Atomic-Scale Theory and Simulations for Colloidal Metal Nanocrystal

Article pubs.acs.org/jced

Atomic-Scale Theory and Simulations for Colloidal Metal Nanocrystal Growth Kristen A. Fichthorn* Department of Chemical Engineering and Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: A significant challenge in the development of functional nanomaterials is understanding the growth of colloidal nanocrystals. Although it is presently possible to achieve the shape-selective growth of colloidal nanocrystals, the process is not well understood and not generally scalable to a manufacturing environment. Advances in our fundamental understanding are hampered by the complexity of the colloidal environment, which makes it difficult to experimentally interrogate the liquid−solid interface of a growing nanocrystal. Theory can be beneficial, but because of the lack of quantitative experimental data, theoretical efforts should be based on first-principles to ensure sufficient accuracy. I review our studies with first-principles, density-functional theory of how polyvinylpyrrolidone (PVP), a widely used structure-directing agent (SDA) in the synthesis of Ag nanocrystals, might function effectively as an SDA. These studies indicate that the beneficial characteristics of PVP are not present in poly(ethylene oxide) (PEO), which is experimentally determined to be less effective as an SDA. I discuss our recently developed force field to characterize the interaction of PVP, PEO, and ethylene glycol solvent with Ag surfaces. The availability of a reliable force field will enable future studies using classical molecular dynamics simulations to probe various aspects of nanocrystal growth.

■

INTRODUCTION A significant challenge in the development of functional nanomaterials is understanding the growth, transformations, and assembly of colloidal nanoparticles. From a practical perspective, this knowledge would benefit numerous applications in energy technology. In the substitution of fossil fuels by renewable energy resources, for example, nanometer-sized particles play a key role as catalysts for synthesizing energy vectors from biomass.1−5 Nanoparticles are further indispensable as electrocatalysts in fuel cells,6−12 and nanostructured materials offer advantages for hydrogen storage.13 The ability of plasmonic Ag and Au nanostructures to concentrate UV−vis radiation in small volumes makes it attractive to use these building blocks in the design of composite photocatalysts for the production of solar fuels.14−21 Nanoscience in both the experimental and the computational arena has played an important role in advancing these catalytic technologies.22−28 Nanoparticles will also figure prominently in emerging solarcell technologies, for example as nanometallic plasmonic structures to enhance the light absorption and the efficiency of photovoltaics14,29−31 or as flexible electrode materials.32 Semiconductor nanostructures are important in films with large surface areas in dye-sensitized solar cells,33−39 where their aggregation and interfacial structure can influence electron transport. In these and many other applications, it has been emphasized that the sizes, shapes, phases, and assembly or dispersion of the nanoparticles can significantly impact their performance. © XXXX American Chemical Society

For most applications, nanoparticles are synthesized in a colloidal environment, involving a precursor salt, solvent, and various additives that can be used to alter the nanocrystal growth process. Due to the complexity of this environment, the fundamental understanding of most colloidal syntheses is still in its infancy. It is experimentally difficult to interrogate nanocrystal growth in situalthough new techniques, such as environmental transmission electron microscopy,40 continue to emerge. Atomic-scale theory and simulations can play an important role in the quest to understand colloidal nanocrystal synthesis. First-principles density-functional theory (DFT) calculations can reveal much about the interactions that dictate nanocrystal growth and structural transformations.41−44 However, it is prohibitively difficult at present to simulate nanometer-sized particles in the presence of solvent (and perhaps additives) entirely from first principles. Such problems fall within the capabilities of classical molecular dynamics (MD) simulations, which can reveal nanocrystal interactions, transformations, and aspects of growth.45−55 The force fields (FF) underlying MD simulations can be parametrized and tested against first-principles calculations and/or experiments to ensure their suitability for a given application.56−58 Special Issue: Modeling and Simulation of Real Systems Received: February 25, 2014 Accepted: May 19, 2014

A

dx.doi.org/10.1021/je500189s | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

In this paper, I review our recent efforts41−44,58 to gain an understanding of Ag nanocrystals grown using solution-phase methods.59−68 The nucleation and growth mechanisms in these syntheses are complicated and not well understood. Central to the selective formation of nanocrystal shapes are additive molecules known as structure-directing agents (SDAs). In the presence of a SDA, a nanocrystal can grow to adopt a different shape from the Wulff polyhedron predicted from the energies of its bare metal surfaces. Polyvinylpyrrolidone (PVP), for example, is a particularly successful SDA that is known for promoting the formation of Ag and Pd nanocrystals bounded by {100} facets such as nanocubes, nanobars, and nanowires,59−68 when the lowest-energy facets of Ag and Pd in vacuum are the {111} facets. However, it is not well understood why PVP and other SDA molecules are successful. A basic understanding of the traits that endow these molecules with structure-directing capabilities might allow us to identify new SDAs with greater selectivity for producing well-known crystal shapes or with capabilities to produce entirely new nanostructures.

