Polymeric Sol-Gel Transition with the Diverging Correlation Length Verified by Small-Angle X-ray Scattering

Sol-gel transitions of polymers are pivotal phenomena in material science, yet the critical phenomenon of structure during gelation has remained unclear. Here, we investigated the sol-gel transition of a fluorous polymer, poly(vinylidene fluoride-co-hexafluoropropylene), in a blend of two ionic liquids. This system features a quite high amount of cross-linker and binding sites with ion-dipole interactions between the cation and C-F dipoles, thereby facilitating easy exchange of the cross-links. Changing the mixing ratio of the two ionic liquids enabled tuning the ion-dipole interactions and inducing sol-gel transition. Notably, the correlation length and molar mass, obtained by small-angle X-ray scattering, diverged at the gelation point. Moreover, the derived critical exponents (ν = 0.85 ± 0.05) aligns remarkably well with the prediction from percolation theory (ν = 0.88). To our knowledge, this is the first report on the evident divergence during polymeric gelation by small-angle scattering and the verification of the critical exponents of the percolation theory.