Amphiphile bilayers · Ohta-Kawasaki free energy · microphase separation
Amphiphiles (soap molecules, lipids) self-assemble due to competing short-range (Flory-Huggins) and long-range electrostatic/entropic interactions. The Ohta-Kawasaki functional F[φ] = ∫[f(φ) + κ|∇φ|²]dr + γ∫∫G(r−r′)(φ−φ̄)(φ′−φ̄)dr dr′ describes microphase separation. Depending on φ and χ: disordered, lamellar (bilayers), hexagonal cylinders, gyroid, or micellar phases.