Random phase approximation for complex charged systems: Application to copolyelectrolytes (polyampholytes)

We study binary polyelectrolytes in the melt state and in concentrated solutions using the random phase approximation (RPA). We compute the thermodynamics and electrostatics of chemically linked polyelectrolytes chains into block copolymer molecules (copolyelectrolytes). Polyelectrolytes blends and copolyelectrolytes in the presence of free ions have Debye-Hückel-type effective monomer-monomer interactions, even when the polymer chains are not charged. Copolyelectrolyte of chemically linked chains of opposite charge in the absence of counterions, have ion-ion effective interactions characteristic of a dielectric medium, contrary to the case of polyelectrolyte blends where these effective interactions are Debye-Hückel type, even on the absence of free ions. The dielectric constant in such a diblock copolymer melt is proportional to the square of the degree of polymerization N_p. In the reference state (without interactions) RPA assumes random walk statistics, which are nearly unperturbed in the dielectric; we find the scaling of the end-to-end vector square of a chain in the dielectric. We also discuss the physics of other copolyelectrolytes (polyampholytes).