U. S. Schwarz, S. A. Safran and S. Komura
Mechanical, adhesive and thermodynamic properties of hollow nanoparticles
Mat. Res. Soc. Symp. Proc. 651: T5.3.1-T5.3.6 (2001)

When sheets of layered material like C, WS$_2$ or BN are restricted to
finite sizes, they generally form single- and multi-walled hollow
nanoparticles in order to avoid dangling bonds.  Using continuum
approaches to model elastic deformation and van der Waals interactions
of spherical nanoparticles, we predict the variation of mechanical
stability, adhesive properties and phase behavior with radius $R$ and
thickness $h$. We find that mechanical stability is limited by forces in
the nN range and pressures in the GPa range. Adhesion energies scale
linearly with $R$, but depend only weakly on $h$.  Deformation due to
van der Waals adhesion occurs for single-walled particles for radii of
few nm, but is quickly suppressed for increasing thickness.  As $R$
is increased, the gas-liquid coexistence disappears from the phase
diagram for particle radii in the range of 1-3 nm (depending on wall
thickness) since the interaction range decreases like $1/R$.