A Force Field for Describing the Polyvinylpyrrolidone-Mediated

Article pubs.acs.org/JPCC

A Force Field for Describing the Polyvinylpyrrolidone-Mediated Solution-Phase Synthesis of Shape-Selective Ag Nanoparticles Ya Zhou,† Wissam A. Saidi,§ and Kristen A. Fichthorn*,†,‡ †

Department of Chemical Engineering, and ‡Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15621, United States ABSTRACT: Polyvinylpyrrolidone (PVP), ethylene glycol (EG), and polyethylene oxide (PEO) are key molecules in the solution-phase synthesis of Ag nanostructures. To resolve various aspects of this synthesis, we develop a classical force field to describe the interactions of these molecules with Ag surfaces. We parametrize the force field through force and energy matching to results from firstprinciples density-functional theory (DFT). Our force field reproduces the DFT binding energies and configurations of these molecules on Ag(100) and Ag(111). Our force field also yields a binding energy for EG on Ag(110) that is in agreement with experiment. Molecular-dynamics simulations based on this force field indicate that the preferential binding affinity of the chains for Ag(100) increases significantly beyond the segment binding energy for PVP decamers, but not for PEO. This agrees with experimental observations that PVP is a more successful structure-directing agent than is PEO.

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INTRODUCTION Metal nanocrystals exhibit unique electrical, optical, and magnetic properties that would benefit various applications in areas such as catalysis,1−5 solar energy,6−8 and sensing.9−12 Because many of these properties and applications are highly sensitive to nanocrystal size and shape, there has been an enormous amount of research centering on the shapecontrolled synthesis of metal nanocrystals. In particular, various metal nanocrystals with different shapes have been produced using solution-phase methods.13−20 The nucleation and growth mechanisms in these syntheses are not fully understood and are considered to be extremely complicated. Yet, it is known that certain additive molecules, known as structure-directing agents (SDAs), can be added purposely to the solution to direct the nanostructures to grow into specific shapes. Depending on the SDA used, the produced nanocrystals can adopt shapes distinctly different from the Wulff polyhedra predicted from the energies of the 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,13−15,18−25 when the lowest-energy facets of Ag and Pd in vacuum are the {111} facets. While SDAs play a crucial role in the shape-controlled synthesis of metal nanocrystals, the mechanisms of their facetselectivity are unclear. In the case of PVP, it is believed that the polymer preferentially adsorbs to the {100} metal facets and reduces their interfacial free energy relative to the {111} facets. The {100} facets are thus passivated, and the addition of solution-phase metal atoms is inhibited.14,19,20 Recent theoretical studies with first-principles, dispersion-corrected density© XXXX American Chemical Society

functional theory (DFT) corroborate that PVP binds preferentially to Ag(100)26,27 and also indicate why PVP is experimentally observed13 to be more successful as an SDA than polyethylene oxide (PEO).28 We also note that previous DFT calculations for citric acid on Ag surfaces29 confirm the experimental finding that this molecule tends to produce {111}-faceted Ag nanostructures.30 While confirmation or prediction of facet-selective binding with DFT calculations is a first step in understanding why nanostructures form with certain shapes, these calculations cannot explain many aspects of nanostructure growth. Unlike the static, zero-temperature, vacuum environment of DFT, experimental studies occur in solution at relatively high temperatures. The experimental solution-phase synthesis of metal nanostructures is a dynamic process that involves the growth, aggregation, and dissolution of metal clusters, as well as the adsorption of SDAs and solvent on the exposed facets of metal nanocrystals. Because of the computational cost, however, it is infeasible to treat the solvent as individual molecules in first-principles calculations. Instead, the solvent is typically modeled as a polarizable continuum to account for its electrostatic effects.31−34 However, popular continuum models neglect or underestimate nonelectrostatic effects, and they do not take into account the role of local molecular structure, both of which are critical in the dynamic interplay between metal, SDAs, and the solvent in the synthesis. We note that such features of solution-phase synthesis could be captured by Received: December 10, 2013 Revised: January 20, 2014

