Binding of Polyvinylpyrrolidone to Ag Surfaces: Insight into a Structure

Article pubs.acs.org/JPCC

Binding of Polyvinylpyrrolidone to Ag Surfaces: Insight into a Structure-Directing Agent from Dispersion-Corrected Density Functional Theory Wissam A. Saidi,*,† Haijun Feng,‡,§ and Kristen A. Fichthorn‡ †

Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States Department of Chemical Engineering and Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, United States § School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou 510640, China ‡

ABSTRACT: We use dispersion-corrected density functional theory (DFT) to resolve the role of polyvinylpyrrolidone (PVP) in the shape-selective synthesis of Ag nanostructures by probing the interaction of its 2-pyrrolidone (2P) ring with Ag(100) and Ag(111). We employ two different semiempirical methods for including van der Waals (vdW) interactions in DFT calculations: DFT+vdWsurf and DFT-D2. We find that DFT-D2, in its original parametrization, overestimates the Ag metal dispersion interaction and causes an unphysical herringbone-like reconstruction of Ag(100). This can be remedied in DFT-D2 by using modified vdW parameters for Ag that account for many-body screening effects. The results obtained using DFT-D2 with the modified parameters agree well with experiment and with DFT+vdWsurf results. We find that 2P binds more strongly to Ag(100) than Ag(111), consistent with experiment. We analyze the origins of the surface-sensitive binding and find that vdW attraction is stronger on Ag(111), but the direct chemical bonding of 2P is stronger on Ag(100). We also study the influence of strain on binding energies and find that tension tends to lower the vdW interaction with the surfaces, while increasing the direct chemical-bonding interaction, consistent with the d-band center model. Overall, our work indicates that strain has little impact on the structure-directing capabilities of PVP, which is consistent with the fact that strained, 5-fold twinned Ag nanowires have extensive {100} facets and relative small {111} facets.

■

INTRODUCTION Solution-phase crystal-growth techniques have been used to synthesize a wide variety of metal nanostructures, including highly anisotropic morphologies, such as nanowires and thinplate nanoparticles with triangular, hexagonal, or circular profiles.1−11 These “bottom-up” chemical methods are ideal routes to nanostructures because they are, in principle, extremely versatile and permit the synthesis of a wide variety of different nanostructures with desirable properties that depend on nanocrystal size and shape. The potential impact of these nanoscale materials on emerging applications is immense, with the possibility for advances in areas as diverse as alternative energy, computing, and medicine. A deep fundamental understanding of these syntheses would allow for tight control over the various nanocrystal sizes and shapes that can be achieved. Central to these chemical methods are structure-directing or capping agents, solution-phase additive molecules that facilitate the formation of a particular nanostructure morphology. These molecules likely play multiple roles in facilitating selective nanocrystal growth. For example, by covering the nanocrystal surfaces, such molecules can prevent growing nanostructures © 2012 American Chemical Society

from random aggregation, which is favored by nonspecific van der Waals (vdW) forces between the metal particles. Capping agents can selectively alter the surface energies of certain crystal facets to promote the growth of shapes that are different from the Wulff shapes expected for the uncapped material.12 The surface-selective binding of structure-directing molecules to certain crystal facets can also kinetically promote the growth of facets on which they are most strongly bound, as their high coverage can prevent or hinder atoms from adding to those facets. A system that likely contains all of these structure-directing functionalities is the growth of 5-fold-twinned, pentagonal Ag nanowires via the polyol process.2,4,8,13−19 In this synthesis, ethylene glycol is both a solvent and a reducing agent for AgNO3, which is the source of Ag atoms. When polyvinylpyrrolidone (PVP) is used as a structure-directing agent, pentagonal nanowires form with long {100} side facets and relatively small {111} end facets, although nanostructures with Received: October 5, 2012 Revised: December 23, 2012 Published: December 27, 2012 1163

dx.doi.org/10.1021/jp309867n | J. Phys. Chem. C 2013, 117, 1163−1171

The Journal of Physical Chemistry C

Article

provide active sites for nanowire growth along their long axes and that Ag atoms are less likely to stick to the less-strained {100} side facets.18 Because the growth of the Ag nanowires is facilitated by PVP and the binding of PVP can be affected by strain, we also study the sensitivity of surface-selective binding to strain.

low-energy {111} facets are expected for face-centered cubic (fcc) Ag. This has been attributed to stronger binding of PVP to Ag(100) than Ag(111),13 and in a recent study,20 we used first-principles, density functional theory (DFT) including vdW interactions to test this idea. We found that PVP binds significantly more strongly to Ag(100) than to Ag(111),20 consistent with experimental findings.4,8,13 In this work, we present a detailed analysis of the origins of this surface-sensitive binding. We also note that strain is relevant in the growth of 5-foldtwinned, pentagonal Ag nanowires. As shown in Figure 1a,

■

METHODS To assess the interaction of PVP with Ag surfaces, we break its repeat unit into submolecules, in a method originally proposed by Delle Site et al.22 This breakdown is shown in Figure 2,

Figure 1. (a) Schematic of a 5-fold twinned pentagonal nanowire consisting of five elongated {100} side facets and 10 small {111} end facets. (b) Each of the five sections of the nanowire consists of a triangular prism, in which the angle of each section is 70.53°. This leads to a deficit of 7.35° after fitting the five sections together. This schematic is similar to previously published figures, for example, in refs 8, 13, 15, and 18.

