The Influence of Chain Length and Branching on the Structure of

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C: Physical Processes in Nanomaterials and Nanostructures

The Influence of Chain Length and Branching on the Structure of Functionalized Gold Nanoparticles Amal Kanta Giri, and Eckhard Spohr J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08590 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 3, 2018

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The Journal of Physical Chemistry

The Influence of Chain Length and Branching on the Structure of Functionalized Gold Nanoparticles Amal Kanta Giri∗,†,§ and Eckhard Spohr∗,‡,¶ †LAQV-REQUIMET, Department of Chemistry and Biochemistry, Faculty of Science, University of Porto, Rua do Campo Alegre, Porto 4169-007, Portugal ‡Fakultät f¨ ur Chemie, Universität Duisburg-Essen, D-45117 Essen, Germany ¶Center for Computational Sciences and Simulations (CCSS), Universität Duisburg-Essen, D-45117 Essen, Germany §former address: Fakultät f¨ ur Chemie, Universität Duisburg-Essen, D-45117 Essen, Germany E-mail: [email protected]; [email protected]

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Abstract Functionalized gold nanoparticles (GNPs) in aqueous NaCl solutions have been studied using molecular dynamics (MD) simulations in order to assess the suitability of various functionalization chemistries to effectively shield the metallic core. Alkane thiol chains of various chain length (Cl ) containing 6, 12, 18 and 24 carbon atoms are grafted onto the surface of the gold core. We compare the properties of GNPs functionalized with non-polar CH3 -terminated and polar COO− - and NH+ 3 -terminated chains, where the nanoparticle charge is compensated by appropriate numbers of excess Na+ or Cl− counterions. In addition to linear chains, we also investigate branched Yshaped chains with the branching sites at the 4th, 8th, or 12th carbon atom from the sulfur atom that connects the chain to the gold core. The penetration depth of water and ions into the diffuse hydrocarbon shell region and its dependence on chain length, branching, and terminating group is found to increase with decreasing chain length irrespective of termination. Long linear chains, however, tend to form bundles independent of terminal group and can thus leave fractions of the nanoparticle surface exposed to small molecules, while shorter and branched chains do not form bundles and can cover the GNPs more homogeneously.

Introduction Functionalized metal nanoparticles (FMNPs) have recently caught attention in materials research due to their wide range of technological applications in electronics, 1 optics, 2,3 chemistry, 4,5 biosensing, 6–9 imaging, 10–12 drug delivery 13–16 or micro-fabrication. 17,18 In addition, functionalization can be a method to package and deliver nanoparticles by preventing coagulation or Ostwald ripening of the bare nanoparticles. Such nanoparticles with a size between 1 and 100 nm bridge the gap between bulk materials and well-defined molecular structures.

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While normal bulk material properties are independent of size or granularity of the material, the properties of nanoparticles are highly dependent on their size. functionalized metal nanoparticles (FMNPs) are often produced by grafting long hydrocarbon chains with specific terminal groups onto a metal core. The hydrocarbon chains are linked chemically to the metal core via different chemical groups, which, in the case of gold, is usually achieved via a sulfur (thiol) bridge. The properties of such FMNPs can be flexibly tuned by varying the functionalization density (i.e. the number of hydrocarbon chains on the metal surface), the length of the chains (i.e. the number of carbon atoms), and the size of the metallic core. Electrochemical and solvation properties of FMNPs can be changed easily by modifying the terminal groups from more hydrophilic groups (both charged or neutral, e.g., COO− , OH, or NH+ 3 termination) to hydrophobic ones (e.g., CH3 or CF3 termination). While many metals and oxides can form the cores of FMNPs, gold in particular is widely used due to its unique properties of non-toxicity and inertness towards forming stable oxides, so that it can be handled with relative ease. Like other nanoparticles, gold nanoparticles (GNPs) have furthermore quite attractive optical properties, and the color of colloidal nanoparticle solutions varies from yellow to dark red depending on nanoparticle size. The scattering properties of GNPs are successfully exploited in biological imaging applications. 19 It has also been shown that the grafting density of chains on the nanoparticle (NP) surface plays an important role for the ability of the NPs to form composite materials. 20 Similarly, chain length and terminal functionalization determine solubility, dispersion and aggregation properties. While GNPs are chemically quite stable, other metallic core NPs are not inert against solute access from the aqueous phase. Thus, it is of some practical importance to be able to assess the accessibility of the core from solution. This even more so as techniques exist 21 to generate, by laser ablation, naked (or partially covered) NPs. Also, the areal density of functional polystyrene chains has been observed to play a role for the location of embedding of such particles in composite materials. 20 3



