and Dirk Zahn* Computer Chemie Centrum/Lehrstuhl für Theoretische Chemie Friedrich-Alexander Universität Erlangen-Nürnberg Nägelsbachstraße 25, 91052 Erlangen, Germany S Supporting Information *

ABSTRACT: The association of Ag+ ions and the early stage of Ag nanoparticle nucleation are investigated from molecular dynamics simulations. Combining special techniques for tackling crystal nucleation from solution with efficient approaches to model redox-reactions, we unravel the structural evolution of forming silver nanoparticles as a function of the redox-potential in the solution. Within a range of only 1 eV, the redox-potential is demonstrated to have a drastic effect on both the inner structure and the overall shape of the forming particles. On the basis of our simulations we identify surface charge and its distribution as an atomic scale mechanism that accounts for creating/avoiding 5-fold coordination polyhedra and thus the degree of (multiple)-twinning in silver nanoparticles. KEYWORDS: Metal nanoparticles, nucleation mechanism, molecular dynamics simulation

T

near quantum-chemical accuracy.12 On this basis, we can elucidate the structural evolution of silver clusters as a function of size at atomic resolution, i.e., upon association of one Ag+ ion after another. After each ion association step, possible reduction of the forming silver particle is considered according to

he wide range of applications for metal nanoparticles has motivated an immense number of studies dedicated to syntheses of increasingly controlled size and shape. Using inexpensive wet chemistry approaches, silver nanoparticles can be prepared as cubes, rods, quasi-spheres, triangular prisms, and star-like shapes.1 Despite these tremendous advances from the experimental side, theory lags behind in providing in-depth understanding of the underlying mechanisms. Indeed, metal clusters pose an ongoing challenge to molecular simulation which requires a reasonable balance between accurate evaluation of atomic interactions and appropriate sampling of the immense manifold of different configurations. While the search for favorable structures for the relatively simple systems of neutral metal clusters in the gas phase already inspired considerable theoretical efforts,2 even more specialized simulation approaches are needed to account for nuclei selforganization during aggregation from solution.3,4 Here, we report on a molecular simulations dedicated to Ag nanoparticle nucleation from ethylene glycol solutions of silver nitrate modeling the popular “polyol” synthesis.5−8 Unlike the characterization of the final products, experimental work on the nucleation mechanisms is rather scarce. However, Sloufova et al. provided surface enhanced Raman scattering evidence for the existence of charged domains on silver nanoparticles,9 thus hinting at the importance of considering the interplay of aggregate growth and redox reactions. For the present molecular simulation study we account for this phenomenon by using a combination of a recently developed method for studying crystal nucleation from solution10,11 with efficient interaction potentials that describe charge transfer between individual Ag atoms within the forming silver nanoparticle at © 2014 American Chemical Society

reducing agent

Ag m x + + Ag + → Ag(mx++11) + ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ Ag m + 1 y +↓

The manifold of possible redox reactions is hereby “coarsened” to a single, tunable parameter, the redox-potential. This allows us to mimic in principle any reducing condition, while explicit ethylene glycol molecules are employed to describe the (nonreactive) solvent effect of embedding the forming nanoparticle. Methods and Models. Interactions within the silver aggregates are evaluated by a combination of the embedded atom method (EAM)13−15 and the extended charge equilibrium method (QEq).16−18 While the former is well-established for uncharged metal clusters and bulk phases, the latter is used as an extension to account for polarization and nonzero net charge in the clusters. The key concept of QEq is to balance partial charges qi for all atoms i of the cluster to ensure (a) a given net charge and (b) minimal electrostatic potential E. Accordingly, electronegativity χi, as described here by a Taylor expansion, must be equalized for all atoms i of the cluster. Received: July 3, 2014 Revised: July 28, 2014 Published: July 31, 2014 4913

dx.doi.org/10.1021/nl502503t | Nano Lett. 2014, 14, 4913−4917

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Scheme 1. Illustration of the Aggregate Growth Schemea

a Starting from the particularly stable Ag13 cluster (left), ion docking from random direction is followed by detailed relaxation from molecular dynamics simulations (right). After each ion association step, possible reduction of the forming nucleus is explored as a function of the redoxpotential in the solution.

Figure 1. Representative snapshots illustrating the evolution of silver clusters as functions of size and redox-potential in the solution. Using a relative scale, strong (top) and weak (bottom) conditions are compared to the reference scenario (middle) which is chosen as the redox potential required to reduce an isolated Ag+ to a silver atom. A color code is used to highlight local charge distribution.

