Spherical shape instability induced changes in the structure of microemulsions

The dispersed phase of a microemulsion in equilibrium with the excess dispersed phase is in the form of spherical globules. A change in the structure of the microemulsion near the transition from two to three phases is predicted on the basis of thermodynamic considerations. This change occurs because the spherical interface of the globules becomes unstable to perturbations. Because this instability is a result of the condition of equilibrium itself, there is a similarity (but not identity) to the behavior near a critical point. The spherical interface can also become unstable to perturbations in some single-phase microemulsions, although it is stable in microemulsions that coexist with the excess dispersed phase. Thermodynamic considerations also indicate that at the transition from two to three phases, the curvature of the spherical globules must be zero. This result is extended to the entire middle-phase microemulsion as the condition of zero mean-time or space-average curvature. Such a condition can be satisfied in the neighborhood of the transition points from two to three phases and again from three to two phases via the oscillations of the globular interface; in the central region of the middle phase, where the volume fraction of oil0.5, this condition is likely to be satisfied via the oscillations of the interface of a bicontinuous sponge.