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.