Figure 2. Breakdown of the repeat unit of PVP into two submolecules: ethane and 2-pyrrolidone. Carbon atoms are turquoise, oxygen is red, nitrogen is blue, and hydrogen is white.

these nanowires consist of five triangular prisms that are joined at internal twin planes, resulting in 10 small {111} end facets and five elongated {100} side facets. The 5-fold symmetry is not space filling, as the angle for each of the five sections is 70.53° and an angle of 72° per section is required to have a space-filling (360°) geometry. Thus, as shown in Figure 1b, there is a gap of 7.35° after fitting the five sections together, and closure of this gap results in lattice strain. There is some disagreement in the literature with regard to the nature of the strain in pentagonal nanowires.15,17,18,21 In early studies, this strain was believed to be primarily tensile at the nanowire surfaces,15,17,21 and it was proposed that the increase in tension with growth of the nanowire diameter would inhibit growth of the {100} side facets, or result in the formation of reentrant grooves along these facets. Recent experimental studies with high-resolution X-ray diffraction and transmission electron microscopy indicate that the distribution of strain in 5-fold twinned nanowires is significantly more complicated than was originally believed.18 These studies show that 5-fold twinned Ag nanowires actually have a body-centered tetragonal (bct) structure. Such a structure emerges from an fcc unit cell for which one of the lattice parameters is compressed relative to the other two. Moreover, the lattice strain was found to be concentrated in the nanowire cores, so that they have a core−shell structure with a highly strained (anisotropically compressed) core, which has many defects and dislocations, surrounded by a relatively unstrained exterior shell on the {100} facets. The core is exposed on the {111} end facets of the nanowires, which are strained, with many defects near the center, and relatively unstrained near the periphery. It has been proposed that these highly strained and defective {111} ends

where we see that two logical submolecules for PVP are ethane, which is an inert and nonpolar molecule whose interaction with Ag is dominated by vdW attraction, and a 2-pyrrolidone (2P) ring. Experimental studies with various spectroscopic techniques14,23−26 indicate that PVP binds to Ag surfaces via the oxygen and, possibly, the nitrogen in the 2P ring. Thus, it is likely that the 2P ring plays a central role in endowing structure-sensitive binding to PVP, and we focus our investigation on 2P. The DFT calculations are carried out using a locally modified version of the Vienna Ab Initio Simulation Package (VASP),27−29 where the DFT+vdW scheme was recently implemented.30 The electron−ion interaction is described using the projector-augmented waves of Blöchl31 in the implementation of Kresse and Joubert.32 The Kohn−Sham wave function is expanded in plane waves up to a cutoff of 400 eV. We use the generalized-gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE).33 Our model slab contains 6 metal layers and 8 vacuum layers, where the bottom 3 layers are fixed at their bulk positions. 2P is adsorbed within a (4 × 4) unit cell cut along the (100) and (111) directions for the Ag(100) and Ag(111) surfaces, respectively. The Brillouin zone (BZ) is sampled using a (4 × 4 × 1) Monkhorst−Pack (MP) k-grid for structure optimization. The reported binding energies are obtained using a denser (6 × 6 × 1) MP k-grid. There are no significant differences between the binding energies obtained with the two k-grids, which indicate that the results are converged with respect to the size of the k-grid. The atom-projected density of states (PDOS) analysis is done using a larger (8 × 8 × 1) MP k-grid. 1164



Article

Table 1. Summary of Parameters for Ag in the Various Dispersion Corrections Employed in This Study along with the Predicted Bulk Lattice Constant a0 and Δ12 = (d12 − dbulk)/dbulk, Which Is the Percentage Change from the Bulk Interlayer Spacing between the First and Second Surface Layers PBE

PBE-D2

PBE+D2surf

PBE+vdWsurf

4.16 −2.05 −0.30

24.67 1.639 4.15 1.30 1.61

6.89 1.34 4.09 −0.67 0.17

6.89 1.34 4.02 −1.54 −0.25

−1

6

C6 (J nm mol ) R0 (Å) a0 (Å) Δ12 Ag(100) (%) Δ12 Ag(111) (%)