Figure 1. Repeat unit of PVP (a) and two related submolecules: 2pyrrolidone (b) and 1-methyl-2-pyrrolidone (c). Carbon atoms are turquoise, hydrogen is white, oxygen is red, and nitrogen is blue.

of these calculations can be found in ref 41. Table 1 summarizes some structural properties of gas-phase 2P, which agree well Table 1. DFT+vdWsurf and Experimental Bond Lengths (dx−y) and Bond Angles (θx−y−z) for Gas-Phase 2Pa

■

FIRST-PRINCIPLES STUDIES OF POLYMERIC SDAS PVP is a widely used polymeric SDA, with a demonstrated capability for producing Ag nanostructures with {100} facets.59−68 The origin of this selectivity has been proposed to be the selective (preferential) binding of PVP to Ag(100). This selective binding may lead to passivation of the Ag(100) facets, so that atoms add to neighboring facets in the crystal for example {111} facetsand thereby selectively grow the {100} facets. By binding more strongly to the {100} facets, PVP may lower the surface energy of these facets relative to the {111} facets, which are energetically preferred for the bare Ag metal. Thus, PVP may promote different thermodynamic crystal shapes than the Wulff shapes predicted for bare Ag nanocrystals. A third possibility is that, by binding more strongly to certain surface features, PVP may alter the diffusion of Ag atoms across the nanocrystal facets and, thus, prevent certain structural transformations of the growing nanocrystals. As a ground-zero effort for testing any of these scenarios, we need to understand how PVP interacts with various Ag surfaces and what might determine its strong selectivity for producing {100} facets. As a test of our ideas, I show that the traits that likely make PVP a successful SDA are not present in PEO, which is not as beneficial.59,60 Computational Methods. First-principles studies of polymer adsorption are challenging because of the macromolecular length scales involved. To make the problem tractable, we studied a logical submolecule of the repeat unit of PVP2-pyrrolidone (2P). This molecule is shown in Figure 1, along with the repeat unit of PVP. Experimental spectroscopic studies indicate that PVP chemically bonds to Ag surfaces via the 2P ring.69−73 Thus, we studied the interaction of 2P with Ag surfaces to gauge the total interaction. We also probed the interaction of 1-methyl-2-pyrrolidone (shown in Figure 1) with the Ag surfaces, and as I will elaborate below, we found that it is similar to the Ag-2P interaction.58 For the DFT studies, we used a locally modified74 version of the Vienna Ab Initio Simulation Package (VASP).75−77 This version includes van der Waals (vdW) interactions using the DFT+vdW method of Tkatchenko and Scheffler.78 To account for screening effects that can mitigate vdW interactions in bulk metals, we used a parametrization of DFT+vdW by Ruiz et al.,79 known as DFT+vdWsurf, for the vdW interactions. Details

PBE+vdWsurf experiment80

dC5−O/Å

dC2−N/Å

dC5−N/Å

dC2−C3/Å

θO−C5−N/deg

1.229 1.238

1.373 1.335

1.455 1.460

1.530 1.518

125.878 125.90

a

Atoms are numbered sequentially along the ring with N = 1 (cf., Figure 1b).

with experimental values.80 We are also able to accurately describe the experimental lattice constant for Ag, as well as the interlayer spacing between the first and second layers of atoms at the Ag(111) and Ag(100) surfaces.42 Results and Discussion. To study the adsorption of 2P to Ag surfaces, we began with various initial 2P molecular configurations on Ag(100) and Ag(111), and we optimized the structure/conformation of the molecule, along the top three Ag surface layers, by minimizing the forces on all the moving atoms until the largest force on any atom is less than 0.01 eV/ Å. Our search produced four and five unique configurations on Ag(100) and Ag(111), respectively. In the insets to Figures 2 and 3, I show top-down views of 2P in its lowest energy binding conformations on Ag(100) and Ag(111), respectively. In all of

Figure 2. Total binding energies Ebind for the four lowest-energy conformations of 2P on Ag(100) (light orange) and the short-range contribution (dark orange). The inset depicts the binding conformations. B



Article

solid surface, there is correlated binding of a number Nc of repeat units that contact the surface as a single unit, due to chain stiffness and the energetic preference for chain binding. Taking a group of Nc segments as the binding unit, we formulated an expression for the relative probability for a unit to bind to Ag(100) relative to Ag(111): P(100)/(111) = exp(NcΔE /kBT )

where ΔE is the difference between the segment binding energies on Ag(100) and Ag(111).41 Equation 4 is an equilibrium constant, i.e., the ratio of partition functions for PVP on Ag(100) and Ag(111), and it contains a number of approximations. Due to the similarity of binding configurations and energies for 2P binding to Ag(100) and Ag(111), we assumed that solvent (present in experiments) affects the segment binding energies equally on both surfaces. Similarly, we assumed that entropic effects are similar on both surfaces. We also assumed that each successive segment adds ΔE to the energy difference. In support of this assumption is our observation41 that the binding potential-energy surface (PES) for the 2P segments is essentially flat, so that there is little variation of the binding energy over various surface locations. We estimated that Nc ≈ 9 PVP segments from the Kuhn length of solution-phase PVP.41 Thus, while eq 4 predicts that 2P (Nc = 1) is ∼10 times more likely to bind to Ag(100) than Ag(111) at 400 K (a relevant temperature for Ag nanostructure synthesis), that affinity increases to ∼109 when Nc = 9. Thus, small differences in the binding energies of repeat units can lead to strong preferences for chain binding to a particular surface. We recently extended our approach for PVP to poly(ethylene oxide) (PEO),43 which is not as successful as a SDA.59,60 As shown in Figure 4, we used dimethyl ether

