General conditions governing the formation of cylindrical microemulsion aggregates

On the basis of classical surface thermodynamics in a general version derived by Melrose, and the Helfrich expression for the bending free energy of an interface, we consider the mechanical and physicochemical conditions which control the formation of cylindrical microemulsion aggregates of water in oil in the presence of an excess water phase (Winsor II case). We find that ultralow interfacial tensions (about 10−7 N/m or less) have to be attained for cylindrical geometry in the range about the spontaneous curvature in order to obtain spherocylindrical water aggregates in appreciable amounts. According to the generalized Young-Laplace equation for interfaces with bending free energy, this corresponds to an excess pressure of a few N/m2. Furthermore, mechanical stability of the cylinder-shaped aggregates requires the interfacial tension at very large radii, γ∝, to fulfill the condition 2k c H 0 2 ⩽ γ ∞ ⩽ ( 8 3 )k c H 0 2 , where kc is the ordinary bending elasticity constant and H0 the spontaneous curvature. Approximately, this condition means that 1 2 ⩽ k c kT ⩽ 2 3 . In addition, the Gaussian curvature elasticity constant, k c , should be positive and fairly large as compared with kc; otherwise spheroidal droplets will predominate. It is inferred that elongated spherocylindrical aggregates might account for the bicontinuity of Winsor II and Winsor III microemulsions observed at comparatively low water contents when H0 differs appreciably from zero.