Atomistic Simulations of Self-Assembled Monolayers on Octahedral

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Atomistic Simulations of Self-Assembled Monolayers on Octahedral and Cubic Gold Nanocrystals Takieddine Djebaili, Johannes Richardi, Stephane Abel, and Massimo Marchi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b05256 • Publication Date (Web): 19 Aug 2015 Downloaded from http://pubs.acs.org on August 25, 2015

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The Journal of Physical Chemistry

Atomistic Simulations of Self-Assembled Monolayers on Octahedral and Cubic Gold Nanocrystals

Takieddine Djebaili1,2, Johannes Richardi1,2, Stéphane Abel3 and Massimo Marchi3 1 Sorbonne Universités, UPMC Univ Paris 06, UMR 8233, MONARIS, F-75005, Paris, France 2 CNRS, UMR, MONARIS, F-75005, Paris, France 3 Commissariat à l’énergie atomique et aux énergies alternatives, Gif-sur-Yvette Cedex, France DSV/iBiTec-S/SB2SM/LBMS & CNRS UMR 9198 4 Institute for Integrative Biology of the Cell (I2BC), CEA, CNRS, Université Paris-Sud, 1 avenue de la terrasse, 91198 Gif-sur-Yvette, France

Abstract This paper reports on a molecular dynamics investigation of the molecular organization of alkanethiolates (from ethane to dodecanethiolate) on octahedral and cubic gold nanocrystals with diameters up to 10 nm. We show that the average surface per adsorbed thiolate only slightly depends on the nanocrystal shape and the alkane chain length. Two different organizations of thiolates are observed on the facet centers and edges of octahedral nanocrystals, while on cubic nanocrystals only one appears. This explains the closer distance between thiolates on the edges of octahedral nanocrystals, which is not observed for nanocubes. The enhanced surface coverage of thiolates on nanocrystals is explained by the new organization for octahedral nanocrystals and can be attributed to the occupation of adsorption sites on the edges for cubic nanocrystals. Small differences observed in the molecular organizations on icosahedral and octahedral nanocrystals can be mainly explained by the larger facets of the latter ones.

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1. Introduction Over the last decade the synthesis of gold nanocrystals (Au NCs) with well-defined shapes has made important progresses1,2. Thus, a whole new family of nanocrystals with various forms has been obtained. E.g. strong reducing conditions using polyol yield singlecrystal and multiply twinned Au nanocrystals enclosed by (111) facets, such as octahedra3, truncated tetrahedra4, icosahedra4,5 or decahedra4. When Ag+ or Br- ions are present during the synthesis, truncated or perfect gold nanocubes enclosed by (100) facets are observed5,6. Under milder reduction conditions, Au nanobelts7 or nanoplates with triangular8 or hexagonal profiles7 are produced. An alternative method is the use of small gold nanocrystals as seeds during the synthesis2. Thus, Au nanorods and nanowires were synthesized. These nanocrystals have a pentagonal cross-section with end surfaces being terminated by (111) facets, while the side surfaces are poorly defined showing (100) or (110) facets9,10. Using specific non spherical nanocrystals as seeds at low concentration, surprising nanostructures may be obtained such as multipods, flower-like structures11, dog bones12 or dumbbells13. The control of nanocrystal shape enables a fine tuning of the electronic, optical and chemical properties of the nanocrystals. This makes non spherical nanocrystals promising candidates for future applications in medicine, catalysis, or sensoring1,2,14. Gold nanocrystals (Au NCs) are often stabilized with organic ligands such as alkanethiolates or phosphines. These ligands form compact monolayers on the nanocrystal surface. These self-assembled monolayers (SAM) have been widely studied on flat gold surfaces in the literature15-20. On Au(111) thiolate headgroups form hexagonal overlayer structures, while on Au(100) a complex distorted hexagonal order denoted by c(2x8) is observed21. Nevertheless, the average surface area occupied per alkanethiolates are very similar on Au(111) and Au(100)15,22,23. DFT calculations and STM experiments24,25 have shown that the sulfur head groups on Au(111) are localized between three gold atoms with a shorter distance to two of the surface atoms. Other studies17,26-33 indicate that surface reconstruction may play an important role during the SAM formation with the presence of vacancies or single adatoms sitting on the flat surface. 2


