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 I m 3 m cubic phase is used to find the Gaussian bending rigidity κ ¯, and a torus with Willmore energy W =2 π2 allows for direct evaluation of the mean bending modulus κ . Consistent with this, the spherical droplet gives access to 2 κ +κ ¯. We observe that κ ¯ 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.
- Publication:
-
Physical Review Letters
- Pub Date:
- January 2018
- DOI:
- 10.1103/PhysRevLett.120.028003
- arXiv:
- arXiv:1711.03760
- Bibcode:
- 2018PhRvL.120b8003V
- Keywords:
-
- Condensed Matter - Soft Condensed Matter
- E-Print:
- 7 pages, 5 figures