Liquid-vapor interface, Gibbs adsorption

With a liquid-vapor interface, Gibbs [36] has developed a thermodynamic treatment of the variation of surface tension with composition. This derivation comes from the book Physical Chemistry of Surfaces by Adamson [2, p. 340]. This derivation sets the stage for adsorption at the solid—liquid interface, which will be discussed next. 

Historically, the first derivation (by Gibbs) of an adsorption isotherm was that for the hquid—vapor interface. This derivation is presented next to put in place the nomenclature used in adsorption on both hquid—vapor and soUd—hquid interfaces. A derivation (by Langmuir) for adsorption at the sohd—hquid interface is presented after that for the hquid—vapor interface. Adsorption at the liquid—vapor interface is... 

Gibb 8 Adsorption Isotherm for the Liquid—Vapor Interface... 

As a first example, consider a pure liquid in equilibrium with its vapor. Because I wish to focus attention on the liquid/gas interface to the exclusion of adsorption effects at solid boundaries, I shall suppose the containing vessel to be chemically inert. The Gibbs-Duhem equation for the system is then... 

Gas-solid equilibria have been studied for over 200 years, since Fontana showed that activated charcoal adsorbs gases and vapors at room temperature [1]. A considerable amoxmt of theoretical and experimental literature is available. The Gibbs isotherm [2] and the multilayer adsorption theory of Brunauer, Emmett and Teller [3], provide serious theoretical guidelines and support in understanding the results of experimental studies. Although, gas-sohd isotherms are difficult to predict quantitatively [4], this branch of adsorption thermod3mamics is much easier than liquid-solid adsorption because of the relative simplicity of the gas-sohd interface as compared to the liquid-solid interface. The Gibbs equation relates the amoimt of a compoimd adsorbed per unit surface area of a hquid-gas or a hquid-hquid interface and the surface or interfacial tensions [2]. This relationship provides a useful theoretical framework. 

Before describing surfactant adsorption at the air/liquid (A/L) and liquid/liquid (L/L) interface it is essential to define the interface. The surface of a liquid is the boundary between two bulk phases, namely, liquid and air (or the liquid vapor). Similarly an interface between two immiscible liquids (oil and water) may be defined providing a dividing line is introduced since the interfacial region is not a layer that is one molecule thick, but usually have a thickness S 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 (Fig. 20.8). 

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