Multistability of graphene nanobubbles.

Using He, Ne, Ar, Kr, and Xe atoms as a model system, it is demonstrated that graphene nanobubbles on flat substrates are multistable systems. A nanobubble can adopt multiple stable stationary states, each characterized by the number of layers l within the cluster of encapsulated atoms. The layers are circular, concentrically stacked, and form an l-stepped pyramid with a flat top. Encapsulation of this pyramid by the graphene sheet is achieved through local stretching of the membrane: the valence bonds elongate only directly above the confined atoms. Outside this coverage zone, the sheet remains undeformed and lies flush against the substrate. The maximum number of possible layers, lm, increases monotonically with the number of encapsulated atoms N, reaching lm = 6 for N = 4000. The graphene membrane, through van der Waals interaction with the substrate, compresses the internal atomic cluster, generating internal pressures on the order of Pin ∼ 1 GPa. Numerical simulations of thermal vibrations reveal that among all l-layer configurations, one ground state always exists. Upon heating, this state smoothly transitions into a layerless liquid configuration. All other stationary states transform into this ground state once a characteristic temperature Tl is reached. For N = 4000, the ground state corresponds to the four-layer packing (l = 4). The coexistence of multiple stable states with distinct layer numbers at low temperatures leads to the absence of a universal shape for the nanobubbles. In this scenario, the height-to-radius ratio, H/R, is not constant and can vary from 0 to 0.28, depending on the number of layers. The commonly reported universal aspect ratio H/R ∼ 0.2 holds only for the ground states of the system. External hydrostatic pressure P does not lead to a change in the multistability of the nanobubbles. An increase in pressure can lead to crystallization of the system of encapsulated atoms, which results in a change in the shape of the nanobubble (a decrease in the H/R ratio). In the absence of crystallization under pressure, uniform compression of the nanobubble occurs, in which the H/R ratio does not change.