Dissecting the thermodynamics of polyelectrolyte complexation and liquid-liquid phase separation using a dual-equilibrium reaction model

The thermodynamics of complexation between charged macromolecules determine their associative liquid-liquid phase separation (LLPS) behavior and condensed phase properties. However, a proper approach to accurately extract full thermodynamic parameters from polyelectrolyte complexation has been missing. In this study, we divide the polyelectrolyte complexation into two correlated equilibrium reactions - ion pairing and coacervation, and introduce a dual-equilibrium reaction model (DER) that successfully fits the binding isotherms obtained from isothermal titration calorimetry (ITC). The binding free energy and equilibrium constant of both ion-pairing and LLPS are obtained and validated against thermogravimetric analysis and coarse-grained molecular dynamics simulations. The equilibrium constant of coacervation exhibits a logarithmic Gaussian distribution along the polyelectrolyte molar ratio and well represents the polymer content distribution between the supernatant and condensed phases. The DER model captures the underlying physical nature and offers a reliable approach for extracting thermodynamic parameters of the complexation and LLPS between charged macromolecules.