A

dx.doi.org/10.1021/jp412098n | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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C6,ij is the dispersion coefficient for interaction between atom pair i and j, and fdamp is a damping function that depends on the vdW radii R0,i and R0,j for atoms i and j. We note that eq 1 can be easily incorporated into our force field for the molecule− surface interaction, ensuring consistency between DFT and the force field. In a previous study of the binding of 2-pyrrolidone (the active group in PVP) to Ag surfaces,27 we found that the accuracy of the DFT-D2 method of Grimme is comparable to that of the DFT+vdWsurf method,51,52 if appropriate parameters are used for Ag to account for Coulomb screening within the metal surface.52 In this work, as in our previous study,27 we use the values of C6 and R0 derived by Ruiz et al. for Ag that account for screening effects.52 Intramolecular Interaction. In our first efforts to obtain a suitable force field for PVP, we use 1-(1-ethylpropyl)-2pyrrolidone, shown in Figure 1, as an analogue molecule.

classical molecular dynamics (MD) simulations, given that atomic interactions can be described with sufficient accuracy. In this work, we present force fields that can be used to model the synthesis of Ag nanostructures in a colloidal system consisting of Ag, PVP and/or PEO, and ethylene glycol (EG) solvent. Metallic interactions between the Ag atoms can be reliably described using an embedded-atom method (EAM) potential,35,36 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 choose to use the CHARMM force field,37−40 which has parameters optimized for EG and PEO, as well as most of the inter- and intramolecular interactions relevant for describing PVP. As we will discuss below, we obtain parameters for several angle and dihedral terms involved in a proper description of PVP. The majority of our effort is focused on describing interactions between Ag atoms and the organics, where we require a force field that is capable of capturing the surfacesensitive binding observed in DFT calculations and implied by experiment. We note that nonreactive force fields for describing metal−organic interactions have been derived in previous studies.41,42 However, the metal−organic force field by Jalkanen and Zerbetto is based on molecular force fields whose applicability to the molecules of interest here is not known.41 Further, it is not clear that their model, which is based on pairwise additive interactions, could yield stronger binding of the species of interest here to Ag(100) than to Ag(111). In the work of Wright et al.,42 fictitious binding sites are introduced within the surface to achieve a good match with molecular binding geometries from first-principles calculations. While such an ad hoc model could yield stronger binding of the organics to Ag(100) than to Ag(111), it is unclear how fictitious sites could be defined in simulations of nanoparticle growth, where the local metal geometry may not be welldefined. Below, we develop a general force field that can predict stronger binding of the organics to Ag(100) than to Ag(111), consistent with first-principles calculations and experiment. Such a force field is suitable for describing the PVP-mediated, solution-phase growth of Ag nanoparticles.

Figure 1. (a) Structure of a 1-(1-ethylpropyl)-2-pyrrolidone molecule, with key atoms involved in bond-angle bending and torsion labeled, and (b) ground-state geometries of 1-(1-ethylpropyl)-2-pyrrolidone predicted by DFT (in yellow) and CHARMM (O in red, N in blue, C in turquoise, and H in white).

Similar to a repeat unit of PVP, this molecule consists of an alkyl backbone and a 2-pyrrolidone ring. To characterize the bonded interactions of this molecule, we employ a set of potentials to describe the bond stretching of all bonded atom pairs, bending of the bond angle formed by two atoms that bond to a common neighbor, and torsion, or internal rotation of one section of the molecule with respect to another about a bond. While CHARMM force-field parameters to describe bond stretching, bending of most of the bond angles, and most torsions are available in the literature,40 there are eight torsions, involving C3−C2−N−C1, C6−C1−C7−C9, N−C1−C6−C8, C6−C1−N−C2, C6−C1−N−C5, H11−C1−N−C5, C4−C5− N−C1, and H51−C5−N−C1, and one bond angle, C1−N−C5 [see Figure 1a], for which the CHARMM parameters were not known. The CHARMM dihedral potential has the form:

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METHODS Computational Details. We obtain force fields for certain intramolecular interactions in PVP, as well as the interaction of PVP, PEO, and EG with Ag by fitting them to results from dispersion-corrected DFT. We perform force-field-based calculations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).43,44 For the DFT calculations, we use the Vienna Ab Initio Simulation Package (VASP)45−47 employing the Perdew−Burke−Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA) and projector augmented wave (PAW) pseudopotentials.48,49 We use Grimme’s method50 to describe van der Waals (vdW) interactions in the DFT calculations. In Grimme’s method, the dispersion correction EvdW is expressed as the sum of pairwise interactions: 1 EvdW = − s6 ∑ fdamp (rij , R 0, i , R 0, j)C6, ijrij−6 2 i≠j

Edihedral = K χ [1 + cos(nχ − δ)]