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Experiment34-40 and simulations41-50 show marked differences between the SAMs on flat surface and nanocrystals. Thus, the average surface per thiolate is about 10 to 20 % smaller for Au NCs35,38,41-43, which means that surface coverage is larger. The transition from an ordered to a disordered SAM is observed at significantly smaller temperatures for NCs41,42. In simulations highly asymmetric arrangements of ligand bundles were attributed to the curvature of the NCs46. Atomistic simulations of gold nanocrystals were mainly focused on nearly spherical particles such as truncated octahedral41,42,44,48, isosahedra43,48,50, or spheres45,46,47,49. To the best of our knowledge gold nanocrystals of nonspherical shapes such as octahedra or cubes have never been simulated before. In a previous paper50, the molecular organization of alkanethiolates on the surface of icosahedral gold NCs has been studied by atomistic molecular dynamics simulations. We have shown that the average surface per thiolate only slowly increases with NC diameter. Thus, even at sizes around 10 nm this average surface is 10 % lower than that on flat surfaces in good agreement with recent experiments51. We have observed a new molecular zig-zag SAM on the edges of the icosahedral facets which explain the reduced surface per thiolate. Here, we will focus on the influence of the NC form on the structure of the thiolate layer. To choose representative forms which will be studied here, we have classified the NC geometries usually obtained in synthesis according to three criteria: the type of facets (111, 100, etc.), the shape of the facets (triangular, rectangular, etc.) and the angles between the facets. The NCs obtained in experiments are often characterized by triangular (111) or rectangular (100) facets. Therefore, we selected octahedral and cubic NCs. On the one hand, octahedral NCs have the same type and form of facets (triangular (111) facets) as the icosahedral NCs previously studied, but with larger facets and larger angles between these facets, thus allowing the investigation of the influence of the size and the angle of the facets. On the other hand, cubic NCs have rectangular (100) facets and right angles between facets. While the simulations of icosahedal or truncated octahedral nanocrystals in the literature were limited to 5 nm41-43, we will here study sizes up to 10 nm for any shape. For very large NCs we expect to observe the same assembly in the facet centers as for planar surfaces. This enables us to understand the transition from SAM observed on NCs to those found on planar surfaces. We have chosen the interaction model proposed by Pool et al.43 because it reproduced many experimental results such as the surface coverage and molecular organization on flat Au(111) and Au(100) surfaces. The use of this simpler model allowed us to carry out the systematic study of very large nanocrystals up to 10 nm which will be difficult to examine 3



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with more complex model. Moreover, to our mind, in future these simple models will be continued to be used where large systems shall be studied and the aim is not a detailed structural information (better obtained by DFT). This is for example the case for the interaction between nanocrystals, where ligand-ligand and ligand-solvent is more important than the S-Au interaction. The paper is organized as follows. In section 2, the interaction model and the simulation method is explained. In section 3, the time evolution of the adsorption of thiolates on the NCs is analyzed. Then, the surface coverage of the NCs is determined and compared to experimental values and our previous results for icosahedral NCs.

The organization of

thiolates is studied in detail, in particular the presence of SAMs typical for Au(111) and Au(100) is analyzed. Finally, the distance between the ligand head groups and the occupation of adsorption sites is investigated.

2. Method 2.1. Interaction model The interactions between the atoms of the coated AuNC are described by a model proposed in the literature43. The S, CH2 and CH3 groups of the alkanethiolates are handled as single interaction sites. A Lennard-Jones (LJ) pair potential is used to represent the repulsive and dispersive interactions between all sites except of those within an alkanethiolate separated by less than two bonds. The LJ interaction is truncated at a cut-off of 12 Å. The intramolecular interactions of the alkanethiolates are described by a sum of bond, bend and torsion energies. The interaction between the gold atoms and the sites of the alkanethiolates is described by the LJ potential proposed by Pool et al.43, in turn derived from a model by Hautman and Klein obtained from quantum chemical calculations52. It is important to mention that the actual nature of the adsorbed molecules as thiol or thiolate radicals has been widely discussed in the literature24,26,53. This question is still open for nanocrystals, while recent experimental and theoretical studies on gold surfaces indicate the presence of thiolate26,53. Here, we use a united atom model, where the hydrogens are not explicitly handled. Therefore, any transformation of thiols to thiolates cannot be taken into account. It is interesting to note that our model yields an adsorption energy for propane thiol molecules in a SAM on Au(111) of around -0.86 eV50. This is actually between the case of the adsorption of a propanethiol (-0.6 eV) and its radical (-1.3 eV) estimated from experiments54. In our previous paper50, we have studied the 4


