Figure 9.

Mechanical interaction between an internalized circular sheet of diameter L and a surrounding vesicle of effective radius a at zero osmotic pressure. (a) Compressive contact force f between the vesicle membrane and encapsulated sheet (assumed to be rigid in the contact force calculation). (b) Buckling phase diagram with respect to the length ratio L/(2a) and bending stiffness ratio κ_p/κ. Insets in (a) correspond to the vesicle configurations at L/(2a)=1.1 and 1.3. Colored strips in (b) mark the regimes in which the corresponding 2D materials would buckle beyond a critical length. Except the bilayer MoS₂ in the magenta regime, the other 2D materials marked in (b) are of monolayer structures. In the case of lateral size L<2a, the encapsulated 2D material would undergo random Brownian motion in the vesicular confinement.