### Adsorption at the fluid/fluid interface

In general, the choice of the position of a Gibbs surface is arbitrary but it is possible to define quantities which are invariant with respect to this choice.

This is particularly useful for fluid/fluid interfaces where no experimental procedure exists for the unambiguous definition of a dividing surface.

The relative adsorption ( or ). If and are the Gibbs surface concentrations of components and 1, respectively, with reference to the same, but arbitrarily chosen, Gibbs surface, then the relative adsorption of component with respect to component 1, defined as

is invariant to the location of the Gibbs surface.

Alternatively, may be regarded as the Gibbs surface concentration of when the Gibbs surface is chosen so that is zero, i.e. the Gibbs surface is chosen so that the reference system contains the same amount of component 1 as the real system. Hence .

In terms of experimental quantities

where

and

and , are the total amounts of and 1 in the system, and is the total volume of the system. and thus defined correspond to .

For liquid/vapour interfaces the following approximate equation may be used in the domain of low vapour pressures:

where and are the mole fractions of and 1 respectively in the bulk liquid phase.

The reduced adsorption ( ) of component is defined by the equation

where , and are, respectively, the total Gibbs surface concentration and the total concentrations in the bulk phases and :

The reduced adsorption is also invariant to the location of the Gibbs surface.

Alternatively, the reduced adsorption may be regarded as the Gibbs surface concentration of when the Gibbs surface is chosen so that is zero, i.e. the Gibbs surface is chosen so that the reference system has not only the same volume, but also contains the same total amount of substance () as the real system.

Hence

In terms of experimental quantities

where now

and

and thus defined correspond to .

For liquid/vapour interfaces the following approximate equation may be used in the domain of low vapour pressures:

Because both and are invariant to the position of the Gibbs surface, it is possible to dispense with the concept of the Gibbs surface and to formulate the above definitions without explicit reference to a dividing surface.

It may happen that component is virtually insoluble in both of the adjoining phases, i.e. , but is present as a monolayer between them. Such a layer can be produced by spreading and is called a spread monolayer11. The relative and reduced adsorption become indistinguishable for such a component as does the difference between surface excess amount ( ) and amount of adsorbed substance , (see §1.1.11). In this case the surface concentration (= surface excess concentration) is defined by

The symbol for the (average) area per molecule (in the surface)12 is or .