Surfactants (Soaps and Detergents) and Physicochemical Properties - Surface and Colloid Chemistry: Principles and Applications - page 55

Gas

Surface

Liquid

FIGure 3.13 Concentration of detergent (shaded with tail) in solution and at the surface.
The shaded area at the surface is the excess concentration due to accumulation.

X X´

Beta

G G

Alpha

P P´

FIGure 3.14 Liquid column in a real system with α-phase and β-phase.

To analyze these data, the well-known Gibbs adsorption equation (Chattoraj and
Birdi, 1984; Birdi, 1989) has to be used. A liquid column containing i number of
components is shown in Figure 3.14, according to the Gibbs treatment of two bulk
phases, that is, α and β, separated by the interfacial region AA′BB′.
Gibbs considered that this interfacial region is inhomogeneous and difficult to
define, and he therefore also considered a more simplified case in which the interfa-
cial region is assumed to be a mathematical plane GG′ (Figure 3.14).
In the actual system (Figure 3.15), the bulk composition of the i i-th component in
α-phase and β-phase are c iα and c iβ , respectively.
However, in the idealized system, the chemical compositions of the α and β
phases are imagined to remain unchanged right up to the dividing surface so that
their concentrations in the two imaginary phases are also ciα iα and c iβ , respectively.
If in iα and n iβ denote the total moles of the i i-th component in the two phases of
the idealized system, then the Gibbs surface excess Γ ni of the i -th component can be
defined as

n i x = n i t − n iα − n iβ (3.12)

where n i t is the total moles of the i i-th component in the real system.