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

TL;DR

This paper develops a modified Poisson-Boltzmann theory incorporating co-solvent polarizability, revealing how co-solvent properties influence electrostatic potential profiles and capacitance in electrolyte solutions.

Contribution

It introduces a new field-theoretical approach that explicitly accounts for co-solvent polarizability in the Poisson-Boltzmann framework, extending Gouy-Chapman theory.

Findings

Increased co-solvent concentration and polarizability enhance differential capacitance.

Electrostatic potential profiles become more long-ranged with higher co-solvent polarizability.

Permanent dipole of co-solvent has minimal effect on capacitance.

Abstract

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.