MD Simulations - American Chemical Society

Article pubs.acs.org/JPCC

Conformational Equilibria of Organic Adsorbates on Nanostructures in Aqueous Solution: MD Simulations Amal Kanta Giri* and Eckhard Spohr* Center for Computational Sciences and Simulations (CCSS), Lehrstuhl für Theoretische Chemie, Fakultät für Chemie, Universität Duisburg-Essen, D-45117 Essen, Germany

ABSTRACT: We have performed atomistic molecular dynamics (MD) simulations of gold nanoparticles (GNPs) in aqueous NaCl solution. Alkanethiol chain-covered GNPs at grafting densities between approximately one-third and full coverage were studied with nonpolar CH3 and charged COO− and NH3+ terminations. Special attention was given to the penetration depth of water and ions into the diffuse shell of the functionalized alkanethiol chains and its dependence on grafting density and functionalization. Solutions with polar terminations were neutralized by an excess of Na+ and Cl− ions. The penetration of water and ions into the hydration shell increases with decreasing grafting density irrespective of termination. High grafting densities lead to more extended hydrocarbon chains. Charged functionalized GNPs produce nonmonotonous counter charge distributions with reduced ion mobility. Partial replacement of first shell solvation water by the charged groups leads to a drastic increase in torsional relaxation times of the chain termini. Due to the large curvature of the GNPs with a diameter of 2 nm, gold cores remain accessible to both ions and water even at the highest studied grafting densities of about 5 chains/nm2.

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or neutral groups (COO−, OH, NH3+) to hydrophobic (CH3, CF3) ones. Various metals and oxides can form the core of such nanoparticles. Gold in particular is widely used due to its unique properties and nontoxicity. Gold furthermore does not form stable oxides, so that it can be handled with relative ease. Gold nanoparticles (GNPs) have in addition quite attractive optical properties, and the color of nanoparticle solutions can vary from yellow to dark red depending on nanoparticle size. Also, its scattering properties are very useful in biological imaging applications.19 While gold NPs are very stable, other metallic core NPs are not inert against solute access through the aqueous phase. Stability issues may become important in such cases, particularly since techniques exist20 to generate, by laser ablation, naked (or partially covered) NPs. In other work, it has been shown that the areal density of functional polystyrene chains on a nanoparticle can play a role for the embedding of such particles in composite materials.21 Hence, it

INTRODUCTION

Functionalized metal nanoparticles (FMNPs) have recently become a focus of materials research, since they can be used in a variety of applications such as electronics,1 optics,2,3 chemistry,4,5 biosensing,6−9 imaging,10−12 drug delivery,13−16 and microfabrication.17,18 In addition, functionalization can be a way to package and deliver nanoparticles by preventing coagulation or Ostwald ripening of the naked particles. Such nanoparticles (1−100 nm in size) bridge the gap between bulk materials and atomic or molecular structures. While normal bulk material properties are independent of size or granularity of the material, the properties of nanoparticles are highly dependent on particle size. FMNPs are often made of long hydrocarbon chains with terminal groups grafted onto a metal core. The hydrocarbon chains are linked chemically to the metal core via different groups, which frequently, in particular with gold nanoparticles, is achieved via a sulfur bridge. Such FMNPs can be flexibly tuned by varying the number of hydrocarbon chains on the metal surface, the length of the chains, and the size of the particle. Electrochemical and solvation properties of FMNPs can be changed easily by modifying the terminal groups from more hydrophilic, charged © 2015 American Chemical Society

Received: June 30, 2015 Revised: October 15, 2015 Published: October 17, 2015 25566

DOI: 10.1021/acs.jpcc.5b06249 J. Phys. Chem. C 2015, 119, 25566−25575

Article

The Journal of Physical Chemistry C

Figure 1. Top row: partially functionalized GNPs with NC = 20 (CH2)11−CH3 (left) and (CH2)11−COO− chains (right). Bottom row: fully functionalized GNPs with NC = 60 (CH2)11−CH3 (left) and (CH2)11−COO− chains (right).