Figure 3. Total binding energies Ebind for the five lowest-energy conformations of 2P on Ag(111) (light blue) and the short-range contribution (dark blue). The inset depicts the binding conformations.

the binding configurations we found, the oxygen atom is the closest to the surface atoms, and the ring maintains a small tilt angle with the surface plane. By calculating atomic projected densities of states,42 we found good agreement with experimental results from various spectroscopic techniques,69−73 which indicate that PVP binds to Ag primarily via the oxygen and, to a lesser extent, via the nitrogen in the 2P ring. We calculated binding energies Ebind using E bind = Esurf + E2P − Esurf + 2P

(4)

(1)

where Esurf is the energy of the bare Ag surface slab, E2P is the energy of an isolated 2P molecule in vacuum, and Esurf+2P is the energy of a Ag surface slab containing a 2P molecule. The binding energies can be partitioned into three components, such that E bind = E Pauli + Edirect + EvdW

(2)

where EPauli is the short-range Pauli repulsion between the molecule and the surface, Edirect is the short-range attraction from direct chemical bonding, and EvdW is the vdW attraction between the molecule and the surface. In DFT calculations, we can distinguish the sum of the short-range terms Eshort−range, i.e., Eshort‐range = E Pauli + Edirect

Figure 4. Breakdown of PEO (a) into its small-molecule analogue dimethyl ether (b).

(3)

(DME) as the small-molecule analogue for PEO. We studied various different initial configurations of DME on Ag(100) and Ag(111) and found that, in its most favored configuration, DME binds more strongly (by 43 meV) to Ag(100) than to Ag(111).43 This energetic preference is smaller than that for 2P (80 meV). As for PVP, we gauged the correlation length using the Kuhn length. The Kuhn length Nc is shorter for PEO than for PVP due to the greater flexibility of the PEO chainour estimates indicate that it is ∼3 repeat units.43 Thus, using eq 4, we estimated that PEO is ∼28 times more likely to bind to Ag(100) than Ag(111) at 400 K. This reduced preference compared to PVP (where it was ∼109) is consistent with experimental trends61 and indicates that a successful polymeric SDA has selective binding at the segment level and is a sufficiently stiff chain.43

from the long-range vdW attraction EvdW. In Figures 2 and 3, I show the total binding energies from eq 1, as well as the shortrange component (and, by inference, the vdW component), for all of the binding configurations on both surfaces. In these figures, we see that 2P forms stronger chemical bonds with Ag(100) than with Ag(111), where the attraction arises almost solely from nonspecific vdW forces. Comparing the binding energies for 2P on Ag(100) and Ag(111), we see that the binding is stronger on Ag(100) and the difference between the two strongest binding energies is ∼80 meV. The binding-energy difference between 2P on Ag(100) and Ag(111) is small, and I note that 2P (actually, 1-ethyl-2pyrrolidone, the analogue molecule for the PVP repeat unit in Figure 1a) is not an effective SDA for Ag nanostructures.59 It is the polymeric nature of PVP that governs its strong, preferential binding to Ag(100). When a polymer binds to a C



■

Article

ATOMISTIC SIMULATION OF THE FUNCTION OF SDAS While DFT calculations provide insight into the interaction of SDAs with metal surfaces, which is a first step in understanding why nanostructures form with certain shapes, these calculations cannot simulate nanostructure growth. Unlike the zerotemperature, vacuum environment in our DFT calculations, experimental studies occur in solution at relatively high temperatures. Due to the computational cost, it is not feasible to simulate this environment entirely from first principles. I note that these features can be captured in classical MD simulations, if the atomic interactions can be described in a FF with sufficient accuracy. To enable such simulations, we developed a classical FF to describe the growth of Ag nanostructures in a colloidal system consisting of Ag, PVP and/or PEO, and ethylene glycol (EG) solvent.58 To successfully describe the colloidal synthesis, we need to capture metallic interactions among the Ag atoms, the structure and interactions among the fluid-phase organics, and the metal−organic interaction. Metallic interactions among Ag atoms can be reliably described using an embedded-atom method (EAM) potential,81,82 which is capable of reproducing a variety of experimental properties of Ag, including the lattice constant, bulk cohesive energy, and various defect energies. Similarly, for intra- and intermolecular interactions among the organic molecules, we used the CHARMM force field,83−86 which has parameters optimized for EG and PEO, as well as most of the inter- and intramolecular interactions relevant for describing PVP, although we computed parameters for several angle and dihedral terms to obtain a complete description of PVP.58 Thus, the majority of our effort was spent in describing interactions between Ag atoms and the organics. Computational Methods. We obtained a FF for the metal−organic interaction by fitting it to results from dispersion-corrected DFT. We performed FF-based calculations and MD simulations using the Large-scale Atomic/ Molecular Massively Parallel Simulator (LAMMPS).87,88 For the DFT calculations, we used VASP.75−77 We used Grimme’s method89 to describe vdW interactions between every Ag atom and every atomic species M in the molecules. In Grimme’s method, the van der Waals potential ϕvdW(rAg,M) between an Ag atom and an atomic species M in a molecule separated by a distance of rAg,M is given by

ϕMorse(rAg,M) = D0,Ag − M [e−2αAg−M(rAg,M − r0,Ag−M) − 2e αAg−M(rAg,M − r0,Ag−M)]

