Casimir-like effect driven self-assembly of graphene on molten metals

Casimir effect, explained by Hendrik Casimir in 1948, is a macroscopic manifestation of quantum electrodynamics. Symmetry breaking due to space confinement of vacuum fluctuations in between two planar mirrors results in an attractive force acting between the two mirrors. Here, we show that spontaneous self-assembly of two-dimensional (2D) layered materials grown on molten metals (rheotaxy) is driven by the mechanical forces exerted by the liquid on the graphene domain and that these forces are subject to a Casimir-like effect. We present in situ environmental and ultrahigh vacuum scanning electron microscopy observations of chemical vapor deposition of graphene on both solid and molten gold and copper, which reveal that the self-assembly occurs via translational and rotational motions of graphene domains during growth on molten metals. Using high-temperature (~ 1300 K) atomic force microscopy measurements of graphene/molten-metal interfaces, coupled with density functional theory and continuum modelling of 2D layers floating on a liquid surface, we attribute the observed phenomena to Casimir-like effect of surface undulations and give further guidance for achieving seamless stitching of 2D layer domains into large scale monolayers.