  Effective pair potentials for hollow nanoparticles like the ones made from
carbon (fullerenes) or metal dichalcogenides (inorganic fullerenes) consist of
a hard core repulsion and a deep, but short-ranged, van der Waals attraction.
We investigate them for single- and multi-walled nanoparticles and show that in
both cases, in the limit of large radii the interaction range scales inversely
with the radius, $R$, while the well depth scales linearly with $R$. We predict
the values of the radius $R$ and the wall thickness $h$ at which the gas-liquid
coexistence disappears from the phase diagram. We also discuss unusual material
properties of the solid, which include a large heat of sublimation and a small
surface energy.