1 2

−6 ∑ fdamp (rAB , RA0 , RB0)C6,ABrAB A,B

6.25 4.07 ±1.5 0.5 ± 0.8

reference 39 40 41 42

effects that lead to the screening of vdW interactions by the bulk metal are absent. As discussed above, DFT+vdWsurf is formulated to account for nonlocal Coulomb screening within the bulk so that interactions involving metal surfaces are described more accurately. Using PBE-D2 with its standard parametrization for C6 and R0, we found that Ag(100) had a herringbone-like reconstruction with a lower energy than Ag(100).20 Because, to our knowledge, such a reconstruction has not been reported experimentally for Ag(100), we conclude that the standard parametrization of PBE-D2 is not suitable to describe Ag surfaces. The failure of this method is likely due to an overestimation of vdW interactions because of the neglect of screening effects in the Ag metal. To remedy this, we reparametrized PBE-D2 using the PBE+vdWsurf parameters for Ag; we use Grimme’s original parameters for all other species. We will refer to this approach as PBE+D2surf to distinguish it from PBE-D2 with its standard parametrization for Ag. In Table 1, we provide the vdW parameters for Ag employed in the different dispersion corrections employed in this study and in our previous study.20 We note that these are parameters for isolated atoms; although for the “surf” entries in Table 1, these parameters include bulk screening effects so they represent single Ag atoms within solid Ag. Table 1 also includes the bulk lattice constant a0 and Δ12, which is the percentage change from the bulk interlayer spacing between the first and second surface layers, for Ag(100) and Ag(111). As compared to the experimental results, we see that the value of C6 in the PBE+vdWsurf approach is consistent with the value of C6 derived from the Hamaker constant measured experimentally for bulk Ag with ultrahigh vacuum atomic-force microscopy.39 The lattice constant for bulk Ag predicted by the dispersion-corrected methods is smaller than the PBE value, making it in better agreement with the experimental lattice constant.40 Overall, dispersion-corrected methods seem better at predicting Δ 12 than the GGA PBE, although the experimental error is significant.

The lattice constant in the surface calculations is determined from the calculated bulk Ag lattice constant. As we will report below, this value varied depending on the level of theory applied. The 2P molecule in the gas phase was modeled using a cubic supercell with side lengths of 15 Å. Geometry optimization was done using a convergence threshold of 0.01 eV/Å on the atomic forces, and 10−6 eV on the energies in the self-consistent step. We performed several tests to verify our computational framework including varying the vacuum spacing, the plane-wave cutoff, and the number of k-points for the first BZ sampling. In our previous study, we accounted for vdW interactions using the DFT+vdWsurf approach,34 which is a variant of the DFT+vdW scheme35 designed to account for the interaction of adsorbates with metal surfaces. The DFT+vdWsurf method combines the DFT+vdW35 scheme with the Zaremba−Kohn− Lifshitz theory36 to account for nonlocal Coulomb screening within the bulk, which modifies the vdW interactions between an adsorbate and a metal surface or between metal atoms in surface slab. In the present study, we also apply a modified version of the DFT-D2 method37 to gain further insight into the system. In both DFT-D2 and DFT+vdWsurf, the dispersion energy EvdW is expressed as a sum of damped pair interactions between atoms in the system. This energy is added to the total self-consistent DFT energy, and it has the form: EvdW = −

expt

(1)

where rAB is the distance between atoms A and B, C6,AB is the dispersion coefficient for the interaction between atoms A and B, R0A and R0B are the vdW radii for atoms A and B, and fdamp is a short-range damping function designed to eliminate the singularity in eq 1 at short distances. In both the DFT+vdW and the DFT-D2 approaches, the C6,AB parameter for an A−B pair is determined using a mixing rule (that is different for each method) based on the values of C6,AA and C6,BB. Although the general form for the dispersion energy is similar in DFT-D2 and DFT+vdWsurf, there are two major differences between these two approaches. First, in DFT-D2, the dispersion parameters, C6 and R0, are fixed for a given atom.37 In the DFT+vdWsurf approach, the dispersion parameters for a given atom depend on its chemical environment, as described using a Hirshfeld partitioning scheme of the total electron density of the system. Thus, hybridization effects due to the formation of chemical bonds are described more accurately in this method. For completeness, we note that in the modified version of DFT-D2, DFTD3,38 C6 depends on the coordination number of the atom, thus accounting for the chemical environment albeit using a different scheme than DFT+vdW. Second, the parametrization of C6 and R0 for metal atoms in DFT-D2 is based on a single atom in the gas phase and not in the bulk. Thus, many-body

■

RESULTS AND DISCUSSION

Binding Energies and Conformations. In our previous study,20 we used PBE+vdWsurf to obtain adsorption energies and geometries of 2P on Ag(100) and Ag(111) using 18 and 13 different initial binding configurations, respectively. After optimization, we found four and five unique binding configurations for Ag(100) and Ag(111), respectively. The optimized structures from that study are shown in Figures 2 and 3 of ref 20. The corresponding optimized structures using PBE+D2surf are shown in Figures 3 and 4. Both methods show binding configurations in which 2P essentially retains its gasphase structure and does not significantly perturb the Ag surface atoms. On Ag(100), 2P prefers binding configurations 1165



Article

Our results show only positive vibrational frequencies, indicative of a stable adsorption configuration. The binding configurations predicted by PBE+vdWsurf in ref 20 and PBE+D2surf (Figures 3 and 4) are relatively similar. In all of these configurations, the 2P ring is nearly parallel to the surface, and the O atom is the closest atom to the surface. Thus, we characterize the structures using the tilt angle θ between the plane of O, C2, and C3 in the 2P ring and the surface plane (atoms are numbered sequentially along the ring with N = 1, and C5 is bonded to both O and N, cf., Figure 2), and the distance dAgO between O and the closest Ag atom, as shown schematically in Figure 5 for configuration 1. Table 2 Figure 3. Top-down view of the binding configurations for 2P on Ag(100) using PBE+D2surf. The O atom is red, N is blue, C atoms are turquoise, and H atoms are white.