(2)

where Kχ is the dihedral angle force constant, χ is the dihedral or torsion angle, n is the periodicity or multiplicity, and δ is the phase. The bond-angle bending potential has the form: Eangle = K θ(θ − θ0)2

(3)

where Kθ is the force constant, and θ is the bond angle whose equilibrium value is θ0. To obtain the unknown parameters for these potentials, we first generated them by analogy to existing CHARMM parameters using the CHARMM General Force Field (CGenFF) program,53,54 version 0.9.6 beta. We accept partial atomic charges generated by the program (Table 1), along with

(1)

where s6 is a global scaling factor that depends on the exchangecorrelation functional used and is 0.75 for the PBE functional, B



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reproduce the ground-state geometry predicted by DFT using these parameters. Ag−Organic Interaction. The second task in fitting a force field is to describe interactions between Ag atoms and the organics. Here, we devise a force field that includes the types of interactions observed in previous DFT studies, namely, shortrange Pauli repulsion, direct (short-range) chemical bonding, and long-range vdW attraction.26−28 In the force field, we model vdW interactions using Grimme’s DFT-D2 method,50 but employing the Ag parameters derived by Ruiz et al.52 Considering that vdW attraction is the most dominant interaction in the adsorption of these organic molecules on Ag surfaces,26−28 the force field is able to capture the majority of the interaction with the same accuracy as DFT. To describe Pauli repulsion and direct chemical bonding, we use Morse potentials between Ag and every atomic species in the molecules. Because both vdW attraction and the short-range interactions provided by the Morse potentials are pairwise, they tend to be nonspecific, and they slightly favor binding on Ag(111), as this is the most densely packed surface of the fcc metal. Hence, to capture the surface-sensitivity of PEO and PVP observed in DFT studies that favors binding on Ag(100), we use an additional EAM-like potential to describe the many-body aspects of the interaction. Considering that binding typically occurs through the O atom in each of these molecules,26−28 we introduce a one-way electron-density function, whereby O can influence the electron density of Ag. In this way, we modify the molecular binding energy by adjusting the embedding energy of the surface Ag atoms. For convenience, the O atoms are given an electron-density function that is proportional to the Ag-atom electron-density function, and we use a constant scaling factor to adjust the amount of electron density that can be supplied from O to the Ag surface. This method was first proposed by Grochola and co-workers55 in simulating the interaction between gold nanoparticles and model Lennard-Jones surfactants, and was found to be instrumental in reproducing shape-selective growth of gold nanorods. The potential for the Ag−Ag and Ag−organic interaction has the form:

Table 1. Partial Charges on Atoms in PVP and 1-(1Ethylpropyl)-2-pyrrolidonea atom

charge (electron charge)

C1 C2 C3 C4 C5 C6, C7 C8, C9 H N O

0.026 (0.020) 0.371 −0.011 −0.188 0.067 −0.186 (−0.168) (−0.285) 0.090 −0.399 (−0.393) −0.490

a

Values in parentheses are given for atoms in 1-(1-ethylpropyl)-2pyrrolidone that do not exist in PVP or have different partial charges than in PVP.

bonded parameters with fair analogy, including the bond-angle terms of C1−N−C5 (Table 2) and dihedrals terms involving Table 2. CHARMM Bond Angle Parameters for the 2Pyrrolidone-Backbone Linkage in PVP angle

Kθ (eV)

θ0 (deg)

C1−N−C5

2.16822

116.0

Table 3. CHARMM Dihedral (Torsional) Parameters for the 2-Pyrrolidone-Backbone Linkage in PVP dihedral

Kχ (eV)

n

δ (deg)

