Nanoparticle dynamics

DOI: 10.1002/smll.200600456

Dynamics of Thiolate Chains on a GoldNanoparticle**

Stefania Rapino and Francesco Zerbetto*

An important difference between the surfaces of bulk mate-rials and nanoparticles is the percentage of surface atoms.In a gold nanoparticle �2 nm in diameter more than 50%of the atoms are on the surface. The surface chemical func-tionalization can both stabilize the particle and avoid aggre-gation. If the molecules at the surface are properly termi-nated, they can modulate the chemical, electronic, and pho-tochemical properties of the particle. Here, molecular-dy-namics simulations of Au309ACHTUNGTRENNUNG(SC6H13)80 show that the thio-lates located at the edge of the antipodal face of the goldnanoparticle are more accessible from the outside. The be-havior is compared with experimental data and explained insimple terms.

In one of the most investigated types of nanoparticle,thiolates form a protective layer and their terminal atomsare often connected to electro- or photoactive groups. Fullsurface coverage of a metal surface with linear thiolatesranges from 33% of the gold atoms for a perfectly planarAuACHTUNGTRENNUNG(111) surface up to a maximum of 60% for particles ofthe size studied here and even up to 70% for smaller parti-cles such as Au25.

[1] To achieve the best packing interactions,the ligands are tilted by at least 20–30 degrees with respectto the metal surface. A variety of experimental techniquesallows the study of the coverage of the particles. These tech-niques can be of spectroscopic nature, such as IR and NMRspectroscopy, belong to the family of scanning probe micro-scopy, or involve chemical reactivity.[2] Molecular-dynamicssimulations can also provide insight about the structure anddynamics that take place at the surface, in consideration ofthe roles played by the length of the thiolate chains and bytheir dynamics, roles that are now becoming apparent. Forinstance, nanoparticles easily exchange thiolates with solu-tions,[2–7] and the kinetics of the reactions vary as a functionof the conditions and the timescale of the experimentalmethods used for assessment.[2–7]

Here we examine the thiolate dynamics on a nanoparti-cle with a model that we have found useful to describe andexplain Au–organic interactions. The thiolate chains are de-scribed by a standard force field.[8] The gold particle is de-

scribed by an embedded-atom model called the “gluemodel”.[9] The metal–organic interactions are the sum oflong-distance and short-distance terms. The former are Cou-lomb interactions, with charges calculated by the charge-equilibration (QEq) scheme of Rappe and Goddard,[10]

while the latter are described by the short-rangeBorn–Mayer potential, which tunes the long-distance terms,accounts for higher-order terms, and avoids nuclear fusionwhen charges interact attractively. Some examples wherethis model has been applied are 1) the adsorption of alkanesand 1-alkenes on AuACHTUNGTRENNUNG(111),[11] where the adsorption energiesof short chains, up to C10, were reproduced with an averageerror of less than 1 kcalmol�1 and the unexpected transitionto disorder occurring for the deACHTUNGTRENNUNGposition of alkyl chains be-tween 18 and 26 carbon atoms in length was explained,2) the apparent symmetry breaking of a macrocyle on theAu surface,[12] 3) the substitution kinetics of thiolates onself-assembled monolayers,[13] 4) the existence of two surfacereconstructions for C60 adsorbed on Au ACHTUNGTRENNUNG(110),[14] and 5) themobility of DNA bases on Au ACHTUNGTRENNUNG(111).[15]

Although not ab initio, the present model does not pre-define the gold–organic connectivity, and molecules are, inprinciple, able to slide on the surface. This phenomenonhardly occurs in the present work and is not relevant to thechain dynamics. In the calculations, after an initial equilibra-tion of 20 ps at 298 K, the atomic charges were frozen; an-other 40 ps were used for further equilibration, while theproduction run was extended for 900 ps. The timestep was0.5 fs. No attempt was made to add solvents or include in-teractions with other particles.

