  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.
