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The structure of the isotropic L3 phase observed in many surfactant-water or surfactant-water-oil systems is analyzed. It is pointed out that the L3 phase generally appears in equilibrium with a dilute solvent phase on one hand and a lamellar liquid crystalline phase on the other. Irrespective of the detailed chemical nature of the system, the one-phase region is remarkably narrow in one direction, indicating that the thermodynamic degrees of freedom are effectively reduced by one due to an internal constraint in the phase. In accordance with previous work it is argued that the basic structural unit in the L3 phase is a surfactant bilayer. Furthermore, we conclude that the L3 phase appears when there is a spontaneous mean curvature toward the solvent at the polar/apolar interface. It is shown that, for a system which has such a curvature toward the solvent, the surface formed by the bilayer midplane has a negative average Gaussian curvature {K). By virtue of the Gauss-Bonnet theorem the bilayer under such circumstances has a multiply connected structure. The conclusion is then that, under conditions when there is a spontaneous mean curvature toward the solvent, it is possible to reach a low free energy state by forming multiply connected bilayer structures, as in many cubic phases, rather than planar bilayers. When interbilayer forces are weak, the structure tends to be disordered, leading to an isotropic solution (L3) rather than an ordered cubic structure. To minimize local variations in curvature at the polar/apolar interface, we demonstrate that the midplane surface should be close to a minimal surface. We then show that a certain dimensionless group associated with a given periodic minimal surface has approximately the same value for all of the well-known isotropic minimal surfaces. Assuming a minimal midplane surface, we can then show that, for a given thickness, a bilayer structure with a prescribed area-averaged mean curvature can only exist at a single volume fraction. This explains the internal constraint in the L3 phase, which is manifested in the narrow character of the L3 phase. Applying the equations that express this constraint, and using results from a theory due to Cantor to account for the effect of water/head-group interactions on water penetration, we present fits of these narrow phase-existence regions to the theory and rationalize the temperature dependence of the L3 phases in a variety of nonionic surfactant systems. For a microemulsion system the analysis shows that the spontaneous monolayer curvature'increases strongly on the addition of hydrocarbon. The emerging picture of the L3 phase is that the solution structure is characterized by a highly connected bilayer, extending in three dimensions, thus appearing bicontinuous in, e.g., NMR self-diffusion experiments, and having an average mean curvature at the polar/apolar interface toward the solvent. The basic driving force forming an L3 rather than a lamellar phase is thus not an entropy increase associated with disorder, as previously sug...

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The strongly repulsive short-range force between amphiphilic surfaces has, since Langmuir, been associated with how these surfaces modify the local water structure. We consider the results of both old and new experiments and conclude that these so-called "hydration" forces are not due to water structure. Instead, they originate from the entropic (osmotic) repulsion of molecular groups that are thermally excited to protrude from these fluid-like surfaces. Genuine hydration effects play a minor role, mainly in determining the hydrated size of the protruding groups. Our conclusions resolve many inconsistencies and observations that were not reconcilable with the hydration model.