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

TL;DR

This study uses self-consistent field theory to analyze the bending rigidities of microemulsion interfaces, revealing a sign switch in Gaussian bending modulus related to segregation strength, which impacts phase transition understanding.

Contribution

It provides a novel molecular-level prediction of curvature energies in microemulsions, highlighting the sign change of Gaussian bending rigidity with segregation strength.

Findings

Gaussian bending rigidity $ar{}$ switches sign with segregation strength

Mean bending modulus $$ remains positive and increases with segregation

Results inform phase transition mechanisms in microemulsions

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, $\bar{\kappa}$, and a torus with Willmore energy $W=2 \pi^2$ allows for direct evaluation of the mean bending modulus, $\kappa$. Consistent with this, the spherical droplet gives access to $2 \kappa + \bar{\kappa}$. We observe that $\bar{\kappa}$ 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, $\kappa$ remains positive and increases with increasing strength of segregation.