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 Waals-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.
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