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influence of the S-Au interaction multiplying or dividing the attraction by a certain factor. We found that even when the attraction is increased by a factor 2, the results do not change within the statistical accuracy of our method. Therefore, we expect our results to be reliable even in the case of a transformation from thiol to thiolates on the NCs. In the following we will usually speak of thiolates, which does not exclude the presence of thiols on the nanocrystals. We have tested two other interaction models proposed in the literature19,41. The models by Pool et al.43 yields the best average surface per thiol for Au(100) and Au(111) surfaces in comparison to experimental values. This model also correctly reproduces the decrease of the average surface per thiol for nanocrystals in good agreement with experiments, while other models fail to do so19. The ratio between the number of adsorbed thiols and gold surface atoms as a function of the nanocrystal size is in good agreement with the model proposed by Olmos-Asar et al.48. Models recently proposed57 better describe the structure of small gold clusters in comparison with DFT calculations. Future simulations would be interesting to study their behaviour for larger nanocrystals in comparison to our simualtions. The Au NCs are described as perfect octahedra or cubes ignoring the presence of defects, adatoms and vacancies. To reduce the computation time, the NC is handled as rigid, fixing the relative positions of the gold atoms. Experimental and theoretical studies show that surface restructuration26,32 may play an important role in the formation of SAMs on gold surfaces. However, very recent simulations taking into account surface reconstruction indicate that the vacancies and adatoms form large islands and only slightly perturb the hexagonal SAM on Au(111)19.

2.2. Simulation method Molecular dynamics (MD) simulations are carried out using the GROMACS 4.5.5 MD package55 allowing massively parallel calculations. The use of up to 120 processors enables us to study NC diameters until 10 nm. As previously our in-house simulation code NATAMOS was employed to set up the system, carry out short test simulations and analyze the trajectories50. In the beginning of the simulations, the bare Au NC is put in the center of the simulation box. Then, the NC is surrounded by an excess of thiolates calculated from the average surface per thiolate typically observed for Au NCs (around 16 Å2). Simulations were carried out at various excess thiolate concentrations and it was observed that the simulation results are the same within the statistical accuracy of the method. A time step of 1 fs is used 5



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and the temperature is kept constant at 300 K with the Nose-Hoover thermostat (time constant: 0.4 ps). 3. Results and Discussion In the following, we will present a comparison between the results of atomistic simulations for cubic and octahedral gold NCs. We have studied the adsorption of butanethiolate (denoted with C4 in the Figures), octanethiolate (C8) and dodecanethiolate (C12) for NCs between 1 and 10 nm. To compare the different NC geometries, the radii of the octahedral, icosahedral and cubic NCs are defined as the square root of the average square distances between the center and the surface atoms including one van der Waals radius of gold (1.66 Å). For this paper, we have carried out additional simulations for icosahedral NCs in particular at some NC diameters not investigated in our previous paper50. The results are in good agreement with the ones already published50. We only discuss the results when they are markedly different from those obtained for octahedral NCs. The figures for the iosahedral NCs can be found in the supporting information. Tables S1 - S3 give the simulation parameters of the studied systems and the tables S4 – S6 give the detailed results of the simulations (see supporting information). 3.1 Time evolution of the adsorption of thiolates on the NCs The snapshot in Figure 1 shows typical configurations obtained at the end of simulation for octahedral and cubic NCs of about 10 nm coated with butanethiolate. To determine the simulation length necessary to obtain a well converged structure, the number of adsorbed thiolate molecules on the surface of 7 nm NCs is plotted as a function of the simulation time, for different alkanethiolates and NC forms in Figure 2. Similar results were obtained for other NC sizes except very small NCs (< 4 nm) which usually converge more rapidly. It should be noted that the presence of an excess of non-adsorbed thiolate molecules has been checked after each simulation run. We find that the time evolution of the adsorption of thiolate molecules on the surfaces of gold NCs depends on the length of the adsorbed thiolates. Figure 2 shows the two phases of the adsorption process: a rapid phase when a large number of thiolate molecules adsorb on the NC surface, is followed by a slower reorganization phase. During this phase, the optimization of the molecular organization of the adsorbed thiolate molecules on the NC facets takes place ensuring a gradual increase of their adsorption. The adsorption process is usually finished after 50 ns with the exception of

