Emulsion curvature

Kralchevsky, P.A., Ivanov, I.B., Ananfhapadmanabhan, K.P. and Lips, A. (2005) On the thermodynamics of particle-stabilized emulsions curvature effects and catastrophic phase inversion. Langmuir, 21, 50-63. 

The most frequent emulsiflcation using phase inversion is known as the PIT (Phase Inversion Temperature) method [81-83] and occurs through a temperature quench. This method is based on the phase behavior of nonionic surfactants and the correlation existing between the so-called surfactant spontaneous curvature and the type of emulsion obtained. 

Figure 1.4. For a nonionic surfactant, influence of the temperature on (a) the surfactant morphology and hence the spontaneous curvature, (b) the type of self-assembly, (c) the phase diagram, the number of coexisting phases is indicated (d) the coexisting phases at equilibrium, and (e) the corresponding emulsions.

Figure 5.3. Scheme explaining the influence of the spontaneous curvature on the activation energy for coalescence in a W/O emulsion. 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

Both the stability and curvature of the emulsions are dependent on the head sizes as is indicated from the following figures for the stability and mean diameter of benzene-water emulsions emulsified with various metallic oleates. 

Evidently the lamp black is more soluble in the benzene than in the water phase. On increasing the concentration of lamp black in the mixture the curvature of the particles increases and the mean diameter of the emulsion decreases as noted by Moore J.AXj.S). xli. 944, 1919) who obtained the following figures. The... 

Many reports are available where the cationic surfactant CTAB has been used to prepare gold nanoparticles [127-129]. Giustini et al. [130] have characterized the quaternary w/o micro emulsion of CTAB/n-pentanol/ n-hexane/water. Some salient features of CTAB/co-surfactant/alkane/water system are (1) formation of nearly spherical droplets in the L2 region (a liquid isotropic phase formed by disconnected aqueous domains dispersed in a continuous organic bulk) stabilized by a surfactant/co-surfactant interfacial film. (2) With an increase in water content, L2 is followed up to the water solubilization failure, without any transition to bicontinuous structure, and (3) at low Wo, the droplet radius is smaller than R° (spontaneous radius of curvature of the interfacial film) but when the droplet radius tends to become larger than R° (i.e., increasing Wo), the microemulsion phase separates into a Winsor II system. 

From the above equation, the variation of equilibrium disjoining pressure and the radius of curvature of plateau border with position for a concentrated emulsion can be obtained. If the polarizabilities of the oil, water and the adsorbed protein layer (the effective Hamaker constants), the net charge of protein molecule, ionic strength, protein-solvent interaction and the thickness of the adsorbed protein layer are known, the disjoining pressure II(x/7) can be related to the film thickness using equations 9 -20. The variation of equilitnium film thickness with position in the emulsion can then be calculated. From the knowledge of r and Xp, the variation of cross sectional area of plateau border Qp and the continuous phase liquid holdup e with position can then be calculated using equations 7 and 21 respectively. The results of such calculations for different parameters are presented in the next session. 

Later we discover another parameter, the phase inversion temperature(PIT), which helps us to predict the structure of emulsions stabilized by nonionic surfactants. The PIT concept is based on the idea that the type of an emulsion is determined by the preferred curvature of the surfactant film. For a modern introduction into the HLB and PIT concepts see Ref. [546],... 

Going higher in temperature results in a negative curvature (towards the hydrophilic head groups) and the surfactants start to favor water-in-oil emulsions. Now the whole sequence is repeated only with water drops in oil. Between 35°C and 37°C we have large water drops which decrease in size with increasing temperature (L2). Then, above 37°C, two phases appear a water phase underneath a water-in-oil microemulsion. 

The interfacial tension is a key property for describing the formation of emulsions and microemulsions (Aveyard et al., 1990), including those in supercritical fluids (da Rocha et al., 1999), as shown in Figure 8.3, where the v-axis represents a variety of formulation variables. A minimum in y is observed at the phase inversion point where the system is balanced with respect to the partitioning of the surfactant between the phases. Here, a middle-phase emulsion is present in equilibrium with excess C02-rich (top) and aqueous-rich (bottom) phases. Upon changing any of the formulation variables away from this point—for example, the hydrophilie/C02-philic balance (HCB) in the surfactant structure—the surfactant will migrate toward one of the phases. This phase usually becomes the external phase, according to the Bancroft rule. For example, a surfactant with a low HCB, such as PFPE COO NH4+ (2500 g/mol), favors the upper C02 phase and forms w/c microemulsions with an excess water phase. Likewise, a shift in formulation variable to the left would drive the surfactant toward water to form a c/w emulsion. Studies of y versus HCB for block copolymers of propylene oxide, and ethylene oxide, and polydimethylsiloxane (PDMS) and ethylene oxide, have been used to understand microemulsion and emulsion formation, curvature, and stability (da Rocha et al., 1999). 