Table 2. Geometrical Parameters for the Different Binding Configurations Obtained with the PBE, PBE+D2surf, and PBE+vdWsurf for Variations of the Different Binding Configurations Shown in Figures 2 and 3a PBE+D2surf

PBE

Figure 4. Top-down view of binding configurations for 2P on Ag(111) using PBE+D2surf, similar to Figure 3.

configuration

dAgO (Å)

θ (deg)

1 2 3 4

2.61 2.50 2.54 2.50

26 25 21 20

1 2 3 4 5

2.67 2.86 2.55 2.69 2.56

24 24 30 24 20

dAgO (Å) Ag(100) 2.71 2.57 2.62 2.50 Ag(111) 2.67 2.77 2.54 2.70 2.57

PBE+vdWsurf

θ (deg)

dAgO (Å)

θ (deg)

15 12 16 12

2.66 2.55 2.72 2.60

14 13 16 11

17 15 14 15 12

2.70 2.81 2.54 2.78 2.60

17 15 16 16 11

a

dAgO is the shortest distance between O and a metal surface atom, and θ is the tilt angle between the plane of O, C2, and C3 in the 2P ring and the surface Ag plane (atoms are numbered sequentially along the ring with N = 1 and C5 is bonded to both O and N). dAgO and θ are illustrated for configuration 1 in Figure 5.

with the O atom in close proximity to the bridge site between two Ag atoms or directly on top of an Ag surface atom. We found binding configurations with the O atom near the bridge, top, and hollow sites on Ag(111). For several of the optimum structures, we computed the harmonic vibrational frequencies in the frozen lattice approximation to examine their stability.

summarizes the values of θ and dAgO for the different binding states. These structures are characterized by low tilt angles that are consistent with the binding of a PVP polymer in a “flat”

Figure 5. Side view of 2P binding showing the tilt angle θ between the plane of O, C2, and C3 in the ring and the surface plane and dAgO, which is the distance between the O and the closest surface atom for configuration 1 on Ag(100) and Ag(111) for the three methods. 1166



Article

Comparing the binding energies from the two vdWcorrected DFT methods, we see that they exhibit similar trends. Both approaches predict that the binding energies of the various conformers on a given surface lie within a relatively narrow range, with essentially the same ordering of energies. On both surfaces, both methods predict that vdW attraction is the dominant contribution to the binding energy and that the contribution from short-range binding is more significant on Ag(100) than on Ag(111). Thus, the balance between shortrange and vdW attraction is surface sensitive with both methods. We note that PBE+vdWsurf predicts larger binding energies on both surfaces. On Ag(100) this arises from the stronger contribution from direct bonding with PBE+vdWsurf, as the vdW contributions are comparable in both methods. On Ag(111), the vdW contribution is stronger with PBE+vdWsurf, but the short-range, direct-bonding contribution is weaker. In addition to differences between the methods with regard to the vdW parameters (i.e., they are fixed in PBE+D2, but they can vary in PBE+vdW), we note that the lattice constant of the Ag substrate is different in the two sets of calculations (cf., Table 1). As we will discuss below, these different lattice constants also contribute to variation in the binding energies. In comparing the PBE-only results to those including vdW interactions, we see that the PBE-only binding energy for a given conformation is always greater than the short-range attraction in the dispersion-corrected DFT results. This occurs because vdW attraction plays a considerable role in determining binding configurations in dispersion-corrected DFT. Nonspecific vdW attraction pulls the ring close to the substrate (so it has low tilt angles in Table 2) at the expense of short-range attraction due to direct bonding. On the other hand, shortrange attraction is the only attraction in PBE-only calculations, and molecules achieve the lowest binding energies in configurations that optimize this interaction, those with the highest tilt angles in Table 2. Interestingly, all of the methods in Table 3 predict that 2P binds more strongly to Ag(100) than to Ag(111). As we discussed previously,20 when PVP binds to these surfaces, there is correlated binding of a number Nc of 2P rings connected to the backbone due to chain stiffness and the energetic preference for chain binding. Using the solution-phase Kuhn length as an estimate, we found Nc = 9 segments for PVP, and we derived an expression for the relative preference of the polymer chain to bind to Ag(100) at a temperature of T as

conformation, with its backbone parallel to the surface and its ring slightly tilted. It is interesting to elucidate the effects of vdW corrections on the binding configurations of 2P on the Ag(100) and Ag(111) surfaces. To this end, we performed structural optimization on the optimum structures shown in Figures 3 and 4 using PBE only with no dispersion corrections. We employed the PBE optimized bulk lattice constant predicted in the PBE calculations. Structural parameters for the PBE-optimized conformers are included in Table 2, and side views of binding conformation 1 are shown in Figure 5. As compared to the binding conformations from vdW-corrected DFT, we see that the PBE conformations assume higher tilt angles with the surface, while dAgO tends to be comparable with the PBE only. Table 3 shows a summary of the binding energy Ebind for the conformers in Figures 3 and 4, as well as the analogous Table 3. Total Binding Energies in millielectronvolts of 2P Obtained with the PBE, PBE+D2surf, and PBE+vdWsurf for Variations of the Different Binding Configurations Shown in Figures 2 and 3, Along with the Short-Range (short) and Dispersion (vdW) Contributions to the Total Energy for the Dispersion-Corrected Methods PBE+D2surf configuration