Gaining knowledge on the stabilization of GNPs by functionalization in solution is also an essential prerequisite to understand the role of these materials in the physiological 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 in this field, mostly as molecular dynamics (MD) simulations. Ghorai and Glotzer 22 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 at 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 Grest 23 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 Weng 24 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 coworkers 25 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 group recently extended their studies by establishing a qualitative measure of solubility of functionalized nanoparticles 26 solutions. They also calculated effective potentials of mean force (PMFs) between nanoparticles in dependence of coating thickness; they 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, hydrogen bond dynamics for mixed monolayer-protected GNPs in solution has been studied, 28 where also a dependence of nanoparticle morphology on ligand 4


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length was observed. In the present work, we have studied the solvation of single charged or uncharged GNPs with partial or full functionalization in one molar NaCl solution. Specifically, we have studied GNPs with a three-layer gold core consisting of 144 Au atoms and functionalized with –(CH2 )11 -CH3 , –(CH2 )11 -COO− and –(CH2 )11 -NH+ 3 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 it was modeled using DFT-based interaction potentials taken from the literature. 29 Of particular interest in the present context is the relative accessibility of the particle surface by water in the presence of the different hydrocarbon chains of varying grafting density, which, for any given core material, can be taken as a rough measure for the probability of possibly destabilizing chemical reactions of the core and thus for the protection which these chains can provide for the nanoparticle. Our simulation results can be regarded to be quite general with respect to the solvent accessibility and protection of nanoparticles with arbitrary cores, but the chemical consequences will have to be assessed individually for different NP cores, since the employed force field models are incapable of describing specific chemistry. In the next section we describe the computational model and methods. Then, our simulation data are analyzed by maps of interchain angles, and surface accessibility as well as some quantitative comparisons between the various studied NPs, followed by a summary.

Computational Methods and Simulation Details The functionalized GNPs consist of a three-layer core of gold atoms (altogether 144 atoms with a diameter of approximately 2 nm). 60 sulfur atoms on the surface of the core serve as anchoring points for the functionalizing hydrocarbon chains. Figure 1a shows the NP and

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b

a

c

Figure 1: (a) Fully functionalized GNP (gold: yellow, sulfur: green) with NC =60 (CH2 )11 + − NH+ 3 chains including few close-by water molecules (red and white) Na (green) and Cl ions (pink) ions. (b) Chains of length 12 branched at the 4th (left) and the 8th (right) carbon atom. (c) Definition of angle for time average angle distribution. a few water molecules. Further details about structure and modeling of the gold and sulfur core atoms can be found in Ref. 30 This gold core was functionalized by linear chains attached to each of the surface sulfur atoms (full functionalization, NC =60). A total of 12 different NPs were simulated by combining four different chain lengths, Cl = 6, 12, 18, 24, and three different end groups, CH3 , − 30 NH+ 3 and COO , (see also Ref. ).

