Mixing order asymmetry in nanoparticle-polymer complexation and precipitation revealed by isothermal titration calorimetry

In recent years, there has been a renewed interest in complex coacervation, driven by concerted efforts to offer novel experimental and theoretical insights into electrostatic charge-induced association. While previous studies have primarily focused on polyelectrolytes, proteins or surfactants, our work explores the potential of using cerium (CeO2) and iron ({\gamma}-Fe2O3) oxide nanoparticles (NPs) to develop innovative nanomaterials. By combining various charged species, such as polyelectrolytes, charged neutral block copolymers and coated NPs, we study a wide variety of complexation patterns and compare them using isothermal titration calorimetry, light scattering and microscopy. These techniques confirm that the titration of oppositely charged species occurs in two steps: the formation of polyelectrolyte complexes and subsequent phase (or microphase) separation, depending on the system studied. Across all examined cases, the entropic contribution to the total free energy surpasses the enthalpic contribution, in agreement with counterion release mechanisms. Furthermore, our investigation reveals a consistent asymmetry in the reaction enthalpy associated with the secondary process, with exothermic profiles observed upon the addition of cationic species to anionic ones and endothermic profiles in the reverse case.