PBE

short

1 2 3 4

266 261 236 266

132 137 118 146

1 2 3 4 5

204 216 233 206 208

65 98 92 74 91

vdW Ag(100) 538 490 508 456 Ag(111) 553 527 495 535 498

PBE+vdWsurf total

short

vdW

total

670 627 626 602

248 234 222 237

530 484 492 449

778 718 714 686

618 625 587 609 589

42 1 58 12 30

651 688 612 653 621

693 689 670 665 651

structures obtained with DFT+vdWsurf and the PBE only. We compute the binding energies using E bind = E2P + ES − E2P + S

(2)

where E2P+S is the energy of the surface slab with the adsorbed molecule, E2P is the energy of the gas-phase 2P molecule, and ES is the energy of the bare surface slab. Positive values of Ebind indicate attraction between the molecule and the surface. These binding energies can be partitioned into three different components: vdW attraction EvdW (which is given by eq 1 and absent in calculations with the PBE only), short-range direct bonding Edirect, and short-range Pauli repulsion EPauli, so that Ebind = EvdW + EPauli + Edirect. To gain further insight into the stabilizing forces for the different adsorption configurations, we also show in Table 3 a breakdown of the total binding energy into the vdW component EvdW and the short-range component, given by EPauli + Edirect. For a given binding configuration, the short-range contribution to the total binding energy can be obtained from a calculation with the PBE alone (i.e., in the absence of vdW interactions). We note that the optimized PBE configurations in Table 3 have lower energies and lower tilt angles than what we found previously20 because in this study we began with different initial structures that gave lower-energy optimized configurations.

P(100)/(111) = exp(NcΔE /kBT )

(3)

where ΔE is the difference between the 2P binding energies on Ag(100) and Ag(111).20 Taking ΔE as the energy difference between the most strongly bound conformer on each surface, we find that at T = 400 K, PVP is ∼109 times more likely to bind to Ag(100) than to Ag(111) (ΔE = 85 meV) in the PBE +vdWsurf method and ∼106 times as likely with PBE+D2surf, where ΔE = 44 meV. Both of these trends are consistent with the experimental observation that Ag forms {100}-faceted nanostructures in the presence of PVP.4,8,13 The atom-projected density of states (PDOS) yields insight into the binding of 2P to these surfaces. Figure 6 summarizes our results for configuration 1 in Table 3 obtained using PBE +D2surf on the Ag(100) and Ag(111) surfaces, respectively. We also examined the other stable configurations shown in Figures 3 and 4 but did not find the results of the PDOS to be sensitive to the conformers on the same surface. Additionally, the 1167



Article

governed by the density of the substrate, which is affected by strain. Strain can also influence the electronic structure of the surface by altering the width of the d band. As we proceed from compression to tension, the width of the d band decreases due to decreasing overlap between the d orbitals on neighboring metal atoms. In metals with a partially filled d band, this causes an upshift in the energies of the d orbitals to maintain a constant d band occupancy.43 For filled d band metals such as Cu, Ag, and Au, an upshift in the d-band center for expanded surfaces arises from a narrowing of the d band due to a lesser orbital overlap and the pinning of the d band top edge with respect to the Fermi energy.44 The center of the d band reflects these changes and has been demonstrated to be a key parameter influencing the interaction strength between adsorbates and metal surfaces.43,45 The two dispersion-corrected DFT methods employed here are both based on the PBE-GGA for the electronic structure, yet the lattice constants for bulk Ag associated with these methods can be considerably different from the inherent PBE GGA value (cf., Table 1) due to vdW interactions. It is of interest to know how the results are affected by the strain associated with the different lattice constants. As discussed above, strain is also relevant in the colloidal growth of pentagonal 5-fold-twinned Ag nanowires,15,17,18 and it is interesting to consider the ramifications of strain for the structure-directing capabilities of PVP. To study the influence of strain on 2P binding to these surfaces, we carried out a series of calculations using DFT +vdWsurf where the Ag metal slab is under a compressive or tensile stress. We study 2P adsorption on Ag slabs for which the bulk lattice constant changes from 3.90 to 4.14 Å or relative strains ranging from ∼−3% to 3%, where the relative strain is given by (a − a0)/a0. The initial guesses for the minimumenergy structures are obtained from the four/five optimized structures with the equilibrium bulk lattice constant a0 on Ag(100)/Ag(111), respectively, from ref 20. Our studies focus on fcc lattices, although recent studies indicate the possibility that the bulk nanowire structure is bct.18 We note that the fcc and bct lattices are similar, so that bct lattices have approximate fcc structures at the surface. Figure 7a shows the binding energy of the lowest-energy conformer on each surface (conformer 1 from ref 20), as well as its breakdown into vdW and, by implication, short-range components, as a function of the relative strain. As can be seen in Figure 7a, the total binding energy of 2P to Ag(100) is relatively insensitive to strain, while on Ag(111), there is an increase in the binding energy as we proceed from compression to tension. Perhaps the most notable observation from Figure 7a is the decrease in vdW attraction and the increase in shortrange attraction with increasing tension. The Ag(100) surface clearly exhibits this trend, where increases in the short-range binding energy are almost exactly compensated by decreases in vdW attraction. We see this trend to a lesser extent on Ag(111). In a purely geometric sense, vdW attraction in our calculations is (essentially) a sum of pair interactions between atoms in the 2P molecule and in the Ag substrates (cf., eq 1). The density of the substrate decreases as we progress from compression to tension, leading to a decrease in vdW attraction. Of course, the terms in eq 1 associated with the closest Ag surface atoms to 2P influence the binding energy the most strongly, so that strain can locally induce changes in the binding conformation, as well as the binding energy. As we will

