Microemulsion phases, periodic surfaces

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

Lattice models have been studied in mean field approximation, by transfer matrix methods and Monte Carlo simulations. Much interest has focused on the occurrence of a microemulsion. Its location in the phase diagram between the oil-rich and the water-rich phases, its structure and its wetting properties have been explored [76]. Lattice models reproduce the reduction of the surface tension upon adsorption of the amphiphiles and the progression of phase equilibria upon increasmg the amphiphile concentration. Spatially periodic (lamellar) phases are also describable by lattice models. Flowever, the structure of the lattice can interfere with the properties of the periodic structures. 

When comparable amounts of oil and water are mixed with surfactant a bicontinuous, isotropic phase is formed [6]. This bicontinuous phase, called a microemulsion, can coexist with oil- and water-rich phases [7,1]. The range of order in microemulsions is comparable to the typical length of the structure (domain size). When the strength of the surfactant (a length of the hydrocarbon chain, or a size of the polar head) and/or its concentration are large enough, the microemulsion undergoes a transition to ordered phases. One of them is the lamellar phase with a periodic stack of internal surfaces parallel to each other. In binary water-surfactant mixtures, or in... 

In the microemulsion the role of A is played by the period of damped oscillations of the correlation functions (Eq. (7)). The surface-averaged Gaussian curvature Ky, = 2t x/ S is the topological invariant per unit surface area. Therefore the comparison between Ryyi = Kyy / in the disordered microemulsion and in the ordered periodic phases is justified. We calculate here R= Since K differs for diffused films from cor-... 

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