We consider an average-sized particle of 309 Au atomswhose shape is a cube octahedron with a diameter of�2.3 nm. Magic numbers for nuclearities of 13, 55, 147, 309,561, 923, and 1415 are known and correspond to completefilling, in a close-packed arrangement, of 1–7 coordinationshells around a central atom. Au309 has 8 surface planes akinto AuACHTUNGTRENNUNG(111) and 6 surface planes akin to Au ACHTUNGTRENNUNG(100). The sur-face was covered in the most symmetric way with 80 SC6H13

chains (out of 162 surface atoms). The initial 32 thiolateswere positioned in the hexagonal-close-packed (hcp) sites ofthe (111) planes (Figure 1), while the subsequent 48 chainswere positioned in the fourfold symmetric hollow site of thec ACHTUNGTRENNUNG(2A2) structures of the (100) planes (Figure 1). In detail:

1) The threefold, hcp sites of the pseudo Au ACHTUNGTRENNUNG(111) surfacesare energetically slightly less favorable than the face-centered-cubic (fcc) sites,[16] but the choice of these sitesresults in a denser surface coverage with four thiolatesfor each (111) face, instead of the two allowed by the fccoccupancy.

2) The centers of the c ACHTUNGTRENNUNG(2A2) superstructures, or pseudo Au-ACHTUNGTRENNUNG(100) faces, give a distance between sulfur atoms of�4.07 C. This superstructure was observed for methyl-thiolates on bulk Au ACHTUNGTRENNUNG(100) surfaces. Further experimentaldata indicates that even for longer alkane chains thec ACHTUNGTRENNUNG(2A2) structure is not completely lost.[17]

[*] S. Rapino, F. ZerbettoDipartimento di Chimica “G. Ciamician”Universit� di BolognaVia F. Selmi 2, 40126 Bologna, ItalyFax: (+39)051-209-9456E-mail: francesco.zerbetto@unibo.it

[**] We would like to thank Professor Francesco Stellacci for usefulcomments. Partial support from the EU is gratefully acknowl-edged.

386 < 2007 Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim small 2007, 3, No. 3, 386 – 388

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The geometrical result ofthe decoration is illustratedin Figure 1, where, for sim-plicity, only the sulfur atomof each thiolate chain isshown.

The molecular dynamicsof the chains were analyzedwith the intent of identifyingthe less crowded terminalatoms. This situation shouldfavor reactivity of the topatom of a chain, if it is prop-erly functionalized. In prac-tice, we sought 1) the ligandswhose terminal (methyl)groups were furthest awayfrom their four closest neigh-bors, and 2) the ligandswhose chains were more per-pendicular from the core sur-face. This is qualitatively il-lustrated in the cartoons of

Figure 2, where, in particular, the room available around thetop atoms is given by the average of the squares of the fourshortest Cmethyl�Cmethyl distances.

Figure 3 shows the largest value in the cluster of theaverages of the squares of the distances as a function oftime. It also gives the number of picoseconds during whicheach of the 80 chains is the most isolated from the othersduring �1 ns of dynamics. If the system had the most sym-metric configuration, only 5 types of atoms/distances wouldbe present, with relative populations of 8:24:12:24:12. How-ever, in the timescale of �1 ns, a handful of ligands aremore “separate” from the others.

Figure 3 also shows the dynamics of the chains thatextend more linearly from the nanoparticle surface as afunction of time and gives the number of picosecondsduring which each of the 80 terminal Cmethyl atoms is themost perpendicular and straight with respect to the goldshell. If the system had the most symmetric configuration,

Figure 1. a) The threefold hollow site of thep3�

p3R308 structure of

the (111) planes; b) the most symmetric decoration of Au309; sulfuratoms are depicted in gray and the point of view shows the decora-tion of the (111) triangular planes; c) the fourfold symmetric hollowsite of the cACHTUNGTRENNUNG(2�2) structure of the (100) planes; d) the most symmet-ric decoration of Au309; sulfur atoms are depicted in gray and thepoint of view shows the decora-tion of the (100) square planes.