Another 10 systems with branched chains were simulated, where only 30 of the 60 sulfur atoms were functionalized, but due to the Y-shape of the molecules, the same number (60) of end groups are present (see Fig. 1b and c, which show the structures of two branched side

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chains and the definitions of angles between them as used below). Since in our previous study we observed no significant differences in the protective quality of the NP-attached molecules + − between positive NH+ 3 and negative COO functionalization, we studied only CH3 and NH3

termination. The branched system had chain lengths (from sulfur to terminal group) of 12 (with two studied branch points at carbon atoms 4, or 8, counted from the sulfur atom) or 18 (with three branch points at carbon atoms 4, 8, or 12). Thus, for CH3 termination, the number of C atoms in the branched chains varied between 16 (Cl =12, branch point 8) and 30 (Cl =18, branch point 4). Since the total number of carbon atoms for NC = 60 linear chains of Cl =12(18) is larger than for 30 branched chains of the same Cl , we have also performed a few simulations in which we increased the number of branched chains to NC = 35 or 40 with a total number of terminal groups of 70 or 80, respectively, in order to be able to further estimate the influence of the total number of CH2 groups covering the NP. The size of the simulation box was increased with increased chain length Cl . Simulation box sizes are 6×6×6 nm3 , 8×8×8 nm3 , 10×10×10 nm3 and 12×12×12 nm3 for Cl = 6, 12, 18 and 24 systems, respectively. These cells contain approximately 6000, 15000, 30000 and 52000 water molecules in the Cl = 6, 12, 18 and 24 systems, respectively. For the charged polar terminal groups, excess Na+ and Cl− counterions are added to neutralize the systems. In addition, 123, 295, 584 and 1017 NaCl ion pairs are solvated as backbone electrolyte in the systems to achieve approximately 1 molal aqueous solution at ambient density. The gold atoms of the GNP core were kept immobile in the center of the simulation box during the dynamics. All other atoms were mobile. Table 1 summarizes the relevant system parameters and Fig. 2 shows the final configurations for all simulations. The TIP3P 31 water model has been used throughout. Parameters for the functionalized chains have been taken from the OPLS-AA force field and parameters for gold atoms were taken from Ref., 32 as these are not available in the OPLS-AA force field. Based on the results

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Table 1: Simulated nanoparticle systems. Cl denotes the total chain length (including terminal group), Nt the number of terminal groups, nw , nNa+ , and nCl− the number of water molecules, Na+ cations and Cl− anions, respectively. L denotes the linear box dimension of the cubic box (in nm). hree i is the simulationaveraged end-to-end distance of the side chains (in nm).

