Nanoscale surface chemistry directs the tunable assembly of silver octahedra into three two-dimensional plasmonic superlattices

A major challenge in nanoparticle self-assembly is programming the large-area organization of a single type of anisotropic nanoparticle into distinct superlattices with tunable packing efficiencies. Here we utilize nanoscale surface chemistry to direct the self-assembly of silver octahedra into three distinct two-dimensional plasmonic superlattices at a liquid/liquid interface. Systematically tuning the surface wettability of silver octahedra leads to a continuous superlattice structural evolution, from close-packed to progressively open structures. Notably, silver octahedra standing on vertices arranged in a square lattice is observed using hydrophobic particles. Simulations reveal that this structural evolution arises from competing interfacial forces between the particles and both liquid phases. Structure-to-function characterizations reveal that the standing octahedra array generates plasmonic ‘hotstrips', leading to nearly 10-fold more efficient surface-enhanced Raman scattering compared with the other more densely packed configurations. The ability to assemble these superlattices on the wafer scale over various platforms further widens their potential applications.


Supplementary Figure 3 | Order analyses of the superlattices.
Voronoi-Delaunay cells for the hexagonal close-packed monolayer formed using PVP (a), the open hexagonal monolayer formed using C3SH (b), and the square lattice of standing octahedra formed using C16SH (c). The three 2D superlattices of Ag octahedra exhibit long-range order. In addition to mapping the radial distribution functions (Fig. 1e, i, m), the Voronoi cells and Delaunay triangulation of the assembled 2D superlattices are also defined. Both the hexagonal close-packed and open hexagonal octahedra monolayer gives rise to a honeycomb network of hexagonal Voronoi cells (blue lines) whereas the Voronoi cells of the square lattice of standing octahedra corresponds to a network of squares (Fig. S6c). Complementary Delaunay triangulation is also observed for the three superlattices (green lines). The overall potential energy (a,c,e) in all cases decreases to reach a more thermodynamically stable state. A decrease in interfacial energy (b,d,f) is observed for PVP, while an increase is observed for C3SH and C16SH. This increase in interfacial energy arises from the particle moving into the oil phase completely.

Supplementary Figure 8 | Topological characterization of the heights of variously functionalized
Ag octahedra remaining in the aqueous phase. The height of the exposed Ag octahedra on the PDMS surface correspond to their heights and orientations in the aqueous phase because the PDMS mold itself replaces the oil phase during the lift-off process. PVP-and C3-octahedra are both planar with the triangular facet parallel to the oil/water interface; the heights of octahedra protrusion from the PDMS surface are (260 ± 17) nm and (240 ± 18) nm respectively. Since the distance between two parallel planes of the 356 nm Ag octahedron is 291 nm, ~ 31 nm (11 %) and 51 nm (18 %) of the PVP-and C3-octahedra are in contact with the oil phase respectively (Supplementary Table 1). The standing configuration for C16-octahedra is also evident in the AFM measurements, with the protrusion height of the Ag octahedra from the PDMS surface at around (215 ± 18) nm. Since the orthogonal distance between two tips of the 356 nm Ag octahedra is 503 nm, approximately 57 % of the Ag octahedra is in contact with the oil phase (Supplementary Table 4). Error bars correspond to standard deviation of the measurements collected from a minimum of 50 particles for each functionality. The low hydrophilic/hydrophobic potential ratio of C16-octahedra implies that they are unable to remain buoyant standing in air in the absence of the oil phase. c,d, The open hexagonal structure remains fixed even when the oil phase is added after the addition of the particles in both cases. There is no energetic incentive to vary the superlattice structure upon the addition of an organic phase since the air/water interfacial energy is much higher than that of the oil/water.

Supplementary Figure 13 | Molecular dynamics simulations of the interfacial behavior of C16SH-
functionalized Ag octahedron at the air/water interface. a,b, Ag octahedron moves across the air/water interface over time. c, The particle-water potential energy remains relatively low due to the hydrophobicity of the C16-octahedron.
Supplementary Figure 14 | Investigating the influence of particle introduction location on the formation of the square superlattice. The locations at which the octahedra are added to the oil/water interface does not matter, since the addition from both the aqueous (a) and oil phase (b) gives rise to standing octahedra for the gel-trapping self-assembly experiments. Particles move to the interface spontaneously to achieve thermodynamic equilibrium and to minimize unfavorable contact between the two immiscible phases, verified through simulations.        CH2-CH2-CH2 109.5 520.0 CH2-CH2-CH3 109.5 520.0

