Graphene origami structures with superflexibility and highly tunable auxeticity

The two-dimensional structure of graphene makes it difficult to realize flexibility and auxeticity (negative Poisson's ratio) in graphene-based structures. Using molecular dynamics simulations, we demonstrate for graphene origami structures effective tuning of both the flexibility and Poisson's ratio through the geometry, including the potential to combine superflexibility with a highly tunable negative Poisson's ratio in contrast to any existing graphene-based structure. Auxeticity even can be achieved under large applied strain, both tensile and compressive.

Figure 1

Schematic of the formation of a GMS by pattern-based hydrogenation of a graphene sheet. (a) Folding pattern showing the areas where the graphene sheet is hydrogenated (magenta, top side; cyan, bottom side). (b) GMS with $L_{x,0}=L_{y,0}=36.7$ nm, $w=3.7$ nm, and $\rho =15$% (GMS 1) in the equilibrium state at 300 K. (c) Definition of geometrical parameters. (d) Potential energy of GMS 1 as function of the simulation time at 300 K.

Figure 2

Mechanical response of GMS 1 under uniaxial stress in the $x$ direction at 300 K: (a) ${\sigma }_{xx}, {\epsilon }_{yy}, \theta$, and $\varphi$ as functions of ${\epsilon }_{xx}$. (b) Structure at points A and B marked in (a). (c) $h^{\text{eq}}$ as a function of ${\epsilon }_{xx}$ for a strain rate of ${10}^8{\mathrm{s}}^{-1}$ and a quasistatic simulation (QS; the dependence on the simulation time is shown).

Figure 3

GMSs with $L_{x,0}=L_{y,0}=36.7$ nm: (a) deformation without buckling for $\rho =20$%, (b) effect of $w$ and $\rho$ on $E_s$ and $E_c$, (c) $Y_{xx}$ as a function of $\theta$ and $\varphi$, and (d) effect of $w$ and $\rho$ on ${\nu }_{xy}$. The legend of (b) applies also to (d).

Figure 4

Effect of $\alpha$ and $\rho$ on (a) $l_x^{\text{eq}}$, (b) $E_s$ and $E_c$, and (c) ${\nu }_{xy}$.