branch point

nw

nN a+

nCl−

L

hree i

60

–

6176

123

123

6

0.60

CH3 CH3 CH3

60 60 60

– 4 8

15067 15163 15257

295 297 299

295 297 299

8 8 8

1.31 1.06 1.03

18 18 18 18 18 18

CH3 CH3 CH3 CH3 CH3 CH3

60 60 60 70 60 80

– 4 8 8 12 12

29991 30106 30184 30103 30280 30092

584 586 588 586 589 586

584 586 588 586 589 586

10 10 10 10 10 10

2.01 1.55 1.35 1.41 1.38 1.44

L24/0

24

CH3

60

–

52618

1017

1017 12

2.38

L6/+ L12/+ L12B4/+ L12B8/+ L18/+ L18B4/+ L18B8/+ L18B8/+/70 L18B12/+ L18B12/+/80 L24/+

6 12 12 12 18 18 18 18 18 18 24

NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3 NH+ 3

60 60 60 60 60 60 60 70 60 80 60

– – 4 8 – 4 8 8 12 12 -

6111 15004 15103 15202 29933 30035 30116 30040 30223 30038 52549

123 295 297 299 584 586 588 586 589 586 1017

183 355 357 359 644 646 648 646 649 646 1077

6 8 8 8 10 10 10 10 10 10 12

0.62 1.29 1.16 1.13 1.96 1.67 1.61 1.65 1.59 1.61 2.62

L6/– L12/– L18/– L24/–

6 12 18 24

COO− COO− COO− COO−

60 60 60 60

– – – –

6116 15013 29936 52545

183 355 644 1077

123 6 295 8 584 10 1017 12

0.60 1.26 1.96 2.59

Key

Cl

terminal Nt group

L6/0

6

CH3

L12/0 L12B4/0 L12B8/0

12 12 12

L18/0 L18B4/0 L18B8/0 L18B8/0/70 L18B12/0 L18B12/0/80

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Figure 2: Final simulation snapshots of functionalized gold nanoparticles with keys as defined in Table 1. Only CH3 - and NH+ 3 -terminated (last characters 0 and +, respectively) are shown for various chain lengths without and with (character B) Y-shaped branching. For details of the nomenclature, see Table 1. of our recent MD simulation studies 33,34 we chose to use geometric combination rules for the Lennard-Jones interactions between unlike atoms. All force field parameters are summarized in Table 2. Simulations were performed using the LAMMPS 35 simulation package (version 31, March, 2011) in the NVT ensemble at 300 K. The NVT ensemble was used in order to avoid slow energy transfer between the heavy central NP and the light solution molecules and possibly large fluctuations of the box volume due to motions of the heavy particle at the center of the simulation box. A Nosé-Hoover thermostat 36 has been used to keep the temperature of the systems constant at 300 K with a time constant of 1 ps. For initial equilibration, several short simulations of the order of several picoseconds were run in order to adjust volume (and thus pressure) to its ambient value of 1 atm. This was followed by a 2 9



Table 2: Force field parameters Bonded interaction Non-bonded interaction Bond Kr (Kcal/(mol/˚ A2 )) r0 (˚ A) Atom (Kcal/mol) σ(˚ A) C–S 222.000 1.810 Au 1.322 2.951 C–C 268.000 1.529 S 0.355 3.600 C–H 340.000 1.090 C 0.066 3.500 C–O 570.000 1.229 O 0.210 2.960 C–N 337.000 1.449 N 0.170 3.250 Angle bend Angle Kθ (Kcal/(mol/rad2 )) θ(degree) S–C–C 50.00 147.7 C–C–C 58.35 112.7 C–C–N 80.00 109.7 C–C–O 80.00 120.4 O–C–O 80.00 126.0 C–N–H 38.00 118.4 H–N–H 35.00 120.0 Torsion Dihedral K1 (Kcal/mol) K2 (Kcal/mol) K3 (Kcal/mol) S–C–C–C 2.62 -0.62 0.25 C–C–C–H 0.00 0.00 0.30 H–C–C–H 0.00 0.00 0.30 C–C–C–C 1.30 -0.05 0.20 C–C–C–N 0.00 0.00 0.46

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ns equilibration run at a pressure of 1 atm. The final production runs lasted 80 ns using an integration step of 2 fs. Histograms and maps were calculated by averaging over stored configurations from the production run. Cutoff for the Lennard-Jones interactions was taken to be 1 nm with a 0.2 nm skin distance so that neighbor tables could be updated every 5 to 10 steps. For long-range Coulomb interaction the particle-particle-particle-mesh (PPPM) algorithm with a relative accuracy setting of 10−4 was used. In addition, the SHAKE algorithm 37 has been used to constrain O-H bonds and H-O-H angles of water molecules. We used the molecular editor Avogadro 38 to construct the functionalized GNPs. Na+ and Cl− ions were solvated in the water box with the use of VMD (1.9.1) 39 by employing the TopoTools plugin. Initially, we constructed functionalized GNPs and equilibrated them in vacuum. We cut out a water sphere from the center of a large water box and immersed the functionalized GNP. This system was then pre-equilibrated for several ns. By choosing the size of the cut-out sphere appropriately, the required solution density at ambient pressure can quickly be reached.

Results and Discussion The snapshots in Figure 2 show the final configurations of the performed GNP simulations of 80 ns length, with water molecules, ions, and chain hydrogen atoms excluded for a clearer view of the chain arrangement. Only CH3 - and NH+ 3 -terminated chains are displayed, since 30 the differences between COO− -termination and NH+ 3 -termination were found to be small.

