The surface excess concentration of an emulsifier can be determined from measurements of the variation in the surface tension of an air-liquid interface as the emulsifier concentration in the bulk liquid is increased (Figure 5.7). There is an equilibrium between emulsifier molecules at the interface and those in the bulk liquid. As the concentration of emulsifier in the bulk liquid is increased, so does their concentration at the interface. The presence of the emulsifier molecules at the interface shields the unfavorable contact between the oil and water molecules and therefore reduces the surface tension. At a certain concentration, the surface tension reaches a constant value because the surface becomes saturated with emulsifier molecules. For small-molecule surfactants, the saturation of the surface occurs at approximately the same concentration as the surfactant molecules form micelles in the bulk liquid (i.e., the critical micelle concentration) (Section 4.5.2). A relationship between the decrease in surface tension with emulsifier concentration and the amount of emulsifier present at the surface can be derived from a mathematical treatment of the thermodynamics of the system (Hiemenz 1986, Hunter 1986). This relationship is known as the Gibbs isotherm equation, which is given by the following expression for an ideal solution:
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