Atomistic Simulations of Coating of Silver Nanoparticles with Poly

Article pubs.acs.org/JPCC

Atomistic Simulations of Coating of Silver Nanoparticles with Poly(vinylpyrrolidone) Oligomers: Effect of Oligomer Chain Length Alexander Kyrychenko,*,† Oleksandr M. Korsun,† Iurii I. Gubin,‡ Sergiy M. Kovalenko,† and Oleg N. Kalugin† †

V. N. Karazin Kharkiv National University, 4 Svobody square, Kharkiv 61022, Ukraine National University of Pharmacy, 53 Pushkinska street, Kharkiv 61002, Ukraine

‡

S Supporting Information *

ABSTRACT: Silver nanoparticles (AgNPs) possess unique physicochemical properties, which are different from those of matter of the same chemical composition on a larger scale. These features open up the opportunity for their use in many promising chemical and biomedical applications. In this study we have developed an atomistic model for molecular dynamics (MD) simulations of AgNP coated by poly(N-vinyl-2-pyrrolidone) (PVP) oligomers. We focus on identifying the relative length of PVP oligomers, enabling effective protecting of a crystalline silver core of 4.5 nm diameter from water contacts. Three different PVP-coated AgNP systems have been compared: (i) a nanoparticle coated by a mixture of short-chain PVP oligomers of the varying size and (ii,iii) the silver core wrapped by a single, long-chain PVP polymer with the number of monomers equal to 816 and 1440, respectively. We have validated the MD models of the PVP−AgNPs using a series of MD simulations reproducing adsorption, wrapping, and coating of PVP around a silver core either as short PVP oligomers or as a single-chain, long polymer of a varying length. Our simulations predict that the saturated coating of PVP around the silver core of the given diameter can occur when the polymer chain length approaches 2600−2800 units.

1. INTRODUCTION

Recently, more attention has been directed to the theoretical understanding of molecular aspects governing specific, regioselective surface adsorption and self-assembly of organic ligands and polymers on inorganic metal nanocrystals. Using the density functional theory (DFT) calculations, the role of PVP in the shape-selective synthesis of Ag nanostructures has computationally been studied by probing the interaction of its 2-pyrrolidone (2P) ring with Ag(100) and Ag(111) facets.17,18 In addition, a combined use of surface-enhanced Raman spectroscopy and DFT calculations has allowed to identify binding sites of PVP toward the crystalline silver surfaces. It has been suggested that N-methyl-2-pyrrolidinone was selectively adsorbed on silver and gold colloid crystalline surfaces preferably via the nonbonding electrons of the carbonyl group.19 Numerous MD simulation studies of bare metal nanostructures20 or nanoparticles protected by organic ligand monolayers,21−30 polymers,31 and dendrimers32 have been conducted. It has also been shown that MD simulations of ligand-functionalized nanoparticles can be used as useful tools for studying interactions of metal nanoparticles with biomolecular species such as nucleic acids,33 DNA,34,35 proteins, 36,37 and lipid membranes, 38−41 opening up the opportunity for their use in nanomedicine.42 While major

A growing body of research has demonstrated potential antimicrobial activity of silver nanoparticles (AgNPs) toward many pathogenic microbes and viruses.1 Along with such antibacterial activity, AgNPs have also shown toxic effects on human health and the environment.2,3 Numerous studies have attempted elucidating the mechanisms of AgNP toxicity, distinguishing between the effects of silver ions (Ag+) and nanoparticles themselves.4−7 However, despite of these efforts the mechanism of antibacterial activity are still not fully understood, because many factors such as nanoparticle size, shape, aggregation state, surface coatings, and solution chemistry could potentially influence the toxicity of AgNPs.8,9 Therefore, to tune and manipulate colloidal silver morphologies, progress in understanding the interfacial interactions between inorganic nanocrystals and organic ligands are still needed.10,11 Several lines of evidence have shown that capping agents such as poly(N-vinyl-2-pyrrolidone) (PVP) essentially dictate a synthetic procedure for the preparation of silver nanoparticles, leading to the formation of different anisotropic size/shaped nanostructures.12−16 It has been shown by using a microwavepolyol synthesis that silver nanosheets and nanoplates were dominantly obtained when short-chain PVP oligomers were used, while nanoparticles were preferentially synthesized by utilizing longer chain PVPs.13 © 2015 American Chemical Society