(6)

where D0,Ag−M, αAg−M, and r0,Ag−M are the Morse-potential parameters for short-range interactions between Ag and species M in the organic molecules. Since both the vdW and Morse potentials are pairwise, they slightly favor binding on Ag(111), as this is the most densely packed surface of the fcc metal. Thus, to capture the preference for PEO and PVP to bind to Ag(100), we added an additional many-body term into the potential. Considering that binding occurs through the O atom in each of these molecules,41−43 we introduced a one-way electron-density function, whereby O can influence the electron density of Ag. This method was first proposed by Grochola and co-workers.90 Using this additional potential, we modified the binding energy by altering the energy of the surface Ag atoms. To retain a simple functional form, the O atoms are given an electron-density function that is proportional to the Ag-atom electron-density function, and we adjusted the proportionality constant to achieve the correct degree of surface-selective binding. Thus, the potential for the Ag−Ag and Ag−organic interaction has the form Ag

E=

Ag

O

∑ FAg(∑ ρAg− Ag (rij) + ∑ ρO→ Ag (rij)) i

+

j≠i

1 [ 2

j≠i

Ag − Ag

∑

Ag − M

ϕAg − Ag (rij) +

i≠j

∑

ϕMorse(rij) + ϕvdW (rij)]

i≠j

(7)

where the superscripts on the sums indicate that the sums run over the specified species or species pairs. FAg is the Ag embedding energy that is a function of the electron density ρ, and ϕA−B is the pair potential between species A and B separated by a distance of rij. The embedding function, the Ag− Ag electron density ρAg−Ag, and the Ag−Ag pair potentials ϕAg−Ag are given by the Ag EAM potential by Williams et al.81,82 The one-way O−Ag electron-density function is given by ρO → Ag (rij) = fO ρAg − Ag (rij)

(8)

where f O is a scaling parameter. To parametrize the Morse potentials and the one-way, O−Ag electron-density functions, we considered EG, DME, and 1methyl-2-pyrrolidone as target species. In our procedure, we first used DFT to perform structural optimizations of these molecules on Ag(100) and Ag(111). From the strongestbinding configuration on each surface, we generated a 20-point grid of molecular configurations by translating the molecule with respect to the surface, so that the distance between each atomic species in the molecule and the Ag surface spans a range that probes both attraction and repulsion. Using a simulated annealing algorithm,91 we adjusted the FF parameters to minimize a cost function based on both force- and energymatching to DFT results at each grid point. More details on our methods, as well as the final parameters of the FF, are given in ref 58. Results and Discussion. In Figure 5, I compare the binding energies predicted by the FF to those from DFT for several different binding configurations of DME, EG, 2P, and 1methyl-2-pyrrolidone on Ag(100) and Ag(111). For DME, 2P, and 1-methyl-2-pyrrolidone, the empirical binding energies are

−6 ϕvdW (rAg,M) = −s6fdamp (rAg,M , R 0,Ag , R 0,M)C6,Ag − MrAg,M

(5)

where s6 depends on the exchange-correlation functional used and is 0.75 for the PBE functional that we used for this study, C6,Ag−M is the dispersion coefficient for interaction between atom pair Ag and M, and fdamp is a damping function that depends on the vdW radii R0,Ag and R0,M for Ag and M atoms. We used eq 5 in our FF to describe vdW interactions between the organic molecules and the Ag surface, so that we exactly matched the vdW interactions from DFT. In a previous DFT study of the binding of 2P to Ag surfaces,42 we found that the accuracy of the DFT-D2 method is comparable to that of the more sophisticated DFT+vdWsurf method,78,79 if appropriate parameters are used for Ag. In this work, we used the values of C6 and R0 derived by Ruiz et al. for Ag that account for screening effects.79 To describe Pauli repulsion and direct chemical bonding, we used Morse potentials between every Ag and M atom. The Morse potential has the form D



■

Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: fi[email protected]. Funding

