Theory for the phase behavior of microemulsions

Abstract

A model has been developed which quantitatively predicts phase behavior in micellar systems or microemulsions. This model treats the interface between a droplet and its contacting external phase as a duplex monolayer of oriented surfactant molecules. The respective hydrophilic heads and lipophilic chains sides of the interface are treated as independent interphases, water interacting with the heads and oil with the chains. Direction and degree of curvature are imposed by a lateral stress gradient in the interface resulting from differences in interaction on either side of the interface. This stress gradient is expressed in terms of physically measurable quantities, surfactant molecular volume, interfacial tension and compressibility. Surfactant volume and compressibility are split into separate contributions by heads and chains. (This lays a quantitative physical basis for describing Hydrophilic versus Lipophilic interactions in the system (HLB).) When the heads volume and compressibility are larger than that of the chains, the interface curves convex to the water phase, the microemulsion is O/W. The microemulsion is W/O when the chains volume and compressibility is larger. Equations are developed for both oil droplets (O/W) and water droplets (W/O) which relate interfacial tension and surfactant head and chain volumes and compressibilities to phase behavior. These equations are generated by the geometry of 2 concentric spherical shells surrounding the droplet and by force balance across these shells. Phase behavior is expressed in terms of water and oil uptake in saturated microemulsions and is described on an idealized ternary phase diagram. The responses are explored of water and oil uptake to temperature and composition. For ethoxylated surfactants, increasing temperature, salt concentration and oil aromaticity result in increased oil uptake and decreased water uptake. Decreasing head/chain volume and compressibility ratios have the same effect. The system tends to become more lipophilic and shifts in the direction of Winsor's micellar solution Types I - III - II. This shift is related to phase regions on the idealized ternary diagram. Types I and II fall in 2 phase regions and Type III in the 3 phase region. The theory predicts shifts in phase boundaries in response to the above variables. Thus, the theory correlates water and oil uptake, the idealized ternary diagram and Winsor's transition in micellar types. Where water and oil uptake are known, interfacial tension can be predicted and vice versa. The theory also predicts droplet size and interfacial concentrations of adsorbed surfactant in terms of molecules/droplet.