Gibbs dividing line

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)... 

Within this definition, argon is more hydrophobic (or less hydrophilic) than krypton at, say, 25X. Thus the more positive AG , the more hydrophobic is the solute. The more negative AG , the more hydrophilic is the solute. One can conveniently choose AG = 0 as the dividing line between H0O and H0I solutes, but this is not necessary. What is important is the relative hydrophobicity, or the difference between the solvation Gibbs energies of two solutes in the same solvent. In the above definition, the same solvent is water. Clearly, the concept can be extended to any solvent or mixture of solvents. 

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... 

The first reason that led Latora and Baranger to evaluate the time evolution of the Gibbs entropy by means of a bunch of trajectories moving in a phase space divided into many small cells is the following In the Hamiltonian case the density equation must obey the Liouville theorem, namely it is a unitary transformation, which maintains the Gibbs entropy constant. However, this difficulty can be bypassed without abandoning the density picture. In line with the advocates of decoherence theory, we modify the density equation in such a way as to mimic the influence of external, extremely weak fluctuations [141]. It has to be pointed out that from this point of view, there is no essential difference with the case where these fluctuations correspond to a modified form of quantum mechanics [115]. 

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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