Twist grain boundaries in cubic surfactant phases

Twist grain boundaries in bicontinuous cubic surfactant phases are studied by employing a Ginzburg–Landau model of ternary amphiphilic systems. Calculations are performed on a discrete real-space lattice with periodic boundary conditions for the lamellar Lα, gyroid G, diamond D, and the Schwarz P phases for various twist angles. An isosurface analysis of the scalar order parameter reveals the structure of the surfactant monolayer at the interfaces between the oil-rich and water-rich regions. The curvature distributions show that the grain boundaries are minimal surfaces. The interfacial free energy per unit area is determined as a function of the twist angle for the G, D, P, and lamellar phases using two complementary approaches: the Ginzburg–Landau free-energy functional and a geometrical approach based on the curvature energy of a monolayer. For the Lα, G, and D phases the interfacial free energy per unit area is very small, has the same order of magnitude, and exhibits a nonmonotonic dependence on the ...