This work was funded by the Department of Energy, Office of Basic Energy Sciences, Materials Science Division, grant number DE-FG02-07ER46414. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF/OCI-1053575. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Cortright, R. D.; Davda, R. R.; Dumesic, J. A. Hydrogen from catalytic reforming of biomass-derived hydrocarbons in liquid water. Nature 2002, 418, 54−57. (2) Huber, G. W.; Shabaker, J. W.; Dumesic, J. A. Raney Ni-Sn catalyst for H2 production from biomass-derived hydrocarbons. Science 2003, 300, 2075−2077. (3) Deluga, G. A.; Salge, J. R.; Schmidt, L. D.; Verykios, X. E. Renewable hydrogen from ethanol by autothermal reforming. Science 2004, 303, 993−997. (4) Raimondi, F.; Scherer, G. G.; Koetz, R.; Wokaun, A. Nanoparticles in energy technology: examples from electrochemistry and catalysis. Angew. Chem., Int. Ed. 2005, 44, 2190−2209. (5) Huber, G. W.; Iborra, S.; Corma, A. Synthesis of transportation fuels from biomass: chemistry, catalysts, and engineering. Chem. Rev. 2006, 106, 4044−98. (6) Wasmus, S.; Küver, A. Methanol oxidation and direct methanol fuel cells: a selective review. J. Electroanal. Chem. 1999, 461, 14−31. (7) Gasteiger, H. A.; Kocha, S. S.; Sompalli, B.; Wagner, F. T. Activity benchmarks and requirements for Pt, Pt-alloy, and non-Pt oxygen reduction catalysts for PEMFCs. Appl. Catal. B: Environ. 2005, 56, 9− 35. (8) Liu, H.; Song, C.; Zhang, L.; Zhang, J.; Wang, H.; Wilkinson, D. P. A review of anode catalysis in the direct methanol fuel cell. J. Power Sources 2006, 155, 95−110. (9) Chen, S.; Gasteiger, H. A.; Hayakawa, K.; Tada, T.; Shao-Horn, Y. Platinum-Alloy Cathode Catalyst Degradation in Proton Exchange Membrane Fuel Cells: Nanometer-Scale Compositional and Morphological Changes. J. Electrochem. Soc. 2010, 157, A82. (10) Wang, C.; Daimon, H. A General Approach to the Size- and Shape-Controlled Synthesis of Platinum Nanoparticles and Their Catalytic Reduction of Oxygen. Angew. Chem., Int. Ed. Engl. 2008, 47, 3588−3591. (11) Chen, J.; Lim, B.; Lee, E. P.; Xia, Y. Shape-controlled synthesis of platinum nanocrystals for catalytic and electrocatalytic applications. Nano Today 2009, 4, 81−95. (12) Wang, L.; Imura, M.; Yamauchi, Y. Tailored Design of Architecturally Controlled Pt Nanoparticles with Huge Surface Areas toward Superior Unsupported Pt Electrocatalysts. ACS Appl. Mater. Interfaces 2012, 4, 2865−2869. (13) Fichtner, M. Nanotechnological aspects in materials for hydrogen storage. Adv. Eng. Mater. 2005, 7, 443−455. (14) Schuller, J. A.; Barnard, E. S.; Cai, W.; Jun, C.; White, J.; Brongersma, M. L. Plasmonics for extreme light concentration and manipulation. Nat. Mater. 2010, 9, 193−204. (15) Chen, K. H.; Pu, Y. C.; Chang, K. D.; Liang, Y. F.; Liu, C. M.; Yeh, J. W.; Shih, H. C.; Hsu, Y. J. Ag-nanoparticle-decorated SiO2 nanospheres exhibiting remarkable plasmonmediated photocatalytic properties. J. Phys. Chem. C 2012, 116, 19039−19045. (16) Bian, Z.; Tachikawa, T.; Kim, W.; Choi, W.; Majima, T. Superior Electron Transport and Photocatalytic Abilities of Metal-NanoparticleLoaded TiO2 Superstructures. J. Phys. Chem. C 2012, 116, 25444− 25453.

Figure 5. Binding energies predicted by the FF as a function of their DFT value for EG, DME, 2P, and 1-methyl-2-pyrrolidone.

within 7 % of DFT values. For EG, most of the binding energies predicted by the FF fall within 4 % of DFT values, although there are two outliers that fall within 11 % and 17 % of DFT. Although experimental data for the binding energies of PEO and PVP on Ag surfaces are not available, the desorption activation energy for EG on Ag(110) was estimated to be 0.65 eV in temperature-programmed desorption experiments by Capote and Madix.92 We used our FF to predict the binding energy of EG on Ag(110), and we find a value of 0.63 eV, which is within 3 % of the experimental value. A reliable FF will enable future studies targeting aspects of how PVP functions as a SDA. For example, questions regarding the influence of PVP on the surface energies of various Ag facets can be resolved using a FF. This information can only be obtained indirectly from experiment at present, making simulations a potentially useful tool in the quest to understand colloidal nanoparticle syntheses.

■

CONCLUSIONS In summary, I reviewed our studies highlighting the role that first-principles calculations can play in understanding the role of SDAs in the colloidal synthesis of metal nanocrystals. I showed how first-principles DFT calculations can be used to understand the binding of PVP and PEO to Ag(100) and Ag(111) and predict their effectiveness as SDAs. Such calculations are important because of the dearth of quantitative experimental data regarding this interaction. By using DFT results to fit a FF, we gain the capability to perform future studies that correctly render the colloidal environment and provide insight into the nanocrystal growth process. Although this is beneficial, I note that classical MD simulations based on detailed all-atom models, such as the one used here, are still limited in the length and time scales they can probe. In the case of PVP-mediated growth, the nanostructures evolve over human time scales and the relevant length scales approach the micrometer range.62 Further coarse graining of the spatial and temporal degrees of freedom in less detailed models may be required to capture large-scale features of the crystal-growth process. E



