Structural Effects of Multivalent Counterions in the Self-Assembly of Polyelectrolyte Copolymers

In this paper, we investigate the effects of multivalent counterion units and linear counterion chains in the self-assembly of polyelectrolyte (PE) copolymers. Both the valent and structural effects of the counterions are discussed. As the valence of counterion units or the length of counterion chains increases, the electrostatic correlations are significantly strengthened. Compared with multivalent counterion units, the linear structure of counterion chains is primarily manifested in two aspects. First, the electrostatic repulsion among the monovalent ions within the counterion chains diminishes near-neighbor electrostatic correlations, resulting in less compact PE coronas and more stretched PE blocks. Second, the linear arrangement of counterions reinforces the remote spatial electrostatic correlations, prompting the formations of ring-like and semiring-like PE coronas. The charge distribution in the PE coronas closely depends on counterion structures. As the counterion valence or length increases, the enhanced electrostatic effects draw more counterions into the inner regions of the PE coronas. The overcompensation of multivalent counterions within the inner regions of the PE coronas results in local charge inversion. The increased absorption of counterion chains not only raises the positive charge in the inner regions but also extends it to the peripheral regions of the PE coronas, thereby reducing the critical interfacial distance required for the transition in the net charge polarity.