Figure 2. Cartoons illustrating how terminal chain atoms becomemore available to the external environment. Left: increase of the“horizontal” distance from the neighbors. Right: increase of theheight from the particle surface.

Figure 3. a) The largest separation found between terminal carbon atoms; b) the number of picosecondsfor which each ligand is the most separate from the others; c) Au309 ACHTUNGTRENNUNG(SC6H13)80; the alkyl chains are notshown, while dark gray spheres represent the sulfur atoms of the chains whose terminal carbon atom isless crowded during 900 ps of simulation; d) the greatest height from the Au surface found for the termi-nal carbon atoms; e) the number of picoseconds for which each chain extends most linearly during900 ps of simulation; f) Au309 ACHTUNGTRENNUNG(SC6H13)80; the alkyl chains are not shown, while dark gray spheres repre-sent the sulfur atoms of the chains whose terminal carbon atom extends most linearly.

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only five types of atoms/distances would emerge. However,on the timescale of approximately 1 ns, a handful of ligandsare taller than the others.

For both mechanisms, the sulfur atoms of the ligandsthat become more accessible from the outside are shown onthe right-hand side of Figure 3. Generally, the more exposedchains are at the antipodal edges of the (111) surfaces. Illus-trative snapshots of the dynamics are shown in Figure 4.

Some issues must be addressed, namely, 1) the length ofthe simulation and its physical meaning, 2) the physicalreason for the breakdown of symmetry that singles outsome chains as more accessible, and 3) the possible conse-quences of the symmetry breakdown.

1) Analysis of the distances of all the carbon atoms fromthe metal surface shows the presence of s-cis conformationsin about one third of the chains. Experimentally, it has beendetermined[3] that the average distance from the Au surfaceof the fifth and sixth carbon atoms of the thiolate chains are6.35 and 7.35 C, respectively. These values agree well withthe present average distances, over slightly less than a nano-second of dynamics, of 6.54 and 7.40 C. It appears that thetimescale of the simulation captures the dynamics of the thi-olates.

2) It is known that one cannot comb the hair on a ballsmoothly so that there is no bald spot. The reason is thesame as the one for why it is not possible to cover a spherewith square magnets so that they do not repel each othersomewhere and is formally expressed by the so-called“hairy-ball theorem”.[18] This theorem of algebraic topologystates, in laymanEs terms, that “one cannot comb the hair ona ball in a smooth manner”. To understand it, one can pic-ture the hairs on a sphere: any attempt to make them math-ematically “smooth” will leave a spot where two hairs pointin “drastically” different directions.

In practice, as soon as the thiolate chains tilt to maxi-mize their mutual interactions, the effects of the theoremkick in and there must be (at least) one chain that standsapart from the others. In time, each chain/hair may play thisrole, but the present simulations show that the chain(s) thatstand(s) apart is/are the same for at least one nanosecond.

3) The existence of terminal atoms more accessible fromthe external environment suggests that, properly functional-ized, they could react more easily and the decoration of thenanoparticle should therefore occur at its antipodes. Themore accessible thiolates could also be involved in the fastexchange dynamics of ligands.[4]

In conclusion, study of the molecular dynamics of thethiolates of a gold nanoparticle shows that during �1 ns ofsimulation some ligands stay apart from the others, eitherbecause they are more separate or because they extendmore linearly. The existence of these special chains is due tothe impossibility of “combing” them smoothly on the nano-particle. These ligands are located in the proximity of theedges of the faces of Au308 and that is where the ligand ex-change with the solution is thought to take place.[4]

Keywords:gold · molecular dynamics · nanoparticles ·self-assembled monolayers

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Received: August 29, 2006Published online on February 5, 2007

Figure 4. Schematic representation of the molecular-dynamics simu-lations. The red thiolate represents the least crowded (left) and themost linearly extended (right) thiolate.

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