Extended Law of Corresponding States: Origins, Challenges, and Applications to Protein Solutions

The phase diagram of colloidal systems strongly depends on the nature of interparticle interactions, which reflect the physical mechanisms that stabilize the particles in the medium. In systems with dominant short-range attractions, where interactions act over distances much shorter than the particle diameter, the extended law of corresponding states asserts that an interaction potential can be described by three key parameters: effective diameter, interaction strength, and second virial coefficient. If these parameters are the same, then different systems exhibit identical phase behavior, structure, and dynamics. In this review, we outline the origin and formulation of this law and the evidence that supports it. We further examine its applicability to protein solutions near liquid-liquid phase separation and to colloidal systems with short-range attraction and long-range repulsion, exploring the possibility of a universal phase diagram and extending its relevance for understanding the nature of these complex fluids.