group recently extended their studies by establishing a qualitative measure of solubility of functionalized nanoparticles26 solutions. They also calculated effective potentials of mean force (PMFs) between nanoparticles vs coating thickness and noted that the force at separations beyond about 2.5 nanoparticle radii is statistically very insignificant, but becomes quickly repulsive for distances smaller than about 2 nanoparticle radii.27 Quite recently, the hydrogen bond dynamics for mixed monolayer-protected GNPs in solution has been studied,28 where also a dependence of nanoparticle morphology on ligand length was observed. In the present work, we have studied the solvation of single charged or uncharged, partially or fully functionalized GNPs in an approximately 1 molar NaCl solution. Specifically, we have studied such GNPs with a three-layer gold core consisting of 114 Au atoms and functionalized with −(CH2)11−CH3, −(CH2)11−COO−, and −(CH2)11−NH3+ chains attached to the gold particle via sulfur bridges. In addition, we have studied the chain length dependence of the hydrocarbon chains (from 6 to 24 atoms) for the fully covered GNPs. The gold core has an approximate diameter of 2 nm, and the core was modeled in the same way as a DFT model taken from the literature.29 Of particular interest is the relative accessibility of the particle surface by water in the presence of the different hydrocarbon chains of varying grafting density. For any given core material the solvent accessible surface can be taken as a rough measure for the probability of possible destabilizing chemical reactions in the core. This, in turn, provides a measure for the protection which these chains can provide for the nanoparticle. In the next section, we describe the computational model and methods. Then, simulation data are analyzed by radial densities, the

is of some practical importance to be able to assess the accessibility of the core from the solution. Gaining knowledge on the stabilization of functionalized GNPs in solution is a prerequisite to understand the role of these materials, for example, in the biological environment, which can be regarded as a very crowded solution of ions, proteins and other molecular components in water. Complementary to experimental studies, computer simulations offer a detailed atomistic view of the interactions of functionalized GNPs in aqueous solution. Few such studies have been performed to date, mostly as molecular dynamics (MD) simulations. Ghorai and Glotzer22 compared the morphology of hydrocarbon-coated GNPs with the structures in monolayers on flat gold surfaces. In the absence of solvent they observed that at room temperature and slightly elevated temperatures ordered arrangements similar to those on the flat surface exist with disclination lines between these patches due to the large surface curvature, whereas at higher temperatures the GNPs become more isotropic. In a pioneering study, the group of Grest23 investigated the emerging shapes of various functionalized nanoparticles dissolved in water, alkane and at interfaces and noted that deviations from spherical symmetry are less dependent on the nature of the functionalization than on packing constraints. Yang and Weng24 studied with MD in much detail the structure and dynamics of pure water around an uncharged polar and nonpolar functionalized GNP with methyl, carboxyl, amine and hydroxyl termination. More recently, Heikkilä and co-workers25 studied charged polar functionalized GNPs in dilute solutions and noted that such charged nanoparticles form very stable complexes with ions and counterions around them. The Grest 25567


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The Journal of Physical Chemistry C solvation shell of counterions, surface access maps and chain conformation, and intrinsic relaxation times, followed by a summary.

