Buckling of shells: from fullerene to ping-pong ball

Deformation of a spherical shell adhering onto a substrate due
to van der Waals attractive interaction is investigated by means
of numerical minimization.  The configuration of the deformed
shell is governed by the two dimensionless parameters, i.e.,
C_s/epsilon and C_b/epsilon where C_s and C_b are respectively
the stretching and the bending constants, and epsilon is the
is the depth of the van der Waals potential.  As C_b/epsilon is
varied systematically, we find both discontinuous and continuous
bucking transitions for large and small C_s/epsilon, respectively,
which is analogous to van der Waals liquids or gels.  Some scaling
arguments are employed to explain the adhesion induced buckling
of spherical shells.