Figure 6. PDOS for 2P adsorbed on Ag(100) and Ag(111) for the most stable configuration 1 shown in Figures 3 and 4, respectively. The inset shows the PDOS for the system in the noninteracting regime, where the 2P molecule is more than 10 Å from the surface.

corresponding PDOS for the PBE+vdWsurf optimized structures are not shown; we discussed these previously,20 and they do not differ appreciably from what is shown for PBE+D2surf. The insets of Figure 6 show the PDOS for 2P when it is far from the surface, that is, in the noninteracting limit of 2P and the metal surfaces. The 2P frontier orbitals bracket the Fermi energy, where the 2P lowest unoccupied molecular orbital (LUMO) is ∼4 eV above the Fermi level, while the highest occupied molecular orbitals (HOMO) and HOMO−1 are 1−2 eV below the Fermi level of the system. The occupied orbitals of 2P are 1−2 eV above the top of the Ag d band. The upper two bonding orbitals are localized to a large extent on oxygen (∼60%) and nitrogen (∼25%). When 2P achieves its optimum bonding configuration with the metal surface, its edge states are broadened for both Ag facets. Additionally, the occupied frontier orbitals move closer to the Ag d band, while the unoccupied orbitals shift closer to the Fermi energy located between the occupied and unoccupied orbitals of 2P. Examining Figure 6, we see that the shift in the occupied orbitals of 2P to lower energies leads to hybridization between the p orbitals of 2P (those of O and N) and the d band for Ag(100). On the other hand, for Ag(111), the shift is not large enough to cause appreciable overlap between the bonding frontier orbitals of 2P and the Ag d band. Effects of Strain. The surface sensitivity of 2P binding to Ag surfaces is affected by strain. In a purely geometric sense, the fit between 2P and the surface can be influenced by strain, and the ability of the molecule to bond to the surface can be influenced by this fit. In the (essentially) pairwise additive forms we employ here (see eq 1), vdW interactions are 1168



Article

(εd−εp is too large in Figure 7c), so that the short-range interaction is essentially zero. We can see this in the PDOS for 2P adsorbed on Ag(111) as described by PBE+D2surf in Figure 6, and we also observed this previously20 in calculations with PBE+vdWsurf. As we increase the lattice constant from the unstrained state, the p−d overlap in Figure 7c increases and the short-range interaction in Figure 7a becomes nonzero on Ag(111), but remains relatively constant with increasing tension. In Figure 7c, the overlap for the highest strain does not follow the nearly linear trend seen for the lower strains, which implies a less-than-expected increase in the short-range interaction. This may also be due to an interplay between vdW interactions and direct bonding, such that the molecule finds binding conformations that better optimize vdW interactions (at the expense of short-range binding) at the highest strain. We monitored the tilt angle θ and dAgO as a function of strain and find that these increase by 2° and decrease by ∼1%, respectively, as the relative strain increases from 0 to 3%. While these are small changes, the energies associated with shifting the d-band center are also small on Ag(111), so that such an interplay could occur. The d-band center energies and the overlap between the p and d bands also correlate with the trend in differences between overall binding energies on the two surfaces. In Figure 7b, we see that εAg(100) > εAg(111) for all strain states, although the d d Ag(100) − εAg(111) decreases as the surface lattice difference εd d expands. Similarly, in Figure 7c, we see that there is better overlap between the p and d bands on Ag(100) than on Ag(111), but that the overlap on Ag(111) is approaching that of Ag(100) with increasing strain. Despite the fact that the total binding energy reflects an interplay between vdW and shortrange bonding, it does appear that, in an overall sense, the shrinking difference between the binding energies with strain can be explained by changes in the electronic structure of the substrate. Regarding the role of PVP in the growth of 5-fold twinned Ag nanowires, our study indicates that if there is increasing tension at the nanowire surfaces with increasing nanowire diameter, as has been proposed,15,17,21 then the structuredirecting capabilities of PVP diminish somewhat with increasing nanowire diameter, assuming that the {100} and {111} are under the same tensile stress. This is because we find (see Figure 7a) less of a difference in the binding energies of 2P on the two facets with increasing tension, although for the strains studied here, we still expect PVP to be highly selective to the {100} facets using eq 3. If, as has also been proposed,18 the {100} side facets are relatively unstrained and the {111} end facets are compressed, then from Figure 7a we expect PVP to have the same structure-directing capabilities as we find for unstrained surfaces. Of course, there are factors other than the PVP binding energy that could influence strain-dependent nanowire growth, including strain-induced changes in the binding energies of Ag atoms to the different facets. Also, because we study relatively low densities of adsorbed 2P, our calculations do not take into account interactions between these molecules, which could lead to a coverage dependence of the binding energies. Nevertheless, our work indicates that strain has little impact on the structure-directing capabilities of PVP, which is consistent with the fact that strained, 5-fold twinned Ag nanowires have extensive {100} facets and relatively small {111} facets.