Received: October 14, 2014 Revised: March 12, 2015 Published: March 12, 2015 7888

DOI: 10.1021/jp510369a J. Phys. Chem. C 2015, 119, 7888−7899

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The Journal of Physical Chemistry C Scheme 1. PVP-Coated AgNPa

efforts have been made to develop MD force-field parameters and engineering nanoparticles with a gold inorganic core, less attention has been paid to computational studies of AgNPs.43−46 Using MD simulations, it has recently been shown that the preferential adsorption of PVP on different facets of silver crystals could modulate the growth kinetics of silver nanocrystals in solution.47,48 The motivation of the present study is to develop a MD model of AgNP coated and stabilized by poly(N-vinyl-2pyrrolidone) (PVP) in aqueous solution. Despite significant progress in theories of polymer/nanoparticle organization, there is no a unified approach that allows us to predict how many monomeric units are able to be coupled to AgNP of a certain diameter. It is known that the ligand coating density and hence the area per ligand strongly depends on the ligand packing arrangements and on the curvature of the NP surface.49 Therefore, to examine a role of the degree of polymerization of PVP in the formation of the equilibrium structure of AgNP, we studied interactions of a crystalline silver core of 4.5 nm diameter with PVP oligomers of different sizes. First, the formation of AgNP was studied in aqueous solution containing a mixture of short-chain oligomers of PVP with the number of repeating units varying from 10 to 20, reaching the total number of 680 monomers. Second, we studied the adsorption of a single, long-chain PVP polymer composed of 816 and 1440 monomers on a bare silver nanoparticle of the same diameter. A main goal of our study is to identify the relative length of PVP oligomers, which enables effective protecting of a crystalline silver core of 4.5 nm diameter from water contacts. It is believed that PVP coating prohibits nanoparticle selfaggregation in the aqueous environment. However, despite extensive MD simulation studies on structure, hydrogen bonding, and conformational behavior of short-chain oligomers of poly(vinylpyrrolidone) in water solution,50,51 suitable interaction potentials and a reliable MD model of PVP-coated AgNPs were still not available. Therefore, here we have analyzed existing force fields for PVP focusing on developing a suitable MD model for large-scale modeling of single, longchain PVP polymers in the aqueous environment, focusing on a better understanding of molecular interactions occurring on an organic−inorganic interface of a silver nanoparticle.

a

(left) Silver nanoparticle core is organized in fcc truncated octahedron with the average diameter of 4.5 nm. (right) Structure of PVP polymer and atom numbering in a vinylpyrrolidone unit.

properties of polymer blends of PVP in a glassy amorphous phase have also been modeled by using the COMPASS (condensed-phase optimized molecular potentials for the atomistic simulation studies) all-atom force field.50,54,55 Recently, the same force field has been used to model the interaction energies between PVP and Ag(110), Ag(100), and Ag(111) facets on silver crystals.47 Our goal is to develop a robust, atomistic MD model of PVP with a variable chain length, enabling long-scale sampling in diluted aqueous solutions. Therefore, we first benchmarked popular united-atom force fields based on the standard GROMOS force fields G45a3 and G53a6 in which CH2 and CH fragments are treated as single interacting sites.56,57 The G53a6 force field has shown the better performance for MD simulations of biopolymers due to improved description of lipids, nucleic acids, and reoptimization of some polar functional groups.56 We adopted the G53a6 parameters for PVP and carried out additional polymer-specific structure reparameterizations by using DFT calculations. First, to determine partial charge distributions in PVP, we optimized the geometry of 2-pyrrolidone ethane using the B3LYP/ccpVDZ calculations, and, after that, the partial electric charges were estimated on the optimized structure by the electrostatic potential (ESP) calculation utilizing the method of Besler− Merz−Kollman. 58 Second, using the same level DFT calculations, torsion angle scan around bond −C7−C8− (Scheme 1) was carried out for vinylpyrrolidone dimer to adjust the rotational barrier heights for dihedral angle rotations in a hydrocarbon backbone of PVP. The repulsion and dispersion terms of nonbonded interactions were computed using the Lennard-Jones (LJ) 12−6 potential energy function (eq 1). Several sets of LennardJones potentials for Ag were considered. Among available potentials, suitable nonbonded interaction parameters, compatible with the G53a6 force field, were adopted from the recent work of Heinz and coworkers,59 in which 12−6 LJ potentials were fitted to reproduce densities, surface tensions, and interface properties of crystalline, face-centered cubic silver, and other metals. The final sets of the nonbonded and bonded interactions parameters are given in Tables 1 and 2, respectively.

