General principles of equilibrium surface thermodynamics

The thermodynamic description of the interfacial state of liquid systems is the basis for the development of relationships between the adsorption density T at a liquid interface, the surface tension and the surfactant bulk concentrations. Beside this the interfacial tension is an intrinsic parameter which determines the shape of a curved interface as well as different other types of capillary phenomena. 

The thickness of the phase s determined by the extension of the molecules forming the interface is given by the boundaries A-A and B-B. Beyond these planes the interaction forces between the molecules become identical to those in the bulk phases a and p. The phase s can therefore be described as a zone of continuously changing properties. The change of properties is related to intrinsic parameters because the surface model is determined by the molecular state and does not depend on the surface area. In other words, all properties of s are constant in the direction parallel to A-A but not in the direction normal to A-A.  

The volume of the s-phase depends on the size and shape of the molecules. There are three extreme possibilities for the molecular composition of s  

According to Gibbs we obtain surface excess quantities as the basic for adsorption isotherms and surface rheology. For flat or only slightly curved surfaces one can define the surface excess quantity convenient for discussion of a particular problem. It is assiuned that this freedom 

The surface excess amount or Gibbs adsorption of component i denoted by n-, may be positive or negative. This amount is given by 

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