⎛ ⎞ ⎛ ⎞ 1 ∂ 3E 1 ∂ 4E χi = χi + 2ηi ·qi + ⎜⎜ 3 ⎟⎟ ·qi 2 + ⎜⎜ 4 ⎟⎟ ·qi 3 2 ⎝ ∂qi ⎠ 6 ⎝ ∂qi ⎠ 0 0 0

+

the OPLS force-field.21 It is known to well reproduce solvent properties such as density and molecular polarization. The Lennard−Jones mixing parameters for the interaction of ethylene glycol with silver are taken from Heinz et al.22 In addition to this, we account for possible reduction of the aggregate after each ion association step as discussed in the following. The evolution of silver nuclei forming in ethylene glycol solution is investigated by the Kawska−Zahn approach which describes aggregate growth ion-by-ion within an iterative procedure (Scheme 1). Therein, Ag+ diffusion to growing silver clusters is mimicked by a simple docking procedure, followed by simulated annealing type molecular dynamics runs to explore aggregate relaxation in solution. The latter is modeled by a periodic cell of ∼4 nm dimensions of ∼700 solvent molecules. Both explicit nitrate ions and the diffuse counter charge model were tested (as discussed in the Supporting Information). From this we confirmed the accuracy

0

1 4πε0

∑ f (rij ; qj) j≠i

Therein, all derivatives are fitted to quantum calculations.17,18 The scaled potential f is applied to effectively model the shortrange Pauli repulsion as well as the long-range Coulomb interactions (including diffuse counter charge to achieve charge neutrality of the overall system) via the damped shifted force approach, originally proposed by Wolf et al.19,20 More details and benchmarks of this approach to model charged silver clusters were assessed from comparison to with density functional theory calculations as reported in ref 12. The nonreactive character of the solvent is described by a classical molecular mechanics model of ethylene glycol using 4914


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of the latter approach whichin terms of computational efficiencywas found much more favorable for the nucleation and growth runs discussed in the following. For each Ag+ association step, we sample the enthalpy of AgnQ+ and Agn(Q−1)+ from parallel runs of 1 ns (using a time step of 1 fs) and decide about the clusters net charge on the basis of the applied redoxpotential. Thus, without going into molecular detail, all kinds of redox-agents in the solutions are accounted for by a single, effective redox-potential ϕredox. Along this line, metal cluster oxidation/reduction is assessed by comparing the corresponding difference in enthalpy with the applied redox-potential:

Despite the relatively moderate change in the redox conditions, the nature of the forming nuclei differs considerably. While the inner core of the clusters is practically uncharged, surface patterning and even roughening by aggregate charge also shows drastic effects on the inner structure of the nuclei. On the one hand side, surface charge implies a “negative pressure” which facilitates the formation of defects in the bulk. Among the possible defects in the fcc lattice, 5-ring motifs are of particular importance because they reflect interfaces to differently oriented fcc domains. Figure 2 shows the average

ΔG = G(AgQn +) − G(Ag(nQ − 1) +) ⎧ ⎪ ΔG + ϕredox < 0 → reduce cluster →⎨ ⎪ ⎩ ΔG + ϕredox ≥ 0 → no reduction

The identification of structural motifs in the forming silver aggregates was based on the common neighborhood analysis which, for a given atom, reflects its coordination number, binding between its neighbors, and the coordination numbers of the neighboring atoms.23−25 Details of this approach are discussed in the Supporting Information. Results. Using the above-described implementation of the Kawska−Zahn approach for investigating nucleation from solution, we studied the evolution of forming silver nuclei under three different redox potential conditions. For each of these nucleation scenarios, a series of three independent simulation runs was performed. Because of computational limitations our data cannot rigorously account for the immense manifold of configurations. However, the findings discussed below were found to be consistent within the corresponding series of independent runs demonstrating the validity of our mechanistic analyses. Starting from the particularly stable Ag13 icosahedron, which reflects a magic-number cluster of considerable stabilization from low surface tension, each of the nine simulation runs were propagated for 150 Ag+ ion association steps. The very early stages of cluster formation are relatively insensitive with respect to the redox potential and largely correspond to the evolution of uncharged metal clusters.11 However, after about 25 ion association steps we observe an increasing trend toward control of the clusters’ shape and structure by surface charge. Figure 1 illustrates representative series of growth runs performed within a ±0.5 eV range of the redox potential applied. Charge neutral metal clusters are well-known for their interplay of favorable bulk interactions and surface stress which leads to an evolution of shape and structure encompassing fccstructures and magic number clusters reflecting polyhedra of compact surfaces.11 An additional degree of complexity is now given by considering various redox conditions leading to net charging. Throughout all of our simulation runs, the forming nuclei exhibit a pronounced heterogeneous charge distribution which results from the interplay of electronegativity and Coulomb interactions. While the former would give rise to homogeneous charging, Coulomb repulsion within the silver cluster and attraction to the embedding solvent favors localized charges according to bulk < faces < edges < corners. An immediate consequence of this trend is the favoring of large and eventually roughened surfaces with increasing cluster charge. This is nicely illustrated by comparing the simulation runs at relative redox potentials of −0.5 to 0.5 eV (Figure 1).

