The Thermodynamics of Fluid Interfaces

Fluid interfaces are those systems in which the two phases forming the interface are mobile. Thus, they include liquid liquid and liquid gas interfaces. The example chosen here to illustrate the application of thermodynamics to these interfaces is a closed system containing both gas and liquid phases consisting of two components, propanol and water. The liquid phase is designated p and the gas phase a. Now imagine a microprobe moving up through p to the interface (see fig. 8.4). The concentration of the alcohol is constant in this phase and equal to In the gas phase, its concentration is much lower. Near the interface the alcohol concentration rises before it falls to the lower gas phase value c%. This observation is 

The second convention, due to Guggenheim [Gl], defines a surface phase a whose width is suflficient to include the inhomogeneities associated with the surface. Placing the boundaries at and xp, the surface excesses may be defined as follows  

The fundamental thermodynamic expression for the infinitesimal increase in Gibbs energy for a multicomponent system which can exchange matter with its surroundings was derived earlier on the basis of the first and second laws of thermodynamics (equation (1.3.21))  

P is the chemical potential of species i and the other symbols have their usual meanings. This expression was derived assuming that the only work done on the system is mechanical. If work is also done to change its area A, then the expression becomes 

Two points should be noted about equation (8.3.6). First, the number of components considered in the summation is that which can be added to the system in an independent way. Thus, if NaCl is a component, Na is not considered separately from Cl , since the concentrations of the two ions are exactly equal. However, local concentrations near the interface may not be equal. If one considers Na and Cl as independent components the total number of variables in equation (8.3.6) increases. In the case of charged components, the chemical potential p,- must be replaced by the electrochemical potential p,-. It also follows 

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