Curvature, of surfactant layers

Figure 8 Schematic change in spontaneous curvature of surfactant layers in the process of spontaneous formation of highly concentrated W/O emulsions (from Ref [58], with permission).

The spontaneous curvature of surfactant layers can be controlled in many ways see Table 7.1. For ionic surfactants, one can control the contribution coming from the counter-ions by adjusting the concentration of salt. As the electrolyte concentration increases, the ionic atmosphere approaches the oil-water interface (Debye length decreases), the transverse pressiue moment decreases and the spontaneous curvature faUs. " Increasing the temperature does the opposite, because the osmotic pressxne (jt) of the counter-ions is proportional to temperature due to the osmotic pressure ideal gas law n = cRT. 

Figure 11.16 Schematic change in the spontaneous curvature of surfactant layers in the process ofspontaneous formation of W/O gel emulsions (Reproduced by permission of the American Chemical Society from ref. 40)...

This (local) double twist configuration clearly involves a hyperbolic deformation of the imaginary layers. In contrast to the hyperbolic layers found in bicontinuous bilayer lyotropic mesophases, the molecules within these chiral thermotropic mesophases are oriented parallel to the layers, to achieve nonzero average twist. The magnitude of this twist is deternuned by the direction along which the molecules lie (relative to the principal directions on the surface), and a function of the local curvatures of the layers (K1-K2), cf. eq. 1.4. Just as the molecular shape of (achiral) surfactant molecules determines the membrane curvatures, the chirality of these molecules induces a preferred curvature-orientation relation, via the geodesic torsion of the layer. 

Solubilization of an insoluble solute molecule in a surfactant solution is primarily governed by fundamental properties linked to thermodynamics and structure. These quantities, also at the origin of the general layout of ternary or quaternary phase diagrams, are spontaneous curvature and surfactant layer bending constants. These notions will be briefly introduced and will allow us to distinguish between the different types of solubilization which are observed experimentally. 

The surface dividing the components of the mixture formed by a layer of surfactant characterizes the structure of the mixture on a mesoscopic length scale. This interface is described by its global properties such as the surface area, the Euler characteristic or genus, distribution of normal vectors, or in more detail by its local properties such as the mean and Gaussian curvatures. 

The type of structure observed is closely related to the spontaneous curvature Co of the surfactant assemblies [7]. By using an analogy with liquid crystals, which can also adopt layered structures, Helfrich [8] introduced the concept of the elastic-free energy associated with thermally excited deviations from the spontaneous curvature of the microstructures. This elastic-free energy per unit area is given by... 

The HLD concept has been recently related to the so-called net-average curvature which indicates the size of the oil and water domains in the micro emulsion. For marginal microemulsions, i.e. of the WI or WII type at some distance from optimum, the inverse of the swollen micelle Sauter diameter is proportional to HLD. The zero net curvature at optimum does not result from infinite radius but rather from the coexistence of finite curvatures of opposite signs. For bicontinuous micro emulsions, it is the inverse of the characteristic length which is maximised at HLD = 0. As discussed elsewhere [38], its value at optimum formulation is the maximum distance that a molecule of oil or water can be separated from the surfactant layer and still interacts with it. In other words, it is the length at which the molecular interaction becomes equal to the molecular entropy. 

Not only do surfactants and cosurfactants lower the interfacial tension, but also their molecular structures affect the curvature of the interface as shown schematically in Fig. 3. The hydrocarbon chains are rather closely packed (about 0.25 nm per chain) they repel one another sideways and as a result have a tendency to bend the interface around the water side. The counterions of the ionic headgroups also repel one another sideways and thus tend to curve the interface around the oil side. The bullQ polar groups of nonionic surfactants have a similar effect. So we understand qualitatively that more cosurfactant promotes W/O rather than O/W microemulsions. More electrolyte compresses the double layer, diminishes the sideways pressure of the double layer, and also promotes W/O microemulsions. The polar groups of PEO nonionics become more compact (less soluble) at higher temperatures, and so with this type of surfactants high temperature leads to W/O microemulsions. 

Figure 3 Schematic representation of the influence of surfactants on the curvature of the interface. The hydrophilic parts of the surfactant molecules repel each other sideways, tend to curve the interface around the oil side, and promote O/W emulsions. This effect is most pronounced with long and/or bullg nonionic polar groups or, in the case of ionic surfactants, at low electrolyte content, where the double layers are extended. On the other hand, the mutual repulsion of the hydrophobic parts of the surfactants tend to curve the interface around the water side and promote W/O emulsions. Here, long hydrocarbon tails and/or close packing, as in combinations with cosurfactants, make the effects more pronounced. (After Refs. 11 and 12.)...

One of the most common structures encountered in microemulsions consists of water or oil droplets dispersed in a continuous phase of oil or water, respectively. The type of dispersion results from the preferred curvature Co of the surfactant layer, which is by convention positive for oil-in-water (O/W) systems and negative for water-in-oil (W/O) systems. Co can be varied by adjusting the surfactant/cosurfactant ratio, which allows swelling of the droplets until a maximum is reached. When the systems become more concentrated, the micellar swelling is mostly limited by attractive interparticle interactions, as observed, for example, for microemulsions close to a critical point. 

By varying several parameters such as the W/O ratio, one can induce an inversion from an O/W to a W/O microemulsion and vice versa. The type of structure in the inversion domain depends essentially on the bending constant a characteristic of the elasticity of the surfactant layer [7]. If Ke is on the order of kT (where k is the Boltzmann constant and T absolute temperature), the persistence length of the film (i.e., the distance over which the film is locally flat) is microscopically small. The interfacial film is flexible and is easily deformed under thermal fluctuations. The phase inversion occurs through a bicontinuous structure formed of water and oil domains randomly interconnected [8,9]. The system is characterized by an average curvature around zero, and the solubilization capacity is maximum. When K kT, is large and the layers are flat over macroscopic distances. The transition occurs through a lamellar phase. 

---