Adsorption of Polyvinylpyrrolidone on Ag Surfaces: Insight into a

Letter pubs.acs.org/NanoLett

Adsorption of Polyvinylpyrrolidone on Ag Surfaces: Insight into a Structure-Directing Agent W. A. Al-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 density functional theory to resolve the role of polyvinylpyrrolidone (PVP) in the shape-selective synthesis of Ag nanostructures. At the segment level, PVP binds more strongly to Ag(100) than Ag(111) because of a surface-sensitive balance between direct binding and van der Waals attraction. At the chain level, correlated segment binding leads to a strong preference for PVP bind to Ag(100). Our study underscores differences between small-molecule and polymeric structure-directing agents.

KEYWORDS: Density functional theory, nanostructure, silver, adsorption, van der Waals, structure-directing agent

I

that endow certain molecules with surface-sensitive binding or other structure-directing abilities are not well understood. Here, we report the results of first-principles calculations based on density functional theory (DFT) aimed at understanding the structure-directing capabilities of PVP. This polymer is widely used as a structure-directing agent in nanostructure syntheses involving a variety of different materials, and its success is generally attributed to its surfaceselective binding, although the origins of this selectivity are not understood. In this work, we focus on the surface-selective binding of PVP to Ag, to address experiments.8−11 Firstprinciples studies of polymer adsorption are challenging because of the wide range of relevant length scales. To assess the interaction of PVP with Ag surfaces at the smallest length scale (over which chemical bonds are formed), we break the repeat unit of PVP into submolecules, in a method originally proposed by Delle Site et al.12 We calculate the interaction of each submolecule with the surface separately to gauge the total interaction. This breakdown is shown in Figure 1, 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 van der Waals (vdW) attraction and a 2pyrrolidone (2P) ring. Experimental studies with various spectroscopic techniques13−17 indicate that PVP binds to Ag surfaces via the oxygen and, possibly, the nitrogen in the 2P ring.

n the past decade, an astounding variety of intricate nanostructures have been synthesized via solution-phase techniques.1−9 A large number of potential and existing applications, (e.g., in sensing, catalysis, photonics, electronics, and medicine) can exploit the unique optical, electronic, and magnetic properties of nanostructures with well-defined sizes and shapes. Despite numerous successes and the promise of new applications, there are still many gaps in the fundamental understanding of these syntheses. In a typical process, seed crystals grow with the help of a structure-directing or capping agent that determines the shape of the final nanostructure. Although there is a great deal of experimental evidence indicating that structure-directing agents can play a pivotal role in selectively producing various nanostructures, their exact role remains elusive. It is often hypothesized that structure-directing molecules exhibit surfaceselective binding to certain crystal facets, which grow at the expense of facets on which they are less strongly bound. An example of such a system is the growth of Ag nanowires from seed crystals that nucleate via the reduction of AgNO3 salt in ethylene glycol and grow with the help of a structuredirecting polymer, polyvinylpyrrolidone (PVP).8−10 The nanowires have long (100) side facets and small (111) end facets, and this is attributed to stronger binding of PVP to Ag(100) than Ag(111).10 Similarly, in the growth of Ag nanostructures in L-ascorbic acid, it has been hypothesized that the strong binding of sodium citrate to Ag(111) promotes the growth of nanosized octahedral crystals with (111) facets.11 When PVP is the structure-directing agent in this system, a mix of (100)faceted nanocubes and nanobars forms, consistent with selective binding to Ag(100).11 The physicochemical attributes © 2011 American Chemical Society

Received: November 22, 2011 Revised: December 21, 2011 Published: December 29, 2011 997

dx.doi.org/10.1021/nl2041113 | Nano Lett. 2012, 12, 997−1001

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experimental systems. Solvent can change the polymer binding affinity, and we expect the binding energies we obtain here to be stronger than solution-phase binding energies. However, as we will elaborate below, differences in binding energies on the two Ag facets are likely representative of solution-phase values. The bulk Ag lattice constants using the PBE only, PBE-D2, and PBE-vdWsurf are 4.16, 4.15, and 4.02 Å, respectively. The lattice constant obtained with PBE-vdWsurf is the closest to the experimental value of 4.07 Å (corrected to the limit T = 0).28 Table 1 summarizes some structural parameters of 2P. The gas-

Figure 1. Breakdown of the repeat unit of PVP into two submolecules: ethane and 2P.