2. METHODS 2.1. MD Model of PVP-Coated AgNP. Silver nanoparticles were modeled as a crystalline, quasi-spherical silver core coated by PVP oligomers in the aqueous environment. For single-crystalline silver nanoparticles, a truncated octahedron has been predicted to be one of the thermodynamic equilibrium shapes.10,52 Therefore, the silver core was approximated by a truncated octahedron with the face-centered cubic ( fcc) crystalline structure containing the fixed number of 3871 silver atoms. The average diameter of such a nanoparticle core equals to 4.5 nm, as shown in Scheme 1. PVP oligomers with atactic chains of variable lengths were constructed in random-coil conformations so that repeating units adopted randomly either a racemo or a meso configuration. To benchmark the effect of the parametrization for determining the equilibrium structure of AgNPs, we performed a series of short MD simulations of PVP-coated AgNPs using various force fields. The MD model of PVP, based on the all-atom AMBER force field, has been employed in computational studies of amorphous glasses of long-chain PVP, containing small amounts of water.51,53 The thermophysical condensed-phase

⎛⎛ ⎞12 ⎛ ⎞6 ⎞ σij σij VLJ(rij) = 4εij⎜⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎟ ⎜⎝ r ⎠ ⎝ rij ⎠ ⎟⎠ ⎝ ij 7889

(1) DOI: 10.1021/jp510369a J. Phys. Chem. C 2015, 119, 7888−7899

Article

The Journal of Physical Chemistry C

with the number of repeating fragments equal to 816 to 1440 units, which corresponds to molar mass of ∼119k and 211k, respectively. The initial structures of PVP816 and PVP1440 were constructed to be in atactic random-coil conformations. These systems are further referred to as PVP816−AgNP and PVP1440− AgNP, respectively. All systems were solvated by explicit water molecules using the simple point charge (SPC) model.60 The size of the water box was chosen to ensure that the systems have at least 10 Å solvation shell in all directions. To study water accessibility toward a silver nanoparticle core, we also carried out control MD simulation of a bare AgNP in water. The details of all simulated systems are summarized in Table 3. Convergence of PVP−AgNPs to equilibrium is an essential requirement for MD simulation output to be accurate and reproducible. Testing for convergence of MD sampling of longchain polymers and polypeptides is, however, challenging because they have multidimensional energy surfaces characterized by many local minima separated by high free-energy barriers, which can lead to kinetic trapping with sampling restricted to localized “metastable” regions. Two computational approaches are often used to escape these kinetic traps: (i) According to the first strategy, simulations must often run for very long times; however, a key challenge remains to determine when a simulation has run “long enough” to reach equilibrium.61 (ii) The second approach involves a series of multiple discrete MD runs, each initiated with random initial structures, enhancing the conformational space searches.62−64 To investigate a role of starting configurations in the coating behavior of the PVP oligomers we used the multiple discrete MD run approach so that a series of five independent MD simulations of each of PVP680−AgNP, PVP816−AgNP, and PVP1440−AgNP were carried out with either different initial orientations of PVP oligomers or different initial configurations of random coil PVP polymers, respectively. Additionally, to examine the convergence of the structure and the physicochemical properties, we also performed the thermal annealing of the some selected AgNP−PVP system with a slow temperature rise up to 360 K, followed by thermal equilibration back to the room temperature. Finally, the structural parameters of PVP680−AgNP, PVP816−AgNP, and PVP1440− AgNP, such as the thickness of the PVP coating and the saturated PVP coverage, were then ensemble-averaged over the set of independent MD runs. More details of the parallel MD simulations of the studied systems are given in the Supporting Information. 2.2. MD Simulation Setup. The MD simulations were carried out for the NVT ensemble. The reference temperature of 303 K was kept constant using the Berendsen weak coupling scheme65 with coupling constant τ = 0.1 ps. The initial atomic velocities were generated with a Maxwellian distribution at the given absolute temperature. Periodic boundary conditions were applied to all three directions of the simulated box. Electrostatic interactions were simulated with the particle mesh Ewald

