Adsorption coefficient
The adsorption coefficient (adsorption constant) is a measure of the speed at which molecules of a surfactant are adsorbed at the surface.
Background
Surfactant molecules become enriched at the surface and align themselves in such a way that molecule groups with higher affinity to the volume phase are aligned inwards and those with less affinity are aligned outwards. In doing so, the surface tension decreases with increasing surface concentration. The transient behavior of the adsorption process, which becomes slower with increasing surface concentration, has been described by Ward and Tordai by means of the following equation:
σt = surface tension at surface age t; σeq = surface tension in dynamic equilibrium; t = surface age; R = universal gas constant; T = absolute temperature; Γ = surface excess concentration; c = molar concentration of the solution; Dl = adsorption coefficient
The surface excess concentration Γ is the area-related concentration of the surfactant at the interface and can be obtained by measuring the CMC. The adsorption coefficient can be determined with the help of a bubble pressure tensiometer which measures the surface tension as a function of surface age.
As well as the adsorption, the rate of change of surface tension is also determined by the diffusion of the volume phase at the interface, as a result of which it is also expedient to determine the diffusion coefficient. Which process requires more time depends on the concentration of the solution and to what extent the interface is already overlaid with surfactant molecules. Depending on the conditions, the diffusion or the adsorption can become the rate determining step.
Bibliography
A. F. G. Ward, L. J. Tordai: Time-Dependence of Boundary Tensions of Solutions I. The Role of Diffusion in Time-Effects. J.Chem.Phys. 14, 453 (1946)