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dodecanethiolate on cubic NCs. Therefore, we have continued the simulation up to 600 ns (see Figure S1 in supporting information) and found that the number of adsorbed dodecanethiolates still increases by 3 % between 100 and 600 ns for cubic NCs (Figure S1A). In our previous paper we have already found that the adsorption of hexadecanethiolate (Figure S1B) is even slower which was here confirmed for cubic NCs (Figure S1A). The formation of bundles41,42,46, observed for thiolates with long alkyl chains, may explain this slower adsorption. Because of this convergence problem, we have excluded the hexadecanethiolate from our study. Moreover, we continued our simulations of the adsorption of octanethiolate and dodecanethiolate up to 600 ns for the cubic NCs of any size, while the simulation time for octahedral and icosahedral NC is at least 90 ns. Nevertheless, we assume that the accuracy of the results obtained for dodecanethiolate for cubic NCs is limited to about 3%. For any system, we have controlled that the number of adsorbed thiolates and all derived properties are stabilized within 2 %. In particular, transitions of head groups from one adsorption site to another are very rare events but we have checked that they occur several times during our simulations.

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Figure 1. Snapshot of the final configuration obtained for an octahedral (a) and cubic (b) NC coated with butanethiolate. The diameters are 10.2 and 9.8 nm for the octahedron and the cube, respectively. The thiolate head groups are in yellow, whereas the CH2 and CH3 groups are in grey.

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Figure 2. Time evolution of the number of adsorbed thiolate molecules for different alkane chain lengths for NCs: (a) octahedron of 7.0 nm, (b) cube of 7.2 nm.

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3.2 Determination of the surface area per adsorbed thiolate Figure 3 shows the evolution of the average surface area per adsorbed thiolate as a function of the NC diameter, for different alkanethiolates on cubic and octahedral NCs. The NC surface accessible to the thiolate molecule is estimated from the usual formula for cubes (6 L2), octahedra (8 √3/4 L2) and icosahedra (20 √3/4 L2). The lengths L of the facet edges are obtained by the construction of cubes, octahedra or icosahedra made of S groups on the vertices which envelop the NC with the corresponding form (see detailed discussion in our previous paper). The distance between the S groups and the closest gold atoms on the vertices of the NC is fixed at the equilibrium S-Au distance (6√2σS,Au=2.97 Å). A geometrical analysis yields the following general equation for the length of the facet edges: L = dAuAu (nAu -1) + d, where nAu is the number of gold atoms on the NC edge. dAuAu is the distance between two neighboring gold atoms (2.88 Å) and d depends on the NC geometry (2.97 Å, 4.20 Å and 3.13 Å for cubes, octahedra and icosahedra, respectively). Please note that the additional parameter d is due to the fact that the enveloping form is slightly larger than the NC due to the distance between S and Au atoms. For the cubic NCs (Figure 3b), despite a different molecular organization of alkanethiols, the area per thiolate is close to those observed for octahedral (Figure 3a) and icosahedral NCs (Figure S2 in supporting information). For the cubic and octahedral NCs of a size larger than 2 nm, the area per thiolate slightly increases with the NC size, unlike the icosahedral NCs for which the area per thiolate is constant. Even considering the error of the simulation results of about 2 %, the values of the area per thiolate for C4 are always significantly lower than the values 21.4 Å2 / thiolate and 20.6 Å2 / thiolate experimentally observed for Au(111) and Au(100) flat surfaces, respectively22,56. To check that the used method correctly reproduces the experimental surface per thiolate on Au(111) and Au(100), we have carried out simulation of the thiolate adsorption on these surfaces. The area per thiolate are 21.2 ± 0.6 Å2 and 21.0 ± 0.6 Å2 for Au(111) and Au(100) in good agreement with the experimental values. Let us now study the influence of the alkyl chain length on the surface per thiol. For octahedral NCs, we observed that the surface per thiolate for octanethiolate and dodecanethiolate molecules is lower than that of butanethiolate (Figure 3a), in agreement with the results previously obtained for icosahedral NCs (Figure S2). The increase of the number of adsorbed thiolate with the alkyl chain length may be explained by more favorable van-der Waals attractions. For cubic NCs, the surface per thiolate for octanethiolate is also lower than that of butanethiolate (Figure 3b), while it is higher for dodecanethiolate. Please note that this 10


