Adsorption of metal nanoparticles on carbon substrates and epitaxial graphene: Assessing models for dispersion forces

Carbon substrates such as graphite or epitaxial graphene can be employed to support metal nanoparticles for applications in diverse areas of surface science. In this paper, we address the computational modeling of such systems by means of semiempirical potentials, and in particular the possible role of long-range London dispersion forces. Following the Grimme (D2) strategy often used in combination with density-functional theory calculations, we propose some analytical extensions taking into account the crystalline and semi-infinite natures of the substrate and, in the case of epitaxial graphene, the possible screening of the van der Waals interaction by the bulk underlying metal. These ideas are tested in the specific case of platinum nanoparticles deposited on graphene, graphite, and graphene epitaxially grown on Pt(111) modeled using a many-body Brenner-type potential, and validated against available electronic-structure calculations. Systematic optimizations carried out at zero temperature indicate the relative stability of various nanoparticle shapes on their support, for adsorbates containing several thousand atoms. Using molecular dynamics simulations, we shed light on the thermal behavior and emphasize the key role of dispersion forces on the stabilization of the adsorbates at finite temperature. The vibrational properties of graphene layers in contact with a Pt nanoparticle or epitaxially grown on Pt(111) also reveal some clear sensitivity on temperature and strain.

Figure 1

Interaction between an adsorbate atom $i$ and a succession of planar layers, smoothly excluding regions within cutoff distances. See text for notations.

Figure 2

High-symmetry adsorption sites of adatoms on graphite: The atoms of the uppermost graphitic layer are represented as black rings, the atoms of the layer below as gray circles. In the implicit models, the alpha and beta sites are equivalent.

Figure 3

Energy profiles of a Pt adatom approaching flat graphitic surfaces along various sites, as obtained from the bond-order potential corrected with different dispersion models. Upper panels (a)–(c): single-layer graphene; lower panels (d)–(f): semi-infinite graphite.

Figure 4

Potential energy of a Pt adatom on a graphite surface with a single vacancy (upper panel) or a 5775 Stone-Wales defect (lower panel) as obtained with the explicit D2 and implicit dispersion models. The defective carbon lattice is explicitly shown for the D2 model. For the Stones-Wales defect, two adsorption sites A and B are highlighted as defined in the text.

Figure 5

Adsorption energies of Pt nanoparticles on graphene and graphite, computed for different treatments of London dispersion forces, and normalized by the number of metal atoms in contact with the substrate. (a) No dispersion correction; (b) explicit correction of the Grimme D2 type; (c) implicit dispersion model. The adsorption energies, as defined in the text, for graphene and graphite are denoted by full and empty symbols, respectively. Icosahedral (ico) and truncated octahedral (toct) adsorbates are indicated by circles and squares, respectively. DFT data from Ref. [43] have been superimposed in panel (b).

Figure 6

Temperature variations of the root-mean-square bond length fluctuation indices measuring the internal rigidity of the ${\mathrm{Pt}}_{64}$ adsorbate $\left({\delta }_{\mathrm{intra}}\right)$ and the mobility of the adsorbate relative to the graphite substrate $\left({\delta }_{\mathrm{inter}}\right)$, and average adsorbate thickness $\sigma$ as obtained from the explicit (Grimme D2) and implicit dispersion models.

Figure 7

Short-time average angle between the ${\mathrm{Pt}}_{64}$ adsorbate and substrate lattices, and center-of-mass velocity of the adsorbate, as obtained from a MD trajectory at 900 K using the implicit model for dispersion corrections. Adsorbates under maximal (left) and minimal (right) alignment are also depicted.

Figure 8

Vibrational spectra for a two-layer ${\mathrm{Pt}}_{64}$ adsorbate on graphite obtained from the velocity time correlation function at finite temperatures (continuous lines) and in the harmonic limit (histograms pointing downward). (a) Spectra of isolated substrate (upper part) and adsorbate (lower part); (b) global spectra of the entire system (upper part) and of adsorbate alone (lower part) but interacting with the substrate. The calculations were performed with the implicit dispersion correction model.

Figure 9

Inventory of moiré sites of the graphene/Pt(111) system with a vanishing in-plane angle ($\xi$ structure).

Figure 10

Edge length of moiré structures obtained for graphene on Pt(111) by varying the in-plane angle between the two lattices obtained by geometric construction (red circles) and observed in experiments (green circles, see also Table 2 for the assignment of the different structures). Full and empty circles refer to simple commensurate lattices and to commensurate lattices of twice the size of the apparent moiré periodicity, respectively.

Figure 11

Variations of (a) adsorption energy and (b) corrugation of the graphene monolayer in epitaxial contact with Pt(111), as obtained from the implicit dispersion model as a function of the screening length $r_{\mathrm{TF}}$. The curves were obtained for various moiré structures corresponding to different in-plane angles $\mathrm{\Theta }=0^{\circ } \left(\xi \right)$, $13.9^{\circ } \left(\gamma \right)$, and $19.1^{\circ } \left(\beta \right)$ and based on local relaxations. In panel (a), the adsorption energies predicted by other dispersion models are also indicated as horizontal lines.

Figure 12

(a) Corrugation $\mathrm{\Delta }z$ and (b) interlayer separation $\delta z$ of a graphene layer epitaxied on Pt(111) as a function of the in-plane angle $\mathrm{\Theta }$, as obtained from different dispersion models at zero temperature. The values predicted by the model with screened dispersion forces lie beyond the respective upper values of the graphs at $\mathrm{\Theta }={30}^{\circ }$ (see text for discussion).

Figure 13

Thermally averaged corrugation $\mathrm{\Delta }z$ (upper panels) and graphene-metal separation $\delta z$ (lower panels) of a graphene layer epitaxied on Pt(111) as a function of temperature, as obtained from different dispersion models for the $\xi$ moiré (in-plane angle $\mathrm{\Theta }=0^{\circ }$, left panels) and the $\gamma$ moiré (in-plane angle $\mathrm{\Theta }=13.9^{\circ }$, right panels).

Figure 14

Position of the intense G peak as a function of temperature, as obtained from MD simulations of freestanding graphene and epitaxial graphene on Pt(111) forming $\xi$ and $\gamma$ moiré patterns. The simulations of epitaxial graphene used the implicit dispersion correction model with a screening length of $r_{\mathrm{TF}}=2.9\text{Å}$.

Figure 15

Lindemann indices of intra-adsorbate mobility and adsorbate-support and thickness of ${\mathrm{Pt}}_{64}$ on graphene/Pt(111) in the $\xi$ moiré structure as a function of temperature for different dispersion correction models.