Figure 2. Average net charge (left) and average number of common neighborhood motifs (right, sampled over the last 75 growth steps) as functions of nucleus size and redox-potential in the solution. In particular for weak redox conditions (high net charge) we find that the inner structure of the forming nuclei comprises a large number of nonfcc type, 5-ring motifs which give rise to rough surface patterns as illustrated in Figure 1.

cluster charge and the average number of packing motifs in the bulk as functions of the redox potential applied to the solution. A moderate degree of twinning, or more precisely multipletwinning, allows for compact surfaces as also observed for the decahedral and icosahedral magic number clusters at zero charge.11 On the other hand, at relatively large surface charge such 5-ring motifs become much more abundant to allow for rugged surfaces. In-between these two extremes, our simulation runs referring to a relative redox potential of 0 eV exhibits most favoring of fcc motifs and the least abundance of 5-fold coordination defects and thus correspond to a moderately enlarged surface at the benefit of particularly favorable interactions in the interior (see Supporting Information for a detailed documentation of the packing motifs analysis and the discussion of magic number clusters as functions of charge). The redox potential is thus identified as a very sensitive parameter for tuning both shape and the inner structure of forming silver nuclei. Interestingly, this phenomenon already applies to very early stages of nucleation, from about 50 Ag atoms onward, and should be considered for both nanoparticles stemming from a single nucleus and particle formation from agglomeration of smaller precursor aggregates. Surfactants may further strengthen the role of redox conditions for controlling the structural evolution of metal nanoparticles: By the example of the final nuclei illustrated in Figure 1 we can clearly outline domains of low surface charge which are susceptible to “covalently” binding surfactants such as thiols (Figure 3, left). On the other hand, edges and corners tend to concentrate partial charges and are thus more readily stabilized by anions (Figure 3, right). In-between these two extremes, a moderate degree of nuclei charging and a combination of both types of surfactants appears particularly 4915


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ASSOCIATED CONTENT

S Supporting Information *

Common-neighbor-analysis, stability of charged “magic” clusters, and influence of nitrate ions. 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]. Notes

Figure 3. Charge distribution in equally sized nuclei formed under different redox-conditions (depicted from Figure 1). Left: strong redox-potential leads to low net charge. Covalently binding surfactants such as thiols are preferred. Center: covalent binding can be used to stabilize faces, while anions appear best suited for association to the charged edges and corners of the nucleus. Right: rough surfaces exhibiting a large number of high partial charges. Stabilization by anions is clearly favored.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge the funding of the Deutsche Forschungsgemeinschaft (DFG) through the Cluster of Excellence Engineering of Advanced Materials.

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REFERENCES

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suited to stabilize particles with plain faces and well-defined edges (Figure 3, center). A further consequence of anions in the solution is the lowering of the effective charge of the nanoparticle-−surfactant complex as experienced in electrophoretic measurements and mass-spectrometry. So far, we used a diffuse background charge in our aggregate growth runs to maintain overall charge neutrality of the solution. However, the consideration of explicit anions in the simulation model may easily be implemented as a postprocessing step. We demonstrate this for nitrate ions by attaching the corresponding number of NO3− ions to the Ag163Q+ nuclei highlighted in Figure 3. Starting from initially fully neutralized effective charge, the colloid was found to gradually release nitrate ions to the solution resulting in average effective charges of +1, +3, and +4 for Q = 3, 8, and 15, respectively (see also Supporting Information). The nitrate ions are associated only temporarily and exhibit considerable mobility either along the aggregate surface and concerning frequent association/dissociation events. Nitrate ions hence do not correspond to explicit surfactants, but rather to a halo of counterions that damp the effective particle charge without effect on the shape and structure as compared to the implicit counter charge model used for the growth simulations. Conclusion. Our simulations demonstrate the crucial role of the redox-potential for directing the inner structure and the overall shape of Ag nuclei forming from solution. Surface charge is preferentially localized at corners and edges. With increasing charge, this trend gives rise to surface roughening and particle deformation, both requiring 5-fold coordination polyhedra in the bulk and thus a degree of (multiple)-twinning. At weak redox conditions, Coulomb repulsion of the highly charged metal clusters may outperform surface tension and thus account for the energetic preference of enlarged, rugged surfaces. While these structures may be considered as seeds to noncompact, branched nanoparticles, we also suggest guides to morphologies based on plain faces and well-defined edges (cubes, prisms, etc.). For this, we suggest nucleation at moderate redox potential and a combination of covalently binding and anionic surfactants for stabilizing faces and edges/ corners, respectively. 4916


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Molecular Simulation of Ag Nanoparticle Nucleation from Solution

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