Gibbs isotherm

For a binary system, the Gibbs adsorption equation in terms of surface excess is where Different influences at the interface may cause changes in the composition of the near-surface layer.

The general principle is: The Gibbs isotherm equation gives the exact quantitative relationship for these trends.

In the idealized model, the chemical components of the α and β bulk phases remain unchanged except when approaching the dividing surface.

In the real system, however, the total moles of a component varies depending on the arbitrary placement of the dividing surface.

The quantitative measure of adsorption of the i-th component is captured by the surface excess quantity.

[1] The surface excess represents the difference between the total moles of the i-th component in a system and the moles of the i-th component in a particular phase (either α or β) and is represented by: where Γi is the surface excess of the i-th component, n are the moles, α and β are the phases, and A is the area of the dividing surface.

The relative surface excess of species i and solvent 1 is therefore: For a two-phase system consisting of the α and β phase in equilibrium with a surface S dividing the phases, the total Gibbs free energy of a system can be written as: where G is the Gibbs free energy.

For a binary system containing two components the Gibbs Adsorption Equation in terms of surface excess is: The chemical potential of species i in solution,

is the chemical potential of the i-th component at a reference state, R is the gas constant and T is the temperature.

Differentiation of the chemical potential equation results in: where f is the activity coefficient of component i, and C is the concentration of species i in the bulk phase.

[3] Values of m are calculated using the Double layer (interfacial) models of Helmholtz, Gouy, and Stern.

[5] As such, surface tension is not a reliable method for determining the relative propensity of ions toward the air-water interface.

A method for determining surface concentrations is needed in order to prove the validity of the model: two different techniques are normally used: ellipsometry and following the decay of 14C present in the surfactant molecules.

The method involves attaining a one square meter portion of air-liquid interface of binary solutions using a microtome blade.

Another method that is used to determine the extent of adsorption at an air-water interface is the emulsion technique, which can be used to estimate the relative surface excess with respect to water.