C3−C2−N−C1 C6−C1−C7−C9 N−C1−C6−C8 C6−C1−N−C2 C6−C1−N−C5 H11−C1−N−C5 C4−C5−N−C1 H51−C5−N−C1

0.04857 0.00867 0.00867 0.03903 0.0 0.0 0.02906 0.0

2 3 3 1 1 1 3 3

180.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Ag

E=

C6−C1−C7−C9 and N−C1−C6−C8 (Table 3). The rest of the parameters were further refined by fitting to DFT results. To obtain the dihedral-angle parameters, we rotate the alkyl group about the C1−N, C2−N, and C5−N bonds [see Figure 1a] and calculate the corresponding torsional surfaces using dispersion-corrected DFT. A plane-wave cutoff energy of 400 eV is used in the calculation with an energy-convergence criterion of 10−8 eV in the self-consistent cycle, and the molecule is placed in a (15 Å)3 cubic supercell with the selected dihedral angle fixed at given values. The rest of the molecule is relaxed until the forces converge to less than 0.01 eV/Å. The CHARMM dihedral potentials are fit to DFT data, and the resulting DFT points and force-field fits are shown in Figure 2, which indicates good agreement of the force field to DFT results. The accepted dihedral parameters are given in Table 3. With the inclusion of these parameters in the CHARMM force field, we optimized the geometry of a 1-(1ethylpropyl)-2-pyrrolidone molecule using the conjugategradient method within LAMMPS until the force on any atom is less than 0.01 eV/Å. Figure 1b shows that, with a rootmean-square deviation (RMSD) of 0.09 Å, we can successfully

Ag

i

+

O

∑ FAg(∑ ρAg− Ag (rij) + ∑ ρO→ Ag (rij)) 1 [ 2

j≠i Ag − Ag

∑

j≠i Ag − M

ϕAg − Ag (rij) +

i≠j

∑ i≠j

ϕAg − M(rij)] (4)

where 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.35,36 The superscripts on the sums indicate that the sums run over the specified species or species pairs. The oneway O−Ag electron-density function is given by: ρO → Ag (rij) = fO ρAg − Ag (rij)

(5)

where f O is a scaling factor that is used to adjust the amount of electron density supplied from O to Ag. The pair potentials describing the interaction between organic species M and Ag are given by: C



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Figure 2. DFT and force-field (FF) torsional surfaces for (a) C6−C1−N−C2, (b) C6−C1−N−C5, (c) C3−C2−N−C1, and (d) C4−C5−N−C1 dihedrals offset by the energy of the optimized structure. Because of geometrical constraints imposed by CHARMM bonded interactions within the 2-pyrrolidone ring, rotation of the alkyl group about the C1−N bond results in simultaneous change of the (a) C6−C1−N−C2 and (b) C6−C1− N−C5 dihedral angles. The force constant of the C6−C1−N−C5 dihedral is made zero, and the C6−C1−N−C2 terms are parametrized to effectively account for the torsional surfaces associated with this rotation (Table 3).

atoms in the molecules into different species based on their bonding nature and geometrical environment, similar to the atom typing in the CHARMM force field. Atoms in the EG molecule are grouped into 4 types, sp3 C, alcohol O, alkane H attached to C, and alcohol H attached to O. In DME and PEO, there are three types of atoms, sp3 C, ether O, and alkane H. In 1M2P and PVP, atoms are classified into six species including carbonyl O, amide N, C double bonded to O, aliphatic C in the five-membered ring, aliphatic C in the backbone, and aliphatic H bonded to C. In our procedure, we first use DFT to perform structural optimizations of EG, DME, and 1M2P on periodic (4 × 4) Ag(100) and Ag(111) surfaces with 4 atomic layers. A vacuum spacing of 8 Ag layers is used, and Ag atoms are fixed at their lattice sites with a0 = 4.09 Å, the 0 K lattice parameter predicted by the EAM potential used. The plane-wave cutoff energy is 400 eV, the energy-convergence criterion is 10−8 eV in the selfconsistent cycle, and a (4 × 4 × 2) Monkhorst−Pack k-point mesh is used for Brillouin-zone integration. Because of the complexity of the intramolecular and Agorganic interactions, the molecules can adopt multiple binding configurations that are distinct from one another. To obtain configurations that are representative of the adsorption of the molecules on Ag surfaces, we relax the structures of the molecules from different initial configurations with the O atoms located at various high-symmetry sites of the surfaces. For each molecule, we consider three initial configurations on Ag(100) with the O atoms near the top, bridge, and hollow sites, respectively, and four initial configurations on Ag(111) with O atoms near the top, bridge, fcc-hollow, and hcp-hollow sites. The structures of the molecules are relaxed until the forces are

ϕAg − M(rij) = D0,Ag − M [e−2αAg−M(rij − r0,Ag−M) − 2e αAg−M(rij − r0,Ag−M)] − s6fdamp (rij , R 0,Ag , R 0,M)C6,Ag − Mrij−6