Table 1. Atomic Names, Atom Types, and Partial Charges Used in PVP−AgNPa name

typeb

partial charge

Ag C1, C2 C3 C4 N5 O6 C7 C8

Ag CH2 CH2 C NE O CH CH2

0 0.050 0.100 0.150 −0.250 −0.300 0.150 0.050

charge group

σ (nm)

ε (kJ/mol)

0 0 1 1 1 1 2

0.2995 0.4070 0.4070 0.5257 0.3137 0.2760 0.5019 0.4070

19.05865 0.4105 0.4105 0.0277 0.6398 1.2791 0.0949 0.4105

a

LJ parameters for Ag were adopted from ref 59. bExcept for Ag, the atom types for PVP are based on GROMOS G53a6 force field with the partial charges adjusted by the B3LYP/cc-pVDZ calculations.

Table 2. Force-Field Parameters for Bonded Interactions in PVP bond stretch bond

rij (nm)

C1−C2, C1−C3, C2−C4 C7−C8 C3−N5, C7−N5 C4−N5 C4−O6

0.154 0.153 0.146 0.138 0.122 angle bend

angles

Θijk (deg)

Krij (kJ/(mol nm2)) 8.0 8.0 8.0 8.0 1.0

× × × × ×

105 105 105 105 106

KΘijk (kJ/mol)

C1−C2−C4 C1−C3−N5 C2−C1−C4 C2−C4−N5 C2−C4−O6 C3−N5−C4, C3−N5−C7 N5−C4−O6 N5−C7−C8

104.2 103.2 103.6 107.3 127.3 122.2 125.5 113.8 torsion

dihedral

φijkl (deg)

Kφijkl (kJ/mol)

n

N5−C7−C8−(+C7) (−C8)−C7−C8−(+C7)

180 180

4.0 4.5

3 3

1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8

× × × × × × × ×

103 103 103 103 103 103 103 103

To study the effects of different degrees of PVP polymerization on the structure of AgNPs, we examined three different Ag-PVP systems: In System I, a quasispherical silver core, consisting 3871 atoms, was surrounded by a mixture of PVP oligomers composed of 44 and 12 oligomers with the degree of polymerization of 10 and 20, respectively. The average molar mass of the PVP oligomer mixture was ∼1.5 k (g/mol). The choice of the oligomer mixture was to mimic the average molar mass for commercial available PVPs. The total number of PVP units in this system is 680, so that it is referred to as PVP680− AgNP through the text. Systems II and III were built on the same size silver core, wrapped by a single-chain PVP polymer Table 3. Simulation Details of Different PVP−AgNP Systemsa system bare AgNP in water PVP680−AgNP PVP816−AgNP PVP1440−AgNP a

number of PVP oligomers 44 PVP10 + 12 PVP20 1 PVP816 1 PVP1440

total number of VP monomers

number of water molecules

680 816 1440

5010 8100−8200 18000−20000 35000−38000

size of simulation box (Å) 60.0 × 60.0 × 84.5 × 84.5 × 95.0 × 95.0 × 105.0 × 125.0

