An Exact Solution to the Electrostatic Interaction between an Ion-Penetrable Sphere and an Ion-Penetrable Rod

Area of Science:

• Physical Chemistry
• Colloid and Surface Chemistry
• Computational Physics

Background:

• Modeling electrostatic interactions in electrolyte solutions is crucial for understanding macromolecular behavior.
• Existing models often simplify complex geometries like sphere-rod systems, limiting accuracy.
• Hindered transport in diffusional systems requires precise interaction energy calculations.

Purpose of the Study:

• To derive an exact analytical solution for the electrostatic free energy of interaction between a charged sphere and an infinitely long rod.
• To compare the derived solution with existing models for nonpenetrable (hard) bodies.
• To assess the impact of ion penetrability on electrostatic interactions in complex geometries.

Main Methods:

• Developed an analytical approach to solve for the electrostatic free energy of interaction.
• Modeled an ion-penetrable (soft) sphere and an infinitely long rod in an electrolyte.
• Compared results with a finite-element analysis of a hard sphere and rod system.

Main Results:

• An exact analytical solution for the electrostatic free energy of interaction was obtained for the ion-penetrable sphere-rod system.
• The ion-penetrable model consistently yielded lower electrostatic free energy values compared to the hard body model.
• The difference in free energy was significant across various ionic strengths and radius ratios.

Conclusions:

• The choice between hard body and ion-penetrable models significantly affects electrostatic free energy calculations.
• Ion-penetrable models provide a more accurate representation of electrostatic interactions in certain macromolecular and fiber-matrix systems.
• Careful consideration of the modeled system's properties is essential for selecting the appropriate interaction model.