Dissecting the Thermodynamics of Polyelectrolyte Complexation and Liquid–Liquid Phase Separation Using a Dual-Equilibrium Reaction Model

The thermodynamics governing complexation between charged macromolecules determine their associative liquid–liquid phase separation (LLPS) behavior and properties of the condensed phases. Despite its fundamental importance, precise extraction of complete thermodynamic parameters from polyelectrolyte complexation and LLPS remains unfulfilled. In this study, we propose a dual-equilibrium reaction (DER) model that decouples the polyelectrolyte complexation process into two interconnected equilibrium reactions: ion pairing and coacervation. The equilibrium constant for coacervation ( K c ) is assigned a logarithmic Gaussian distribution as a function of the polyelectrolyte ratio. This DER model quantitatively describes the evolution of the coacervation tendency and successfully fits the binding isotherms obtained from isothermal titration calorimetry. The derived binding free energies and equilibrium constants are validated against thermogravimetric analysis (TGA) and coarse-grained molecular dynamics simulations, where the K c is consistent with the polymer content ratio between coacervate and supernatant phases. Both the ion-pairing and coacervation are proven to be entropy-driven, which could become entropically and energetically unfavorable when reducing polyelectrolyte charge density and hydrophobicity. The DER model not only offers a robust approach for the thermodynamic characterization of polyelectrolyte complexation but also enlightens the physical nature of LLPS with respect to polyelectrolyte charge stoichiometry, providing implications for biological and artificial LLPS.