The finite size effect of monomer units on the electrostatics of polyelectrolyte solutions

The effective interactions between two test counterions and two test solvent dipoles in a semidilute/concentrated weakly charged polyelectrolyte solution are studied using the field-theoretical approach on the mean-field level. From the effective Hamiltonians in terms of the two test counterions and the two test solvent dipoles, respectively, analytical expressions for the effective interactions in the real space are derived. It is unambiguously demonstrated that, at a Theta solvent condition, both the effective interactions between two counterions and two parallel-oriented solvent dipoles consist of an attractive part at intermediate distances of separation. As the electrostatic screening effect from counterions and salt ions quantified by the Debye-Hückel screening parameter becomes stronger, the magnitude of the attraction decreases and the minimum of the attractive profile shift to a shorter distance of separation. On the other hand, when the excluded volume effect is dominant, the effective interactions are purely repulsive. This nontrivial and seemingly counterintuitive result originates from the finite size effect of the monomer units of the polymer chains on the electrostatics of the polyelectrolyte solution. As the size of the monomer units goes to zero, at the Theta solvent condition, the effective interactions between two counterions and two parallel-oriented solvent dipoles are purely repulsive.