Universality in the phase behavior of soft matter: A law of corresponding states

We show that the phase diagram of substances whose molecular structure changes upon varying the thermodynamic parameters can be mapped, through state-dependent scaling, onto the phase diagram of systems of molecules having fixed structure. This makes it possible to identify broad universality classes in the complex phase scenario exhibited by soft matter, and enlightens a surprisingly close connection between puzzling phase phenomena and familiar behaviors. The analysis presented provides a straightforward way for deriving the phase diagram of soft substances from that of simpler reference systems. This method is applied here to study the phase behavior exhibited by two significative examples of soft matter with temperature-dependent molecular structure: thermally responsive colloids and polymeric systems. A region of inverse melting, i.e., melting upon isobaric cooling, is predicted at relatively low pressure and temperature in polymeric systems.