Article

(17) Thimsen, E.; Formal, F. L.; Grätzel, M.; Warren, S. C. Influence of plasmonic Au nanoparticles on the photoactivity of Fe2O3 electrodes for water splitting. Nano Lett. 2011, 11, 35−43. (18) Thomann, I.; Pinaud, B. A.; Chen, Z.; Clemens, B. M.; Jaramillo, T. F.; Brongersma, M. L. Plasmon enhanced solar-to-fuel energy conversion. Nano Lett. 2011, 11, 3440−3446. (19) Linic, S.; Christopher, P.; Ingram, D. Plasmonic-metal nanostructures for efficient con-version of solar to chemical energy. Nat. Mater. 2011, 10, 911−921. (20) Warren, S. C.; Thimsen, E. Plasmonic Water Splitting. Environ. Sci. 2012, 5, 5133−5146. (21) Tong, H.; Ouyang, S.; Bi, Y.; Umezawa, N.; Mitsutake, O.; Ye, J. Nano-photocatalyticMaterials: Possibilities and Challenges. Adv. Mater. 2012, 24, 229−251. (22) Rolison, D. R. Catalytic nanoarchitecturesthe importance of nothing and the unimportance of periodicity. Science 2003, 299, 1698− 1701. (23) Bell, A. T. The impact of nanoscience on heterogeneous catalysis. Science 2003, 299, 1688−1691. (24) Mao, S. S.; Chen, X. Selected nanotechnologies for renewable energy applications. Int. J. Energy Res. 2007, 31, 619−636. (25) Kamat, P. V. Meeting the clean energy demand: nanostructure architectures for solar energy conversion. J. Phys. Chem. C 2007, 111, 2834−2860. (26) Somorjai, G. A.; Park, J. Y. Colloid science of metal nanoparticle catalysts in 2D and 3D structures. Challenges of nucleation, growth, composition, particle shape, size control and their influence. Top. Catal. 2008, 49, 126−135. (27) Prieto, G.; Zečević, J.; Friedrich, H.; de Jong, K. P.; de Jongh, P. E. Towards stable catalysts by controlling collective properties of supported metal nanoparticles. Nat. Mater. 2013, 12, 34−39. (28) Li, Y.; Somorjai, G. A. Nanoscale advances in catalysis and energy applications. Nano Lett. 2010, 10, 2289−2295. (29) Beck, F. J.; Polman, A.; Catchpole, K. R. Tunable light trapping for solar cells using localized surface plasmons. J. Appl. Phys. 2009, 105, 114310. (30) Atwater, H. A.; Polman, A. Plasmonics for improved photovoltaic devices. Nat. Mater. 2010, 9, 205−213. (31) Ding, I.-K.; Zhu, J.; Cai, W.; Moon, S. J.; Cai, N.; Wang, P.; Zakeeruddin, S. M.; Grätzel, M.; Brongersma, M. L.; Cui, Y.; McGehee, M. D. Plasmonic dye-sensitized solar cells. Adv. Energy Mater. 2011, 1, 52−57. (32) Hu, L.; Kim, H. S.; Lee, J.-Y.; Peumans, P.; Cui, Y. Scalable Coating and Properties of Transparent, Flexible, Silver Nanowire Electrodes. ACS Nano 2010, 4, 2955−2963. (33) Trindade, T.; Brien, P. O.; Pickett, N. L. Nanocrystalline Semiconductors: Synthesis, Properties, and Perspectives. Chem. Mater. 2001, 13, 3843−3858. (34) Frank, A.; Kopidakis, N.; Lagemaat, J. Electrons in nanostructured TiO2 solar cells: transport, recombination and photovoltaic properties. Coord. Chem. Rev. 2004, 248, 1165−1179. (35) Law, M.; Greene, L. E.; Johnson, J. C.; Saykally, R.; Yang, P. Nanowire dye-sensitized solar cells. Nat. Mater. 2005, 4, 455−459. (36) Robel, I.; Subramanian, V.; Kuno, M.; Kamat, P. V. Quantum dot solar cells. Harvesting light energy with CdSe nanocrystals molecularly linked to mesoscopic TiO2 films. J. Am. Chem. Soc. 2006, 128, 2385−2393. (37) Parussulo, A. L. A.; Bonacin, J. A.; Toma, S. H.; Araki, K.; Toma, H. E. Unravelling the chemical morphology of a mesoporous titanium dioxide interface by confocal Raman microscopy: new clues for improving the efficiency of dye solar. Langmuir 2009, 25, 11269− 11271. (38) Adachi, M.; Murata, Y.; Takao, J.; Jiu, J.; Sakamoto, M. Highly Efficient Dye-Sensitized Solar Cells with a Titania Thin-Film Electrode Composed of a Network Structure of Single-Crystal-like TiO2 Nanowires Made by the “Oriented Attachment” Mechanism. J. Am. Chem. Soc. 2004, 126, 14943−14949.