Our DFT calculations are performed using a locally modified version of the Vienna Ab Initio Simulation Package (VASP).18−20 We use projector-augmented waves21 and the generalized-gradient approximation (GGA) by Perdew, Burke, and Ernzerhof (PBE).22 For reference calculations of the structure/energy of gas-phase 2P, we use a cubic supercell with side length of 15 Å. Ag surfaces are modeled by periodic slabs using a (4 × 4 × 14) supercell with six Ag layers and eight vacuum layers. The bottom three Ag layers are held fixed to the bulk positions, while all other atomic degrees of freedom are relaxed until the forces are less than 0.01 eV/Å. 2P is adsorbed only on one side of the slab, and we verified that the dipole correction is negligible. The in-plane lattice spacing in the surface calculations is determined from the calculated bulk lattice constant. All structure optimizations were done using a (4 × 4 × 1) Monkhorst−Pack k-point grid with a 400 eV planewave cutoff. The reported binding energies that include vdW interactions are obtained using a denser (6 × 6 × 1) k-grid. In addition to the length-scale challenge, a second challenge associated with DFT calculations involving macromolecules is accounting for vdW interactions, which are expected to play a significant role in the binding of PVP to Ag surfaces. We account for vdW interactions using both Grimme’s PBE-D2 method23 and the Tkatchenko−Scheffler PBE+vdW schemes.24 These methods describe the vdW energy as a sum of pairwise additive dispersion terms between atoms, whose strength is modulated by the C6 coefficient. In PBE-D2, the C6 coefficient is constant and independent of its local environment. By contrast, in the PBE+vdW method, the C6 coefficients depend on the ground-state electron density through a Hirshfeld charge−decomposition scheme that includes hybridization effects. In this way, the dispersion contribution for each atom depends on its chemical environment. It has been noted25 that screening can mitigate vdW interactions in bulk metals, and neither the PBE-D2 nor the PBE+vdW method properly accounts for this effect. As a consequence, these methods are expected to overestimate vdW interactions for adsorbed species on metal surfaces. Recently, Ruiz Lopez et al.26 combined the PBE+vdW scheme with the Zaremba−Kohn theory27 to account for nonlocal Coulomb screening within the bulk. We utilize this new method in our study (PBE+vdWsurf), which amounts to a reparametrization for C6 and the cutoff radius R0 from the original PBE+vdW method (cf., ref 24). To assess the surface sensitivity of binding, we compare binding energies for the submolecules in Figure 1 on Ag(100) and Ag(111). The binding energy Ebind is given by

Ebind = EA + ES − EA + S

Table 1. PBE-vdWsurf, B3LYP, and experimental bond lengths (dx−y) and bond angles (θx−y−z) for gas-phase 2Pa surf

PBE+vdW B3LYP29 experiment30

dC5−O (Å)

dC2−N (Å)

dC5−N (Å)

dC2−C3 (Å)

θO−C5−N (°)

1.229 1.221 1.238

1.373 1.372 1.335

1.455 1.458 1.460

1.530 1.530 1.518

125.878 125.783 125.90

a

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

phase 2P reference structures obtained using all these methods are similar and agree well with experimental values30 as well as with previous results obtained using B3LYP/aug-cc-pVDZ.29 Hirshfeld charge decomposition shows that oxygen and nitrogen are negatively charged with net a charge of 0.3 and 0.1 electron, respectively. This is in relatively good agreement with the Mulliken charges of 0.4 and 0.2 electron obtained in a previous study.29 We first probed the binding of 2P and ethane to the two Ag surfaces using the PBE functional with no vdW interactions. In these calculations, ethane does not bind to either surface. However, 2P binds to Ag surface atoms via the O atom. We found distinct binding conformations in which the O atom of 2P is near each of the high-symmetry sites on Ag(100) (top, bridge, and four-fold hollow) and Ag(111) (top, bridge, fcc hollow, and hcp hollow). While oxygen is in close proximity to the Ag surfaces, the rest of the 2P ring is repelled from the surfaces, so that the molecule assumes conformations in which the ring is tilted away from the surface. On Ag(100), the angle between the plane of O, C2, and C3 in the ring and the surface plane ranges between 61−65°, and on Ag(111), this angle ranges between 65− 69°. We found similar binding energies for all sites on both surfaces. The strongest binding site for 2P on Ag(100) has Ebind = 0.22 eV, while on Ag(111), the strongest binding energy is 0.27 eV. This slight preference for 2P to bind to Ag(111) is inconsistent with experiment.10,11 When we include vdW interactions via the PBE-D2 description, 2P causes a herringbone-like reconstruction of Ag(100). This reconstruction has a lower energy than Ag(100) in the absence of the 2P adsorbate, contrasting experimental studies in which no reconstruction is observed. Thus, we conclude that PBE-D2, in its original parametrization, is not appropriate to describe vdW interactions involving Ag surfaces. In contrast to PBE-D2, PBE-vdWsurf leaves Ag(100) intact. Beginning with initial sets of 18 and 13 different binding configurations for Ag(100) and Ag(111), respectively, we found 4 and 5 different binding configurations for these surfaces. Figures 2 and 3 depict these binding configurations. In all of the configurations, 2P essentially retains its gas-phase structure and does not significantly perturb the Ag surface atoms. When we include vdW attraction, the angle between the 2P ring and the Ag surface plane reduces considerably compared to the case

