Surfactant
Adsorption

For a dilute solution in which the activity of the surface active component can be related to concentration, the equation can be written in a form involving the slope of surface tension against logarithmic activity. For nonionic surfactants under ideal dilute conditions, Γ is proportional to −dγ/dln c divided by RT.

Ionic surfactants require careful treatment of dissociation, counterions, ionic strength and the thermodynamic component convention. The common appearance of a stoichiometric factor should not obscure the underlying point: Gibbs' equation is fundamentally an activity-based thermodynamic relation.

Experimentally, the Gibbs equation transforms a sufficiently accurate equilibrium surface-tension isotherm into an estimate of adsorbed amount.

Because Γ depends on a derivative, data quality and smoothing strategy matter. Small systematic errors in γ can become amplified when slopes are evaluated.

Equilibration must also be demonstrated: differentiating a dynamic γ(c,t) data set as if it represented equilibrium can produce a physically misleading adsorption isotherm.

As surfactant concentration increases, interfacial coverage typically increases and γ decreases.

At sufficiently high bulk concentration, micelles or other aggregates can form in the solution bulk. Above the critical micelle concentration, the monomer activity often changes much less strongly with total concentration, and the surface tension is correspondingly less concentration sensitive.

The CMC is therefore frequently identified from a break or transition in γ versus log c, but the interpretation can be complicated by impurities, non-equilibrium state of adsorption, mixed surfactants and nonideal solution behavior.

Liquid–liquid interfaces introduce additional phenomena. Hydrocarbons can participate in the interfacial layer; a surfactant may partition into both phases; competitive and cooperative adsorption can occur; and the apparent concentration in one phase may change because of transfer across the interface.

A rigorous experiment must therefore define not only nominal composition but also phase volumes, equilibration history and the possibility of component redistribution.

1. 1.J. W. Gibbs, The Collected Works of J. Willard Gibbs, Vol. 1: Thermodynamics, Longmans, Green and Co., 1928.
2. 2.A. I. Rusanov and V. A. Prokhorov, Interfacial Tensiometry, Studies in Interface Science, Vol. 3, Elsevier, Amsterdam, 1996.
3. 3.V. B. Fainerman, D. Möbius and R. Miller (Eds.), Surfactants: Chemistry, Interfacial Properties, Applications, Studies in Interface Science, Vol. 13, Elsevier, Amsterdam, 2001.