Multiscale Ab-initio Modelling of Helium Droplet-mediated Deposition of Metallic Nanoparticles on Solid Surfaces

Multiscale Ab-initio Modelling of Helium Droplet-Mediated Deposition of Metallic Nanoparticles on Solid Surfaces

Soft landing of free metal clusters onto surfaces at low collision velocity has been discussed in the literature (see, e.g., [Popov et al. Mater Sci. Eng. R 72 (2011) 137] and [Popov et al., Surf. Sci. Rep. 66 (2011) 347]) as an attractive technique for the isolation of nanoclusters for subsequent use in various experiments. Recently, it has been shown that soft deposition can be achieved upon encapsulation in cold (0.4 K) He nanodroplets (see, e.g., [Mozhayskiy et al., J. Chem. Phys. 127 (2007) 094701], [Loginov, Gómez, and Vilesov, J. Phys. Chem. A 115 (2011) 115] and [Volk et al., J. Chem. Phys. 138 (2013) 214312]). It has also been suggested that the He droplet assembly/deposition technique can be useful in different applications, since metallic and bimetallic core-shell nanoparticles with tunable size, shape, and composition can be produced  (see, e.g. [Thaler et al., Phys. Rev. B 90 (2014) 155442]). For example, a very recent experimental study [Ridge et al. J. Phys. Chem. Lett. 7 (2016) 2919] has shown that the 4He droplet technique yields a narrow distribution of gold nanoparticles on a TiO2 surface. Moreover, the one-dimensional confinement induced by the presence of vortex filaments in the droplet (see, e.g., [Gómez, Loginov, and Vilesov, Phys. Rev. Lett. 108 (2012) 155302]) can be exploited to induce the formation of ultrathin wires of metallic nanoparticles whereas the experimental set-up  can be arranged to produce metallic nanoparticle films also beyond the submonolayer regime and in pre-reactive states (see e.g., [Emery, Rider, Lindsay, Propellants, Explos., Pyrotech. 39 (2014) 161]). Very recent experimental efforts are being driven to the optimal control of the metallic nanoparticle parameters by Wolfgang Ernst's experimental group (Graz University of Technology), as measured by the high-resolution atomic-resolved imaging by Ferdinand Hofer's group [G. Haberfehlner et al., Nature Communications 6 (2015) 8779]. Novel properties of these metallic nanoparticles are expected to be highly relevant in different fields of material science such as heterogeneous catalysis and photocatalysis.

The complete simulation of helium droplet-mediated deposition processes must consider: (1) the metallic nanoparticles growth inside the droplet; (2) the collision dynamics of (doped and pure) helium droplet with the surface; (3) the detailed forms of the helium-metal, helium-surface, and metal-surface potential energy surfaces; (4) the phonon-mediated desorption of the helium atoms from the droplet at impact with room temperature surfaces; (5) the influence of defects and finite temperature of the surface on the dynamics of the deposited nanoparticles; (6) the mobility and subsequent aggregation of the deposited nanoparticles due to the interaction with incoming helium droplets; (7) and the characterization of the nanopartilces properties. We have dedicated much effort to get a fundamental understanding of helium droplet-mediated deposition processes during the last five years. Our first theoretical effort of one elementary step, the helium droplet collision dynamics, was accomplished in 2012 [Aguirre et al., J. Chem. Phys. 136 (2012) 124703]. These earliest first-principles simulations demonstrate the paramount importance of including nuclear delocalization on the helium droplet dynamics to characterize the deposition process. In contrast with a pure classical picture predicting the splashing of helium droplets at impact, simulations with the TDDFT method revealed that the helium droplet spreads on the surface (see figure below), which is consistent with the soft-landing deposition of the embedded nanoparticles. These studies used TiO2 as the targeted hard-side surface whereas carbon-based substrates were considered in more recent quantum-mechanical simulations [de Lara-Castells et al., J. Chem. Phys. 141 (2014) 151102].