Table 1. Force Field Parameters bonded interaction

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COMPUTATIONAL METHODS AND SIMULATION DETAILS Functionalized GNPs with gold core (consisting of 114 Au atoms) have been modeled as in ref.29 The gold core is composed of three shells and possesses nearly spherical geometry. The first gold shell contains 12 Au atoms, the second shell 42 Au atoms, and the third shell contains 60 Au atoms. The surface layer of the gold core is covered by 30 additional Au atoms, each of which is connected to two bridging sulfur atoms (S−Au−S)25,30,31 (Figure 1). The GNPs with approximate diameters of 2 nm are then (partially or fully) functionalized by attaching NC = 20, 40, or 60 −(CH2)11−CH3, −(CH2)11−COO−, or − (CH2)11−NH3+ chains to the 60 sulfur atoms, leading to degrees of functionalization df of 1/3, 2/3, and 1. A total of 9 systems with coverage varying between 1/3 and 1, chain length of 12 atoms, and total charge varying between −60e and +60e (with e the proton charge) have thus been prepared. For the highest coverage of 1, we have prepared 9 additional systems with chain lengths of 6, 18, and 24 atoms. The box size is 8 × 8 × 8 nm3 and contains a single functionalized GNP and approximately 15 000 water molecules. Na+ and Cl− counterions are added to the system to compensate the net charge of the GNP and create an overall neutral system. In addition, 300 NaCl ion pairs are introduced as background electrolyte, leading to an approximately one molar aqueous solution. The choice of a one molar solutions was made in order to produce a compact screening layer around the nanoparticles, so that the system size could be kept in a computationally efficient range. A lower value would, however, have been more realistic with respect to typical experimental or physiological conditions. The TIP3P32 water model has been used for all simulations together with the CHARMM-27 force field parameters for Na+ and Cl− ions.33,34 Parameters for the functionalized chains have been taken from the AMBER-99 force field,35 and parameters for gold atoms were taken from ref.,25,36 as they were not available in the AMBER-99 force field. The CHARMM dihedral style37,38 has been used for the C−C−C−C dihedral angles. All parameters are given in Table 1. Simulations are performed with the LAMMPS39 simulation package (version 31, March 2011) using the NVT ensemble, where the number of atoms, volume and temperature of the system are held constant. A Nosé-Hoover thermostat40 has been used to keep the temperature of the systems constant at 300 K, with a time constant of 1 ps. The number of water molecules was arranged in preliminary runs to produce a bulk density very close to the experimental density. We ran the simulations at constant volume in order to avoid possible instabilities leading to large volume fluctuations due to the very disparate masses of the objects in the simulation cell. Production runs are performed for about 40 ns with a time step of 1 fs and a skin distance for the neighbor tables of 0.1 nm, which are updated every 5 steps. The particle−particle− particle−mesh (PPPM) method to compute long-range Coulomb interactions has been employed with a relative accuracy of 10−4. The SHAKE algorithm41 has been used to constrain O−H bonds and H−O−H angles. The Lennard− Jones interactions are cut off at a distance of 10 Å.

nonbonded interaction

bond

Kr (kcal/(mol/Å2))

C−S C−C C−H C−O C−N

222.000 260.000 340.000 510.000 367.000

r0(Å)

atom

ϵ (kcal/mol)

σ (Å)

0.1553 0.250 0.109 0.210 0.170

3.2 3.563 3.996 2.960 3.250

1.810 Au 1.540 S 1.090 C 1.296 O 1.471 N angle bend

θ (deg)

Kθ (kcal/(mol/rad2))

angle Au−S−Au Au−S−C S−Au−S S−C−C C−C−C C−C−O O−C−O C−N−H

55 55 155 50 40 80 80 50 torsion

88.0 90.0 180.0 147.7 109.5 115.2 120.0 109.5

dihedral

K(kcal/mol)

n (integer)

d (deg)

weighting factor

C−C−C−C

0.18

3

0.0

0.0

The functionalized gold nanoparticles were constructed with the molecular editor Avogadro.42 Na+ and Cl− ions were solvated with the use of VMD (1.9.1)43 employing the TopoTools plugin. Initially, the GNPs were equilibrated in vacuum. Then the box was filled with water and ions. The number of water molecules was adjusted to yield the experimental value of 33 water molecules per nm3 at ambient conditions. Following a 5 ns equilibration run, the dynamics of the GNPs in solution was followed over 40 ns in production runs.

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RESULTS AND DISCUSSION Figure 1 shows system snapshots for partially and fully functionalized CH3 (left) or COO−-terminated GNPs (number of chains NC = 20, top; NC = 60, bottom) after about 35 ns. While in the top snapshots the chains seem to be mostly folded around the nanoparticle, the chains on the fully functionalized GNPs are predominantly in an extended form. However, significant bunching occurs as a consequence of the large curvature of the GNP and the interchain interactions (see also Figure 3). The chain bunches are more ordered in the case of the nonpolar chains, because the nonpolar-nonpolar van der Waals interactions between the chains are not mitigated by electrostatic repulsion between the charged end groups. This behavior is not surprising. At low coverage, the systems with few nonpolar chains are stabilized by reducing the exposure of the nonpolar (CH2)11-CH3 chains to the polar aqueous environment, leading to the collapse of the chains onto the particle. Thus, a GNP forms, which is covered by disordered alkyl chains. In the system with many chains, the chains stretch out mainly due to the crowded environment close to the GNP, where not much room for gauche defects in the individual chains exists. At larger distance the chains become bundled since stabilization is again driven by reduction of the solvent accessible surface area of the nonpolar chain backbone. The bundling of the grafted chains leads to asymmetric NPs even if, as in our case, the chains are isotropically grafted onto the NP surface. Evidence for such an asymmetry of isotropically 25568