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may be partly due to a slow adsorption process for long thiolates as discussed above (see Figures 2b and S1a). In our previous study50, the average surface per thiolate obtained for icosahedral NCs was shown to be in good agreement with experimental data obtained by elemental analysis using electronic microscopy, thermogravimetry or mass spectrometry35,38,51. The shape of the Au NCs used in the experimental studies was usually not well defined and the particle surface is presumably made of (111), (100) and other facets. Our simulations indicate that the presence of (100) facets will not markedly influence the average surface per thiolates. This explains the good agreement between experimental and theoretical results previously observed even when icosahedral particles with only Au(111) surface were used in the simulations.

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Figure 3. Average surface area per adsorbed thiolate as a function of the NC diameter for octahedral (a) and cubic (b) NCs. The NC surface is described as an octahedron or cube (see main text for details).

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3.3. Molecular organizations of thiolate headgroups In the same way as for the icosahedral NCs in the previous paper50, we studied several snapshots of the facets of octahedral and cubic NCs during the simulation in order to better understand their occupation by thiolates. Figure 4 shows the positions of the thiolate head groups marked as small circles of different colors obtained at the end of simulation. Headgroups with the same color belong to the same assembly which will be defined below. The octahedral NCs feature two different molecular organizations (Figure 4a) in good agreement with the results observed for the icosahedral NCs50. The head groups mainly occupy the 3-fold hollow adsorption sites (see sketch in Figure 4a). In the facet centers the hexagonal SAM typically observed on Au(111) is found, while on the edges the new zig-zag arrangement appears. In contrast, this difference is absent for the cubic NCs (Figure 4B). In fact, we have observed only one type of molecular organization of the adsorbed thiolate molecules on the cubic NCs. The assembly of thiolate headgroups is made of stripes with two or three lines. Within the stripes a simple square organization is observed, where the head groups occupy the 4f hollow sites. The stripes are separated by two lines of the grid of gold atoms. We turned the sketch in Figure 4b by 45° (Figure 5a) to compare this organization with the SAM derived from diffraction (Figure 5b). Figure 5b shows the c(2x8) top structure for the surface methyl groups proposed from helium X-ray diffraction data22. The nearestneigbour distance of 4.7 Å obtained for this structure is in good agreement with other experimental data58. It is also made of stripes with three lines starting with a first one with the head groups on top position due to a restructuration of the surface. A comparison between the assemblies observed in our simulations and the experiments shows that within a stripe the same horizontal distance between the groups is observed. However, in vertical direction, the distance between the lines is slightly contracted with a preference of the hollow sites. This high preference of sites with 4 contacts between S and Au atoms may be an artifact of the additional LJ potential chosen for the S-Au potential. Another difference with the experiment is that in the simulations the separation lines between the stripes do not follow the horizontal or vertical directions of the Au(100) grid but evolve in an angle of 45°. This may be partly due to the presence of edges of the NCs, which may induce this direction. Thus, in a simulation of the planar Au(100) surface we observed a mixture of separation lines which evolve along the grid (0°) (such as in Figure 5B) and in 45°. We can conclude that our model partly reproduces the SAM derived from experiments.

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Figure 4. Snapshots of 10 nm NCs facets, taken at the end of the simulation. (a) octahedral NC. (b) cubic NC. The Au atoms on the edges of the NCs are shown with a grey color. The S groups belonging to the same SAM are represented by the same color.