Figure 7. (a) Effect of strain on the binding energy (computed with PBE+vdWsurf for configuration 1 in ref 20) of 2P on Ag(100) and Ag(111). For each case, we show the total binding energy, as well as the vdW contribution. (b) Effect of strain on d-band center for bare Ag(100) and Ag(111) surfaces. (c) Difference between the d-band center and the center of the p band for the HOMO and HOMO−1 of 2P for both the substrate and 2P in configuration 1 (i.e., the lowestenergy configurations for the two surfaces) of ref 20.

elaborate below, this might explain the nonmonotonic trend in the vdW interaction on Ag(111). To understand the increase in short-range attraction with increasing strain, we examine its effects on the d-band center εd of the Ag substrates. We computed εd (with respect to the Fermi energy) for bare Ag(100) and Ag(111) slabs. The effect of the strain on the d-band center, an upshift in εd with increasing strain, can be seen in Figure 7b. To understand the effect of strain on the short-range interaction of 2P with the Ag substrates, we also calculated the difference between the d-band center and the center of the p band for the HOMO and HOMO−1 of 2P for both the substrate and 2P in configuration 1 (i.e., the lowest-energy configuration) of ref 20. A smaller value of εd−εp indicates better overlap between the p states of 2P and the Ag d band. As we see in Figure 7c, the overlap improves with increasing strain on both surfaces. For Ag(100), the increasing overlap in Figure 7c correlates well with the increase in short-range binding as we go from compression to tension in Figure 7a. Although we see the same overall trend on Ag(111) as we do on Ag(100), changes in the short-range binding energy do not mirror changes in the d-band center and the p−d overlap as well as they do on Ag(100). This is likely due to the fact that there is virtually no overlap between the bonding orbitals of 2P and the Ag(111) d band for compressed or unstrained surfaces 1169



■

Article

(3) Murphy, C. J.; Sau, T. K.; Gole, A. M.; Orendorff, C. J.; Gao, J.; Gou, L.; Hunyadi, S. E.; Li, T. J. Phys. Chem. B 2005, 109, 13857− 13870. (4) Wiley, B.; Sun, Y.; Mayers, B.; Xia, Y. Chem.-Eur. J. 2005, 11, 454−463. (5) Xiong, Y.; Xia, Y. Adv. Mater. 2007, 19, 3385−3391. (6) Weber, J.; Singhal, R.; Zekri, S.; Kumar, A. Int. Mater. Rev. 2008, 53, 235−255. (7) Grzelczak, M.; Perez-Juste, J.; Mulvaney, P.; Liz-Marzan, L. M. Chem. Soc. Rev. 2008, 37, 1783−1791. (8) Xia, Y.; Xiong, Y.; Lim, B.; Skrabalak, S. E. Angew. Chem., Int. Ed. 2009, 48, 60−103. (9) Tiano, A. L.; Koenigsmann, C.; Santulli, A. C.; Wong, S. S. Chem. Commun. 2010, 46, 8093−8130. (10) Xia, X.; Xia, Y. Nano Lett. 2012, 12, 6038−6042. (11) Xia, X.; Zeng, J.; Zhang, Q.; Moran, C. H.; Xia, Y. J. Phys. Chem. C 2012, 116, 21647−21656. (12) Bealing, C. R.; Baumgardner, W. J.; Choi, J. J.; Hanrath, T.; Hennig, R. G. ACS Nano 2012, 6, 2118−2127. (13) Sun, Y.; Mayers, B.; Herricks, T.; Xia, Y. Nano Lett. 2003, 3, 955−960. (14) 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.; Zhang, J. M.; Shen, D. Y. J. Phys. Chem. B 2004, 108, 12877−12881. (15) Lofton, C.; Sigmund, W. Adv. Funct. Mater. 2005, 15, 1197− 1208. (16) Elechiguerra, J. L.; Reyes-Gasga, J.; Yacaman, M. J. J. Mater. Chem. 2006, 16, 3906−3919. (17) Zhang, W.; Liu, Y.; Cao, R.; Li, Z.; Zhang, Y.; Tang, Y.; Fan, K. J. Am. Chem. Soc. 2008, 130, 15581−15588. (18) Sun, Y.; Ren, Y.; Liu, Y.; Wen, J.; Okasinski, J. S.; Miller, D. J. Nat. Commun. 2012, 3, 971. (19) Sun, Y.; Xia, Y. Adv. Mater. 2002, 14, 833−837. (20) Al-Saidi, W. A.; Feng, H.; Fichthorn, K. A. Nano Lett. 2012, 12, 997−1001. (21) Marks, L. D. Rep. Prog. Phys. 1994, 57, 603−649. (22) Delle Site, L.; Abrams, C. F.; Alavi, A.; Kremer, K. Phys. Rev. Lett. 2002, 89, 156103. (23) Bonet, F.; Tekaia-Elhsissen, K.; Sarathy, K. Bull. Mater. Sci. 2000, 23, 165−168. (24) Huang, H. H.; Ni, X. P.; Loy, G. L.; Chew, C. H.; Tan, K. L.; Loh, F. C.; Deng, J. F.; Xu, G. Q. Langmuir 1996, 12, 909−912. (25) Mdluli, P. S.; Sosibo, N. M.; Revaprasadu, N.; Karamanis, P.; Leszczynski, J. J. Mol. Struct. 2009, 935, 32−38. (26) Zhang, Z.; Zhao, B.; Hu, L. J. Solid State Chem. 1996, 121, 105− 110. (27) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251−14269. (28) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15−50. (29) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (30) Al-Saidi, W. A.; Voora, V.; Jordan, K. J. Chem. Theory Comput. 2012, 8, 1503−1513. (31) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953−17979. (32) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758−1775. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (34) Ruiz, V. G.; Liu, W.; Zojer, E.; Scheffler, M.; Tkatchenko, A. Phys. Rev. Lett. 2012, 108, 146103. (35) Tkatchenko, A.; Scheffler, M. Phys. Rev. Lett. 2009, 102, 073005. (36) Zaremba, E.; Kohn, W. Phys. Rev. B 1976, 13, 2270−2285. (37) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (38) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (39) Eichenlaub, S.; Chan, C.; Beaudoin, S. P. J. Colloid Interface Sci. 2002, 248, 389−397. (40) Khein, A.; Singh, D. J.; Umrigar, C. J. Phys. Rev. B 1995, 51, 4105−4109. (41) Li, H.; Quinn, J.; Li, Y. S.; Tian, D.; Jona, F.; Marcus, P. M. Phys. Rev. B 1991, 43, 7305−7307.