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Figure 2. Radial density distributions around the center of the nanoparticles for the CH3 terminated (top row), the COO− terminated (center row) and the NH3+ terminated systems (bottom row) for df = 1/3 (left column), 2/3 (center column), and 1 (right column). Red lines of varying thickness show the density distribution of the terminal atoms(C of CH3, C of COO−, N of NH3+; widest red lines) and the second, fourth, and sixth (narrowest lines) carbon atom of the alkyl chain (counting from the terminal one toward the GNP). In addition, the water oxygen (blue line with diamonds), Na+ (blue squares) and Cl− (blue circles) densities are shown. Vertical density scales have been adjusted to bring all densities to the same scale using identical scale factors for all red curves, one for water oxygen, and one for ions.

When increasing the degree of functionalization to 2/3 and above, the spatial constraints for the relatively densely packed chains become more pronounced. This leads first to a progression of the density maxima of chain atoms toward larger distances when moving from atom C6 toward the end of the chain. Second, it manifests itself in a significant broadening of all chain distributions for df = 2/3 (center column). Compared to df = 2/3, the plots at df = 1 (right column) show a more regular progression of maxima. Naturally, the width of the distribution becomes the wider the farther the chain atom is located away from the sulfur pivot point. At df = 2/3, the conformational freedom of the chain is obviously still quite large, whereas at df = 1 only the outer part of the chains appear to be able to sustain a significant fraction of gauche defects (see also below). The water oxygen distribution at df = 1/3 shows that only about half the amount of water penetrates the relatively compact layer for nonpolar chain termination (top left) compared to the polar chain termination (center and bottom left), which is visible as a step in the density at around 1.2 nm. Another structural feature is visible at around 1.7 nm as a slight depression in the water oxygen density. At the higher values of df, the step feature vanishes. Instead, the water distribution increases more or less monotonically from zero toward the bulk value at a distance of around 2.4 nm. While few water

functionalized nanoparticles was recently obtained on the basis of light scattering experiments.44 Figure 2 summarizes the time and ensemble averaged radial distribution of various atomic species of interest. At the low degree of functionalization (1/3, left column), the distributions of the chain atoms (red lines) are significantly closer to the GNP (within about 1.5−2 nm from the center or 0.5 to 1 nm from the surface) than for the higher degrees of functionalization. For the nonpolar CH3 terminated chains at df = 1/3, it is particularly obvious that all carbon distributions have the maximum at the same distance (around 1.2 nm from the GNP center), only the distributions of the outer chain atoms are somewhat wider and more asymmetric than those of the carbon atoms with less bonds between them and the GNP. Thus, the nanoparticle surface is more or less covered with hydrocarbon chains, which wind around the curved surface. When the chains are polar functionalized (with COO− or NH3+ groups), the thickness of the hydrocarbon shell is larger than for the nonpolar CH3-terminated GNP. The distributions of the atoms near the polar headgroups are much wider than in the top-left figure, indicating a certain competition between pulling the individual chains to the surface and solvating the polar head groups in a more stable manner further out into the aqueous solution. 25569