60.0 84.5 95.0 × 105.0

In all of the simulated systems, a silver core was composed of the fixed number of 3871 Ag atoms. 7890

DOI: 10.1021/jp510369a J. Phys. Chem. C 2015, 119, 7888−7899

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The Journal of Physical Chemistry C (PME) approach66 using the long-range cutoff of 0.8 nm. The cutoff distance of Lennard-Jones interactions was also equal to 0.8 nm. The MD simulation time step was 2 fs with the neighbor list updates every 10 fs. All bond lengths were kept constant using the LINCS routine.67 The MD simulations were carried out using the GROMACS set of programs, version 4.5.5.68 Molecular graphics and visualization were performed using VMD 1.8.6.69

3. RESULTS AND DISCUSSION 3.1. AgNP Interacting with PVP Oligomers. Recent experiments have shown that PVP polymers can be used to control the growth of AgNPs.10,11,13,14,70 Therefore, one of our goals is to study the adsorption of PVP polymer on a bare AgNP in aqueous solution and to understand better how PVP assembly may modulate the nanoparticle structure. Depending on the length of oligomer chains, conformational dynamics of PVP backbone can govern its adsorption behavior on a nanoparticle surface.12,15,16,71 This is the reason why we first studied the formation of a silver nanoparticle coated by a mixture of short-chain oligomers of PVP with the number of repeating units equal to 10 and 20, respectively. The oligomer mixture was composed of 44 oligomers with the size of 10 units (PVP10) and 12 oligomers with 20 units (PVP20) so that the total number of vinylpyrrolidone monomers was 680. An initial configuration of AgNP was built by placing randomly distributed PVP oligomers around a nanoparticle core. The inorganic core diameter was 4.5 nm, which is a typical value for small silver nanoparticles estimated experimentally by the transmission electron micrograph (TEM) imaging.10,72 This initial structure was then solvated and equilibrated in aqueous solution for 2 ns. The details of the simulated systems PVP680− AgNP are given in Table 3. The initial configuration of the AgNP is shown in Figure 1a. PVP adsorption on the inorganic core was studied by five independent MD samplings of free distribution of the PVP oligomers between bulk water and the Ag surface (Figure S1 in the Supporting Information). We observed that the PVP oligomers moved from water and became adsorbed on the AgNP core during the first 20 ns. Figure 1b shows an instantaneous snapshot of the PVP680− AgNP structure taken at the end of the 300 ns long MD simulation. The PVP10 and PVP20 oligomers are randomly adsorbed on the surface of the silver core. They are well-mixed and show no oligomer-size-specific segregation, as seen in Figure S2 in the Supporting Information. One of roles of PVP coating in synthesis of metal nanoparticle is to protect them from self-aggregation in solution.10,11,14 To study the efficiency of nanoparticle coating by PVP oligomers, we carried out the control MD simulation of a bare AgNP of the same size solvated in the aqueous environment. For this system, we estimated maximal possible solvent accessibility to AgNP as the number of water molecules residing in the first solvation shell around the silver core at distances shorter than 3.5 Å. The analysis reveals that the average number of the water contacts is decreased from 4170 ± 65 for the bare AgNP to 1864 ± 42 for that of the oligomerprotected PVP680−AgNP, so that the coating coverage of the silver surface by the mixture of the PVP oligomers reaches a value of 55.3 ± 7.5%. (Detailed analysis is given in Section 3.3.) 3.2. AgNP Coated by PVP Polymer. Molecular theories and modeling of behavior and macroscopic properties of nanoparticle−polymer systems, where nanoparticles are grafted with chains of polymers or embedded into polymer matrices,