(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, and the second term accounts for the vdW interaction between Ag and species M in Grimme’s method [eq 1]. We use a cutoff radius of 5.5 Å for the Morse potentials and 12 Å for the vdW interactions. To parametrize the Morse potentials and the one-way electron-density functions from O to Ag, we consider EG, a structural analogue of PEO, dimethyl ether (DME), and a structural analogue of PVP, 1-methyl-2-pyrrolidone (1M2P). A diagram depicting the structures of EG, DME, and 1M2P is shown in Figure 3. To describe the interactions between Ag surfaces and various atoms in the organic molecules, we classify

Figure 3. Molecular structures of (a) EG, (b) DME, and (c) 1M2P (O in red, N in blue, C in turquoise, and H in white). D



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smaller than 0.02 eV/Å. The binding energy of each configuration is calculated using: E bind = Es + Em − Es + m

Table 4. Morse Potential Parameters and the Scaling Factors for the Electron-Density Function for Short-Range Interactions between Ag and Atomic Species in EG, PEO, and PVP

(7)

where Es is the energy of the Ag surface, Em is the energy of an isolated, relaxed molecule in vacuum, and Es+m is the total energy of the Ag surface with an adsorbed molecule. From the strongest-binding configuration on each surface, we generate a 20-point grid of molecular configurations by translating the molecule with respect to the surface, so that the distance between Ag surface and each atomic species in the molecule is varied through a range that probes both attraction and repulsion on that atom. To obtain the forces resulting from Ag−organic interactions, forces from intramolecular interactions are subtracted from the total forces on atoms in the organic molecule. The intramolecular forces are calculated using an isolated molecule in the same configuration, in the same supercell with the same k-point mesh as when the Ag surfaces are present. Using a simulated annealing algorithm,56 we adjust the Morse-potential parameters to minimize a cost function based on both force- and energy-matching to DFT results at each grid point. The cost function is defined as:

molecule EG EG EG EG PEO PEO PEO PVP PVP PVP PVP PVP PVP

interaction Ag−alkane H Ag−alcohol H Ag−sp3 C Ag−alcohol O Ag−alkane H Ag−sp3 C Ag−ether O Ag−aliphatic H Ag−C bonded to O Ag−aliphatic C in backbone Ag−aliphatic C in ring Ag−amide N Ag−carbonyl O

D0 (eV)

α (Å−1)

r0 (Å)

0.00480 0.00448 0.00216 0.00217 0.00480 0.00498 0.00296 0.00480 0.00722 0.00244

1.30 1.06 1.26 2.09 1.30 1.08 2.97 1.30 1.14 1.01

1.94 2.13 4.99 3.43 1.94 5.00 2.84 1.94 4.85 4.92

0.00230 0.00492 0.00325

1.03 1.76 3.34

4.92 3.26 2.65

fO

0.55

3.5

5.5

force on any atom is less than 0.02 eV/Å. The resultant binding configurations and binding energies are shown in Figure 4 and Table 5, in comparison with DFT results.

⎛ ∑ ∑ ∑ (f FF − f DFT )2 jiγ ⎜ j γ i jiγ χ = ∑ ⎜ ∑ ∑ ∑ (f DFT )2 Ag(001),Ag(111) ⎝ j γ i jiγ 2

+b

∑j (Ejinteraction,FF − Ejinteraction,DFT)2 ⎞ ⎟ ⎟ ∑j (Ejinteraction,DFT)2 ⎠

(8)

−1

where b = (number of atoms per molecule) is used to give less weight to the energy measurements considering the number of observations of energies relative to forces, f FF jiγ is the γ Cartesian component of the empirical force exerted by the Ag surface on atom i in molecular configuration j, and f DFT is jiγ the corresponding force from DFT. The interaction energy between molecular configuration j and Ag surface is defined as: Ejinteraction = Es + Ej ,bind − Es + j

(9)

where Es is the energy of the Ag surface, Es+j is the energy of the molecule and the surface together, and Ej,bind is the energy of isolated molecule j while maintaining the binding geometry that it has on the surface. The parametrization of the Morse potentials is first done with f O = 0 in eq 5. When the fitting is converged, ρO→Ag is turned on and is used in combination with the Morse parameters to optimize the structure of the molecule on the Ag surfaces. At this stage, we adjust the value of f O to modify the relative binding preference of the molecule on Ag(100) and Ag(111). The value of f O that best reproduces the amount of binding-energy difference between Ag(100) and Ag(111) predicted by DFT is accepted and is used in the next round of fitting. With the EAM-like potential accounting for part of the atomic forces and interaction energies, we reparameterize the Morse potentials to minimize the cost function defined in eq 8. The final parameters of the potentials and f O values are given in Table 4. With the parametrized potentials, we relax the structures of EG, DME, and 1M2P on rigid Ag(100) and Ag(111) surfaces around the binding sites predicted by DFT. The structural optimization is performed using the FIRE algorithm57 until the

Figure 4. Top and side views of representative binding configurations for EG (top row), DME (middle row), and 1M2P (bottom row) on (a) Ag(100) and (b) Ag(111), predicted by DFT (Ag in gray, organic molecules in yellow) and the force field (O in red, N in blue, C in turquoise, and H in white).

