Gibbs-Duhem equation surface adsorption

Gibbs approach, for treating surfactant adsorption, 24 134-138 Gibbs dividing surface, 24 135 Gibbs-Duhem equation, 3 744 24 134, 135, 672, 677... 

The Gibbs-Duhem equation is used in several cases in electrochemistry, e.g., in the derivation of - Gibbs adsorption equation or -> Gibbs-Lippmann equation since Eq. (4) can be extended by surface work ... 

Adsorption is described by the Gibbs-Duhem equation. Considering only a single vapor at constant temperature, electric potential, and elastic strain, the change in surface tension is given by... 

Gibbs [2] derived a thermodynamic relationship between the surface or interfacial tension y and the surface excess F (adsorption per unit area). The starting point of this equation is the Gibbs-Duhem equation, as given above [see Eq. (5.1)]. At equilibrium, where the rate of adsorption is equal to the rate of desorption, dG = 0. Hence, at a constant temperature, but in the presence of adsorption. 

Surface solution theories should be consistent with the Gibbs adsorption equation (Equation 1.24), just as the bulk solution theories should be consistent with the Gibbs-Duhem equation. It is readily shown that ideal surface solution theory, as discussed above, satisfies this criterion (see Problem 1.15). However, regular surface solution theory does not, owing to the limitations of modeling the interfacial region by a single composition. This matter is discussed in some detail by Defay et al. (1966). 

This is essentially the equation widely used in conventional descriptions where the adsorption complexes AR and BR are simply A and B in the adsorbed state.By combination of these equations with a Gibbs-Duhem equation formulated for the sorption phase treated as a homogeneous solution, expressions are derived for -yar, 7br, In and In Kc for three cases (a) adsorption of a single substance (presumably from the vapour), (6) adsorption from a binary mixture in which a certain constant number of adsorption sites remain empty, and (c) adsorption from a binary mixture which fully saturates the surface (cr = 0). 

This is the Gibbs-Duhem equation for surface adsorption. Now y can be expressed in terms of i independent intensive variables, which is consistent with the phase rule. The important point is that the coefficient of the second term is the relative adsorption of component i with respect to component 1. Then, we have... 

---