Sign Switch of Gaussian Bending Modulus for Microemulsions: A Self-Consistent Field Analysis Exploring Scale Invariant Curvature Energies.

Bending rigidities of tensionless balanced liquid-liquid interfaces as occurring in microemulsions are predicted using self-consistent field theory for molecularly inhomogeneous systems. Considering geometries with scale invariant curvature energies gives unambiguous bending rigidities for systems with fixed chemical potentials: the minimal surface Im3m cubic phase is used to find the Gaussian bending rigidity κ[over ¯], and a torus with Willmore energy W=2π^{2} allows for direct evaluation of the mean bending modulus κ. Consistent with this, the spherical droplet gives access to 2κ+κ[over ¯]. We observe that κ[over ¯] tends to be negative for strong segregation and positive for weak segregation, a finding which is instrumental for understanding phase transitions from a lamellar to a spongelike microemulsion. Invariably, κ remains positive and increases with increasing strength of segregation.