Total free energy, emulsions

Unlike micelles, an emulsion is a liquid system in which one liquid is dispersed in a second, immiscible liquid, usually in droplets, with emulsiLers added to stabilize the dispersed system. Conventional emulsions possess droplet diameters of more than 200 nm, and are therefore optically opaque or milky. Conventional emulsions are thermodynamically unstable, tending to reduce their total free energy by reducing the total area of the two-phase interface. In contrast, microemulsions with droplet diameters less than 100 nm are optically clear and thermodynamically stable. Unlike conventional emulsions that require the input of a substantial amount of energy, microemulsions are easy to prepare and form spontaneously on mixing, with little or no mechanical energy applied (Lawrence and Rees, 2000). 

Emulsions made by agitation of pure immiscible liquids are usually very unstable and break within a short time. Therefore, a surfactant, mostly termed emulsifier, is necessary for stabilisation. Emulsifiers reduce the interfacial tension and, hence, the total free energy of the interface between two immiscible phases. Furthermore, they initiate a steric or an electrostatic repulsion between the droplets and, thus, prevent coalescence. So-called macroemulsions are in general opaque and have a drop size > 400 nm. In specific cases, two immiscible liquids form transparent systems with submicroscopic droplets, and these are termed microemulsions. Generally speaking a microemulsion is formed when a micellar solution is in contact with hydrocarbon or another oil which is spontaneously solubilised. Then the micelles transform into microemulsion droplets which are thermodynamically stable and their typical size lies in the range of 5-50 nm. Furthermore bicontinuous microemulsions are also known and, sometimes, blue-white emulsions with an intermediate drop size are named miniemulsions. In certain cases they can have a quite uniform drop size distribution and only a small content of surfactant. An interesting application of this emulsion type is the encapsulation of active substances after a polymerisation step [25, 26]. 

Let us assume that the total free energy of the emulsion can be separated into several independent contributions. Considering hypothetically the formation or coalescence of emulsion of two immiscible liquids (e.g. oil and water), such that external field forces are absent. The total free energy (Gg) of the system just before emulsification process can be expressed in the form (10)... 

As mentioned in Chapter 10, the preparation of an emulsion requires oil, water, a surfactant, and energy. This can be considered on the basis of the energy required to expand the interface, AAy (where AA is the increase in interfacial area when the bulk oil with area Aj produces a large number of droplets with area Aj Aj Aj, where y is the interfacial tension). Since y is positive, the energy to expand the interface is large and positive. This energy term cannot be compensated by the small entropy of dispersion TAS (which is also positive), and the total free energy of formation of an emulsion, AG is positive. 

Consider two emulsion droplets joined by a neck, as illustrated in Fig. 12. The surfactant film is highly curved in the region of the neck while it is virtually planar elsewhere. As the neck grows or shrinks there is a change in both the area of the film and in its curvature. We can write the total free energy of the film, Gp, as a sum of three terms ... 

Y is positive, the energy to expand the interface is large and positive. This energy term cannot be compensated by the small entropy of dispersion TAS (which is also positive) and the total free energy of formation of an emulsion, AG is positive. 

The thermodynamic stability of emulsions can readily be assessed by comparing the free energy to that of an undispersed system (Fig. 3.15). The total free energy in the undispersed system (I), excluding surface terms, is given by... 

Let us first consider interfaces at equilibrium. Any stress (osmotic or shear stress) imposed to the emulsion increases the amount of interface, leading to a modification of the free energy. For a monodisperse collection of N droplets of radius a, the total interfacial area of the undeformed droplets is So = 47t No. If the emulsion is compressed up to each droplet is pressing against its neighbors through... 

Coalescence. This is caused by rupture of the film between two emulsion drops or two foam bubbles. The driving force is the decrease in free energy resulting when the total surface area is decreased, as occurs after film rupture. The Laplace equation (Section 10.5.1) plays a key role. 

The scaled surface area and its variation with d> are of crucial importance in the definition and evaluation of the osmotic pressure , H, of a foam or emulsion. We introduced the concept in Ref 37, where it was referred to as the compressive pressure , P. It has turned out to be an extremely finitful concept (22,27,38). The term osmotic was chosen, with some hesitation, because of the operational similarity with the more familiar usage in solutions. In foams and emulsions, the role of the solute molecules is played by the drops or bubbles that of the solvent by the continuous phase, although it must be remembered that the nature of the interaetions is entirely different. Thus, the osmotic pressure is denned as the pressure that needs to be applied to a semipermeable, freely movable membrane, separating a fluid/fluid dispersion from its continuous phase, to prevent the latter from entering the former and to reduce thereby the augmented surface free energy (Fig. 4). The membrane is permeable to all the components of the continuous phase but not to the drops or bubbles. As we wish to postpone diseussion of compressibility effects in foams until latter, we assume that the total volume (and therefore the volume of the dispersed phase) is held constant. 

Emulsions are dispersions of one liquid in another liquid, most commonly water-in-oil or oil-in-water. The total interfacial area in an emulsion is very large, and sinee flie interfacial area is associated with a positive free energy (the interfacial tension), the emulsion system is thermodjmam-ically unstable. Nevertheless, it is possible to make emulsions with an excellent long-term stability. This requires the use of emulsifiers that accumulate at the oil/water interface and create an energy barrier towards flocculation and coalescence. The emulsifiers can be ionic, zwitterionic, or nonionic surfactants, proteins, amphiphilic polymers, or combinations of polymers and surfactants. The structure of the adsorbed layer at the water/oil interface may be rather complex, involving several species adsorbed directly to the interface as well as other species adsorbing on top of the first layer. 

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