(39) Chen, X.; Mao, S. S. Titanium dioxide nanomaterials: synthesis, properties, modifications, and applications. Chem. Rev. 2007, 107, 2891−2959. (40) Li, D.; Nielsen, M. H.; Lee, J. R. I.; Frandsen, C.; Banfield, J. F.; De Yoreo, J. J. Direction-Specific Interactions Control Crystal Growth by Oriented Attachment. Science 2012, 336, 1014−1018. (41) Al-Saidi, W. A.; Feng, H.; Fichthorn, K. A. Adsorption of Polyvinylpyrrolidone on Ag Surfaces: Insight into a StructureDirecting Agent. Nano Lett. 2012, 12, 997−1001. (42) Saidi, W. A.; Feng, H.; Fichthorn, K. A. The Binding of PVP to Ag Surfaces: Insight into a Structure-Directing Agent from DispersionCorrected Density-Functional Theory. J. Phys. Chem. C 2013, 117, 1163−1171. (43) Zhou, Y.; Saidi, W. A.; Fichthorn, K. A. Comparison of the Binding of Polyvinylpyrrolidone and Polyethylene Oxide to Ag Surfaces: Elements of a Successful Structure-Directing Agent. J. Phys. Chem. C 2013, 117, 11444−11448. (44) Fichthorn, K. A. Molecular phenomena in colloidal nanostructure synthesis. Mol. Simul. 2014, 40, 134−140. (45) Qin, Y.; Fichthorn, K. A. A molecular-dynamics simulation study of forces between colloidal nanoparticles in a Lennard-Jones liquid. J. Chem. Phys. 2003, 119, 9745−9754. (46) Qin, Y.; Fichthorn, K. A. Solvation forces between colloidal nanoparticles: directed alignment. Phys. Rev. E 2006, 73, 020401. (47) Fichthorn, K. A.; Qin, Y. Molecular dynamics simulation of colloidal nanoparticle forces. Ind. Eng. Chem. Res. 2006, 45, 5477− 5481. (48) Qin, Y.; Fichthorn, K. A. Solvophobicity at large and intermediate length scales: size, shape, and solvent effects. Phys. Rev. E 2006, 74, 020401. (49) Qin, Y.; Fichthorn, K. A. Molecular dynamics simulation of the forces between colloidal nanoparticles in n-decane solvent. J. Chem. Phys. 2007, 127, 144911. (50) Fichthorn, K. A.; Qin, Y. Molecular dynamics simulation of the forces between colloidal nanoparticles in Lennard-Jones and n-decane solvent. Granul. Matter 2008, 10, 105−111. (51) Raut, J. S.; Bhagat, R. B.; Fichthorn, K. A. Sintering mechanisms of aluminum nanocrystals: a molecular-dynamics study. NanoStruct. Mater. 1998, 10, 837−851. (52) Alimohammadi, M.; Fichthorn, K. A. Molecular dynamics simulation of the aggregation of titanium dioxide nanocrystals: preferential alignment. Nano Lett. 2009, 9, 4198−4203. (53) Sathiyanarayanan, R.; Ali-Mohammadi, M.; Zhou, Y.; Fichthorn, K. A. The role of solvent in the shape-controlled synthesis of anisotropic colloidal nanostructures. J. Phys. Chem. C 2011, 115, 18983−18990. (54) Zhou, Y.; Fichthorn, K. A. Microscopic view of nucleation in the anatase-to-rutile transition. J. Phys. Chem. C 2012, 116, 8314−8321. (55) Raju, M.; van Duin, A. C. T.; Fichthorn, K. A. Mechanisms of oriented attachment of TiO2 nanocrystals in vacuum and humid environments: Reactive molecular dynamics. Nano Lett. 2014, 14, 1836−1842. (56) Alimohammadi, M.; Fichthorn, K. A. A force-field for the interaction of water with TiO2 surfaces. J. Phys. Chem. C 2011, 115, 24206−24214. (57) Raju, M.; Kim, S.-Y.; van Duin, A. C. T.; Fichthorn, K. A. ReaxFF reactive force field study of the dissociation of water on anatase and rutile surfaces of TiO2. J. Phys. Chem. C 2013, 117, 10558−10572. (58) Zhou, Y.; Saidi, W. A.; Fichthorn, K. A. A Force Field for Describing the Polyvinylpyrrolidone-Mediated Solution-Phase Synthesis of Shape-Selective Ag Nanoparticles. J. Phys. Chem. C 2014, 118, 3366−3374. (59) Sun, Y.; Xia, Y. Large-Scale Synthesis of Uniform Silver Nanowires through a Soft, Self-Seeding, Polyol Process. Adv. Mater. 2002, 14, 833−837. (60) Sun, Y.; Mayers, B.; Herricks, T.; Xia, Y. Polyol Synthesis of Uniform Silver Nanowires: A Plausible Growth Mechanism and the Supporting Evidence. Nano Lett. 2003, 3, 955−960. F



Article

(81) Williams, P. L.; Mishin, Y.; Hamilton, J. C. An Embedded-Atom Potential for the Cu−Ag System. Modell. Simul. Mater. Sci. Eng. 2006, 14, 817−833. (82) http://www.ctcms.nist.gov/potentials. (83) Guvench, O.; Greene, S. N.; Kamath, G.; Brady, J. W.; Venable, R. M.; Pastor, R. W.; Mackerell, A. D., Jr. Additive Empirical Force field for Hexopyranose Monosaccharides. J. Comput. Chem. 2008, 29, 2543−2564. (84) Vorobyov, I.; Anisimov, V. M.; Greene, S.; Venable, R. M.; Moser, A.; Pastor, R. W.; MacKerell, A. D., Jr. Additive and Classical Drude Polarizable Force Fields for Linear and Cyclic Ethers. J. Chem. Theory Comput. 2007, 3, 1120−1133. (85) Lee, H.; Venable, R. M.; MacKerell, A. D., Jr.; Pastor, R. W. Molecular Dynamics Studies of Polyethylene Oxide and Polyethylene Glycol: Hydrodynamic Radius and Shape Anisotropy. Biophys. J. 2008, 95, 1590−1599. (86) Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr. CHARMM General Force Field: A Force Field for Drug-Like Molecules Compatible with the CHARMM All-Atom Additive Biological Force Fields. J. Comput. Chem. 2010, 31, 671−690. (87) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1−19. (88) http://lammps.sandia.gov. (89) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (90) Grochola, G.; Snook, I. K.; Russo, S. P. Computational Modeling of Nanorod Growth. J. Chem. Phys. 2007, 127, 194707. (91) Goffe, W. L.; Ferrier, G. D.; Rogers, J. Global Optimization of Statistical Functions with Simulated Annealing. J. Econometrics 1994, 60, 65−99. (92) Capote, A. J.; Madix, R. J. O-H and C-H Bond Activation in Ethylene Glycol by Atomic Oxygen on Ag(110): Heterometallacycle Formation and Selective Dehydrogenation to Glyoxal. J. Am. Chem. Soc. 1989, 111, 3570−3577.