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Figure 5. Self-assembled monolayers on Au(100) and cubic NCs. The large golden cercles show the position of the gold atoms. The smaller circles indicate the position of the thiolate head groups. Different colors are used to distinguish the stripes. The structures obtained by simulations (a) are compared to those proposed from helium atom and X-ray diffraction data22 (b). To quantify the observations made above on assemblies, we have calculated the percentage of adsorbed thiolate molecules participating in the formation of a typical SAM of at least 3 members. For octahedral and icosahedral NCs we have searched for the hexagonal SAM observed on flat Au(111). For cubic NCs, we tried to detect thiolates belonging to the same stripe, where the headgroups occupy hollow sites forming a square SAM. In order to detect these SAMs, we used the percolation method explained in our previous paper50. Briefly, we calculate the distances of a headgroup randomly chosen with its neighbors on the same facet. The neighbors are counted as members of the same SAM when its distances to the other headgroups correspond to those usually found for the hexagonal or cubic subsets of SAMs within 10%. Then, the neighbors of the new members are analyzed in the same way. The analysis is continued with a new S group belonging to no SAM previously detected. For the SAMs on cubic NCs, the distances of the first and second neighbors are given by √2 dAuAu and 2 dAuAu, respectively, where dAuAu =2.88 Å. For the octohedral and icosahedral NCs, the distance criteria from our previous paper are used. The results of the SAM analysis are shown in Figure 6. We distinguish between the thiolates on the center and edges of the facets. A thiolate is counted for the edge when its headgroup is closer to a hollow adsorption site in contact with a gold atom on the edge (colored in grey in Fig. 4) than to any site of the facet centre. In agreement with the results found for icosahedral NCs, 90% of the adsorbed thiolates

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in the facet center of octahedral NCs (larger than 3 nm) take part in a SAM, against only 70% of the adsorbed thiolates on the edges. This low value is explained by the formation of the zigzag organization observed in Figure 3A. In Figure S3b and S4 the frequency of zigzag organizations on the facet edges is quantified using the percolation method explained above. It shows the presence of zig-zag organization at any particle size. Figure 6b indicates the presence of only one type of SAM on the edges and in the center of the NCs facets. Thus, the quasi-totality of the adsorbed thiolate molecules participates in the formation of stripes with square organization. Unlike the icosahedral NCs (see Figure S3a in supporting information), for which the percentage of adsorbed thiolate molecules participating in SAMs continues to increase gradually with the diameter of the NCs, the percentages of the SAMs are almost constant for the octahedral NCs and cubic NCs larger than 3 and 2 nm, respectively. This can be explained by the larger facets of these NCs compared to the icosahedral ones. This interpretation is supported by Figure S5 (supporting information), which show that the SAM frequencies for icosahedral and octahedral NCs are in good agreement when they are plotted as a function of the facet length. The preceding observations concerning the molecular organizations of ligands will explain the results for the average distances between the neighboring S groups (S-S) on the edges and in the centers of the NC facets (Figure 7 for octahedral and cubic NCs, Figure S6 for icosahedral NCs). Two S groups are taken as neighbors when their distance is smaller than 1.1

, where the Lennard-Jones parameter

is equal to 4.45 Å. On the one hand,

Figure 7a shows that the values of S-S distances differ between the centers and the edges of octahedral NCs by more than 0.1 Å. This has already been observed for icosahedral NCs in our previous paper (see Figure S6) and can be explained by the two different molecular organizations, more compact on the edges in comparison to the center of the facets. On the other hand, Figure 7b shows that the average distance S-S on the edges is the same as the one found in the center of cubic NC facets, thus confirming the presence of a single molecular organization. This latter is much more compact than the molecular organizations of octahedral and icosahedral NCs. It can be also noted that the S-S distance does not markedly depend on the alkyl chain length of the thiolates for the octahedral and cubic NCs.

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Figure 6. Frequencies of S groups participating in the formation of a SAM of at least 3 members for octahedral (a) and cubic (b) nanocrystals. The upper red curves in each figure correspond to the facet center, while the lower blue ones show the results for the edges.

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Figure 7. Average distances between the neighboring S groups on the edge and in the center of the NC facets. Panels (a) and (b) show the results for octahedral and cubic NCs, respectively, for the different alkanethiolates.