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The short chains (top row) point predominantly outward from the NPs. Water access (as manifest in predominantly yellow regions) is somewhat reduced for the nonpolar chains, which tend to fold and cover the nanoparticle surface (see Figure 1). For the polar chains, which are more likely to be extended and pointing away from the particle core, water access is slightly higher. The folding of the nonpolar chains of length 12 (second row left) is still not sufficient to cover the NP surface fully. The polar chain of length 12, on the other hand, covers the NP somewhat better, presumably due to repulsion between the terminal groups. The longer chains of length 18 and 24 naturally cover larger and larger fractions of the GNP with methylene groups, but even for the longest studied chains there remain open patches of surface which are accessible by solutes over a time scale of 40 ns. The behavior is not strongly dependent on the polarity of the terminating group. One can extrapolate that with chain lengths above about 30, most of the metal atoms should be inaccessible to aqueous solutes. Corresponding data sets for the polar COO− terminated systems show features similar to the polar NH3+ terminated ones. In summary, water access (and thus access of small aqueous solutes) to the surface is possible for all studied and functionalized systems over time spans of at least 40 ns. Figure 4 (left) shows the distribution of coordination numbers for Na+ ions around (CH2)11−COO−-terminated GNPs, separately for water coordination, COO− coordination, and total coordination (from top to bottom in each bold frame). Coordination numbers are defined as the number of oxygen atoms within a distance of 0.32 nm from the Na+ ion. The most probable coordination number far from the GNP is 5 when using these definitions. For all values of df (bold frames from top to bottom), the Na+ ions shed part of their water solvation shell when penetrating the chain domain. At intermediate distances (≈ 1.8 to 2.7 nm), the COO− coordination can compensate the loss in water coordination. COO− groups replace water molecules in the ion solvation shell, and the distribution of total coordination numbers is roughly independent of distance between a distance of about 2−2.3 nm from the GNP center and the bulk. At very small distances from the GNP, however, coordination by the chain-terminating COO− groups cannot compensate for this loss of hydration water, and thus the total coordination number distribution shifts toward smaller values. An analogous behavior to the Na+ ions around the (CH2)11− COO− functionalized GNPs can be observed for the coordination of hydrogen around Cl− ions in the (CH2)11NH3+ functionalized GNPs. The right side of Figure 4 shows water, NH3+, and total coordination number distributions for degrees of functionalization between 1/3 and 1 (bold frames from top to bottom). With the chosen settings (H−Cl− distance less than 0.29 nm), the most probable coordination number is 7 or 8. Again, NH3+ functional groups replace almost completely some solvation water at intermediate distances between approximately 2 and 2.5 nm; close to the GNP, the compensation is incomplete and the coordination number distribution shifts toward smaller values, as in the Na+/ (CH2)11−COO− case. By and large, the partial loss of water molecules around the Cl− ions is less than around the Na+ ions. Also, the total coordination number distribution seems to be somewhat less affected at smaller distances than for Na+ (left side of Figure 4).

molecules penetrate the chain domain almost up to contact with the GNP in all cases, the overall number tends to become smaller, more due to an increase in hydrocarbon coverage near the GNP surface than due to an increase in polarity. Figure 3 shows color-coded maps of the distribution of closest atoms to the GNP surface for GNPs with fully covered

Figure 3. Color maps of surface access. Values of 1 (yellow) indicate that exclusively (over the entire 40 ns simulation length) a water molecule is closest to the GNP surface element, while a value of 0 indicates exclusively a chain atom being closest to the surface. Left column: NC = 60 CH3 terminated chains with 6, 12, 18, and 24 carbon atoms (from top to bottom). Right column: NC = 60 NH3+ terminated chains with 5, 11, 17, and 23 carbon atoms. All maps show the entire surface of the unit sphere (in the laboratory frame) with the cosine of the polar angle θ between −1 and 1 and the angle ϕ between 0 and 2π.

surface atoms (NC = 60). Along the horizontal direction the azimutal angles ϕ vary between 0 and 2π, and the cosines of the polar angles ϑ vary between −1 ≤ cos ϑ ≤ 1 along the vertical direction. The largest values (1; yellow) indicate that water oxygen atoms cover the surface almost exclusively, while purple values indicate a preferential coverage of the GNP surface by chain atoms. Since the map contains about 10 times more pixels than atoms can fit on the GNP surface, the smallest values are usually larger than 0 due to the fact that slight motions of surface-covering chain atoms occur. The left column shows maps for nonpolar CH3 terminated chains of varying chain length with 6, 12, 18, and 24 carbon atoms (from top to bottom). The right column shows analogous data for NH3+ terminated chains with 5, 11, 17, and 23 carbon atoms. The variation of colors is to some extent a consequence of the limited sampling time of around 40 ns, but also a consequence of the not entirely isotropic distribution of anchoring points for the chains. 25570


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Figure 4. Left: Solvation number in systems with COO− terminated chains. The color code shows the probability to find given coordination numbers (vertical axes) around Na+ ions in dependence of the distance of the ion from the GNP center. Each bold frame shows coordinated water, coordinated COO− oxygen atoms, and total coordination number. Bold frames from top to bottom are for increasing degrees of functionalization between 1/3 and 1. Coordinated oxygen atoms are defined as those O atoms within a sphere of radius 0.32 nm around Na+ ions. Right: analogous solvation number distributions of Cl− around NH3+ terminated chains. Here, coordination number is defined as the number of hydrogen atoms within a sphere of radius 0.29 nm around Cl− ions.

