Self-consistent analytical solutions to the Voorn-Overbeek model

Area of Science:

• Physical Chemistry
• Polymer Science
• Biophysics

Background:

• Complex coacervation, driven by electrostatic interactions between oppositely charged macromolecules, is crucial for the phase behavior of charged polymers like nucleic acids and intrinsically disordered proteins.
• The Voorn-Overbeek model offers a fundamental mean-field description, integrating polymer mixing entropy and Debye-Hückel level electrostatics.
• Traditional analysis of the Voorn-Overbeek model for phase coexistence relies on numerical methods or approximations due to the lack of closed-form solutions.

Purpose of the Study:

• To derive a self-consistent analytical solution for the binodal concentrations in the simplest Voorn-Overbeek model.
• To provide explicit analytical expressions for phase boundaries in systems of two oppositely charged polymers in a neutral solvent.
• To establish an analytically tractable framework for studying complex coacervation.

Main Methods:

• Reformulating phase coexistence conditions as a fixed-point problem.
• Deriving self-consistent analytical solutions for binodal concentrations.
• Applying Debye-Hückel theory for electrostatic interactions under local electroneutrality.

Main Results:

• Obtained explicit analytical expressions for phase boundaries of the simplest Voorn-Overbeek model.
• Demonstrated accuracy of the derived expressions across the entire phase-separated regime.
• Developed a self-consistent analytical solution for binodal concentrations.

Conclusions:

• The derived analytical solution provides an accessible framework for understanding complex coacervation.
• This work simplifies the study of liquid-liquid phase separation in charged polymer systems.
• The findings lay the groundwork for future research incorporating more complex electrostatic and compositional factors.