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3.4. Preferred adsorption sites and their occupation In our atomistic simulations on flat gold surfaces we observed that the preferred adsorption sites are 3-fold hollow and 4-fold hollow sites for the Au(111) and Au(100), respectively. The study of the snapshots in Figure 4a confirms that the 3f-hollow sites are favored for the octahedral NCs. For cubic NCs the 4f-hollow sites are preferred in the facet centers, whereas on the edges the S groups also occupy sites made of three gold atoms. We have calculated the frequency of occupation of the adsorption sites, where the S groups are in contact with one, two, three or four gold atoms, denoted as on-top, bridge, 3f-hollow (or edge for the cubic NCs) and 4f-hollow, respectively. To calculate the occupation frequency of the adsorption sites, the same distance criterion was used as in section 4.1. The results in Figure 8a show that for octahedral NCs, the frequency of occupation of hollow sites slightly increases with the NC size, to reach 60 %, a value close to the 65 % found in the case of icosahedral NCs (Figure S7). We also found a high frequency of occupation of bridge sites, which decreases with the NC size to reach 35 %. An investigation of snapshots has shown that this is due to the asymmetrical positions of these head groups close to a hollow site with a shorter distance with two of the three gold atoms. It is interesting to note that DFT calculations and STM experiments24,25 have shown that the geometry of adsorption is actually well described by such a shifted bridge position. The occupation frequency of the cubic NCs shown in Figure 8b is quite different compared to the octahedral particles. While the occupation frequencies are nearly constant for octahedral NC larger than 2 nm, they markedly change even for large cubic NCs. The occupation frequency of 4f-hollow sites slowly increases up to 85 %, while the occupation of the edge sites decreases with NC size from 35 % for small NCs to 10 % for larger ones. This is explained by the fact that the proportion of adsorption sites found on the edges of the facets is substantially higher for small NCs and only slowly decreases with NC size.

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Figure 8. Occupation frequencies of the different adsorption sites for octahedral (a) and cubic (b) NCs and different alkanethiolates.

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3.5. Ratio between the numbers of adsorption sites and adsorbed thiols In the previous two sections, the molecular organization and occupation of adsorption sites was analyzed in detail. This information will be very useful to understand the ratios Rst between the numbers of adsorption sites and adsorbed thiolates shown in Figure 9 (and S8 for the icosahedral NCs). The results are given distinguishing the adsorbed thiolates on the edges and in the centers of the NC facets. We only take into account 3f- and 4f-hollow sites for octahedral/icosahedral and cubic NCs, respectively. Figure 9 shows that Rst is nearly constant for the octahedral and cubic NCs larger than 2 nm, both for the centers and the edges of the NCs facets. This does not apply to the centers of icosahedral NC facets, for which this ratio only begins to stabilize for NCs larger than 6 nm. This may be explained by the smaller size of facets in comparison to octahedral and cubic facets as discussed in section 3.3. The influence of the length of thiolates can be usually neglected for the values of Rst. Figure 9a shows that for octahedral NCs of large size, the ratio Rst in the facet centers reaches values around 5.4, which is close to the value of 6 typically found for the SAMs adsorbed on Au(111). The ratio Rst on the edges is around 2.9 for octahedral NCs, which is typical for the zigzag organization of the thiolate head groups50. This value is lower than the ratio of 3.2 found for the edges of icosahedral NCs. This corresponds to a higher adsorption of thiolate molecules on the edges of the octahedral NCs, which may be explained by the larger angles between the octahedron facets compared to icosahedra. For cubic NCs, Figure 9b gives a ratio close to 2.3 in the facet centers, which can be explained by the formation of stripes shown in Figure 5a. Thus, in the first two rows of a stripe the ratio between adsorption sites and adsorbed thiolate is 2 to 1, while it is 3 to 1 for the third row due to the presence of voids between the stripes. This leads to a total ratio of (2+2+3)/3 ≈ 2.3 in good agreement with our results. A ratio close to 1.0 is found on the edges which is explained by the fact that half of the 4f-hollow and half of the edge sites are occupied (see Figure 4b). Since only the hollow sites are counted and the number of hollow and edge sites is very close, this leads to a total ratio of 1.

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Figure 9. Ratio between the number of adsorption sites and adsorbed thiolates for octahedral (a) and cubic (b) NCs and different alkanethiolates.