Naturally, the overall number of trans conformations increases with increasing df because the increased crowding of the chains close to the nanoparticles to some extent prohibits the establishment of gauche defects, which need more space than the corresponding trans configurations. As the bottom frame, which compares the data at df = 1 for the three different functionalizations, shows, the overall trends of the number of trans configurations and the heterogeneity are similar in all cases, with the notable exception of the terminal dihedral. Obviously, the larger degree of gauche defects and the larger static heterogeneity of dihedral 1 is associated with the polarity of the terminal group, since the CH3 terminated chains do show neither a significant decrease of trans conformations nor a broader distribution for dihedral 1 relative to the neighboring dihedrals. Whereas Figure 5 and also Figure 3 provide a more or less static view (averaged over 40 ns) of chain conformations and bundle structure, Figure 6 provides a dynamic view of the intrachain dynamics. Figure 6 shows the relaxation times of dihedral conformations. Similarly as for Figure 5, the relaxation times are calculated individually for each dihedral angle in each chain. Figure 6 contains the averages over equivalent dihedrals

Figure 5 shows the simulation-averaged percentage of trans conformations (defined as dihedral angles φ between 120 and 240°) of the individual dihedrals along the chain. Average angles have been calculated separately for each individual chain. The error bars in the figure denote plus or minus one standard deviation from the mean, and they thus provide a measure of the static heterogeneity of the chains. Torsion angle 1 is defined as the torsion angle along the chain starting at the terminal group (CH3, NH3+, or COO−) toward the GNP; angle 2 is the next torsion angle starting at the second chain atom (counted from the terminus of the chain), angle 3 is the third one, and so on. The top frame shows the data for the NH3+ terminated chains for different degrees of functionalization, which exemplifies the general trends. The first dihedral angle involving the polar groups shows increasing static heterogeneity with increasing df (characterized by the larger error bars). On average, it exhibits less trans and more gauche conformations than the second to fifth dihedral. Dihedral angles closer to the attachment point on the nanoparticle (larger indices) have again more gauche defects. At the same time, the static heterogeneity of the chains increases for those dihedrals. 25571


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[240−360°]). Then, for each class in turn, the normalized autocorrelation function (acf) fdih = ⟨hc(0) hc(t )⟩

with hc(t) = pc(t|pc(0) = 1) − pc(∞). pc(t|pc(0) = 1) indicates the probability of a specific dihedral to be in class c at time t, given that it was in class c also at time t = 0. pc(∞) denotes the (static) equilibrium probability of finding a specific dihedral in class c, and hc(0) = 1, obviously. The top of Figure 6 shows data for the NH3+ terminated system for different degrees of functionalization. The terminal dihedrals (index 1) show significantly larger relaxation times than their neighbors. Also the dynamic heterogeneity of the chains increases with increasing chain density. Naturally, the relaxation times (and their distribution) increase drastically in the inner part of the chain region, where, as a consequnce of the large curvature of the GNPs, the sterical hindrance between neighboring chains, becomes large. The bottom part compares the fully functionalized GNPs for the different functionalizations. The overall trend is similar for all chain terminations. However, it also becomes evident that the increased relaxation times of the terminal dihedral are a consequence of the polarity of the chain terminus, which thereby can interact more strongly with the Na+ or Cl− counterions. This retarding effect is absent in the case of CH3 termination. Figure 7 demonstrates that the retardation of the conformation of the polar terminated chains is accompanied by a reduction of ion mobility. The figure shows the SDCs of Na+ and Cl− ions, calculated from the final value of the mean square displacement after 0.8 ns. Data are shown for ions selected to be initially in spherical shells of 0.3 nm thickness centered around the distance values given on the horizontal axis. For better readability, data for Na+ ions are shifted downward by 0.15 cm2 s−1, and the values for Cl− ions are shifted upward by 0.15 cm2 s−1. The data demonstrate that ion mobility increases in general slightly toward the bulk region, which is quite expected due to the decreasing sterical hindrance effects along this direction. It also shows that for the CH3 terminated nonpolar chains the effect on both cations and anions is not very pronounced. For GNPs functionalized with polar chains both counterions and co-ions are slowed down in the region of overlap with the chains. This effect is significantly more pronounced for the counterions than for the co-ions. Near COO− terminated chains Na+ counterions are slowed down significantly in the region r < 3 nm. For the Cl− co-ions the effect is smaller and pronounced only for the highest df. Results for the NH3+ terminated GNPs are very similar to the roles of Na+ and Cl− ions reversed.

