Sponge-like structures in polymer blends: Visualization, physico-mathematical analysis, and universality

Mesoscopic structures formed during an ordering process in thermodynamically unstable, isometric, binary molecular mixtures were explored by time-resolved scattering (TRS) and laser scanning confocal microscopy (LSCM). Three-dimensional (3D) bicontinuous structures, which were constructed for the first time by time-resolved LSCM, were found to have a "sponge-like" structure composed of two phases. The structure factor obtained by 3D Fourier transformation of the sponge was found to be identical to that obtained by TRS, confirming that the sponge truly reflects the structural entities evolving in the system. Furthermore, the sponge was shown for the first time to be theoretically predictable by using 3D computer simulations based on the time-dependent Ginzburg-Landau theory. The sponge was subjected to differential geometrical analysis: its Gaussian curvature K, mean curvature H, and their distributions were successfully determined for the first time. The result revealed that the sponge has hyperbolic interfaces with area-averaged curvatures satisfying <K > < 0 and <H > congruent to 0 and that its interface has some deviations from a minimal surface. The sponge was found to be strikingly similar to that occurring in oil/water/surfactant systems at the hydrophile-lipophile-balance, though their characteristic length scales are diversely different (mum vs nm), implying universality of the sponge.