Sponge-like structures and their Gaussian curvatures in polymer mixtures and microemulsions

Bicontinuous structures formed in the late stage of spinodal decomposition (SD) in polymer mixtures were explored experimentally by time-resolved light scattering (TLS) and laser scanning confocal microscopy (LSCM) and computationally by three-dimensional (3D) simulations based on time-dependent Ginzburg-Landau (TDGL) theory. The 3D structures constructed by LSCM exhibited a sponge-like structure and were found to be statistically identical to those constructed by the computer simulations through equality of their scattering structure factors. Moreover, their structure factors were found to be identical to that obtained by TLS, revealing that the 3D structures truly reflect the structure entities occurring in the polymer mixtures and that the TDGL theory accounts for the phase structures evolving in the late stage SD. Gaussian curvature K and mean curvature H were evaluated from the 3D structures, the results of which were compared with the "scattering-mean-curvature" determined by using the Kirste-Porod theory and with K determined by using a Gaussian random-field theory. The sponge-like structure was found to be strikingly similar to that occurring in an equilibrium microemulsion system at the hydrophile-lipophile balance temperature, though their characteristic length scales are different by two-three orders of magnitude.