ABSTRACT
The first attempt to provide a model approach to the theoretical description of adsorption phenomena based on a certain model of the surface layer was developed almost a hundred years ago by Irving Langmuir [1]. While the physical model on which the approach was based is, possibly, the simplest one (the adsorbed molecule occupies a certain fixed area on the surface, which prevents other molecules to adsorb therein; the interactions between the molecules are disregarded), this model remains extremely popular even at present. This popularity can easily be explained: the Langmuir model, as applied to the adsorption of a surfactant at the solution/air interface, is (in mathematical terms) expressed by a pair of well-known simple expressions:
G =
+ 1
1w bc
bc the adsorption isotherm (5.1)
g g
w = - +( )0 1RT bcln the equation of state (5.2)
Here Γ is the adsorbed amount γ is the surface tension γ0 is the surface tension of pure solvent c is the bulk equilibrium concentration of the adsorbed species R and T are the universal gas constant and the absolute temperature
The only parameter involved in the model is the molar area of the adsorbate molecule ω (the area covered by the surfactant molecule at the interface); the other parameter b, which is the adsorption equilibrium constant, is seen to be a scaling factor (as it enters the equations only via the product bc). As long as the physical quantities that one is interested in are only the equilibrium adsorbed amount and the equilibrium surface tension, Equations 5.1 and 5.2 can be dealt with by a suitable matrix processor (e.g., Excel) and even by a pocket calculator.