Figure 1. MD simulations of PVP680−AgNP. Snapshots of MD simulations of AgNP interacting with PVP oligomers in the aqueous environment. (a) An initial configuration of an Ag nanoparticle core surrounded by a mixture of PVP oligomers. The mixture was composed of 44 and 12 oligomers of PVP10 and PVP20, respectively. (b) Equilibrium structure of PVP680−AgNP estimated at the end of the 300 ns MD simulations. Silver atoms are shown by van der Waals model colored in mauve. PVP backbone is shown in green. Water molecules are not shown for clarity.

have made large contributions in recent years,73 providing comprehensive overviews of recent developments in the simulation area.74−78 Because of the very broad range of system sizes and long time scales governing the behavior of such composite nanomaterials, most of these studies use computational models of nanoparticles and polymers with various degrees of coarse-graining, so that many important atomistic details become missing. A limited number of computational studies have reported detailed all-atom models for nanoparticle/polymer systems.31 To model a nanoparticle coated by a single, long-chain PVP polymer, we used the same size of the silver core of 4.5 nm diameter, organized into an fcc truncated octahedron (Scheme 1). A PVP polymer, designed in a random-walk coil conformation and consisting of 816 repeating monomers (PVP816) was wrapped around the nanoparticle core, so that the shortest distance between the polymer and the nanoparticle is kept to be >5 Å. An initial configuration of PVP816−AgNP system was solvated by explicit water molecules. The size of a MD simulation box was chosen to have at least 10 Å solvation shell in all directions. The solvated system was energy7891

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Figure 2. MD Simulations of PVP816−AgNPs and PVP1440−AgNPs. Representative snapshots of MD simulations of (a,b) PVP816−AgNP and (c,d) PVP1440−AgNP in water solution: (a) An initial configuration of a single-chain PVP816, built in a random coil configuration and wrapped around an Ag core. (b) Equilibrium structure of PVP816-coated AgNP taken at the end of the 300 ns MD simulation. (c) Initial configuration of PVP1440− AgNP. (d) Equilibrium structure of PVP1440−AgNP estimated at the end of the 300 ns MD simulation. (See the legend of Figure 1 for more detail.)

the same size with a longer chain PVP1440. An initial configuration of the PVP1440−AgNP shown in Figure 2c was constructed as previously described for the shorter chain PVP816 nanosystem. In this configuration, the PVP1440 oligomer was also wrapped around the silver core and formed the multiple layer coating. The 300 ns long MD simulation was carried out to study the equilibrium structure of the nanoparticle. During the simulations, the PVP1440 chain was gradually adsorbed on the nanoparticle surface adopting the energetically favorable conformation. Representative snapshots of the five independent MD runs of PVP1440−AgNP are shown in Figure S4 in the Supporting Informatin. The typical equilibrium structure of PVP1440−AgNP is shown in Figure 2d. The structure analysis of PVP1440−AgNP shows that the increase in the length of the PVP chain primarily leads to the formation of additional external coating layers around the inorganic core. In PVP1440−AgNP, water penetration to the Ag core decreased so that PVP coating reached the ensembleaveraged value of 93.5 ± 8.8%.

minimized and equilibrated for 5 ns. The initial equilibrated configuration and MD simulation details of PVP816−AgNP are presented in Figure 2a and Table 3. Our MD simulations reveal that the wrapped PVP816 chain became adsorbed on the silver core during the first 50 ns. After that, the PVP chain relaxed and adopted the favorable backbone conformation on the crystalline silver surface. In the equilibrium conformation at the end of 300 ns MD sampling, the PVP816 molecule wraps around the silver core to form the coating structure composed of several PVP layers, as demonstrated in Figure 2b. Representative snapshots of the five independent MD runs showing the formation of PVP816− AgNP are also given in Figure S3 in the Supporting Information. The analysis of the water accessibility to the silver core shows that the PVP816 coating protects the AgNP surface from water penetration for ∼68.9 ± 8.1%, as compared with 100%, which is assumed in the control bare no-PVP− AgNP system. To increase the coverage of the nanoparticle surface by the PVP polymer, we have studied the interaction of the Ag core of 7892

