Fractals and phase separation

Abstract

Fractal patterns are typically observed in systems that develop far from equilibrium. Because phase separating systems are far from equilibrium following a quench, we searched for fractal correlations in two quenched systems: borosilicate glasses and micellar solutions. Because scattering techniques are used, we review the expected scattering profiles expected for spinodal decomposition, nucleation and growth, and kinetic aggregation. In the borosilicate glasses, no non-classical structures are observed unless the boron-rich phase is leached out. Upon leaching, a peak appears in the scattering profile and, depending on leaching conditions, surface fractal porosity develops. We trace the observed structure to the leach process itself, which we believe produces phase separation by nucleation and growth. Short-range structure is explained in terms of reaction-limited dissolution. In micelle solutions, we find fractal patterns following a quench along the critical isochore into the unstable régime. A quench of equivalent depth off the critical isochore into the metastable régime produces no unusual structures. Fractal scattering profiles are also observed in the single-phase régime near the critical point. These observations suggest growth of polymeric structures in the single-phase régime.