text: Coacervates are a type of lyophilic colloid; that is, the dense phase retains some of the original solvent – generally water – and does not collapse into solid aggregates, rather keeping a liquid property. Coacervates can be characterized as complex or simple based on the driving force for the LLPS: associative or segregative. Associative LLPS is dominated by attractive interactions between macromolecules (such as electrostatic force between oppositely charged polymers), and segregative LLPS is driven by the minimization of repulsive interactions (such as hydrophobic effect on proteins containing a disordered region).
  The thermodynamics of segregative LLPS can be described by a Flory-Huggins polymer mixing model (see equation). In ideal polymer solutions, the free-energy of mixing (ΔG) is negative because the mixing entropy (ΔS, combinatorial in the Flory-Huggins approach) is positive and the interaction enthalpies are all taken as equivalent (ΔH or χ = 0). In non-ideal solutions, ΔH can be different from zero, and the process endothermic enough to overcome the entropic term and favor the de-mixed state (the blue curve shifts up). Low molecular-weight solutes will hardly reach such non-ideality, whereas for polymeric solutes, with increasing interactions sites N and therefore decreasing entropic contribution, simple coacervation is much more likely.
  The phase diagram of the mixture can be predicted by  experimentally determining the two-phase boundary, or binodal curve. In a simplistic theoretical approach, the binodes are the compositions at which the free energy of de-mixing is minimal (
  ), across different temperatures (or other interaction parameter). Alternatively, by minimizing the change in free energy of de-mixing in regards to composition (), the spinodal curve is defined. The conditions of the mixture in comparison to the two curves defines the phase separation mechanism: nucleation-growth of coacervate droplets (when the binodal region is crossed slowly) and spinodal decomposition.
  Associative LLPS is more complex to describe, as both solute polymers are present in the dilute and dense phase. Electrostatic-based complex coacervates are the most common, and in that case the solutes are two polyelectrolytes of opposite charge. The Voorn-Overbeek approach applies the Debye-Hückel approximation to the enthalpic term in the Flory-Huggins model, and considers two polyelectrolytes of the same length and at the same concentration. Complex coacervates are a subset of aqueous two-phase systems (ATPS), which also include segregatively separated systems in which both phases are enriched in one type of polymer.