(1)

where EA+S is the total energy of the optimized Ag slab with an adsorbed molecule A, EA is the energy of gas-phase molecule A, and ES is the energy of the bare Ag slab. We compare the binding of PVP to Ag(100) and Ag(111) in vacuum, neglecting the influence of solvent, although solvent is present in the 998


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roughly three times the values without vdW interactions, and 2P binding is stronger on Ag(100) than on Ag(111). Another notable aspect is that we observed similar energies to those in Figure 4 for a wide range of different conformations as these structures converged. This indicates that the potential energy surface (PES) for binding of the 2P ring is relatively “flat”, with low barriers for surface diffusion and transformations between various binding configurations. Thus, vdW interactions play a key role in the binding of PVP to Ag surfaces: They significantly influence binding conformations, they “flatten” the molecule surface PES, they contribute substantially to the total binding energy, and they determine the surface selectivity for 2P binding. To gain insight into the surface selectivity for 2P binding, we partition Ebind into three components: short-range Pauli repulsion EPauli and direct bonding Edirect contributions and long-range vdW attraction EvdW, i.e.,

Figure 2. Top-down view of the binding configurations for 2P on Ag(100). The O atom is red, N is blue, C atoms are turquoise, and H atoms are white.

Ebind = E vdW + EPauli + Edirect

(2)

We obtain the short-range contribution (i.e., EPauli + Edirect) for each conformation by freezing the geometries of the slab, slab +2P, and gas-phase 2P molecule to those predicted using PBEvdWsurf and calculating Ebind via eq 1 using self-consistent energies from the PBE only. This contribution to binding is shown in Figure 4 (denoted as “Short Range”), where we see that on Ag(100) the short-range contribution is attractive, while it is negligible on Ag(111). This indicates that attractive direct binding outweighs Pauli repulsion on Ag(100), so short-range binding is dominated by Edirect. In contrast, EPauli ≈ Edirect on Ag(111), so the net contribution from direct binding is negligible. The long-range vdW contribution to the binding energy is given by the difference between the total and short-range binding energies in Figure 4. Although vdW attraction is often described as “nonspecific”, short-range atom pairs contribute the most strongly to the total vdW interaction. Because Ag(111) has denser packing than Ag(100), the vdW attraction of 2P to Ag(111) is stronger. The total binding energy represents a balance between short- and long-range effects: On Ag(100), 2P achieves optimal conformations for which there is a synergy between direct bonding and vdW attraction. In contrast, stronger vdW attraction dominates the binding of 2P to Ag(111). We further characterized the bonding between 2P and the Ag surfaces using atomic projected densities of states. When the molecule is far from the surface (∼10 Å), the 2P lowest unoccupied molecular orbital is 4 eV above the Fermi level, while the highest occupied molecular orbitals (HOMO) and HOMO-1 are 1.7 eV below the Fermi level of the system and ∼1 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%). As 2P attains its optimum bonding configuration with the Ag surface, the molecular levels are substantially broadened and the HOMO and HOMO-1 move closer to the Ag d-band. On Ag(100), this leads to a hybridization between the p-orbitals of 2P and the d-band of Ag(100), which confirms the attractive short-range binding seen in Figure 4. This binding is consistent with spectroscopic studies for the PVP−Ag system.13−17 On the other hand, for Ag(111), the bonding orbitals of 2P make no substantial overlap with the Ag d-band, confirming the virtual absence of short-range binding on that surface (cf., Figure 4).