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IV.3 Conclusion We have studied the influence of the form of gold NCs on the organization of thiolates molecules on their surface. For cubic NCs, our simulations converge more slowly compared to octahedral and icosahedral NCs, especially for long alkyl chains. We have observed that the average area occupied per adsorbed thiolate depends little on the NC form. It slightly increases with the NC size for cubic and octahedral NCs, whereas it is virtually constant for icosahedral NCs. Nevertheless, the coverage of the surface of the three NCs remains more important compared to that of flat Au surfaces in quantitative agreement with experiments. The fact that, whatever the form of the NC, the ratio between the number of adsorption sites and adsorbed thiolates is lower on the edges compared to the center of the NC facets explains the higher surface coverage. We show that it is related to a different molecular organization on the edges of octahedral and icosahedral NCs and to the occupation of specific edge sites for cubic NCs. Thus, the analysis of the organization of the thiolates has shown the presence of two different molecular organizations on the edges and in the center of octahedral and icosahedral NCs facets. In contrast, a single molecular organization is observed for cubic NCs. This explains why the differences between the distances S-S on the facet edges and centers are only observed in the case of octahedral and icosahedral NCs, while it is absent for cubic NCs. The molecular organization on cubic NCs is made of stripes of two or three lines of S atoms. In comparison to experiments, the thiolate stripes have a different direction with respect to those on the Au(100) grid. Even if the results observed for octahedral and icosahedral NCs which share the same type of facets (111) are relatively similar, we observed differences in the molecular organizations of these two NC types, in particular when the size of the NCs is less than 6 nm. These results can be mainly explained by the fact that the icosahedra have smaller facets compared to octahedra for the same NC size. We would like to emphasize the very important role of the edges of the NCs facets in the adsorption of thiolate molecules, both for the NCs with (111) and (100) facets. Without a doubt, the doubling of the number of adsorbed thiolates on the edges as compared to that of adsorbed thiolates at the facet centers mainly leads to the higher surface coverage of NCs compared to Au flat surfaces. Interestingly, the origin of the higher number of thiolate on the edges is quite different for both types of facets. For (111) facets it is related to a new zigzag organization of the thiols, while for (100) facets it is due to the occupation of new adsorption sites on the edges.

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Nanocubes are usually coated by other ligands than thiols which limits a direct comparision between theory and experiment. However, many nanocrystals coated by thiols are made of (100) and (111) facets59. The simulations here have shown that the molecular organizations are only slightly influenced by those on neighboring facets. Therefore, the results obtained here for (111) and (100) facets should apply also to nanocrystals made of both types of facets. To conclude, the aim of this preliminary study was to understand possible differences in the molecular organization of ligands on large metallic nanocrystals with various shapes. Future studies will also consider the effects of polarization and surface restructuration on the self-assembled monolayers on nanocrystals. Supporting Information Tables S1−S6 gives the parameters and results for the simulations carried out for this study. Figures S1−S8 show additional results discussed in the paper. This material is available free of charge via the Internet at http://pubs.acs.org. Acknowledgements This work was performed using HPC resources from GENCI-CINES/IDRIS (Grant 2013x2013086946, 2014-x2014086946) and the CCRE-DSI of Université P. M. Curie. REFERENCES 1. Xia, Y.; Xiong, Y.; Lim, B.; Skrabalak S. E. Shape-Controlled Synthesis of Metal Nanocrystals: Simple Chemistry Meets Complex Physics? Angew. Chem. Int. Ed. 2009, 48, 60-103. 2. Murphy, C. J.; San, T. K.; Gole, A. M.; Orendorff, C. J.; Gao, J. X.; Gou, L.; Hunyadi, S. E.; Li, T.C. Anisotropic metal nanoparticles: Synthesis, assembly, and optical applications. J. Phys. Chem. B 2005, 109, 13857-13870. 3. Li, C.; Shuford, K. L.; Park, Q.-H.; Cai, W.; Li, Y.; Lee, E. J.; Cho, S. O. High-Yield Synthesis of Single-Crystalline Gold Nano-Octahedra. Angew. Chem. 2007, 119, 3328–3332. 4. Seo, D.; Yoo, C. I.; Chung, I. S.; Park, S. M.; Ryu, S.; Song, H. Shape Adjustment between Multiply Twinned and Single-Crystalline Polyhedral Gold Nanocrystals:   Decahedra, Icosahedra, and Truncated Tetrahedra. J. Phys. Chem. C 2008, 112, 2469– 24


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a

b

Figure 1 ACS Paragon Plus Environment


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Au(111)

b Au(100)



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Hexagonal SAM

Zigzag SAM

b

4f-‐hollow site

edge site


Square SAM

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bridge

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Atomistic Simulations of Self-Assembled Monolayers on Octahedral

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