Snapshots showing the dynamical evolution of the helium density profiles associated to a 4He300 drop at impact with the TiO2(110)-(1×1) surface. The display frames are 80 × 50 Å2. The TiO2(110) surface is located at 2.4 Å from the bottom edge of the box. Left-hand panel: 2D contours of the helium density profiles. Red arrows indicate the current field with a size proportional to the current intensity at a local point. The panels correspond to times t = 0, 8, 16, and 22 ps. The clearer the color, the higher the helium density. Right-hand panel: iso-probability helium density surfaces. [URL: J. Chem. Phys. 136 (2012) 124703].

Helium-mediated deposition processes are naturally strongly determined by the specific interactions between the three basic components (helium, metal, and surface) so that their accurate descriptions via first-principles methods are necessary. Moreover, as explicitly shown in [de Lara-Castells et al., J. Chem. Phys. 141 (2014) 151102], the role played by dispersion effects in the soft-landing is crucial, accounting e.g. for the fast spreading and evaporation of the helium droplet and the formation of solid-like helium structures. Although standard codes for extended systems include dispersion-corrected methods based on density functional theory (DFT), difficulties can be found in dealing with helium/surface (see, e.g., [de Lara-Castells et al., J. Phys. Chem. A 118 (2014) 6367]) and helium/metal interactions [de Lara-Castells et al., J. Chem. Phys. 144 (2016) 244707]. As extensively described in recent works (see, e.g., [de Lara-Castells et al., J. Chem. Phys. 143 (2015) 194701] and [de Lara-Castells et al., J. Chem. Phys. 143 (2015) 102804]), we have developed a cost-efficient methodological scheme capable of providing accurate He/surface and van der Waals-dominated metal/surface potentials. More recently, we have extended and modified the scheme to deal with metallic surfaces and nanoparticles (see, e.g.,  [de Lara-Castells et al., J. Chem. Phys. 144 (2016) 244707]) different noble-gases (see, e.g., [de Lara-Castells et al., J. Chem. Phys. 143 (2015) 194701]) and to determine the nuclear bound states of H2 physisorbed on graphene and graphite surfaces [de Lara-Castells and Mitrushchenkov, J. Phys. Chem. A 119 (2015) 11022].

The ab-initio scheme recently developed in collaboration with Alexander Mitruschenkov (Université Paris-Est) and Hermann Stoll (University of Stuttgart) (see, e.g., [de Lara-Castells et al., J. Chem. Phys. 143 (2015) 102804] for the details) has been applied to determine the necessary He/surface and metal/surface interaction potentials. This ab-initio scheme combines periodic density functional and post Hartree-Fock incremental approaches [de Lara-Castells et al., J. Chem. Phys. (Communication) 141 (2014) 151102]. First, it extends dispersionless density functional theory (the so-called dlDF treatment, see [Pernal et al., Phys. Rev. Lett. 103 (2009) 263201]) by including periodic boundary conditions to calculate the dispersionless interaction contribution. Second, the dispersion energy is evaluated at CCSD(T) level by applying either the method of increments [H. Stoll, J. Chem. Phys. 97 (1992) 8449]  or symmetry-adapted perturbation theory on surface cluster models of increasing size (see figure below, from [de Lara-Castells, J. Chem. Phys. Communication 142 (2015) 131101]). Extended versions of the ab-initio scheme have been also developed to deal with He/metal interactions (see, e.g., [de Lara-Castells et al., 144 (2016) 244707]). For this specific purpose, we have collaborated with Celine Leonard (Université Paris-Est) and Elena Voloshina (Free University of Berlin) (see also [Grenier et al., J. Phys. Chem. A 119 (2015) 6897]). 

Figure illustrating the hydrogen-saturated clusters chosen to model the TiO2(110) surface. The interaction energies obtained with the dispersionless density functional (dlDF) and periodic dlDF + incremental Das/Das approaches are also shown along with the clusters used for dlDF and Das parametrizations. [URL: J. Chem. Phys. 142 (2015) 131101]