The HLB concept assumes that the emulsion type is mainly governed by the curvature of the interface. Large headgroups may need considerable space on the outside of oil droplets in a continuous water phase and cause a positive curvature of the interface. On the other hand, small hydrophilic headgroups can be forced together inside a water droplet whereas large hydrophobic moieties extend into the continuous oil phase. The interface now has a negative curvature. 

Unfortunately this theory, in its original simple form at any rate, does not seem tenable, for several reasons. First, it requires the soap molecules to be closely packed in the interface this does not appear always to be the case second, it requires that the metallic ions should be rigidly attached to the hydrocarbon chains, which is not possible as they are, at any rate in the case of the soaps of the alkali metals, dissociated. Finally, unless the taper of the molecules, from one end to the other, were excessively small, the radius of curvature imposed by the interfacial film on the droplets should be comparable with the length of the soap molecules, and the only really stable sizes of droplets in emulsions should be of the order perhaps 100 A. in diameter. Actually, the droplets are generally about a hundred times larger than this. 

Oh et al. [16] have demonstrated that a microemulsion based on a nonionic surfactant is an efficient reaction system for the synthesis of decyl sulfonate from decyl bromide and sodium sulfite (Scheme 1 of Fig. 2). Whereas at room temperature almost no reaction occurred in a two-phase system without surfactant added, the reaction proceeded smoothly in a micro emulsion. A range of microemulsions was tested with the oil-to-water ratio varying between 9 1 and 1 1 and with approximately constant surfactant concentration. NMR self-diffusion measurements showed that the 9 1 ratio gave a water-in-oil microemulsion and the 1 1 ratio a bicontinuous structure. No substantial difference in reaction rate could be seen between the different types of micro emulsions, indicating that the curvature of the oil-water interface was not decisive for the reaction kinetics. More recent studies on the kinetics of hydrolysis reactions in different types of microemulsions showed a considerable dependence of the reaction rate on the oil-water curvature of the micro emulsion, however [17]. This was interpreted as being due to differences in hydrolysis mechanisms for different types of microemulsions. 

It was discussed that the structure created by the ternary system oil/water/ nanoparticle follows the laws of spreading thermodynamics, as they hold for ternary immiscible emulsions (oil 1 /oil 2/water) [114,116,117]. The only difference is that the interfacial area and the curvature of the solid nanoparticle has to stay constant, i.e., an additional boundary condition is added. When the inorganic nanoparticles possess, beside charges, also a certain hydrophobic character, they become enriched at the oil-water interface, which is the physical base of the stabilizing power of special inorganic nanostructures, the so-called Picker-... 

In spatially evolving multiphase media (e.g., during dissolution of a porous medium, or phase separation in a polymer blend), the mean curvature of the interface between two phases is of interest. Curvature is a sensitive indicator of morphological transitions such as the transition from spherical to rod-like micelles in an emulsion, or the degree of sintering in a porous ceramic material. Furthermore, important physicochemical parameters such as capillary pressure (from the Young-Laplace equation) are curvature-dependent. The local value of the mean curvature K — (1 /R + 1 /Ri) of an interface of phase i with principal radii of curvature Rx and R2 can be calculated as the divergence of the interface normal vector ,... 

A conclusion has been drawn in [67] that the extinction of the luminous flux (7//o, where, 7o is the intensity of the incident light and 7 is the intensity the light passed through the foam) is a linear function of the specific foam surface area. A similar dependence has been used also for the determination of the specific surface area of emulsions [68]. Later, however, it has been shown [69,70] that the quantity 7//o depends not only on the specific surface area (or dispersity) but also on the liquid content in the foams, i.e. on the foam expansion ratio, that during drainage can increase without changing the dispersity. Since foam expansion ratio and dispersity are determined by the radii of border curvatures and film thicknesses, all the structural elements of the foam will contribute to the optical density of foams. This means that... 

---