Figure 5. Fraction of trans conformations for individual dihedral angles in NH3+ terminated systems (top) and for all fully functionalized systems (bottom). The numbering of dihedral angles along the chain starts at 1 for the angle containing the terminal atom (CH3 or COO− carbon or NH3+ nitrogen).

Figure 6. Relaxation time of individual torsional angles in NH3+ terminated systems (top) and for all fully functionalized systems (bottom). The numbering of dihedral angles along the chain starts at 1 for the angle containing the terminal (CH3 or COO− C or NH3+ N atom). See text for the procedure to calculate the relaxation times.

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SUMMARY AND CONCLUSIONS

We have studied small GNPs of approximately 2 nm diameter, functionalized with C11 hydrocarbon chains terminated with nonpolar CH3 and polar COO− and NH3+ groups. Particle size and structure match some of those synthesized by various groups45−48 from almost spherical gold cores and sulfur bridged functional shells.49 The GNPs are solvated in an approximately 1 molar aqueous NaCl solution and the excess functional charge on the polar GNPs is compensated by a corresponding excess of Na+ or Cl− counterions.

in different chains. The error bars again denote plus or minus one standard deviation from the mean value as a measure of dynamic heterogeneity of equivalent chains. The procedure to calculate the relaxation times is the following: dihedrals are categorized into three classes, depending on the dihedral angles ([0−120°], [120−240°](trans), and 25572


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indicate. Surface access naturally diminishes with increasing chain length. Although this temporary accessibility might be a possible contribution to the observed increased dispersion stability of NPs with increasing chain length,50 the nature of our NP model is such that no predictions can be made concerning differences between different metal cores. Patch formation similar to that observed by Grest and co-workers23,26 is stabilized by strong ion pair formation with counterions, as can be derived from the radial distribution functions (data not shown, but see also Figure 4). This stabilization is achieved by the free counterions exchanging part of their hydration shell water molecules with polar functional groups (see Figure 4). The free counter charges also screen most of the radial charge built up by the grafted charged end groups (see Figure 2). Both effects together lead to a significant slow-down of the counterions in the headgroup region (see Figure 7), which, in turn, acts back on chain conformation and dynamics. Owing to the stronger interactions with the counterions the dihedral angle which involves the charged chain terminus shows substantially more static disorder (less trans conformations) than the corresponding methyl group terminated chains (see Figure 5). Also, the local variation of this disorder (as measured by the static heterogeneity expressed in the mean square displacements) is larger in the presence of the counterion shell than for the nonpolar groups, and it increases with grafting density. Simultaneously, the terminal dihedral angles show significantly longer relaxation times as compared to the nonpolar chains (see Figure 6). The simulated particles serve as models to study the influence of an aqueous environment on functionally protected nanoparticles. Our results demonstrate that, at least for such small and compact nanoparticles, a very high degree of functionalization with relatively short polar or nonpolar molecules does not prevent water access to the nanoparticle surface for access times of 40 ns or more. Thus, nanoparticles whose cores consist of water-soluble or acid−base instable substances or of non-noble metals can be expected to be readily attacked by the aqueous environment, even if the degree of functionalization is high. If it is not possible, or undesirable, to cover the nanoparticles with thick polymer layers, a possible remedy for stabilization of such particles in an aqueous environment might be the use of branched or dendritic molecules as functional protection. Specially “curvature”designed molecules might actually selectively stabilize a particular nanoparticle size distribution.

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AUTHOR INFORMATION

Corresponding Authors

Figure 7. Ion self-diffusion coefficients (in units of 10−5 cm2 s−1) for CH3 termination (top), COO− termination (center), and NH3+ termination (bottom) as a function of the distance from the GNP center. For better legibility, values are shifted downward by 0.15 units for Na+ (larger symbols) and upward by 0.15 units for Cl− (smaller symbols).

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge computational support by the Center for Computational Sciences and Simulation (CCSS). This work is supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft.

For each terminal group we have compared systems with degrees of functionalization, df, of approximately 1/3, 2/3, or 1, corresponding to grafting densities of about 2, 3, and 5 chains per nm2. Nonpolar methyl-terminated chains extend less into the solution than the polar charged chains. Instead, the nonpolar chains tend to wrap around the GNP and cover the surface somewhat better, but even at df = 1 parts of the surface remain water-accessible, as the surface access maps of Figure 3

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REFERENCES

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