(61) Wiley, B.; Sun, Y.; Mayers, B.; Xia, Y. Shape-Controlled Synthesis of Metal Nanostructures: The Case of Silver. Chem.Eur. J. 2005, 11, 454−463. (62) Xia, Y.; Xiong, Y.; Lim, B.; Skrabalak, S. E. Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics? Angew. Chem., Int. Ed. 2008, 48, 60−103. (63) Xia, X.; Zeng, J.; Oetjen, L. K.; Li, Q.; Xia, Y. Quantitative Analysis of the Role Played by Poly(vinylpyrrolidone) in SeedMediated Growth of Ag Nanocrystals. J. Am. Chem. Soc. 2012, 134, 1793−1801. (64) Xia, X.; Zeng, J.; Zhang, Q.; Moran, C. H.; Xia, Y. Recent Developments in Shape- Controlled Synthesis of Silver Nanocrystals. J. Phys. Chem. C 2012, 116, 21647−21656. (65) Singh, M.; Singh, A. K.; Mandal, R. K.; Sinha, I. Synthesis of Anisotropic Silver Nanostructures in Presence of Polyvinyl Pyrrolidone (PVP): LSPR and SAXS Analysis. Colloid Surf., A 2011, 390, 167−172. (66) Samanta, S.; Sarkar, P.; Pyne, S.; Sahoo, G. P.; Misra, A. Synthesis of Silver Nanodiscs and Triangular Nanoplates in PVP Matrix: Photophysical Study and Simulation of UV−Vis Extinction Spectra Using DDA Method. J. Mol. Liq. 2012, 165, 21−26. (67) Li, L.; Sun, J.; Li, X.; Zhang, Y.; Wang, Z.; Wang, C.; Dai, J.; Wang, Q. Controllable Synthesis of Monodispersed Silver Nanoparticles as Standards for Quantitative Assessment of Their Cytotoxicity. Biomaterials 2012, 33, 1714−1721. (68) Xiong, Y.; Luo, G.; Chen, C.; Yuan, H.; Shen, Q.; Li, M. In Situ Synthesis of Zero-Valent Silver Nanoparticles in Polymethylmethacrylate under High Temperature. Appl. Surf. Sci. 2012, 258, 5822− 5826. (69) Bonet, F.; Tekaia-Elhsissen, K.; Sarathy, K. Study of interaction of ethylene glycol/PVP phase on noble metal powders prepared by polyol process. Bull. Mater. Sci. 2000, 23, 165−168. (70) Huang, H. H.; Ni, X. P.; Loy, G. L.; Chew, C. H.; Tan, K. L.; Loh, F. C.; Deng, J. F.; Xu, G. Q. Photochemical formation of silver nanoparticles in poly (N-vinylpyrrolidone). Langmuir 1996, 909−912. (71) Mdluli, P. S.; Sosibo, N. M.; Revaprasadu, N.; Karamanis, P.; Leszczynski, J. Surface enhanced Raman spectroscopy (SERS) and density functional theory (DFT) study for understanding the regioselective adsorption of pyrrolidinone on the. J. Mol. Struct. 2009, 935, 32−38. (72) Zhang, Z.; Zhao, B.; Hu, L. PVP Protective Mechanism of Ultrafine Silver Powder Synthesized. J. Solid State Chem. 1996, 121, 105−110. (73) Gao, Y.; Jiang, P.; Liu, D. F.; Yuan, H. J.; Yan, X. Q.; Zhou, Z. P.; Wang, J. X.; Song, L.; Liu, L. F.; Zhou, W. Y.; Wang, G.; Wang, C. Y.; Xie, S. S. Evidence for the monolayer assembly of poly (vinylpyrrolidone) on the surfaces of silver nanowires. J. Phys. Chem. B 2004, 108, 12877−12881. (74) Al-Saidi, W. A.; Voora, V. K.; Jordan, K. D. An Assessment of the vdW-TS Method for Extended Systems. J. Chem. Theory Comput. 2012, 8, 1503−1513. (75) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals. Phys. Rev. B 1993, 47, 558−561. (76) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (77) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (78) Tkatchenko, A.; Scheffler, M. Accurate Molecular van der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data. Phys. Rev. Lett. 2009, 102, 073005. (79) Ruiz, V. G.; Liu, W.; Zojer, E.; Scheffler, M.; Tkatchenko, A. Density-Functional Theory with Screened van der Waals Interactions for the Modeling of Hybrid Inorganic-Organic Systems. Phys. Rev. Lett. 2012, 108, 146103. (80) Goddard, R.; Heinemann, O.; Krüger, C.; Magdfio, I.; Mark, F.; Schaffner, K. A Low-Temperature Phase of 2-Pyrrolidone. Acta Crystallogr., Sect. C 1998, 54, 501−504. G


Atomic-Scale Theory and Simulations for Colloidal Metal Nanocrystal

Recommend Documents