Self-consistent field theory study of the solvation effect in polyelectrolyte solutions: beyond the Poisson–Boltzmann model

Abstract

We developed a self-consistent field theory to study the solvation effect in polyelectrolyte solutions by taking into account the dipolar feature of polar solvents. A Langevin Poisson–Boltzmann equation describing the electrostatic interactions was derived at the mean-field level and numerically solved by an ad-hoc direct spectral algorithm. This method enables the SCFT to be implemented in real space. The developed self-consistent field model was applied to salt-free concentrated solutions of diblock polyampholytes and charged–neutral diblock copolymers. It was found that an increase in the magnitude of dipole moments can lead to an increase in the effective dielectric constant and thereby the change of the phase behaviors. As the magnitude of the dipole moment increases, the segregation between dissimilar blocks becomes strong, and the lamellar spacing undergoes a non-monotonic variation where the spacing first decreases and then increases to reach a plateau. The proposed calculation method can be extended to the solutions of polyelectrolytes with different architectures and polar solutions containing added salts.