For DME and 1M2P, the empirical binding energies are within 7% of DFT values. For the most part, the binding configurations also agree well with DFT. Here, the greatest discrepancy with DFT occurs when DFT predicts that the O atoms are in close proximity to a top site on the Ag surfaces. We see this for configurations 2 and 3 for DME on Ag(100), 3 for 1M2P on Ag(100), 1 for DME on Ag(111), and 4 for 1M2P on Ag(111). We note that in all of these configurations, the RMSD is relatively high, indicating the worst agreement between the force field and DFT. In Figure 4, we see that the O atoms tend to move away from the Ag atom underneath them during relaxations based on the force field. This is due to the semimetallic nature of the O−Ag bonding in our model, which makes the top sites on the Ag surfaces the least energetically favorable for O. E



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Table 5. Binding Energies of EG, DME, and 1M2P on Ag(100) and Ag(111) Predicted by DFT and the Force Field (FF) Developed in This Worka DFT/FF binding energy (eV), (RMSD (Å) of geometry) configuration

a

molecule

surface

EG EG DME DME 1M2P 1M2P

Ag(100) Ag(111) Ag(100) Ag(111) Ag(100) Ag(111)

1 0.57/0.55 0.51/0.51 0.39/0.39 0.36/0.36 0.69/0.68 0.64/0.61

2 (1.28) (1.19) (0.24) (1.00) (0.40) (0.34)

3

0.54/0.55 0.51/0.51 0.39/0.39 0.34/0.36 0.67/0.67 0.63/0.61

(1.12) (1.21) (1.04) (0.22) (0.33) (0.32)

0.49/0.57 0.50/0.51 0.37/0.35 0.34/0.34 0.66/0.65 0.61/0.63

4 (0.37) (1.39) (0.74) (0.30) (0.80) (0.49)

0.46/0.51 (1.22) 0.33/0.34 (0.26) 0.60/0.64 (0.80)

For each configuration, RMSD of the FF-predicted geometry with respect to DFT prediction is shown in parentheses.

EG molecule and the top 3 layers of the Ag(110) surface are allowed to relax. The distribution of the resultant binding energies is shown in Figure 6. The maximum binding energy is 0.63 eV, which is within 3% of the experimental value.

For EG, most of the binding energies predicted by the force field fall within 4% of DFT values, although there are two outliers that fall within 11% and 17% of DFT. The difference between the empirical and DFT-predicted binding configurations is also more evident for EG, which has its O atoms dangling from a flexible chain, making its empirical binding geometry susceptible to slight deviations from DFT. To further test the force field, we use it to describe the adsorption of 2-pyrrolidone on Ag surfaces. Unlike PVP and 1M2P, the N in 2-pyrrolidone is attached to a polar H atom instead of an alkyl group. Here, we continue to use the Ag− amide N parameters in Table 4, as well as the Ag-aliphatic H parameters to approximate the Ag−polar H interactions. Starting from four different initial configurations on Ag(100) and five on Ag(111), we relax the structure of 2-pyrrolidone using the force field and compare the binding energies with DFT predictions. As shown in Figure 5, although the Ag−N and Ag−polar H parameters are not optimal, the binding energies predicted by the force field are in line with DFT results.

Figure 6. Distribution of binding energies of EG on Ag(110) predicted by the force field from structural optimization of 101 different initial configurations.

