Interfaces Gibbs dividing line

The standard approach for describing surfactant adsorption at the gas-liquid interface is based on the Gibbs methodology [16]. The Gibbs dividing surface was introduced and is mathematically defined by the interface line that divides the surface excess of the solvent into two equal parts with opposite signs, and the total surface excess of the solvent is, therefore, equal... 

When surfactant molecules concentrate at the interface, some solvent molecules are displaced, so the surface solvent concentration is lower than the bulk solvent concentration. The Gibbs convention defines the dividing line between the two phases so that the (negative) surface excess of solvent equals zero. Then equation 4 gives the surface excess of (say) laurylsulfonic acid at the air-water interface. When the actual interfacial concentration of surfactant is needed, the situation is more complicated. Methods for handling these complications have been discussed (1,7). 

Before describing surfactant adsorption at A/L and L/L interfaces, it is essential first to define the interface. The surface of a liquid is the boundary between two bulk phases, namely liquid and air (or the liquid vapour). Similarly, an interface between two immiscible liquids (oil and water) may be defined, provided that a dividing line is introduced as the interfacial region is not a layer of one-molecule thickness rather, it usually has a thickness 8 with properties that are different from the two bulk phases a and p [1]. However, Gibbs [2] introduced the concept of a mathematical dividing plane in the interfacial region (Figure 5.1)... 

Figure 5 Density profiles for the binary hard sphere fee [100] crystal-melt interface plotted on a fine scale. The dashed, vertical line is the Gibbs dividing surface defined in Section 2.2. The dotted grid is commensurate with the lattice planes in the bulk crystal and is included to better visualize the expansion of the lattice constant in the interfacial region. (Reprinted by permission of the American Institute of Physics from Davidchack and Laird )...

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