Solvation and dissociation in weakly ionized polyelectrolytes

We present a Ginzburg-Landau theory of inhomogeneous polyelectrolytes with a polar solvent. First, we take into account the molecular (solvation) interaction among the ions, the charged monomers, the uncharged monomers, and the solvent molecules, together with the electrostatic interaction with a composition-dependent dielectric constant. Second, we treat the degree of ionization as a fluctuating variable dependent on the local electric potential. With these two ingredients included, our results are as follows. (i) We derive a mass reaction law and a general expression for the surface tension. (ii) We calculate the structure factor of the composition fluctuations as a function of various parameters of the molecular interactions, which provides a general criterion of the formation of mesophases. (iii) We numerically examine some typical examples of interfaces and mesophase structures, which strongly depend on the molecular interaction parameters.