We note several characteristic trends: • With increasing chain length there is an increasing tendency for chains to ’bundle’ together due to their mutual dispersive attraction and the hydrophobic repulsion by the polar solution. This was discussed already in Ref. 30 11



• Bundling can occur with three bundles for shorter chains (L12/0), two bundles for Cl =18 chains, and only one bundle for the longest chains with Cl =24. • Due to repulsion between the charged head groups, bundling does not occur for shorter NH+ 3 -terminated chains (compare L12/0 with L12/+) and is more ordered for the longer NH+ 3 -terminated chains (particularly visible for the pair L18/0 and L18/+). • Due to the shortness of the chains, bundling does not occur in the Cl =6 chains, but wedge-like gaps occur (see L6/+) in the NH+ 3 -terminated chain, while the nonpolar CH3 -terminated chains in L6/0 collapse somewhat onto the surface due to hydrophobic repulsion by the aqueous phase. • All branched chains (particularly for Cl =18) produce more compact shells than their linear counterparts, which can also be inferred from the mean end-to-end distances of the chains (see Table 1). For example, the average end-to-end chain length for the Cl =18 CH3 -termination decreases from 2.01 nm for L18/0 to 1.35 nm for L18B8/0 or 1.38 nm for L18B12/0. Similar decreases can be found for the Cl =12 chains and the NH+ 3 -terminated chains. • This decrease of the mean end-to-end distance is not the consequence of the altogether smaller number of methylene groups in the branched chains, as the comparisons of L18B8/0 with L18B8/0/70 and of L18B12/0 with L18B12/80 (and similarly for the NH+ 3 -terminated GNPs) show. The end-to-end distance does not increase back to the values of the unbranched chains in the simulations with more than 60 terminal atoms (and a similar number of methylene groups. Thus, it appears that the disorder introduced by the branching gives rise to the chains reduced tendency to stretch; instead, they partially fold around the NP core. • Again, for branched chains with charged NH+ 3 -termination, the end-to-end distances 12


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Figure 3: Color maps of chain-chain-angle distributions. Each frame shows, for all pairs of chains, the distribution of the chain-chain angle (as defined in Fig. 1c) along the x-axis for each equivalent pair of atoms (starting from pairs of atom 1 (carbon atoms bonded to sulfur) to the terminating group (12, 18, or 24) along the y axis. Keys are defined in Table 1. are larger than for the corresponding chains with nonpolar CH3 -termination. The bundling phenomenon can be inferred in a statistically meaningful way by studying the distribution of the angle between two chain-specific vectors. Any choice of vector can be made, the end-to-end vector (sulfur to terminal group) being the most obvious one. In order to learn more about the chain conformations in addition to the end-to-end-vector all vectors from sulfur to any of the intermediate methylene carbon atoms can be used, enumerated from 1 (the carbon atom bonded directly to sulfur), 2 (the next-nearest bonded neighbor of sulfur) up to, say 18, for the chains of Cl =18. Figure 3 shows the distribution of these 13



vectors, averaged over stored configurations of the 80 ns simulation run. If all chains would be in an extended (all-trans) form sticking out radially from the NP core, the distribution would follow roughly a sin θ shape with a maximum around an angle θ ≈ π/2. For the terminal atoms, we observe, in agreement with Fig 2, a sin θ shape distribution for all sulfur-to-Ci atoms in the unbranched NH+ 3 -terminated Cl =12 chain (L12/+). CH3 termination (L12/0), on the other hand, shows two maxima around π/6 and a broader one around 3π/4 which is compatible with the bundling visible in the snapshots. Similar bundling characteristics are evident for the terminal groups in the longer unbranched chains L18/0, L18/+, L24/0 and L24/+. The details, however, vary in accordance with Figure 2. L12/0 exhibits three bundles, which manifests itself in a narrow maximum around π/6 and a broad maximum between about 0.6π-0.8π, while the two-bundle configurations of L18/0 and L18/+ have a narrower maximum around 3π/4 in addition to the one at π/6. The presence of only a single bundle on the surface of the long-chain NPs L24/0 and L24+ leads to a complete suppression of the second maximum in L24/+ or a less pronounced one shifted towards smaller angles for L24/0. While all linear chains with Cl =18 show bundling, all branched chains cover the NP core more uniformly (see Fig. 2). Thus, for the branched chains the angular distributions in Fig. 3 are relatively symmetric and do not change much with increasing distance of the carbon (or the nitrogen atom of the terminal NH+ 3 group) from the sulfur atom. Thus, both polar and nonpolar branched chains can coat the NP surface without significant sideways distortion towards the NP core. For the linear chains, on the other hand, only the atoms closest to the core (small numbers) show symmetric distributions. The distributions become more asymmetric starting with the third- or fourth-nearest neighbor of the sulfur bridges. Taken altogether, Fig. 3 proves that the bundling structure is rather static on a time-scale of 80 ns.

