Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Area of Science:

• Polymer Science
• Physical Chemistry
• Materials Science

Background:

• Associative phase separation (complex coacervation) of oppositely charged polyelectrolytes yields diverse complexes.
• Previous models incorporated ionization but neglected complex density's impact on electrostatic free energy.

Purpose of the Study:

• To develop a model for electrostatic free energy as a function of complex density.
• To determine equilibrium complex density by minimizing total free energy.
• To investigate the thermodynamic basis of polyelectrolyte film formation.

Main Methods:

• Utilized cylindrical cells and the Poisson-Boltzmann equation to calculate electrostatic free energy.
• Integrated Flory-Huggins mixing free energy terms.
• Minimized total free energy to find equilibrium complex density and composition.

Main Results:

• The model predicts equilibrium complex density based on charge ratio and density.
• Calculations for polyelectrolyte film formation suggest a thermodynamic origin for exponential growth in weakly charged systems.
• Strongly charged polyelectrolytes exhibit minimal composition differences between equilibrium states, preventing exponential growth via absorption.

Conclusions:

• Complex density significantly influences electrostatic free energy in polyelectrolyte complexes.
• Thermodynamics, specifically shifts between equilibrium states of varying densities and compositions, drives exponential polyelectrolyte film growth for weakly charged polymers.
• This mechanism is not viable for strongly charged polyelectrolytes due to minimal compositional differences.