Within the framework of our collaboration with Martí Pi's group (University of Barcelona), we have reported a “proof-of-concept” communication [de Lara-Castells, J. Chem. Phys. Communication 142 (2015) 131101] providing the first theoretical evidence of the soft, 4He droplet-mediated, deposition, with a focus on the key role of quantum nuclear delocalization. TiO2(110) surface was first chosen as a technological relevant surface and a prototype transition metal-oxide substrate with very well-characterized properties. To simulate the “soft-landing” process, the nuclear dynamics of the 4He droplet was followed by the TDDFT method while the heavier metal species was treated as a classical particle. This study showed that the 4He droplet essentially carries the gold atom to the minimum of the gold/surface interaction potential, with an energy (< 0.15 eV) much smaller than the metal cohesive energy. After the metal sticking, the remaining 4He droplet evaporates (see figure below, from [de Lara-Castells, J. Chem. Phys. Communication 142 (2015) 131101]).

Snapshots showing the time evolution of the Au@4He300 droplet at impact with the solid surface. The z axis (in Å) is oriented at the surface normal direction. The density values (in Å−3) are given in the legends. [URL: J. Chem. Phys. 142 (2015) 131101]

The natural step forward has consisted in upscaling the first-principles modelling to the typical metallic nanoparticles and helium nanodroplets sizes synthesized in the experiments, considering also the corrugated nature of the support (e.g., a Transmission Electron Microscopy - TEM - grid of amorphous carbon). Thus, within the framework of our collaboration with Andrey Vilesov (University of Southern California), we have reported experiments and calculations of the deposition and aggregation of silver clusters embedded in helium droplets onto an amorphous carbon surface at room temperature (see figure below, from [Fernández-Perea et al., J. Phys. Chem. C 121 (2017) 22248]). Calculations were also performed for deposition onto a graphene surface. They involve potentials for the interaction of carbon atoms with silver and helium atoms, provided by ab-initio calculations. The numerical simulations were performed for few-nanometer-sized silver clusters including up to 5000 Ag atoms and He droplets with up to 105 4He atoms. The fluid nature of the 4He droplet is accounted for by the renormalization of the He-He interaction potential. The numerical results are consistent with deposition experiments with an average number of 3000 Ag atoms per 4He droplet and indicate that the aggregation of the silver clusters on the carbon surface is mediated by secondary droplet impacts. They also reveal nontrivial dynamics of the Ag clusters within the carrier droplet, showing a tendency to drift toward the droplet surface. These findings are of relevance in understanding the heterogeneous deposition patterns (large ramified islands) developed for very large droplets with an average number of Ag atoms per droplet within the million range. Finally, the simulations of large (5000 atoms) Ag cluster deposition on graphene reveals strong superdiffusive behavior. In stark contrast, the diffusion is negligible on the amorphous carbon surface.

TEM images of AgN clusters deposited on a film of amorphous carbon at room temperature. Helium droplets containing ∼1.7 × 1010 He atoms were produced at a nozzle temperature (T0) of 5.5 K and doped with ∼2 × 106 Ag atoms. The TEM micrographs were taken at magnifications of 10 × 103 for panel (a) and 3 × 103 for panels (b) and (c). The samples were obtained by exposing the surfaces to the doped helium droplet beam during 4 s (a), 2 min (b), and 30 min (c)  [URL: J. Phys. Chem. C 121 (2017) 22248].


Top panel: Snapshots showing the evolution of an Ag5000 cluster embedded in an 4He100000 droplet (Ag atoms are shown in gray; He atoms are blue) at impact with an Ag5000 cluster previously deposited onto an amorphous carbon surface (C atoms are turquoise). Bottom panel: Evolution of the velocity component along the surface normal. The blue line corresponds to the center of mass of the two colliding Ag5000 nanoparticles shown in the top panel. The green line refers to the bare colliding Ag5000 clusters, and the black one (Vz, right y axis) corresponds to the center of mass of the soft landing of the bare Ag5000 nanoparticle. The black dashed line indicates the first passage by zero velocity shifted to 60 ps in all cases, whereas the blue dashed line marks the time associated with snapshot (e), when the He droplet can be considered evaporated. Notice that the scale of the right y axis corresponding to the single nanoparticle is double. With this scaling, the left y axis can also be interpreted as the momentum in Ag5000 mass units for all cases [URL: J. Phys. Chem. C 121 (2017) 22248].