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

with the PBE only: For Ag(100), the angles range between 14− 16° and for Ag(111) the range is 12−18°. These configurations are consistent with the binding of a PVP polymer in a “flat” conformation, with its backbone parallel to the surface and its rings slightly tilted. A similar configuration has been proposed based on experiment.17 Figure 4 shows the binding energies (denoted as “Total”) of the configurations depicted in Figures 2 and 3. We note that when we include vdW interactions, the binding energies are

Figure 4. Total binding energies of 2P for the configurations shown in Figures 2 and 3, along with the contribution of short-range interactions to the total energy. 999


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Ag(100), even for modest values of Nc. For Nc = 9, as suggested by our estimate of the Kuhn length, we see that PVP is 109 times more likely to bind to Ag(100) than to Ag(111). In a recent study, Kilin, Prezhdo, and Xia used DFT (without including vdW interactions) to probe the binding of citric acid (another effective structure-directing agent)11,31 to Ag(100) and Ag(111).36 They found one binding configuration for citric acid on each surface and observed that the binding of citric acid to Ag(111) was significantly stronger than to Ag(100), consistent with experiment.11,31 They attributed this strong preference to a better geometric match between citric acid and Ag(111) than Ag(100). Thus, their results suggest that symmetry matching with the substrate is an important aspect of a successful structure-directing molecule. Our results lead to a different conclusion, namely, that there are many different ways for PVP to bind to Ag(100) and Ag(111) surfaces and that small differences in the binding energies of repeat units can lead to strong preferences for chain binding to a particular surface. The differences between our results and those of Kilin et al. underscore differences in the workings of small molecule and polymeric structure-directing agents. Thus, we identify several physicochemical elements that likely contribute to the success of a structure-directing polymer. Ultimately, the surface-sensitivity in this system arises from a surface-sensitive balance between direct bonding and vdW attraction, where the role of vdW attraction is significant. These studies indicate a promising method for identifying appropriate structure-directing polymers. Future work aimed at incorporating the results of such calculations into multiscale models and including solvent effects could lead to new insights and predictions in efforts to synthesize nanostructures with welldefined sizes and shapes.

Comparing the strongest binding energies of 2P on Ag(100) and Ag(111), we see that there is a preference of 80 meV for 2P to bind to Ag(100). This difference is small, and we note that 2P (actually, 1-ethyl-2-pyrrolidone, which is the analog molecule for the PVP repeat unit in Figure 1) is not an effective structure-directing agent in the shape-selective synthesis of Ag nanostructures.32 Studies have shown that the structure-directing capabilities of PVP depend on its molecular weight.32,33 When PVP adsorbs to a solid surface, 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. We can estimate the value of Nc from the Kuhn length of solution-phase PVP. This estimate provides a lower bound, as the Kuhn length accounts for chain stiffness but not the energetic preference for chain binding. In water at room temperature, PVP has a characteristic ratio of C∞ = 12.3.34 The Kuhn length b is given by b = C∞l/ cos(θ/2).35 Here, l (= 1.54 Å) is the main-chain bond length and θ (= 68°) is the bond angle for the chain in a trans configuration, which yields b ≅ 2.3 nm, about 9 PVP segments. Taking a group of Nc segments as the binding unit, we can formulate an expression for the relative probability for a unit to bind to Ag(100) relative to Ag(111). Since the PVP surface interaction is dominated by the ring, we assume that the surface sensitivity of binding is due to the ring only. Due to the apparent flatness of the PES indicated by our calculations, we assume that the binding energy of the ring is relatively insensitive to the local binding site. Given that we observe similar binding energies and conformations of the ring on both surfaces, it is reasonable to assume that solvent effects are similar on both surfaces, so that the segment energy difference is unaffected by the solvent. Finally, if entropic effects are similar on the two surfaces, the preference for Ag(100) binding at a temperature of T is given by

P(100)/(111) = exp(NcΔE /kBT )

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

(3)

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where ΔE is the difference between the 2P binding energies on Ag(100) and Ag(111). Figure 5 shows a plot of eq 3 at 400 K

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. H.F. thanks the China Scholarship Council for support. We acknowledge help from Rajesh Sathiyanarayanan, Alexandre Tkatchenko, Victor Ruiz Lopez, Matthias Scheffler, Scott Milner, and Jian Zhou.

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REFERENCES

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Figure 5. A plot of eq 3 as a function of the number of correlated 2P rings Nc when PVP binds to the solid surfaces. The inset shows a portion of a syndiotactic PVP chain.

for ΔE = 0.08 eV. Here, we see that while 2P (Nc = 1) is ∼10 times more likely to bind to Ag(100) than Ag(111), the preference for PVP binding to Ag(100) increases exponentially with Nc so that PVP has a strong preference for binding to 1000


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Adsorption of Polyvinylpyrrolidone on Ag Surfaces: Insight into a

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