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Fullerene-based sandwiches have excellent controllable physical properties such as cross-plane thermal conductivity and charge transfer, which provide new possibilities for advancing the field of thermoelectricity. Because the pattern of the fullerene cluster impacts the physical properties of the sandwiches, it is important to understand the mechanisms for their structural transformations. In the present work, we find that the graphene/fullerene/graphene sandwich structure transforms among three configurations in an ideal environment, depending on the fullerene to graphene area ratio. Molecular dynamics simulations show that there are two critical values for the area ratio. The fullerene pattern transforms from circular to rectangular at the first critical area ratio of 1 π. The critical value of 1 π is successfully derived by comparing the geometrical perimeter of the circular and rectangular shapes for the fullerene cluster without any physical parameters. At the second critical area ratio, the graphene layers surrounding the fullerene cluster become separated due to the competition between the bending energy and the cohesive energy. The vacuum space is predicted to be 34 Å based on the analytic model. These findings provide fundamental insights into the mechanisms driving structural transformation of fullerene-based sandwiches, which will enable the selection of appropriate structures and materials to guide the design of future electronic and energy storage applications. [Display omitted] • The stable fullerene-based sandwich structure evolves among three typical configurations, which are governed by two critical ratios for the area ratio. • The fullerene pattern transforms from circular to rectangular at the first critical area ratio of 1 π. • At the second critical area ratio, the graphene layers surrounding the fullerene cluster are separated by the fullerenes. • It is demonstrated that the analytic models are universal and are applicable to other sandwich structures such as the MoS 2 /fullerene/MoS 2 structure. [ABSTRACT FROM AUTHOR]

Edge effects play an important role for many properties of graphene. While most works have focused on the effects from isolated free edges, we present a novel knotting phenomenon induced by the interactions between a pair of free edges in graphene, and investigate its effect on the buckling of monolayer graphene. Upon compression, the buckling of graphene starts gradually in the form of two buckling waves from the warped edges. The collision of these two buckling waves results in the creation of a knot structure in graphene. The knot structure enables the buckled graphene to exhibit two unique post-buckling characteristics. First, it induces a five-fold increase in graphene’s mechanical stiffness during the buckling process. Second, the knotted structure enables graphene to exhibit a mechanically stable post-buckling regime over a large (3%) compressive strain regime, which is significantly larger than the critical buckling strain of about 0.5%. The combination of these two effects enables graphene to exhibit an unexpected post-buckling stability that has previously not been reported. We predict that numerical simulations or experiments should observe two distinct stress strain relations for the buckling of identical graphene samples, due to the characteristic randomness in the formation process of the knot structure. [ABSTRACT FROM AUTHOR]