CONCLUSIONS In summary, we used dispersion-corrected DFT to study the role of PVP in the shape-selective synthesis of Ag nanostructures by probing the interaction of its 2P ring with Ag(100) and Ag(111) surfaces. We employed two different semiempirical methods for including vdW interactions in DFT calculations: DFT+vdWsurf and DFT-D2. DFT-D2, in its original parametrization, overestimates the Ag metal dispersion interaction and causes a herringbone-like reconstruction of Ag(100). Such a reconstruction has not been observed experimentally. This feature vanishes from DFT-D2 calculations if we use modified vdW parameters for Ag, those employed in DFT+vdWsurf, that account for many-body screening effects. The results obtained using DFT-D2 with the modified parameters show the same trends as the DFT +vdWsurf results. Both methods predict that 2P binds more strongly to Ag(100) than to Ag(111), consistent with experiment.4,8,13 We analyzed the origins of the surface-sensitive binding and found that vdW attraction is stronger on Ag(111), but the direct chemical bonding of 2P is stronger on Ag(100). Differences in short-range bonding may be understood in terms of overlap between the bonding orbitals of 2P and the Ag metal d band, which can be seen in the PDOS of the adsorbate−metal systems. On Ag(100), there is good overlap between the p orbitals of 2P and the metal d band that hallmarks a bonding interaction. Such overlap is minimal on Ag(111). In contrast, the high vdW interaction on Ag(111) as compared to that on Ag(100) can be understood in terms of the greater local density of atoms on this surface. We studied the influence of strain on 2P binding energies and found on both surfaces that tension tends to lower the vdW interaction and increase the direct chemical bonding interaction. The trend in the chemical bonding interaction is consistent with the d-band center model.43,45 Although there is controversy regarding the exact nature of strain at the surfaces of 5-fold twinned Ag nanowires, our study indicates that strain has little impact on the PVP-mediated growth of Ag nanowires, which is consistent with experimental studies.2,4,8,13−19

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

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 National Science Foundation grant number OCI-1053575. H.F. thanks the China Scholarship Council for support.

■

REFERENCES

(1) Tian, Z. R.; Voight, J. A.; Liu, J.; McKenzie, B.; McDermott, M. R.; Rodriguez, M. A.; Konishi, H.; Xu, H. Nat. Mater. 2003, 2, 821− 826. (2) Xia, Y.; Yang, P.; Sun, Y.; Wu, Y.; Mayers, B.; Gates, B.; Yin, Y.; Kim, F.; Yan, H. Adv. Mater. 2003, 15, 353−389. 1170



Article

(42) Chelvayohan, M.; Mee, C. H. B. J. Phys. C: Solid State Phys. 1982, 15, 2305−2312. (43) Mavrikakis, M.; Hammer, B.; Norskov, J. K. Phys. Rev. Lett. 1998, 81, 2819−2822. (44) Sakong, S.; Groß, A. Surf. Sci. 2003, 525, 107−118. (45) Hammer, B.; Norskov, J. In Impact of Surface Science on Catalysis; Bruce, C., Gates, H. K., Ed.; Advances in Catalysis; Academic Press: New York, 2000; Vol. 45, pp 71− 129.

1171


Binding of Polyvinylpyrrolidone to Ag Surfaces: Insight into a Structure

Recommend Documents