Electric-field-based Poisson-Boltzmann theory: Treating mobile charge as polarization

Area of Science:

• Physical Chemistry
• Continuum Electrodynamics
• Materials Science

Background:

• Mobile charge in electrolytes is typically described by ionic polarization.
• Existing models often lack explicit solvent polarization, limiting their scope.
• Poisson-Boltzmann theory is a cornerstone of electrolyte modeling.

Purpose of the Study:

• To develop a novel theoretical framework for mobile charge in electrolytes.
• To incorporate explicit solvent polarization into a dielectric continuum model.
• To derive equilibrium equations for electric potential and ion concentration.

Main Methods:

• Representing mobile charge as the divergence of ionic polarization.
• Treating electrolytes as composite nonuniform dielectric bodies.
• Utilizing a variational procedure based on electric-field energy density and Maxwell's equations.

Main Results:

• Demonstrated the convexity of the Poisson-Boltzmann functional in the new formulation.
• Derived equilibrium equations for electric potential and ion concentration via variational methods.
• Incorporated transverse polarization, overcoming limitations of electrostatic potential-based theories.

Conclusions:

• The proposed dielectric continuum model offers a more comprehensive description of electrolytes.
• This formulation explicitly accounts for mutual screening between ions and solvent.
• The method provides a robust foundation for studying complex dielectric systems.