A modified Poisson-Boltzmann theory: Effects of co-solvent polarizability

In this paper within a field-theoretical approach taking into account explicitly a co-solvent with a nonzero dipole and a polarizability tensor, we derive a modified Poisson-Boltzmann equation. Applying the modified Poisson-Boltzmann equation, we formulate a generalized Gouy-Chapman theory for the case when an electrolyte solution is mixed with a polar co-solvent having a large polarizability. We show that an increase of the co-solvent concentration as well as the co-solvent polarizability lead to a significant increase of differential capacitance at sufficiently high surface potentials of the electrode, whereas the profile of the electrostatic potential becomes considerably more long-ranged. On the contrary, an increase in the permanent dipole of the co-solvent only weakly affects the differential capacitance.