Supplementary Note 1: Molecular Dynamics Simulations
The aim of utilizing molecular dynamics simulations is to seek a fundamental understanding on the interfacial behavior of a single anisotropic nanoparticle at an oil/water interface. We make use of the simulations to gain insights on how changes to the surface wettability of Ag octahedron arising from the use of various ligands (PVP, C3SH, C16SH) leads to structural changes observed in the self-assembly experiments. For this purpose, we employ an all-atomic molecular dynamics simulation model rather than a coarse-grain model to focus on the surface interactions occurring on the nanoparticle surface with the solvents. The thiol molecules are assumed to form a self-assembled monolayer on the octahedron surface, with experimental density of ~4.5 × 10 14 molecules/cm 2, 1 ; we also assume monolayer coverage for PVP, with the PVP chain non-specifically adsorbed on the octahedron surface.
Computational details. The GROMACS 4.07 simulation package 2 and GROMOS96 force field 3 were used for all our MD simulations. Two neighboring atoms interact with each other through van der Waals interactions, which is treated using a 12-6 Lennard -Jones (LJ) potential summed over all pairs of atoms i and j. The LJ potential may also be written in the following form: where r ij is the distance between the interacting pairs of atoms, σ ij and ε ij are the LJ parameters between atoms. The GROMACS LJ potential parameters C i (6) and C i (12) can be defined using the combination rules: The combinations for different atom-types can be computed according to the combination rule: To investigate the configuration evolution of Ag octahedron with various ligands at the oil/water interface, the LJ parameters (σ 0 = 0.2955 nm and ε 0 = 19.0790 kJ/mol) for Ag atoms were used 4 . The oil phase (hexane or decane), poly(vinylpyrrolidone) (PVP), 1-propanethiol (C3SH), and 1-hexadecanethiol (C16SH) molecular models employed in this study were generated from the small-molecule topology generator PRODRG and the C (6) and C (12) parameters are listed in Supplementary Tables 3, 4, and 5. The water phase was modeled using the single point charge (SPC) model, with the bond lengths and angles held constant through the use of the SETTLE algorithm. Bond lengths of molecules were constrained using the LINCS algorithm. The cutoff distance for short-range non-bonded interactions was chosen to be 12 Å and long-range electrostatic forces were computed using the reaction-field approach 5,6 .
The Ag octahedron used in the simulation was constructed by an all-atomic model using 10425 Ag atoms, as shown in Fig. S17a, corresponding to an edge length of ~ 7.5 nm. 129 PVP chains each built with 8 repeat units are randomly adsorbed onto the surface Ag atoms, as shown in Fig. S17b; 768 thiol molecules (C3SH and C16SH) were chemisorbed onto the Ag atoms to form a self-assembled monolayer, as shown in Fig. S17c and d. Simulations were run over 4 ns with steps of 2 fs, over the course of which the potential energies of the systems became stable. The above described setups demanded 53-66 24-core CPU hours on 2.13 GHz Intel Xeon Nehalam processors per simulation. As such, the size of the Ag octahedron was fixed at 7.5 nm to alleviate the computational demands while retaining the ability to focus on the events occurring at the surface of the Ag octahedron at the oil/water interface.
The simulations were started from the preassembled system consisting of two abutting thick slabs of water and hexane, with various ligand-functionalized Ag octahedron immersed in the aqueous phase. The water slab was composed of 11955 water molecules, and the oil slab was composed of 2341 hexane molecules. The dimensions of the simulation box were 16×16×24 nm 3 . Simulations were performed using the NPT ensemble. The temperature was maintained at 300 K using the Berendsen temperature coupling method and Berendsen bath coupling scheme was used to keep a constant normal pressure of 1 bar 7 .
The last 400 ps trajectory was used for analysis to derive the density distribution profile of the four components (Ag for Ag octahedron, surface ligands, water, and oil) during which the potential energy, the dimensions of the simulation box remained stable. The density profiles of the components aforementioned (Ag, water and oil) along the vertical direction of the simulation box were used to determine the interfacial positions of the variously functionalized Ag octahedron and to obtain the detailed potential energy profiles of the surface ligands. The interface between oil and water was defined by the decrease in the density of water to 10 %. The extent of Ag and ligand density profiles rising above this position was used to estimate the simulated height ratio of Ag octahedron in contact with the oil phase. In addition, snapshot pictures at various time intervals during the simulation were prepared using VMD to show the interfacial configuration of the Ag octahedron 8 .

Supplementary Note 2: Overall Potential Energy and Interfacial Energy Changes
Thermodynamic stability drives the variously functionalized Ag octahedron towards the oil/water interface over the course of the all-atomic molecular dynamics simulations. The total potential energies of all the systems are lower at the end of the simulation than at the beginning, reaching constant values after the simulation (Supplementary Fig. 7). In conjunction with the movement of the Ag octahedron in the three cases to the oil/water interface (Fig. 2), the decrease in overall potential energies indicates that this movement is a spontaneous process. The Ag octahedron breaches the oil/water interface and subsequent deforms the interface to minimize the energetically unfavorable contact between the immiscible oil and aqueous phases 9,10 . Consequently, the Ag octahedron is trapped at the oil/water interface.
In addition, the interfacial potential energies (E interfacial ) of the systems were derived using the following relationship: where E water is the total potential energy of the aqueous phase; E oil is the total potential energy of the oil phase; E Ag+ligand is the total potential energy of the ligand and Ag core; E system is the total potential of the entire system.
The interaction of the octahedron with the aqueous (E water-(Ag+ligand) ) and oil phases (E oil-(Ag+ligand) ) are derived from the following equations: where E water is the total potential energy of the aqueous phase, E oil is the total potential energy of the oil phase, E Ag+ligand is the total potential energy of the ligand and Ag core, E water+Ag+ligand is the total potential energy of aqueous phase and the ligand and Ag core, E oil+Ag+ligand is the total potential energy of oil phase and the ligand and Ag core.