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Figure 4: Color maps of surface access. Values of 1 (yellow) indicate that exclusively (over the 80 ns simulation length) a water molecule is closest to the GNP surface element, while a value of 0 indicates exclusively a functionalizing chain atom being closest to the surface. Keys are defined in Table 1. Only CH3 - and NH+ 3 -terminated (characters 0 and +, respectively) are shown for various chain lengths without and with (character B) Y-shaped branching. While Fig. 3 seems to indicate that all GNPs covered with branched chains are well protected, Fig. 4 shows a more detailed picture. The figure contains color coded maps of the distribution of closest atoms (oxygen of water or carbon of hydrocarbon chains) to the GNP surface averaged over the 80 ns simulation run. Along the horizontal direction the azimuthal angle φ varies between 0 and 2π and along the vertical direction the cosine of the polar angle θ varies between -1 and +1. The largest value 1 (yellow) in these maps indicates that an oxygen atom of a water molecule is always closest to the gold surface, and a value 0 indicates that a carbon atom of a chain is always closest to the surface. The maps correspond to a

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two-dimensional projection of the sphere surface in the laboratory frame. Due to the choice of cos θ as the y-axis, equal areas on the map refer to equal areas on the sphere, different from the commonly used Mercator projection in geography. These maps are best interpreted by inspecting the yellow areas and their distribution. It is obvious that short and medium linear (L6, L12) chains leave vast areas of the NP surface exposed to water. The longer linear chains (L18, L24) reduce the overall wateraccessible area, but cannot prohibit exposition of several open patches (particularly visible in L18/0 and L24/+ due chain bundling. The branched chains contain more methylene groups at a given chain length (L18) when moving the branching point from B12 over B8 to B4, and consequently the protective coating increases in this order. This is true both for the nonpolar CH3 -terminated chains (in the series L18B12/0→L18B8/0→L18B4/0) as well as for polar NH+ 3 -terminated chains (in the series L18B12/+→L18B8/+→L18B4/+). Increasing the number of branched chains (L18B12/0/80 vs. L18B12/0) improves the coating efficiency roughly to the level at earlier branching (compare L18B12/0/80 with L18B4/0). Again, this behavior is similar for the non-polar and the charged chains. Figure 5 summarizes various quantitative informations about the simulated GNPs. The top four graphs analyze the end-to-end distances and measures of heterogeneity of the grafted chains. Let ree (i, t) denote the end-to-end distance of chain i at simulation time t, and let h. . .iT and h. . .iE denote time and ensemble averages, respectively. The average end-toend distance r¯ee (i) of chain i can be calculated as r¯ee (i) = hree (i, t)iT . Similarly, the average 2

2 standard deviation (over time) of the ith chain is given by σee (i) = [hree (i, t)iT −hree (i, t)iT ]1/2

and is related to the dynamic heterogeneity of the individual end-to-end distance. The ensemble average of the individual average end-to-end distances yields the average of the endto-end distance, and the ensemble average of the time-series standard deviations of individual chains in the top row of Fig. 5 as hree i = h¯ ree (i)iT (left) and hσee i = hσee (i)iT (right). The

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The Influence of Chain Length and Branching on the Structure of

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