  We theoretically study the polarizability and the interactions of neutral
complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an
oppositely charged spherical colloid. In the systems we studied, the bending
energy of the chain is small compared to the Coulomb energy and the chains are
always adsorbed on the colloid. We observe that the polarizability is large for
short chains and small electrical fields and shows a non-monotonic behavior
with the chain length at fixed charge density. The polarizability has a maximum
for a chain length equal to half of the circumference of the colloid. For long
chains we recover the polarizability of a classical conducting sphere. For
short chains, the existence of a permanent dipole moment of the complexes leads
to a van der Waal's-type long-range attraction between them. This attractive
interaction vanishes for long chains (i.e., larger than the colloidal size),
where the permanent dipole moment is negligible. For short distances the
complexes interact with a deep short-ranged attraction which is due to
energetic bridging for short chains and entropic bridging for long chains.
Exceeding a critical chain length eventually leads to a pure repulsion. This
shows that the stabilization of colloidal suspensions by polyelectrolyte
adsorption is strongly dependent on the chain size relative to the colloidal
size: for long chains the suspensions are always stable (only repulsive forces
between the particles), while for mid-sized and short chains there is
attraction between the complexes and a salting-out can occur.
