Properties of polyelectrolytes in tetravalent salt solutions are intensively investigated by a coarsegrained 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 morphologicalquantities. 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.

The effect of adding tetravalent salt of different sizes to a solution of linear and flexible polyelectrolytes is investigated by molecular dynamics simulations. Upon the addition of salt, a chain reexpansion takes place, following a well-known collapsed conformation. The degrees of collapse and reexpansion increase with ion size. In the solution, tetravalent counterions replace monovalent ones and condense onto the chains. The condensation for small ions displays a profile different from that for large ones. In a high-salt region, ions can form layering orders around a polyelectrolyte and locally overcompensate the charge inside. Consequently, the integrated charge distribution reveals an oscillatory behavior away from a chain. By studying the radial distribution function between monomers on different polyelectrolytes, like-charge attraction between chains is demonstrated. This attraction is a prerequisite to chain aggregation or precipitation. The results show a strong dependence of salt concentration and ion size on the properties of polyelectrolyte solutions.

We study salt-induced charge overcompensation and charge inversion of flexible polyelectrolytes via computer simulations and demonstrate the importance of ion excluded volume. Reentrant condensation takes place when the ion size is comparable to monomer size, and happens in a middle region of salt concentration. In a high-salt region, ions can overcharge a chain near its surface and charge distribution around a chain displays an oscillatory behavior. Unambiguous evidence obtained by electrophoresis shows that charge inversion does not necessarily appear with overcharging and occurs when the ion size is not big. These findings suggest a disconnection of resolubilization of polyelectrolyte condensates at high salt concentration with charge inversion.

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