Sign switch of Gaussian bending modulus for microemulsions; a self-consistent field analysis exploring scale invariant curvature energies

Abstract

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, $\barκ$, and a torus with Willmore energy $W=2 π^2$ allows for direct evaluation of the mean bending modulus, $κ$. Consistent with this, the spherical droplet gives access to $2 κ+ \barκ$. We observe that $\barκ$ 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 sponge-like microemulsion. Invariably, $κ$ remains positive and increases with increasing strength of segregation.