DOI: 10.1021/jp510369a J. Phys. Chem. C 2015, 119, 7888−7899

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The Journal of Physical Chemistry C

Figure 3. AgNP Structure. (a,b) Inner structure of PVP1440−AgNP. (a) Front view of the slice of PVP1440−AgNP showing the (111) crystal facet of the Ag core. (See the legend of Figure 1 for more detail.) The dotted-line red circle shows a radius of PVP-coated AgNP (RPVP−AgNP). (b) The coating diameter of PVP816−AgNP and PVP1440−AgNP was estimated by averaging mass density of all PVP atoms and plotted with respect to the nanoparticle center. The density of PVP was multiplied by a factor 10 for clarity. (c) Radial distribution functions calculated from the center-of-mass (RDF−COM) of the inorganic core. RDF−COM profiles for PVP reveal three peaks attributed to the formation of the multiple layer coating around the Ag core.

3.3. Structure of PVP-Coated AgNPs. MD simulations allow us to explore time evolution and molecular aspects of the process of nanoparticle assembly and to monitor adsorption events of PVP polymers on the nanoparticle surface. Such an analysis provides valuable insight into the assembly routes and favorable structures of the PVP-coated AgNPs. Figure 3a shows the inner structure of PVP1440−AgNP, as estimated by the MD simulations. The inorganic core is organized as the truncated octahedron with fcc packing of the silver atoms assembled into the perfect crystal lattice. The flexible PVP1440 polymer wraps around the nanoparticle core as the random coil assembling into the multilayer coating, as seen in Figure 3a. 3.3.1. Size of PVP-Coated AgNPs. The size of adsorbed PVP coating in PVP816−AgNP and PVP1440−AgNP was estimated with the mass density distributions averaged along the three spatial axes xyz for all PVP atoms. Figure 3b shows the mass density distribution of PVP816 and PVP1440 plotted from the nanoparticle center. In addition, PVP mass densities are superimposed on the density distribution of the inorganic core. The diameter of a PVP-coated AgNP was calculated as full width at half-maximum (fwhm) of the mass density distribution shown in Figure 3b. The size of a ligand-coated nanoparticle can be measured experimentally as a hydrodynamic radius (Rh) by dynamic light scattering, fluorescence spectroscopy, and other techniques (Figure 3a).79,80 The nanoparticle radius (RPVP−AgNP) for PVP816−AgNP and PVP1440−AgNP is calculated to be 2.9 and 3.2 nm, respectively. The effective hydrodynamic and steric shielding of an AgNP core by protecting polymers is crucial to reach the stability of colloidal silver. So another important parameter of polymer-capped nanoparticles is a polymer coating thickness around an inorganic core.80 Taking into account that the average radius RAgNP of the nanoparticle core is 2.25 nm, the thickness of the PVP coating for PVP816−AgNP and PVP1440−AgNP, defined as RPVP−AgNP − RAgNP, is estimated to be 0.65 and 0.95 nm, respectively. Spatially averaged mass densities provide information about bulk size properties of the PVP-coated AgNPs. In the case of spherically symmetric systems, such as nanoparticles, fine structure details of assembling and packing of ligands or polymers can be extracted by analyzing the 3D radial distribution functions calculated from the center-of-mass (RDF−COM) of a nanoparticle core. Figure 3c shows RDFs calculated for PVP coating and water molecules in three

