Universal scaling of phase diagrams of polymer solutions: A successful isomorphism between theoretical conjectures and experimental results

Polymer chains diffuse 100 times slower than small molecules, taking from a few days to several months to reach the equilibrium of phase separation. Using methods for small molecules to map the phase diagrams of polymer solutions is painfully time-consuming. This is why different theoretical conjectures had not been validated for a long time, owing to the scarcity of good and systematic experimental data. This Review outlines the evolution of different phase transition theories of polymer solutions, mainly focusing on the classical Flory-Huggins mean-field theory, de Gennes' scaling theory, and Muthukumar's field-theoretical model based on the vanishing of the two-body interactions near the critical point for sufficiently long polymer chains. We also illustrate a method of combining small-angle laser light scattering with microfluidic droplet technology to quickly and precisely map phase diagrams of different polymer solutions. Using this novel method, we established a universal scaling of phase diagrams of polymer solutions, (ϕH - ϕL) ∼ N-2/9ε1/3, near the critical temperatures, where ϕH, ϕL, N, and ε are the volume fractions of the concentrated and dilute phases, the number of Kuhn segments, and the reduced temperature, respectively, agreeing well with Muthukumar's conjecture.