# Thermodynamics

The thermodynamic instability of an emulsion is readily demonstrated if one agitates a sealed vessel containing pure oil and pure water and then observes the change in the appearance of the system with time. The optically opaque emulsion which is initially formed by agitation breaks down over time until a layer of oil is observed on top of a layer of water (Figure 6.1).

The origin of this thermodynamic instability can be illustrated by comparing the free energy of a system consisting of an oil and an aqueous phase before and after emulsification (Hunter 1989). To simplify this analysis, we will initially assume that the oil and water have similar densities so that no creaming or sedimentation occurs. As a consequence, the final state consists of a single large droplet suspended in the continuous phase (Figure 7.1), rather than a layer of oil on top of a layer of water (see Figure 6.1). In its initial state, prior to emulsification, the free energy is given by:

and in its final state, after emulsification, it is given by: Separated Emulsion

Phases

Separated Emulsion

Phases

FIGURE 7.1 The formation of an emulsion is thermodynamically unfavorable because of the increase in surface area between the oil and water phases.

where GO, GW, and Gj are the free energies of the oil phase, water phase, and the oil-water interface, respectively; T is the absolute temperature; and S is the configurational entropy of the droplets in the system. The superscripts i and f refer to the initial and final states of the system. The free energies of the bulk oil and water phases remain constant before and after homogenization: G'O = GO and G'W = GW and so the difference in free energy between the initial and final states is given by (Hunter 1989):

AGformation = Gf - G' = GI - GI - (TSconfig - TSronfig) = AGJ - TASconfig (7.3)

By definition, the difference in interfacial free energy between the initial and final states (AGI) is equal to the increase in surface area between the oil and aqueous phases (AA) multiplied by the interfacial tension (y): AGI = yAA. Hence,

Aformation = YAA - TASconfig (7.4)

The change in interfacial free energy (yAA) is always positive, because the interfacial area increases after homogenization, and therefore it opposes emulsion formation. On the other hand, the configurational entropy term (-TASconfig) is always negative, because the number of arrangements accessible to the droplets in the emulsified state is much greater than in the nonemulsified state, and therefore it favors emulsion formation. An expression for the con-figurational entropy can be derived from a statistical analysis of the number of configurations emulsion droplets can adopt in the initial and final states (Hunter 1989):

ASConfig = - — [\$ ln \$ + (1 - \$) ln(1 - \$)] (7.5)

where k is Boltzmann's constant, n is the number of droplets, and \$ is the dispersed-phase volume fraction. In most food emulsions, the configurational entropy is much smaller than the interfacial free energy and can be ignored (Hunter 1989). As an example, consider a 10% oil-in-water emulsion containing 1-|im droplets (y = 0.01 N m-1). The interfacial free energy term (yAA) is about 3 kJ/m3 of emulsion, whereas the configurational entropy term (TAS) is about 3 x 10-7 kJ/m3.

The overall free energy change associated with the creation of a food emulsion can therefore be represented by the following expression:

Thus the formation of a food emulsion is always thermodynamically unfavorable, because of the increase in interfacial area after emulsification. It should be noted that the configura-tional entropy term can dominate the interfacial free energy term in emulsions in which the interfacial tension is extremely small and that these systems are therefore thermodynamically stable (Hunter 1989). This type of thermodynamically stable system is usually referred to as a microemulsion, to distinguish it from thermodynamically unstable (macro)emulsions.

In practice, the oil and water phases normally have different densities, and so it is necessary to include a free energy term which accounts for gravitational effects (i.e., the tendency for the liquid with the lowest density to move to the top of the emulsion). This term contributes to the thermodynamic instability of emulsions and accounts for the observed creaming or sedimentation of droplets (Section 7.3.2). 