different PVP−AgNPs. The RDF−COM profiles of the PVP coating reveal the first peak located at 2.67, 2.70, and 2.73 nm for PVP680−AgNP, PVP816−AgNP, and PVP1440−AgNP, respectively. These peaks correspond to the formation of the first adsorption layer of PVP around the Ag core. In the cases of PVP680−AgNP, PVP816−AgNP, and PVP1440−AgNP, the second peak was characterized by a broad band centered at 3.15, 3.30, and 3.41 nm, respectively. The RDF−COM profile of PVP680−AgNP also reveals the presence of the third peak located at 3.65 nm. This third peak was also observed as a shoulder in the outer side of the second peak in the profiles of PVP816−AgNP and PVP1440−AgNP. Therefore, it could be attributed to the third outer layer of PVP formed around the Ag core. Water penetration profiles were also estimated by RDF− COM, as shown by color-coded dotted lines in Figure 3c. Except for PVP680−AgNP, for which the corresponding RDF− COM water profile reveals a well-defined peak located at 2.59 nm from the nanoparticle center, the corresponding water profiles of PVP816−AgNP and PVP1440−AgNP are broad and unstructured, pointing out restricted water penetration toward the inorganic core of the nanoparticles. 3.3.2. PVP Adsorption Sites. Structural details of adsorption of PVP oligomers on the surface of AgNP were analyzed using calculations of RDFs between silver atoms and those of PVP, and water, as shown in Figure 4. The RDF between Ag atoms of the inorganic core shows narrow peaks, whose pattern reflects the high local fcc crystalline order81,82 (Figure S5 in the

Figure 4. Radial distribution functions. Radial distribution function g(r) calculated between: Ag and PVP carbonyl oxygen (Ag−O, in red) and Ag and nitrogen (Ag−N, in blue) atoms. g(r) between Ag and water oxygen (Ag−OW) atoms are shown in green. 7893

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Figure 5. PVP anchoring sites. (a,b) Structural arrangement of the PVP chain adsorbed on the surface of the Ag core is shown in the top and side views according to MD simulations of PVP1440−AgNP in the aqueous environment. (Carbonyl oxygen atoms, identified as the major anchoring sites of PVP on the Ag surface, are shown by red balls. Carbon atoms of PVP backbone are rendered in green. Water is not shown for clarity.) (c) Distributions of the number of contacts calculated between the Ag atoms and all the PVP heavy atoms located to each other closer than 3.5 Å. The distributions were estimated for the three different PVP-coated AgNPs from the last 100 ns of the MD sampling.

Supporting Information). The first peak position of g(r)Ag−Ag is found to be 2.76 Å. The RDF peaks were calculated between Ag atoms and the major binding sites of PVP, carbonyl oxygen O6 (g(r)Ag−O) and pyrrolidone nitrogen N5 (g(r)Ag−N) atoms, equal to 3.02 and 3.06 Å, respectively. However, the g(r)Ag−N function shows very weak peaks characterized by the unstructured pattern, which points out weak and unspecific adsorption (Figure 4). The RDF calculated between Ag atoms and oxygen atoms of water molecules shows the first peak at 3.28 Å. The orientational preferences of capping ligands and polymers on a nanoparticle surface are believed to be important in determining shape control upon silver nanoparticle growth.10,12−14,16,19,83 Therefore, we have investigated structural arrangement and preferential orientations of the PVP chain backbone on the crystalline surface of the Ag nanoparticle core. Figure 5a,b shows snapshots of the PVP fragment adsorbed onto the Ag surface. The PVP polymer is in direct contact with the surface, and its backbone conformation approaches a flat-on structure. The intrinsic flexibility of the PVP oligomers plays an ambiguous role in its adsorption onto the crystalline Ag. A rigid polymer or peptide that cannot adopt a conformation in which the potential Ag-binding monomer units are able to interact with the Ag surface will be a poor Ag adsorbate. We identified that the carbonyl oxygen atoms of PVP are most frequently found to be in contact with the Ag surface (Figure 5a,b). These findings agree well with the previous DFT and MD simulation studies.19,47 Recently, dispersion-corrected DFT calculations showed that the carbonyl oxygen tends to stay closer to Ag than the pyrrolidone nitrogen.17−19 To study the percentage of PVP adsorption sites bound to the surface, we estimated the number of contact atoms between Ag and PVP for the three studied PVP-coated AgNPs for the last 100 ns of the MD trajectory sampling. The atoms were defined to be in contact with the silver surface when a distance to the outermost Ag atom layer was