To test the performance of the force field in capturing surface-sensitive binding of the molecules at the chain level, we performed MD simulations of rigid and mobile (18 × 18) Ag(100) and (18 × 20) Ag(111) slabs interacting with an EG molecule, as well as PEO and syndiotactic PVP oligomer chains consisting of 10 repeat units. The rigid surfaces consist of 4 atomic layers with all Ag atoms sitting in perfect lattice sites. The mobile surfaces consist of 6 atomic layers, where Ag atoms in the bottom 3 layers are fixed and those in the top 3 layers are allowed to move during the simulation. The in-plane dimensions of the periodic simulation cells correspond to a Ag lattice parameter of a0 = 4.09 Å. Initially, the PEO chain and the PVP backbone are given an all-trans conformation. The simulations are conducted in the canonical ensemble with a time step of 1.0 fs at 300 K. The systems are first equilibrated until the total energy fluctuates about a constant value. Subsequently, we continue the simulations for 5 ns and compute the adsorption energy EA of the molecules on both rigid and mobile Ag surfaces as:

Figure 5. Binding energies of 2-pyrrolidone relaxed from four initial configurations on Ag(100) and five on Ag(111). The bars represent DFT values, and the symbols represent the force-field (FF) values.

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 (TPD) experiments by Capote and Madix.58 To assess this activation energy within our force field, we place an EG molecule on a rigid, periodic (10 × 14) Ag(110) surface with 6 atomic layers and perform MD simulation for 1 ns in the canonical ensemble at 300 K. We save instantaneous configurations of the molecule-slab system every 10 ps and use these 101 different configurations as initial configurations for structural optimization, where atoms in the

EA = ⟨Es⟩ + ⟨Em⟩ − Es + m

(10)

where ⟨Es⟩ and ⟨Em⟩ are the average potential energies of the bare Ag surface and an isolated molecule during the 5 ns production runs, and Es+m is the instantaneous potential energy of the surface with an adsorbed molecule. Figure 7 shows the adsorption energy as a function of time for EG, PEO, and PVP on rigid Ag(100) and Ag(111). The average values of the adsorption energy for both rigid and F



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than that for a monomer (0.05 eV), while for PEO, this difference is comparable for the monomer and the decamer. The difference between PVP and PEO is consistent with the predictions of a model that we developed recently,26,28 which attributes facet-selective binding to differences in the monomer binding energies on two different facets and the chain stiffness. For PVP, the enhancement of surface-sensitive binding at the polymer level relative to the monomer level can be attributed to the strong binding per repeat unit, in combination with a relatively stiff chain. While not all O atoms in PVP can reside close to the Ag surfaces simultaneously due to steric effects, those within the bonding range remain close to the surfaces and contribute to the surface-sensitive binding over the entire time of the production runs. PEO, on the other hand, is a highly flexible chain with a relatively weak binding energy per repeat unit. We observe significant rotation of bonds around the PEO backbone during the simulations, with O atoms frequently moving in and out of the bonding range with the surface. The facet sensitivity of PEO binding is therefore much weaker than that expected for the stiffer PVP chain. We note that the stronger (weaker) facet-selective binding of PVP (PEO) is consistent with experimental studies,13 which indicate that PVP is a more effective SDA than PEO.

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CONCLUSIONS In summary, we developed a force field that is capable of reproducing the binding energies and geometries, as well as surface-sensitive adsorption predicted by first-principles DFT for PVP, PEO, and EG on Ag surfaces. This force field can be used in large-scale MD simulations to model PVP- or PEOmediated growth of various Ag nanostructures in EG solvent. Such simulations can reveal atomistic details of the growth process, which is beyond the capabilities of current experiments, and indicate possible strategies for solution-phase synthesis of Ag nanostructures.

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Figure 7. Adsorption energy of (a) an EG molecule, (b) a decamer PEO chain, and (c) a decamer PVP chain as a function of time on rigid Ag(100) and Ag(111) surfaces at 300 K.

Corresponding Author

*E-mail: fi[email protected].

mobile surfaces are given in Table 6. Here, we see that PVP exhibits significantly stronger binding on both Ag(100) and

Notes

The authors declare no competing financial interest.

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Table 6. Average Adsorption Energy of EG, and PEO and PVP Decamers on Rigid and Mobile Ag(100) and Ag(111) at 300 K molecule

surface

EA, rigid surface (eV)

EA, mobile surface (eV)

EG EG PEO PEO PVP PVP

Ag(100) Ag(111) Ag(100) Ag(111) Ag(100) Ag(111)

0.51 0.49 1.83 1.79 4.50 4.13

0.46 0.44 1.78 1.74 4.51 4.19

AUTHOR INFORMATION

ACKNOWLEDGMENTS 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.

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A Force Field for Describing the Polyvinylpyrrolidone-Mediated

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