  Properties of polyelectrolytes in tetravalent salt solutions are intensively
investigated by a coarse-grained model. The concentration of salt and the size
of tetravalent counterions are found playing a decisive role on chain
properties. If the size of tetravalent counterions is compatible with the one
of monomers, the chains show extended structures at low and at high salt
concentrations, whereas at intermediate salt concentrations, they acquire
compact and prolate structures. The swelling exponent of a chain against salt
concentration behaves in an analogous way as the morphological quantities.
Under certain condition, the electrostatics gives a negative contribution to
the persistence length, in companion with a salt-induced mechanical instability
of polyelectrolytes. Nearly at the same moment, it appears like-charge
attraction between chains. The equal size of the tetravalent ions and the
monomers is the optimal condition to attain the strongest attraction between
chains and the most compact chain structure. Moreover, the ions form a
multi-layer organization around a chain and, thus, the integrated charge
distribution reveals an oscillatory behavior. The results suggest that charge
inversion has no direct connection with redissolution of polyelectrolytes at
high salt concentrations.
